Conservapedia - User contributions [en]

The Church of Jesus Christ of Latter-Day Saints

2017-10-25T01:50:26Z

Bogart12: Added important details to the polygamy section.

[[Image:Birmingham temple.jpg|right|Birmingham temple]]
'''The Church of Jesus Christ of Latter-Day Saints''',<ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=ca07ae4af9c7e010VgnVCM1000004e94610aRCRD Style Guide - The Name of the Church] LDS.org</ref> known as the '''LDS Church''' or, more colloquially, the '''Mormon Church''', is the largest denomination originating from the Latter-Day Saint movement founded by [[Joseph Smith]]. Its members are colloquially referred to as "Mormons." As of 2015, the Church reports over 15.3 million members worldwide.<ref>[http://www.mormonnewsroom.org/article/2014-statistical-report-for-2015-april-general-conference "2014 Statistical Report for 2015 April General Conference"], ''Mormon Newsroom'', April 4, 2015.</ref><ref>[http://www.adherents.com/largecom/com_lds.html Geographic statistics]</ref> This authentic American-founded religious group has contributed greatly to the United States. As just one example, they have devoted millions of man hours to humanitarian efforts around the globe.

==Overview==
The church was organized in 1830 in the [[Burned-over district|Burned-Over District]] of upstate New York, by [[Joseph Smith]]. As the Church grew, new converts gathered in [[Ohio]] and [[Missouri]]. While the Latter-day Saints in [[Kirtland]], Ohio, experienced persecution, those gathered in Missouri were repeatedly driven from town to town by angry mobs. Having been forced from Missouri in 1839, Church members gathered in Illinois and built a thriving city called [[Nauvoo]] in a swampy bend of the Mississippi River. However, within seven years they were again forced from their homes. Led by [[Brigham Young]], these pioneers trekked 1,300 miles (2,092 kilometers) westward to the Salt Lake Valley, to escape persecution, and founded [[Salt Lake City]], [[Utah]], where the Latter-Day Saint Church continues to be headquartered today. The church has now expanded to more than 13 million members.<ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=86e6635a56d8f010VgnVCM100000176f620aRCRD&vgnextchannel=3e0511154963d010VgnVCM1000004e94610aRCRD LDS Newsroom - Early Church History]</ref><ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=d10511154963d010VgnVCM1000004e94610aRCRD Worldwide Church Statistics] LDS.org</ref>

Church members follow a law of health known as the [[Word of Wisdom]] that promotes healthy eating as well as avoiding tobacco, alcohol, coffee, tea, and illegal drugs.<ref>[http://scriptures.lds.org/dc/89 The Word of Wisdom] Scriptures.lds.org</ref>
The U.S religious landscape survey published in February 2008 shows that [[Mormon]]s have the largest families closely followed by Muslims.<ref>[http://www.iht.com/articles/2008/02/25/america/25usreligion.php U.S religious landscape survey]</ref>

==Mormons' relationship to Christianity==
According to the [[Lutheran Missouri Synod]], "The Lutheran Church--Missouri Synod, together with the vast majority of Christian denominations in the United States, does not regard the Mormon church as a Christian church." <ref>http://www.lcms.org/pages/internal.asp?NavID=2239</ref> In addition, the [[Southern Baptist Convention]] states that the Mormon religion is "not consistent with biblical Christianity." <ref>http://www.onenewsnow.com/2007/02/southern_baptist_convention_wa.php</ref> The [[United Methodist Church]] has stated that the Morman faith has "some radically differing doctrine on such matters of belief as the nature and being of [[God]]; the nature, origin, and purpose of [[Jesus Christ]]; and the nature and way of [[salvation]]." <ref>http://www.apologeticsindex.org/news/an200513.html#21</ref> According to Beliefnet.com there are a number of differences between the Mormon faith and traditional Christianity.<ref>http://www.beliefnet.com/features/mormonism.html</ref> Dr. James White, a Christian pastor, has stated that Mormonism is more different from Christianity than Islam because, he states, Mormonism is polytheistic, while Islam is monotheistic, and whether a religion is monotheistic or polytheistic is the basic element to a religion, according to White. He went on to say that part of the reason that Mormonism was, he felt, often mistaken for Christianity was his perception that Mormonism uses the same words Christians use, but it gives them completely different meanings.<ref>http://www.reformationtheology.com/2007/02/mormonism_v_christianity_a_quo.php</ref> The Roman Catholic Church does not accept Mormon baptisms as Christian baptisms.<ref>http://www.christiancentury.org/article/2012-01/are-mormons-christian-its-complicated</ref>

==Beliefs==
Latter-day Saints (Mormons) believe in the deity of [[Christ]]. They affirm the deity of Christ and their Church bears his name. From the organization of the LDS Church in 1830, the Church's doctrine focused on matters concerning theological issues related to Jesus Christ. Joseph Smith, Jr. wrote in 1842 to ''Chicago Democrat'' editor John Wentworth a statement of Church beliefs. The first of these 13 doctrinal declarations, later called the Articles of [[Faith]], stated the following:<blockquote>“We believe in [[God]] the Eternal Father, and in His Son, Jesus Christ, and in the [[Holy Ghost]]."<ref>[http://www.lds.org/portal/site/LDSOrg/menuitem.b12f9d18fae655bb69095bd3e44916a0/?vgnextoid=2354fccf2b7db010VgnVCM1000004d82620aRCRD&locale=0&sourceId=4ebe76e6ffe0c010VgnVCM1000004d82620a____&hideNav=1 The Marvelous Foundation of Our Faith] from the October 2002 General Conference</ref></blockquote> However, the Mormon understanding of Christ's deity is very different from the Christian understanding. Mormons believe Jesus is a god, but not a unique god. They believe Jesus is a created being, is only unique in mission, not in claims to godhood, and that he is the spirit brother of Satan.<ref>What Do Mormons Really Believe
By John Ankerberg, John Weldon [https://books.google.com/books?id=USylAQAAQBAJ&pg=PT48&dq=Mormons+reject+Christ+deity&hl=en&sa=X&ei=g1tRVaLQMMPwoAS42oGACQ&ved=0CB4Q6AEwAA#v=onepage&q=Mormons%20reject%20Christ%20deity&f=false]</ref>

"The Articles of Faith are thirteen statements written by the Prophet Joseph Smith describing some of the basic teachings and ordinances of the Church".<ref>[http://scriptures.lds.org/en/a_of_f/1]</ref><ref>[http://library.lds.org/nxt/gateway.dll/Curriculum/home%20and%20family.htm/gospel%20principles.htm?fn=document-frameset.htm$f=templates$3.0 ''Gospel Principles'', The Church of Jesus Christ of Latter-day Saints, Utah. 1997]</ref>

The LDS website states: <blockquote>"We believe in the Jesus of the [[New Testament]], and we believe what the New Testament teaches about Him. We do believe things about Jesus that other Christians do not believe, but that is because we know, through revelation, things about Jesus that others do not know."<ref>[http://www.mormon.org/question/faq/category/answer/0,9777,1601-1-56-16,00.html Is The Church of Jesus Christ of Latter-day Saints a Christian church?] As answered on the LDS Church's website</ref></blockquote>

Members of the church believe that [[God the Father]] and Jesus Christ are separate and distinct glorified beings, that God, the Father of all spirits (even including Lucifer) and Jesus Christ appeared to Joseph Smith in a vision in the spring of 1820 in response to Joseph's prayer requesting to know which of the many local [[Christian]] denominations he should join himself with, and that They told him that he should join with none of them. The reason behind this direction was as follows, according to LDS beliefs: the organization or "church" put in place by Jesus Christ during His ministry both before and after His resurrection was meant to remain as long as there were faithful followers, although there was clear understanding that a "falling away" (see 2 Thessalonians 2:3) or apostasy would take place, destroying for a time this organization (though not destroying faith in Jesus Christ, which did persist). This church organization provided a structure whereby two key components were maintained: the Priesthood, and continuing and direct revelation from the ascended Jesus Christ to His chosen Apostles.

According to LDS beliefs, the Priesthood is the authority given by Jesus Christ to His [[Apostles]] and others, both to direct the Church, as well as to perform the associated and necessary ordinances, such as baptism by water immersion, and giving the gift of the Holy Ghost by the laying on of hands. Without this authority, it would be impossible to perform them in an authorized manner (see [[Book of Acts|Acts]] 8:18-23). This authority, in actuality a covenant of service, only placed on men and not at all a legitimate source of self-aggrandizement, could only be passed from one authorized holder to another worthy man through the laying on of hands. Thus, while although initially the full quorum of 12 Apostles was maintained (see Acts 1:15-26), the Apostles were killed one by one and the Lord, in His mercy, ceased to give these murderers further opportunity of condemning themselves as more Apostles were not chosen. Thus, without the Priesthood and without the continuing revelation that the Lord provided to His Apostles to lead and guide the church, it fell way, as had been prophesied.

Therefore, LDS doctrine teaches of the necessity of a complete restoration rather than simply a reformation, and for this reason, Joseph Smith was called by God to be the first prophet, in the same sense as [[Moses]], [[Isaiah]], or [[Peter]], since the times of the New Testament. Mormons believe that since Joseph Smith, the leaders of the Church, from Brigham Young to [[Gordon B. Hinckley]] today, were and are prophets, with the complete Priesthood authority (restored through the laying on of hands by first [[John the Baptist]] and then by Apostles Peter, [[James]] and [[John]]). Mormons revere these men just as the Biblical prophets are revered and in particular, honor Joseph Smith for being the man through whom God and Jesus Christ chose to restore Their church to the earth.

===JesusChrist.lds.org===
[[Image:FaithinChrist.jpg|thumb|right|A screen shot of the new JesusChrist.lds.org Web site.]]
The Church has a multimedia website about the life and teachings of Jesus Christ at [http://jesuschrist.lds.org/?cid=wpats1 JesusChrist.lds.org].

Elder [[Russell Nelson|Russell M. Nelson]] speaks about the new website ''JesusChrist.lds.org''. [http://www.lds.org/ldsnewsroom/media/mediaplayer.swf?media=http://broadcast.lds.org/newsroom/video/flv/2-29-08_Nelson.flv&type=FLV video]

===Scriptures===

The four standard works of the Church are:
*The King James Version of the [[Bible]] - both the Old and New Testaments
*[[The Book of Mormon|The Book of Mormon: Another Testament of Jesus Christ]] - Translation of the spiritual record of two ancient civilizations in the western hemisphere, one from the time of the [[Tower of Babel]] to about 600 B.C., and the other from 600 B.C. to 421 A.D.
*[[Doctrine and Covenants]] - Modern-day revelation as received by the Prophet Joseph Smith and other modern-day prophets
*[[Pearl of Great Price]] - Selection of translations, revelations and narrations from the Prophet Joseph Smith

====Book of Mormon====

President [[Gordon B. Hinckley]] said the following about the [[Book of Mormon]] in an October, 2002 [[General Conference]] address entitled "The Marvelous Foundation of Our Faith": <blockquote>"This remarkable book stands as a testimonial to the living reality of the Son of God. The Bible declares that 'in the mouth of two or three witnesses every word may be established' (Matt. 18:16). The Bible, the testament of the Old World, is one witness. The Book of Mormon, the testament of the New World, is another witness.</blockquote><blockquote>I cannot understand why the Christian world does not accept this book. I would think they would be looking for anything and everything that would establish without question the reality and the divinity of the Savior of the world."<ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=e74c4d4297602110VgnVCM100000176f620aRCRD Mormons Reflect Christianity in Lifestyle] as stated in the April, 2007 newsroom article at lds.org</ref></blockquote>

===Restoration of the Priesthood===
Members of the [[Church of Jesus Christ of Latter-day Saints]] believe that on May 15, 1829 A.D., the resurrected [[John the Baptist]] appeared to [[Joseph Smith|Joseph Smith, Jr.]] and [[Oliver Cowdery]] and conferred upon them the [[Aaronic priesthood]], which includes the authority to baptize.<ref>[http://scriptures.lds.org/en/dc/13 Doctrine and Covenants 13]</ref> Later, the resurrected Peter, James, and John appeared to them and conferred the [[Melchizedek priesthood]].

==Special Witnesses of Christ==
These prophets and apostles have given their testimonies as special witnesses of Jesus Christ.

*President [[Gordon Hinckley|Gordon B. Hinckley (1910-2008)]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/president-gordon-b-hinckley-1910-2008-garden-tomb Special Witnesses of Christ], President Gordon B. Hinckley at the Garden Tomb, video at ''JesusChrist.lds.org''.</ref><ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/president-gordon-b-hinckley-1910-2008-sacred-grove Special Witnesses of Christ], President Gordon B. Hinckley at the Sacred Grove, video at ''JesusChrist.lds.org''.</ref>
*President [[Thomas Monson|Thomas S. Monson]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/president-thomas-s-monson Special Witnesses of Christ], President Thomas S. Monson, video at ''JesusChrist.lds.org''.</ref>
*President [[Henry Eyring|Henry B. Eyring]]
*President [[Dieter Uchtdorf|Dieter F. Uchtdorf]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/president-dieter-f-uchtdorf Special Witnesses of Christ], President Dieter F. Uchtdorf, video at ''JesusChrist.lds.org''.</ref>
*President [[Boyd Packer|Boyd K. Packer]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/president-boyd-k-packer Special Witnesses of Christ], President Boyd K. Packer, video at ''JesusChrist.lds.org''.</ref>
*Elder [[L. Tom Perry]]
*Elder [[Russell Nelson|Russell M. Nelson]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/elder-russell-m-nelson Special Witnesses of Christ], Elder Russell M. Nelson, video at ''JesusChrist.lds.org''.</ref>
*Elder [[Dallin Oaks|Dallin H. Oaks]]
*Elder [[M. Russell Ballard]]
*Elder [[Joseph Wirthlin|Joseph B. Wirthlin (1917-2008)]]
*Elder [[Richard Scott|Richard G. Scott]]
*Elder [[Robert Hales|Robert D. Hales]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/elder-robert-d-hales Special Witnesses of Christ], Elder Robert D. Hales, video at ''JesusChrist.lds.org''.</ref>
*Elder [[Jeffrey Holland|Jeffrey R. Holland]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/elder-jeffrey-r-holland Special Witnesses of Christ], Elder Jeffrey R. Holland, video at ''JesusChrist.lds.org''.</ref>
*Elder [[David Bednar|David A. Bednar]] <ref>[http://jesuschrist.lds.org/SonOfGod/eng/special-witnesses/video/elder-elder-david-a-bednar Special Witnesses of Christ], Elder David A. Bednar, video at ''JesusChrist.lds.org''.</ref>
*Elder [[Quentin Cook|Quentin L. Cook]]
*Elder [[D. Todd Christofferson]]

==Wards==
[[Image:DCTemple.jpg|right|Washington DC Temple]]
Wards are geographically-defined congregations of the church. The Bishop is the spiritual leader of the ward and he serves with two counselors, all three chosen from among the body of the Ward. Bishops are usually called to serve for a period of five years and do so on a volunteer and unpaid basis, without formal ecclesiastical training, and while maintaining their secular professions.

The entire ward meets every week on Sunday to worship the Lord Jesus Christ and to receive counsel. The meetings are divided into three different hours:
*First hour - '''Sacrament meeting'''. Our main purpose in attending sacrament meeting is to renew our covenants through partaking of the sacrament and to worship our Heavenly Father through hymn singing and prayer. Sacrament meeting provides an opportunity for members to strengthen their faith, find inner peace and spiritual healing, receive inspiration, and be instructed in the gospel. A member of the bishopric begins the meeting welcoming all members and visitors. There is an opening hymn followed by an opening prayer (invocation). This is followed by conducting ward business where members are released and sustained from callings. Then the sacrament of bread and water is prepared, blessed by the priesthood, and passed to the congregation. The sacrament is a renewal of the covenants each member made at baptism to remember the Lord Jesus Christ and to keep his commandments. On the first Sunday of the month, the meeting conductor starts off the bearing of testimonies by offering his own personal testimony. A testimony is a personal witness that the gospel of Jesus Christ is true. As inspired by the Spirit, other members give their testimonies. On the other three Sundays, there are talks from members. The sacrament meeting concludes with a closing hymn and prayer.
*Second hour - '''Sunday School''', '''Primary''' and '''Nursery'''. Its purposes are to teach the gospel of Jesus Christ and strengthen individuals and families by encouraging them to study the scriptures, obey the commandments, receive the essential ordinances, and keep the associated covenants. All the adults and youth meet in Sunday School classes. Children younger than twelve and three or older attend Primary. Children who are at least 18 months old but who are not yet 3 years old on 1 January may attend nursery at the discretion of their parents.
:'''Adult Sunday School''' - The adults meet in several different classes. New members to the Church usually attend a Gospel Essentials class where they learn the basic teachings of the Church. Most of the other adults attend a Gospel Doctrine class where they are instructed in the Gospel of Jesus Christ from the scriptures. The main subjects rotate every four years: Old Testament, New Testament, Book of Mormon, and the last year is Doctrine and Covenants, Pearl of Great Price and Church history. The bible used by Church members is the King James Version.
:'''Youth Sunday School''' - The youth meet in several different classes according to their ages. There are usually separate classes for twelve and thirteen year olds, fourteen and fifteen year olds and sixteen and seventeen year olds. When they turn eighteen, the member starts attending the adult classes.
:'''Primary''' - The purpose of Primary is to teach children the gospel of Jesus Christ and help them learn to live it.
:'''Nursery''' - The purpose of the nursery class is to provide a loving, safe, organized place where young children can increase their understanding of and love for Heavenly Father and Jesus Christ, have positive experiences in a Church setting, and grow in feelings of self-worth.
*Third hour - '''Priesthood''', '''Relief Society''', '''Young Men''', '''Young Women''', '''Primary''' and '''Nursery'''. The men meet in Priesthood, the adult women meet in Relief Society,the male youth meet in Young Men, the female youth meet in Young Women and the children continue to meet in Primary or Nursery.
:'''Priesthood''' - The purpose of the priesthood meetings are to increase priesthood holders’ knowledge of the gospel; strengthen their dedication to becoming better husbands, fathers, sons, and neighbors; and help them become active participants in fulfilling the mission of the Church.
:'''Relief Society ''' - The purpose of Relief Society is to provide relief for the poor and needy and to bring people to Christ.
:'''Young Men''' - The purpose of the Young men group is to prepare the young men of the Aaronic Priesthood to receive the Melchizedek Priesthood, to receive the ordinances of the temple, and to serve a full-time mission.
:'''Young Women''' - The purpose of the Young Women organization is to help each young woman, ages 12 to 18, "come unto Christ".

==General Conference==
The church holds a semi-annual General Conference (in April and October, five two-hour sessions over two days) during which members listen to spoken messages from the Prophet and President of the church, his two counselors, members of the Quorum of the Twelve Apostles and other Church leaders. These messages are received by members of the church as modern-day revelation, just as the words of Peter were received by the followers of Jesus Christ in his day. Many members travel to Salt Lake City for the two-day conference, but the proceedings are broadcast via satellite throughout the world (as well as streamed on the internet) so that the entire church can participate.

The semi-annual conference was held in the Salt Lake Tabernacle for 132 years, but in 2000, the church completed construction of the Conference Center and has held the conference there since April 2000. The Conference Center's primary feature is an auditorium that seats 21,000.

==History of the Church in Utah ==
After the move to what would eventually become Utah, members of the Church founded the Territory of Deseret. While this was soon scaled down to the Utah territory by the United States government, the name Deseret was retained in the form of a newspaper (the Deseret Times) and the symbol on the state's highways (the beehive). Brigham Young, the then president of the Church was appointed governor of the Territory. The territory thrived, with the Saints in all positions of power (a territory consisting almost entirely of Saints unsurprisingly elected a territorial legislature that was entirely Mormon).

When federal officials, placed as patronage positions, arrived in Utah and found they could not profit in the usual way (skimming money off the top of deals, insisting on bribes and kickbacks for contracts), they started a drumbeat of negativity towards the Church in Washington. This led to the United States government marching an army of 2,500 troops towards Utah in 1857. This exercise of a nation taking arms against its own people failed miserably, with the troops poorly supplied and forced to march through the Rocky Mountains in the winter. Armed conflict was averted by Thomas Kaine, who convinced the governor of the territory at the time, Alfred Cummings, to order the army to pass by Salt Lake City and camp miles away. This failed expedition helped the Saints maintain a greater part of their independence from the federal government for a while longer.

==Controversy==

====Position of the Church of Jesus Christ of Latter-day Saints, with respect to Christianity====
Members of the Church of Jesus Christ of Latter-day Saints consider themselves Christians. They worship Jesus Christ as their Creator (see John 1:3), their Savior and Redeemer, and ultimately their eternal Judge. They believe that the events described in the New Testament in reality occurred, including Jesus Christ's virgin birth, his sinless life and miraculous ministry, and his suffering, death, and literal resurrection, through which forgiveness of sin, salvation (understood in LDS doctrine to indicate resurrection and immortality, a free gift to all; see 1 Corinthians 15:22), and ultimately exaltation (returning to and eternally dwelling in the presence of God and Jesus Christ and becoming "joint-heirs with Christ"; see Romans 8:17), are made possible.

The eleventh of the above-mentioned thirteen articles of faith contains the following statement:
<blockquote>“We claim the privilege of worshiping Almighty God according to the dictates of our own conscience, and allow all men the same privilege, let them worship how, where, or what they may." (see Articles of Faith 1:11)</blockquote>

====African Americans and the Priesthood====
African Americans were banned from the priesthood until, in June 1978, President Spencer W. Kimball is said to have received a revelation extending priesthood ordination to all worthy males of The Church of Jesus Christ of Latter-day Saints (Official Declaration 2).
<ref name="Black">Emmanuel Abu Kissi, [http://byustudies.byu.edu/Reviews/Pages/reviewdetail.aspx?reviewID=117 Book review of Black and Mormon] BYU Studies Review, October 2006.</ref><ref>[http://www.pbs.org/mormons/themes/prohibition.html The Prohibition Against Blacks in the Priesthood], Public Broadcasting Service.</ref><ref>[http://www.lds.org/ldsorg/v/index.jsp?vgnextoid=bbd508f54922d010VgnVCM1000004d82620aRCRD&locale=0&sourceId=36f2ce9566a43110VgnVCM100000176f620a____ LDS.org - Topic Definition - Priesthood Ordination before 1978]</ref>

The Book of Mormon attests that God invites “all to come unto him and partake of his goodness; and he denieth none that come unto him, black and white, bond and free, male and female; . . . and all are alike unto God” (2 Nephi 26:33). In our present day the First Presidency and Quorum of the Twelve Apostles have stated that all human beings are created in the image of God and that each is a beloved spirit son or daughter of Deity.<ref>“The Family: A Proclamation to the World,” 23 Sept. 1995, published in Ensign, Nov. 1995</ref>

<blockquote>In the twentieth century, various Church leaders continued to offer possible reasons why a race of people was prohibited from holding the priesthood. One explanation, carried over from the previous century, stated that blacks were descendants of Cain, the first murderer, and therefore were denied the priesthood because of lineage. Another theory held that blacks were less valiant in the premortal existence and therefore had certain spiritual restrictions placed upon them during mortality. Priesthood denial was perceived to be one of these spiritual restrictions. But by mid-century, President David O. McKay stated, "There is not now, and there never has been, a doctrine in this Church that the negroes are under a divine curse. . . .It is a practice, not a doctrine, and the practice will some day be changed".<ref name="Black" /></blockquote>

===Views on Same-Gender Attraction===
In October 2007, Elder Jeffrey R. Holland, of the Quorum of the Twelve Apostles, wrote an article in the Ensign magazine entitled "Helping Those Who Struggle with Same-Gender Attraction".<ref>[http://www.lds.org/portal/site/LDSOrg/menuitem.b12f9d18fae655bb69095bd3e44916a0/?vgnextoid=2354fccf2b7db010VgnVCM1000004d82620aRCRD&locale=0&sourceId=e5cbba12dc825110VgnVCM100000176f620a____ Helping Those Who Struggle with Same-Gender Attraction]</ref> In 2007, the Church published a pamphlet "God Loveth His Children", for those suffering from same-gender attraction.<ref>http://www.lds.org/topics/pdf/GodLovethHisChildren_04824_000.pdf God Loveth His Children</ref>

On June 7, 2006, ABC’s Nightline ran a story on members and former members of The Church of Jesus Christ of Latter-day Saints who struggle with same-gender attraction. The Church published a response to the inaccuracies in the Nightline story.<ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=d4ec39628b88f010VgnVCM100000176f620aRCRD&vgnextchannel=f5f411154963d010VgnVCM1000004e94610aRCRD Church Responds to Nightline Story on Mormons and Homosexuality]</ref>

The Church has a section on same-gender attraction on the Newsroom website.<ref>[http://www.lds.org/ldsnewsroom/v/index.jsp?vgnextoid=27f71f1dd189f010VgnVCM100000176f620aRCRD&vgnextchannel=726511154963d010VgnVCM1000004e94610aRCRD&vgnextfmt=tab1 Same-Gender Attraction]</ref>

===Polygamy===

Critics try to associate the Church with polygamy, but in fact the Church has denounced polygamy for most of its existence, and at least since 1905. Other belief systems, such as the [[ACLU]]'s, are more supportive of polygamy than this Church is.

A 1998 statement by current LDS President Gordon B. Hinckley states:
:This Church has nothing whatever to do with those practicing polygamy. They are not members of this Church. . . . If any of our members are found to be practicing plural marriage, they are excommunicated, the most serious penalty the Church can impose. Not only are those so involved in direct violation of the civil law, they are in violation of the law of this Church.<ref>[http://www.mormon.org/question/faq/category/answer/0,9777,1601-1-114-1,00.html What is the Church’s position on polygamy?] LDS website</ref>

However, current LDS practice allows men to be sealed to more than one woman at a time<ref>[https://file.wikileaks.org/file/mormon-handbook-of-instructions-2006.pdf]Church Handbook of Instructions, page 85</ref>, where it is believed they will be a single polygamous family in the afterlife.<ref>https://religionnews.com/2016/08/03/polygamy-lives-on-in-mormon-temple-sealings/</ref>

==References==
{{reflist|2}}

==See also==
*[[List of LDS temples]]
*[[Christianity]]
*[[Christianity in Conservapedia]]

==External links==

====Links to websites favorable to the Mormon Church====

*[http://www.lds.org Official Church Website]
*[http://www.mormon.org Official Church Website for Investigators]
*[http://scriptures.lds.org Official Online Version of the LDS Scriptures]
*[http://www.familysearch.org/ Official Church Genealogy Website, "the largest collection of free family history, family tree and genealogy records in the world."]
*[http://www.ldschurchtemples.com "News, schedules, photographs, and interesting facts of the temples of the LDS Church"]
*[http://www.fairlds.org Mormon Apologetics]
*[http://www.maxwellinstitute.com BYU Theologians]
*[http://www.lightplanet.com/mormons/ About Mormons]
*[http://en.wikipedia.org/wiki/The_Church_of_Jesus_Christ_of_Latter-day_Saints Wikipedia article] on the LDS Church
*[http://www.intellectualconservative.com/article3282.html Are Mormons Conservative?]
*[http://www.foxnews.com/story/0,2933,317272,00.html 21 Questions Answered About Mormon Faith]
*[http://www.newsroom.lds.org/ldsnewsroom/eng/news-releases-stories/what-you-will-find-when-you-step-inside-a-mormon-chapel What You Will Find When You Step Inside a Mormon Chapel], LDS Newsroom, 19 August 2008

====Links to Groups Not in Favor of the Mormon Church====
*[http://jesusnotjoseph.com JesusNotJoseph]
*[http://www.mrm.org Mormonism Research Ministry]
*[http://www.evangelicalbible.com/jw.htm#LDS The Mormon Church & the Nature of God]

[[Category:Churches]]
[[Category:LDS Church]]
[[Category:Featured articles]]
[[Category:Utah]]

Talk:Todd Akin

2012-08-22T21:22:15Z

Bogart12:

Nothing in Akin's comment suggests he wanted to distinguish between "legitimate" rape and false accusations of rape.

:The context of the remark, as well as common sense, demonstrate that meaning. No other meaning is plausible.--[[User:Aschlafly|Andy Schlafly]] 14:15, 22 August 2012 (EDT)

:I suspect that a large part of what has worked so many people up is his idea that the female body has ways of shutting down a pregnancy due to rape. --[[User:Bogart12|Bogart 12]] 15:22, 22 August 2012

Talk:Majoring in Mathematics

2012-02-28T01:46:22Z

Bogart12: /* Homomorphism */

This is an extremely rough outline for this new article. I will continue to expand it over the next few weeks based on feedback about the appropriateness of the problems and other suggestions for improvements. Please let me know what you think! --[[User:MarkGall|MarkGall]] 23:12, 4 October 2009 (EDT)
::well I was a math major in college many years ago (before Rubic's cube!) Suggest adding statistics.
:::Ah, good idea. At my undergrad school mathematics and statistics were separate programs, but I guess this isn't typical. I'll throw in a new section. I'm not much for statistics -- can anyone suggest some good problems? --[[User:MarkGall|MarkGall]] 23:20, 4 October 2009 (EDT)

Tremendous work, Mark. I'll try to add something for probability or statistics, which I studied.--[[User:Aschlafly|Andy Schlafly]] 23:22, 4 October 2009 (EDT)
:Great, thanks. These are subjects in which I'm inexpert. Now I'm inclined to move Probability/Statistics to a "field" along with algebra, analysis, etc. Please add a nice problem or theorem if you have any in mind! --[[User:MarkGall|MarkGall]] 23:24, 4 October 2009 (EDT)

Terrific analysis on what college mathematics is not. That should be required reading for many seeking to major in math!--[[User:Aschlafly|Andy Schlafly]] 22:30, 15 October 2009 (EDT)

Why is there no mention of the bible or theology in this article? It should be mentioned, as it is in [[Axiom_of_Infinity]], that the notion of an infinite set is somewhat blasphemous. [[User:Tomkup32|Tomkup32]] 10:58, 9 December 2009 (EST)

For Bezout's theorem, you have some inaccurate claims: the line x+y=0 and x+y=1 never interset. We need to move to projective space for the degree of the intersection to be exactly mn.

== Liberal bias ==

How can there be liberal bias in math? Does saying 1+1 = 2 have a motive?[[User:SusanP|SusanP]] 23:29, 9 February 2012 (EST)

:College math is not completely immune to liberal influences that have destroyed other subjects like physics.--[[User:Aschlafly|Andy Schlafly]] 23:37, 9 February 2012 (EST)

:Can you give an example of liberal bias in math? --[[User:Bogart12|Bogart12]]
:Possible liberal bias--the study of so-called "homomorphisms" in modern liberal algebra could be part of the gay agenda?--[[User:Bogart12|Bogart12]]
::No, sorry, that's absurd and I think you know it. "Homo" simply means same and is used in a wide variety of contexts that have nothing to do with liberal bias. Is homogenized milk liberal bias? Or homonyms? Homophones? I've already reverted your addition to the article once, so I won't do it again just yet, but please consider removing or modifying it yourself.--[[User:JustinD|JustinD]] 19:32, 24 February 2012 (EST)
::There is a crucial difference between your examples and my claim. A homophone describes two words sounding the same but being different. Bat is not a homophone with bat, that doesn't make sense. Saying wind and wind are homophones acknowledges that they sound the same but are different words. A homomorphism allows groups that are different, like Z_2xZ_2 and the Klein four group, to be treated as equal. Additionally the global warming obsession is prolific. I didn't mean my writing to sound flippant, and perhaps its tone can be improved, but it was certainly not meant as a joke.
:::I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs. --[[User:JustinD|JustinD]] 01:23, 26 February 2012 (EST)
::::Haha you are absolutely right, my apologies. I thought I had picked a word specifically with no homophones. Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine. But consider a statement like "there is only one group of order 3." There are clearly many, because you can define one on any set with 3 elements. Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms. Compare this with the professor value of refusing to distinguish between men and women. To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even. To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same. I hope that clarifies what I was struggling to say before. --[[User:Bogart12|Bogart12]]
:::::They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between male and female. So yes, in many situations, women and men are essentially the same.[[User:KenShomer|KenShomer]] 15:15, 26 February 2012 (EST)

::::::If that statement were true, then why are the top achievers on difficult math contests (such as the Putnam exam) more than 90% male, and less than 10% female?--[[User:Aschlafly|Andy Schlafly]] 16:32, 26 February 2012 (EST)\
::::::: I can't vouch for this on a national level, but when I took the Putnam at UConn last year, about 90% of the participants were male. If that's true at a national level (and I don't know if it is) then it stands to reason. [[User:Gregkochuconn|Gregkochuconn]] 21:28, 26 February 2012 (EST)
::::::: It's gotten so bad that now they make women put red stickers on the exams so they can graded differently! Women often have separate prizes too.--Bogart12

::::::::I don't know why anyone (i.e., liberals) would expect or pretend that God created men and women to have absolutely identical aptitudes in everything. Men and women are physically very different.--[[User:Aschlafly|Andy Schlafly]] 01:06, 27 February 2012 (EST)
:::::::::Mr. Schlafly, lets assume you represent the average conservative male. We know that conservatives are smarter than liberals. However, you assume that women are somehow poorer at math than a male of comparable upbringing, and conservative women usually listen to their fathers and other good, conservative influences. This subtle (or overt) bias leads to scores of smart, conservative women turning away from math in favor of biology and social science. This leads to the only potential female math majors being liberal, who then reinforce this stereotype. Otherwise, if women were biologically incapable of doing math as well as men can, the percentage of female mathematics PHD holders would remain at a constant 0%, instead of gradually increasing as the years pass on.[[User:KenShomer|KenShomer]] 17:35, 27 February 2012 (EST)

:::::I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms.
:::::This is getting a bit off topic, but if Andy and you are right and (liberal?) universities improperly equate the aptitude of men and women (by analogy, posit a homomorphism between men and women), we shouldn't conclude that the positing of all equivalences is liberal bias (by analogy, that homomorphisms are the result of liberal bias), but instead should conclude that universities are mistaken and that no such equivalence exists in this case (by analogy, there is no homomorphism between a group of order 3 and a group of order 4, say).--[[User:JustinD|JustinD]] 17:01, 26 February 2012 (EST)
:::::Again though, the university claims more than "these sets have similar group structures on them," and goes so far as to insist that there is no reason to distinguish between them. [[User:Bogart12|Bogart12]]
::::::Okay, so then universities are wrong to equate men and women in this way. What does that have to do with homomorphisms? Are we still disagreeing whether they serve a legitimate mathematical purpose or are instead the product of improper liberal bias?--[[User:JustinD|JustinD]] 21:54, 26 February 2012 (EST)
:::::::It's central to liberal ideology to view these blasphemous notions as "useful." Next, you'll be defending relativity as useful, and that is a slippery slope my friend. We draw the line here at Conservapedia where ideas that are wrong are rejected, regardless of how useful we have been told they are.[[User:Bogart12|Bogart12]]
::::::::Maybe you weren't joking before, but this is clearly just a goof, right? You don't really intend that as an argument do you?--[[User:JustinD|JustinD]] 01:25, 27 February 2012 (EST)

== Examples of Liberal Math ==

The purported proof of [[Fermat's Last Theorem]] would be an example of liberal math.--[[User:Aschlafly|Andy Schlafly]] 16:48, 26 February 2012 (EST)
:This may quickly move outside my area of understanding, but could you clarify this at all? Is the concern the use of the [[axiom of choice]] and/or non-[[ZF]] axioms? I've read our article and vaguely remember a book I read in high school, but other than the use of some non-standard techniques, I wasn't aware there was any serious doubt as to the validity of the proof. --[[User:JustinD|JustinD]] 17:10, 26 February 2012 (EST)
:: What would be an example of Conservative Math? --[[User:BradleyS|BradleyS]] 17:13, 26 February 2012 (EST)

:::[[Godel's Incompleteness Theorems]], and [[liberals]] ostracized [[Kurt Godel]] for it.--[[User:Aschlafly|Andy Schlafly]] 17:41, 26 February 2012 (EST)
:::: What is there that evidence that liberals ostracized Gödel? And what makes the Incompleteness Theorem conservative? --[[User:BradleyS|BradleyS]] 19:12, 26 February 2012 (EST)

:::::Liberals kept Godel from obtaining tenure at most university math departments, and ostracized him in other ways. [[Bertrand Russell]], a leading leftist of that time, was humiliated by Godel's insight, which was conservative in how it debunked intellectual arrogance.--[[User:Aschlafly|Andy Schlafly]] 19:33, 26 February 2012 (EST)

:::::Exactly Andy, Whitehead and Russell were both in the middle of trying to "prove" everything when Godel administered a much-needed dose of humility. [[User:Bogart12|Bogart12]]

::::::Right. A liberal claims to know almost everything. A conservative recognizes that the liberal actually knows almost nothing of value.--[[User:Aschlafly|Andy Schlafly]] 22:39, 26 February 2012 (EST)

:::::::When did you become a liberal? [[User:DaveF|DaveF]] 09:16, 27 February 2012 (EST)
===Carbon Dating===
Using the most advanced scientific & mathematical calculations, the dating process is still prone to error. The [[Shroud of Turin]] is claimed as fabrication by the scientific community but the liberals fail to grasp their errors in calculating exposure to contamination, such as soot. --[[User:Jpatt|Jpatt]] 19:37, 26 February 2012 (EST)
:That's not necessarily mathematics, but, archaeology + ''applied'' mathematics.[[User:JonM|JonM]] 19:50, 26 February 2012 (EST)

::Good point, but applied math is still math, and the example illustrates liberal use of math to convey an unjustified claim of "proof".--[[User:Aschlafly|Andy Schlafly]] 20:10, 26 February 2012 (EST)
:::Hammers have been used throughout history for the construction of buildings intended to promote both liberal and conservative ideals. The hammer has no inherent political philosophy. The hammer is a tool, and though it can be used for liberal or conservative purposes, it is inherently a neutral party. Math is the same way. While math can be used to promote liberal ideals, and is often studied by liberals, it is not liberal or conservative. Math is a tool.[[User:KenShomer|KenShomer]] 22:11, 26 February 2012 (EST)

::::But hammers are not courses of study or an ideology. Math is. And all courses of study and ideologies are susceptible to liberal bias. Engineering, with its grounding in what works, is probably the most immune to [[liberal bias]]. Women's studies and English literature are probably the most susceptible to liberal bias.--[[User:Aschlafly|Andy Schlafly]] 22:37, 26 February 2012 (EST)

== atheist and liberal idiocy extends to math: 2+2=5? (Lawrence Krauss vs William Lane Craig) ==

[http://www.youtube.com/watch?v=NOrlIOm6eGM 2+2=5? (Lawrence Krauss vs William Lane Craig)] [[User:Conservative|Conservative]] 20:33, 26 February 2012 (EST)

== Homomorphism ==

A homomorphism is a function/relation that maps one algebraic structure to another and preserves its structure. It does not equate them, so I removed it because its definition was erroneous. A comparison illustrates why the original definition is incorrect. If <math>f(x) = x+2</math>, then <math>f(3) = 5</math>. This is a relation that maps <math>\mathbb{R}</math> to <math>\mathbb{R} + 2</math>. It does not, however, equate them. Even though <math>f(x)</math> maps 3 to 5, it is not stating that <math> 3 = 5</math>. This is a simple example, but hopefully it illustrates the proper definition. Thank you! [[User:KevinDavis|Kevin Davis]] [[User talk:KevinDavis|Talk]] 09:09, 27 February 2012 (EST)
:This is incorrect, the map you've described is not a homomorphism. A homomorphism <math>\phi:A\rightarrow B</math> satisfies, for all a,b in A, <math>\phi(ab)=\phi(a)\phi(b).</math> I am not talking about claiming that 3=5, I am talking about claiming that the Klein 4-group is the same as Z_2xZ_2.--[[User:Bogart12]]

Liberal

2012-02-27T05:22:47Z

Bogart12: typo

[[File:President Barack Obama.jpg|thumbnail|right|180px|President [[Barack Obama]] advocates the use of [[Keynesian economics|Keynesian economic concepts]] despite the fact that John Maynard Keynes was incompetent and a fraud.<ref>
*[http://centurean2.wordpress.com/2011/03/20/fabian-john-maynard-keynes-the-stealthy-enemy-of-human-freedom/ John Maynard Keynes the stealthy enemy of human freedom]
*[http://www.bloomberg.com/news/2010-02-22/deathbed-of-keynesian-economics-will-be-in-u-k-matthew-lynn.html Deathbed of Keynesian Economics will be in the UK]
*[http://www.iwf.org/inkwell/show/23102.html Will the G8 Repudiate the Philosophy of Living Beyond Our Means?]
*[http://www.keynesatharvard.org/book/KeynesatHarvard-ch09.html KEYNES AT HARVARD Economic Deception as a Political Credo BY ZYGMUND DOBBS]
*[http://www.theatlantic.com/daily-dish/archive/2008/01/keyness-jew-boy-quickie/220620/ Keynes's "Jew Boy" Quickie, The Atlantic]
</ref> ]]
A '''liberal''' (not to be confused with a ''leftist''), is someone who represents or is in support of some form of liberalism. This often includes social progressivism. Particularly in the [[United States]], the term may also be associated with irreligious people, or those who otherwise disagree with moral or social standards held as traditional by American [[Christian|Christians]]. Some may be [[Christian]], but they are rarely immensely committed to Christianity. Liberalism began as a movement for individual liberties, but today is increasingly [[statist]] and, as in Europe, [[welfare state]]-ist. Liberalism has changed over the years and degenerated into a delusional (in the sense of economic views) and anti-traditional ideology.

For example, [[Franklin Delano Roosevelt]] firmly believed in private sector unions, but vehemently opposed and condemned public sector unions, stating that the idea of collective bargaining can't be transferred to the public sector, as that would result in the government being unable to carry out its duties. Yet today, decades later, [[Democrats]] and liberals are almost in cahoots with public sector unions, as they "donate" money to the reelection campaign in exchange for more taxpayer money in their wallets and fluffed up pensions.

Liberals currently use two clauses to try and expand their power: the Commerce Clause and the General Welfare Clause. The general welfare clause mentions "promoting the general welfare". This to a liberal means taxing the rich out of existence and redistributing that money. The commerce clause on the other hand is in the constitution and says that Congress has the power to regulate trade with foreign nations, between the states and with the indian tribes. Since the days of FDR this clause has been interpreted very loosely and has resulted in the federal government vastly expanding its power. The latest example is Obamacare. In Obamacare, the liberals justify the individual mandate by saying it regulates commerce between the states. This is clearly a stretched interpretation of the clause as there is a difference between regulating commerce and forcing citizens to participate in commerce that Congress can regulate.

Polling data over several decades has consistently shown that more Americans identify as conservative than as liberal, by a ratio of 2:1.<ref>http://pewresearch.org/pubs/1042/winds-of-political-change-havent--shifted-publics-ideology-balance</ref> A liberal generally supports many of the following political positions and practices:

* Spending money on government programs.
* Government solving economic problems<ref>http://www.studentnewsdaily.com/conservative-vs-liberal-beliefs</ref>
* The belief that terrorism is not a huge threat, and that the only reason Muslim extremists hate us is because of bad foreign policy <ref>http://www.studentnewsdaily.com/conservative-vs-liberal-beliefs</ref>
* Taxpayer-funded and/or legalized [[abortion]]
* Prohibition of teacher-led [[prayer]] in classrooms and school/state-sponsored religious events
* Support for [[gun control]]
* Affirmative action<ref>http://www.studentnewsdaily.com/conservative-vs-liberal-beliefs</ref>
* Support of obscenity, pornography and violence in video games as a [[First Amendment]] right<ref>The [[Warren Court]], led by [[liberal]] Justices [[William O. Douglas]], [[Hugo Black]], [[Abe Fortas]], [[William Brennan]] and Chief Justice [[Earl Warren]] issued 36 decisions granting [[First Amendment]] rights to obscenity and pornography. These decisions remain fully supported by liberals today.</ref>
* Government-funded medical care, such as [[Obamacare]]
* Taxpayer-funded and government-controlled [[public education]]
* The denial of traditional [[gender roles]]
* Insisting that men and women be placed in the same jobs in the [[military]]
* Legalized [[same-sex marriage]] and homosexual adoption
* [[Tax and spend]]
* Support for economic sector regulations<ref>http://www.studentnewsdaily.com/conservative-vs-liberal-beliefs</ref>
* Trying to impede the economic freedom of [[Job Creators]]
* Support and spreading of [[political correctness]]
* Support of non-syndicalist [[labor union|labor unions]]
* Encouraging promiscuity through sexual education (the teaching of safe sex) rather than teaching [[abstinence]] from premarital sex<ref> [http://www.foxnews.com/story/0,2933,286671,00.html Democrats Aim To Kill Abstinence-Only Program Funding], [[Fox News]], Monday, June 25, 2007</ref>
* A "[[living Constitution]]" that is reinterpreted as liberals prefer, rather than how it was intended
* Government programs to [[rehabilitate criminals]]
* Abolition of the death penalty
[[File:Johnwaynegacyrosalynncarter.jpg|right|300px|thumbnail|[[Serial killer]] [[John Wayne Gacy]] was a [[Democratic Party]] activist who had his picture taken with First Lady [[Rosalynn Carter]] in 1978. In an interview where he denied killing any of his victims, John Gacy said he was [[bisexuality|bisexual]] and "very liberal".<ref>http://s151.photobucket.com/albums/s151/candypop_02/Serial%20Killers/John%20Wayne%20Gacy/?action=view&current=SERIAL_KILLER_John_Wayne_Gacy_In-1.mp4</ref>]]
* [[Environmentalism]]<ref> and environmental organizations, for example [[Greenpeace]]</ref>
* [[Globalism]]
* Opposition to the integration of church and state.
* Opposition to full private property rights.<ref> For example, the liberal wing of the [[U.S. Supreme Court]] issued the 5-4 [[Kelo v. City of New London]] decision authorizing the taking of private property by government in order to give the property to another private entity rather than convert it to a public use.</ref>
* Reinstating the [[Fairness Doctrine]]
* In 2005, it was reported by CBS News that [[Theory of evolution and liberalism|liberals were the most likely supporters of the theory of evolution]].
* Opposition to domestic wire-tapping as authorized in the [[Patriot Act]]
* Opposition of [[Operation Iraqi Freedom]], a major part of the [[War on Terrorism]]
* Withholds support to the [[War on Terrorism]] and the [[War in Iraq]]
* Tolerance of different ideas and lifestyles
* Supports financially irresponsible policies
* Following policies which are proven to be incorrect
* Do not support a laissez-faire capitalist economy and support regulation of business
* Encouragement of [[Global Warming|global warming alarmism]]

According to current dictionaries and their own beliefs, a liberal is "a person who favors a political philosophy of progress and reform and the protection of civil liberties" or "a person who favors an economic theory of laissez-faire and self-regulating markets,"<ref>http://wordnetweb.princeton.edu/perl/webwn?s=liberal&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=00</ref> or "open-minded or tolerant, especially free of or not bound by traditional or conventional ideas, values, etc." or "favorable to or in accord with concepts of maximum individual freedom possible, especially as guaranteed by law and secured by governmental protection of civil liberties."<ref>http://dictionary.reference.com/browse/liberal</ref>

==Liberals and Uncharitableness==
[[Image:228130875 35181424e3.jpg|thumb|right|175px|[[United States|American]] liberals give less to charity than American conservatives.<ref>http://www.realclearpolitics.com/articles/2008/03/conservatives_more_liberal_giv.html</ref> In addition, [[per capita]] [[atheism|atheists]] and [[agnosticism|agnostics]] in the United States [[Atheism and charity|give significantly less to charity than theists even when church giving is not counted for theists]].[http://www.barna.org/barna-update/article/12-faithspirituality/102-atheists-and-agnostics-take-aim-at-christians][http://findarticles.com/p/articles/mi_qa3647/is_200310/ai_n9340592/][http://abcnews.go.com/2020/Story?id=2682730&page=2] ]]
''For more information please see'': [[Liberals and uncharitableness]] and [[Atheism and charity]]

In March of 2008, [[George Will]] wrote at [[RealClearPolitics]] concerning the [[United States]]:
{{cquote|Sixteen months ago, Arthur C. Brooks, a professor at [[Syracuse University]], published "Who Really Cares: The Surprising Truth About Compassionate Conservatism." The surprise is that liberals are markedly less charitable than [[conservative]]s....

If many conservatives are liberals who have been mugged by reality, Brooks, a registered independent, is, as a reviewer of his book said, a social scientist who has been mugged by data. They include these findings:

-- Although liberal families' incomes average 6 percent higher than those of conservative families, conservative-headed households give, on average, 30 percent more to charity than the average liberal-headed household ($1,600 per year vs. $1,227).

-- Conservatives also donate more time and give more blood.<ref>http://www.realclearpolitics.com/articles/2008/03/conservatives_more_liberal_giv.html</ref>}}
[[Atheism|Atheists]] and [[agnosticism|agnostics]] often reject [[Bible|Biblical]] [[morality]] (and therefore [[conservative Christianity]] ) and hold to [[moral relativism]].<ref>http://www.barna.org/FlexPage.aspx?Page=BarnaUpdate&BarnaUpdateID=152</ref> Therefore, it is not surprising that [[per capita]] atheists and agnostics in [[United States|America]] [[Atheism and charity|give significantly less to charity than theists even when church giving is not counted for theists]].[http://www.barna.org/barna-update/article/12-faithspirituality/102-atheists-and-agnostics-take-aim-at-christians][http://findarticles.com/p/articles/mi_qa3647/is_200310/ai_n9340592/][http://abcnews.go.com/2020/Story?id=2682730&page=2]

=== Liberal politicians and uncharitableness ===
The political magazine the [[American Spectator]] featured an article which focused on [[liberal politicians and uncharitableness]] exposing the hypocrisy of the liberal politicians it featured.<ref>http://www.liveleak.com/view?i=1c5_1238044128&c=1</ref>

In addition, [[Barack Obama]] has been criticized concerning [[Barack Obama and uncharitableness|his lack of charitable giving]].

== Liberalism and bestiality ==

See also: [[Liberalism and bestiality]]

[[File:Peter-Singer.jpg|right|thumbnail|260px|The [[atheist]] philosopher [[Peter Singer]] defends the practice of [[bestiality]] (as well as [[abortion]], infanticide and [[euthanasia]]). Despite holding these immoral views the liberal and pro-[[evolution]] academic establishment rewarded his views with a bioethics chair at [[Princeton University]].<ref>
*[http://creation.com/the-basis-of-a-christian-worldview The Basis of a Christian Worldview - Creation Ministries International]
*[http://creation.com/answer-to-philosophy-religion-professor-on-biblical-exegesis-and-the-problem-of-evil CMI answers philosophy/religion professor on biblical exegesis and the problem of evil]
*[http://www.firstthings.com/onthesquare/2011/06/the-dangerous-mind-of-peter-singer ''The Dangerous Mind''] by Joe Carter, ''[[First Things]]''</ref> See: [[Atheism and bestiality]] ]]
[[Bestiality]] is the act of engaging in sexual relations with an animal. The [[atheist]] philosopher [[Peter Singer]] defends the practice of bestiality (as well as [[abortion]], infanticide and [[euthanasia]]). Despite holding these immoral views the liberal and pro-[[evolution]] academic establishment rewarded his views with a bioethics chair at [[Princeton University]] (Princeton University is a very liberal school - see: [[Liberalism and bestiality]]).<ref>
*[http://creation.com/the-basis-of-a-christian-worldview The Basis of a Christian Worldview - Creation Ministries International]
*[http://creation.com/answer-to-philosophy-religion-professor-on-biblical-exegesis-and-the-problem-of-evil CMI answers philosophy/religion professor on biblical exegesis and the problem of evil]
*[http://www.firstthings.com/onthesquare/2011/06/the-dangerous-mind-of-peter-singer ''The Dangerous Mind''] by Joe Carter, ''[[First Things]]''</ref> Peter Singer was installed as the Ira W. DeCamp Professor of Bioethics at the University Center for Human Values at Princeton University in 1999 and in 2006 it was reported that he still worked part-time in that capacity. <ref>[http://creation.com/the-basis-of-a-christian-worldview The Basis of a Christian Worldview]</ref> In 2006, it was also reported that Singer worked part-time as Laureate Professor at the University of Melbourne in the Centre for Applied Philosophy and Public Ethics since 2005.<ref>[http://creation.com/the-basis-of-a-christian-worldview The Basis of a Christian Worldview]</ref>

Joe Carter's ''[[First Things]]'' article entitled ''The Dangerous Mind'' declares concerning Peter Singer declared:
{{cquote|Singer has spent a lifetime justifying the unjustifiable. He is the founding father of the [[Animal rights|animal liberation movement]] and advocates ending “the present speciesist bias against taking seriously the interests of nonhuman animals.” He is also a defender of killing the aged (if they have dementia), newborns (for almost any reason until they are two years old), necrophilia (assuming it’s consensual), and bestiality (also assuming it’s consensual).<ref>[http://www.firstthings.com/onthesquare/2011/06/the-dangerous-mind-of-peter-singer ''The Dangerous Mind''] by Joe Carter, ''[[First Things]]''</ref>}}

On October 5, 2011, the British newspaper The Telegraph wrote an article which discussed how homosexuality "rights" have emboldened individuals to ask for so called bestiality "rights" (see: [[Homosexuality and bestiality]]).<ref>[http://blogs.telegraph.co.uk/news/timstanley/100108943/the-gay-rights-movement-has-emboldened-americas-bestiality-advocates/ The dark side of sexual freedom: American 'zoophiles' take on the language of equality - October 5, 2011 - The Telegraph]</ref>

In 2010, the liberal state of [[Washington]] has the highest number of reported cases of bestiality in the United States even though it was merely the 13th most populous state according to the 2010 United States census. (for more information please see: [[Washington state and bestiality]]).<ref>[http://www.pet-abuse.com/pages/cruelty_database/statistics/state_ranking.php?year=2010&search=go Pet Abuse -2010]</ref><ref>[http://2010.census.gov/2010census/data/apportionment-pop-text.php 2010 United States Census data]</ref><ref>[http://politicalticker.blogs.cnn.com/2011/02/25/new-poll-identifies-most-liberal-and-conservative-states/ 2011 Political map - CNN]</ref>

In 2005, four legislators in the liberal state of [[Massachusetts]] tried to soften it bestiality laws.<ref>[Massachusetts bill to repeal fornication, adultery, and blasphemy, and to soften bestiality laws]</ref>
[[File:NBC Tower.jpg|thumbnail|200px|[[LifeSiteNews]] reported:"In 46 hours of programming, [[NBC]] contained only one reference to marital sex, but 11 references to non-marital sex and one reference to [[adultery]] were made. References to incest, pedophilia, partner swapping, prostitution, threesomes, transsexuals/transvestites, [[bestiality]], and necrophilia combined outnumbered references to sex in marriage on NBC by a ratio of 27 to 1.<ref>[http://www.lifesitenews.com/news/archive/ldn/2008/aug/08080602 Study Finds TV Treats Marital Sex as Burdensome, Adultery as Positive]</ref> See also: [[Liberalism and bestiality]] ]]
The Bible says that bestiality is a perversion and, under the [[Old Testament]] [[Pentateuch|Jewish Law]], punishable by death (Exodus 22:19, Leviticus 18:23, Leviticus 20:15 and Deuteronomy 27:21). The atheistic worldview does not lend itself to the establishment of morality within society and individuals (see: [[Atheism and morality]] and [[Atheism and deception]]). The atheistic worldview does not lend itself to the establishment of morality within society and individuals (see: [[Atheism and morality]] and [[Atheism and deception]]).

A study found that "Psychiatric patients were found to have a statistically significant higher prevalence rate (55%) of bestiality than the control groups (10% and 15% respectively)."<ref>[http://www.ncbi.nlm.nih.gov/pubmed/1778686 A prevalence study of bestiality (zoophilia) in psychiatric in-patients, medical in-patients, and psychiatric staff - Int J Psychosom. 1991;38(1-4):45-7.]</ref> The atheist population [[Atheism and suicide|has a higher suicide rate]] and [[Atheism and marriageability|lower marriage rates]] than the general population (see: [[Atheism and suicide]] and [[Atheism and marriageability]] and [[Atheism and health]]). In addition, ''[[Wired (magazine)|Wired]]'' magazine made the observation that atheists tend to be quarrelsome, socially challenged men.<ref>http://voxday.blogspot.com/2007/08/socially-autistic-atheist.html</ref>

For more information please see:

*[[Atheism and bestiality]]

*[[Evolutionary belief and bestiality]]

*[[Liberalism and bestiality]]

*[[Homosexuality and bestiality]]

*[[Liberal American entertainment industry and bestiality]]

*[[Wikipedia on bestiality]]

*[[Bestiality and Sweden|Liberal Sweden and bestiality]]

*[[Bestiality and Britain|Godless Britain and bestiality]]

*[[Denmark, Sweden, evolutionary belief and bestiality]]

*[[Netherlands and bestiality|The liberal Netherlands and bestiality]]

*[[Skeptic Skatje Myers' comments on bestiality]]

*[[Joseph Stalin's ape-men experiments]]
=== Occupy Wall Street and bestiality chant ===

''See also:'' [[Occupy Wall Street and bestiality chant]]

[[Bestiality]] is the act of engaging in sexual relations with an animal. A crowd at Occupy Wall Street was led to repeat various chants which included a chant involving bestiality and the incident was videotaped.<ref>[http://rightwingnews.com/john-hawkins/the-10-greatest-moments-from-the-occupy-wall-street-protests-so-far/ The 10 Greatest Moments From The Occupy Wall Street Protests So Far]</ref>

Below is an excerpt of the chant:
{{cquote|Everything seems to be possible. [Crowd Parrot Chant] You can travel to the moon. [CPC] You can become immortal [CPC] by biogenetics. You can have sex with animals, or whatever. [CPC].<ref>[http://rightwingnews.com/john-hawkins/the-10-greatest-moments-from-the-occupy-wall-street-protests-so-far/ The 10 Greatest Moments From The Occupy Wall Street Protests So Far]</ref>}}

==Liberals and Superstition==
[[Image:2384975035_230a0eac30.jpg‎‎|right|150px]]

The [[Wall Street Journal]] reported: "A comprehensive new study released by Baylor University, shows that [[Conservative Christianity|traditional Christian religion]] greatly decreases belief in everything from the efficacy of palm readers to the usefulness of [[astrology]]. <ref>[http://online.wsj.com/article/SB122178219865054585.html]</ref>

Also, in September of 2008, the [[Wall Street Journal]] reported:
{{cquote|The reality is that the [[New Atheism|New Atheist]] campaign, by discouraging [[religion]], won't create a new group of intelligent, skeptical, enlightened beings. Far from it: It might actually encourage new levels of mass superstition. And that's not a conclusion to take on faith — it's what the empirical data tell us.

"What Americans Really Believe," a comprehensive new study released by Baylor University yesterday, shows that [[Conservative Christianity|traditional Christian religion]] greatly decreases belief in everything from the efficacy of palm readers to the usefulness of [[astrology]]. It also shows that the irreligious and the members of more liberal Protestant denominations, far from being resistant to superstition, tend to be much more likely to believe in the paranormal and in pseudoscience than evangelical Christians....

This is not a new finding. In his 1983 book "The Whys of a Philosophical Scrivener," skeptic and science writer Martin Gardner cited the decline of traditional religious belief among the better educated as one of the causes for an increase in [[pseudoscience]], cults and superstition. He referenced a 1980 study published in the magazine Skeptical Inquirer that showed irreligious college students to be by far the most likely to embrace paranormal beliefs, while born-again Christian college students were the least likely.<ref>http://online.wsj.com/article/SB122178219865054585.html</ref>}}

== Liberalism in North America Today ==
[[File:Smear merchants.jpg|right|200px]]
[[Democrats]] and most media outlets in the [[U.S.]] are blatantly liberal.<ref>{{cite web|url=http://www.mrc.org/biasbasics/biasbasics1.asp|title=Media Bias basics|publisher=Media Research Center}}</ref> Liberalism in North America today practices three primary tactics to attack the Republican Party, and sometimes to attack American values in general. These three liberal tactics can be pronounced using the following [[acronym]]: SIN. Liberals (1) '''s'''hift the subject, they (2) '''i'''gnore the facts, and they (3) '''n'''ame call.<ref>Scott Baker. [http://www.theblaze.com/stories/did-herman-cain-give-the-dont-miss-speech-at-cpac/ Did Herman Cain Give the ‘Don’t Miss’ Speech at CPAC?], ''[[The Blaze]], February 12, 2011.</ref><ref>[[YouTube]]. [http://www.youtube.com/watch?v=-N3-j3HM7-A& Herman Cain: "Stupid People Are Ruining America"], February 11, 2011.</ref>

* Liberals typically support a "mixed" economy, a policy similar to that of [[fascism]]. <ref>{{cite web|url=http://fora.tv/2008/01/30/Liberal_Traits_of_Fascism|title=Video discussion about how modern liberalism is actually fascist by author Jonah Goldberg.}}</ref>

* Liberals claimed a monopoly on [[compassion]], [[decency]], and [[social justice]] (as defined by themselves), posing as the sole defenders of [[civic virtue]] against a horde of backwoodsmen, racists, and religious fanatics. [http://www.americanthinker.com/2008/03/the_disgrace_of_liberalism.html]
{{cquote|There's another goal, from my point of view, which is to try to lay the groundwork for a radical political force which would conceive of itself as distinctly to the left of moderate, reformist American liberals. And that has two aspects. One is to try to change that liberalism, to transform it by analysis, critique, and activism; the second is to build a radical movement which would be an autonomous force in its own right, which would be distinct from the traditional American liberal consensus. This radical part of the program involves not simply supporting the liberal students against conservative students and conservative professors, but trying to act on them, to push them to the left. It also involves trying to find and support, even trying to help create, networks of radical students in law school and of radical professors around the country — students and teachers who see themselves as wanting to go a lot further than most people want to go. <ref> [http://66.218.69.11/search/cache?ei=UTF-8&p=liberal+teachers&fr=yfp-t-501&fp_ip=MX&u=duncankennedy.net/documents/Liberal%2520Values%2520in%2520Legal%2520Education.pdf&w=liberal+liberals+teachers+teacher&d=BNZFhPReRjC1&icp=1&.intl=us Liberal Values in Legal Education] Duncan Kennedy (professor at Harvard Law School)</ref>}}

===Liberal Rankings of Congress Members===

The National Journal compiles the votes of each congress member each year and uses the information to create rankings<ref>http://nationaljournal.com/voteratings/index.htm</ref> of how liberal each member of the United States [[Congress]] is. In addition to showing the voting records of each member and given an overall all ranking of liberalness, the National Journal also ranks congress members by liberalness in the areas of social, economic, and foreign policy.

==Liberalism in Europe today==

In Europe, on the other hand, parties that call themselves ''liberal'' are moderate in outlook, ranging from centre-left to centre-right, promote typically economic and business freedom. The Alliance of Liberals and Democrats for Europe<ref>http://www.alde.eu</ref> is a party of the European Parliament that represents most ''liberal'' parties from European countries. Similar policies are promoted by many ''liberal'' parties throughout the world,<ref>http://www.liberal-international.org/</ref> such as the Liberal Party of Australia.<ref>[http://www.liberal.org.au/]</ref>

Trade unions and socialist parties often criticize politicians for promoting lower taxes on business, or more flexible hiring and firing laws, by calling them "liberals" or [[neoliberal|neoliberals]]. Thus, just as in the US, "liberal" may occasionally be used as a term of abuse. But when someone is called "liberal" in Europe, it has an entirely different meaning than in the US. In fact, the US meaning of liberal is more similar to the politics of European [[socialist]] or [[social democracy|social democratic]] parties.<ref>[http://www.pes.org]</ref>

==Historical Liberalism ==
In history, the word "liberal" has meant different things at different times, and was associated with individual liberty in prior centuries. In the postwar period, liberals supported government intervention in the economy and welfare state policies, as well as peaceful coexistence with the communist block, which are not liberal policies in the sense of classical liberalism. After the end of the cold war, with the demise of socialism and communism, many liberals embraced some ideas from economic neo-liberalism, and coined it the "Third Way". In the area of national security and foreign policy liberals in the [[U.S.]] failed to define a consistent stance, even after the events of 9/11 and the beginning of the war in Iraq. Liberals generally support affirmative action, gay marriage, and abortion.<ref>"Political liberals tend, for whatever reason, to be ardent supporters of both gay rights and pro-choice programs." Greenberg and Bailey [http://ai.eecs.umich.edu/people/conway/TS/Bailey/Greenberg-Bailey/Homosexual%20Eugenics.pdf] </ref>

==Original meaning: Classical Liberalism==
Liberalism is a political philosophy with freedom as its core value. The term was originally applied to supporters of individual liberties and equal rights, but, in America, the term has come to represent a movement of social change that often conflicts with [[conservative]] values such as moral values and tradition.

See [[Classical Liberal|Classical Liberalism]]. Compare [[Libertarianism]].

== Infamous liberals ==

''See also:'' [[Infamous liberals]]

* [[Margaret Sanger]]

*[[John Wayne Gacy]] - In an interview where he denied killing any of his victims, [[serial killer]] John Wayne Gacy said he was [[bisexuality|bisexual]] and "very liberal".<ref>http://s151.photobucket.com/albums/s151/candypop_02/Serial%20Killers/John%20Wayne%20Gacy/?action=view&current=SERIAL_KILLER_John_Wayne_Gacy_In-1.mp4</ref> Gacy was also a [[Democratic Party]] activist who had his picture taken with [[Rosalynn Carter]].<ref>http://www.digitaljournal.com/image/45527</ref>

==Liberal Organizations ==
*[[AARP|AARP - American Association of Retired People]]
*[[ACLU|ACLU - American Civil Liberties Union]]
*[[ACORN|ACORN - Association of Community Organizations for Reform Now]]
*[[AFL-CIO|AFL-CIO - American Federation of Labor and Congress of Industrial Organizations]]
*[[Amnesty International|AI - Amnesty International]]
*[[A.N.S.W.E.R.|ANSWER - Act Now to Stop War and End Racism]]
*[[CAIR|CAIR - Council on American-Islamic Relations]]
*[[Committees of Correspondence for Democracy and Socialism]]
*[[Democratic National Committee]]
*[[Greenpeace]]
*[[MoveOn.org]]
*[[NARAL|NARAL - National Abortion and Reproductive Rights Action League]]
*[[NAACP|NAACP - National Association for the Advancement of Colored People]]
*[[National Committee for an Effective Congress]]
*[[National Education Association]]
*[[National Organization of Women|NOW - National Organization of Women]]
*[[PETA|PETA - People for the Ethical Treatment of Animals]]
*[[Planned Parenthood|Planned Parenthood Federation of America]]
*[[Progressives for Obama]]
*[[Rainbow/PUSH Coalition]]
*[[SEIU|SEIU - Service Employees International Union]]
*[[U.S. Peace Council]]
Source: [http://www.politixgroup.com/lo.htm The Politix Group]

==References==
{{reflist|2}}

==See Also==

* [[Conservative resources]]
* [[Conservapedia:Articles about liberals|Articles about liberals]]
* [[Classical liberal]]
* [[Drinking Liberally]]
* [[Godless liberal]]
* [[Last wordism]]
* [[Essay:Liberal celebrity obsession|Liberal celebrity obsession]]
* [[Essay:Liberal Behavior on Conservapedia|Liberal Behavior on Conservapedia]]
* [[Liberal Christianity]]
* [[Liberal Democrats]]
* [[Liberal Elite]]
* [[Essay: Liberal Falsehoods|Liberal Falsehoods]]
* [[Liberal Fascism]]
* [[Liberal friendship]]
* [[Liberal Gloss]]
* [[Liberal grading]]
* [[Liberal hypocrisy]]
* [[Essay:Liberal hysteria|Liberal hysteria]]
* [[Essay:Liberal Intellectualism|Liberal Intellectualism]]
* [[Liberal labels]]
* [[Slander: Liberal Lies About the American Right|Liberal Lies About the American Right]]
* [[Liberal logic]]
* [[The Liberal Mind: The Psychological Causes of Political Madness|Liberal Mind]]
* [[Liberal Party]]
* [[Liberal supremacist]]
* [[Massachusetts liberal]]
* [[Progressives]]
* [[Scientific Illiteracy and Liberals]]

==Further Information==
* [[Best_New_Conservative_Words#New_Liberal_Terms|New Liberal Terms]]
* [[Conservative Links]]
* http://www.studentnewsdaily.com/conservative-vs-liberal-beliefs/

{{liberalism}}

[[Category:Political Ideologies]]
[[Category:Politics]]
[[Category: Liberals]]

Talk:Majoring in Mathematics

2012-02-27T05:04:38Z

Bogart12: signed a comment

This is an extremely rough outline for this new article. I will continue to expand it over the next few weeks based on feedback about the appropriateness of the problems and other suggestions for improvements. Please let me know what you think! --[[User:MarkGall|MarkGall]] 23:12, 4 October 2009 (EDT)
::well I was a math major in college many years ago (before Rubic's cube!) Suggest adding statistics.
:::Ah, good idea. At my undergrad school mathematics and statistics were separate programs, but I guess this isn't typical. I'll throw in a new section. I'm not much for statistics -- can anyone suggest some good problems? --[[User:MarkGall|MarkGall]] 23:20, 4 October 2009 (EDT)

Tremendous work, Mark. I'll try to add something for probability or statistics, which I studied.--[[User:Aschlafly|Andy Schlafly]] 23:22, 4 October 2009 (EDT)
:Great, thanks. These are subjects in which I'm inexpert. Now I'm inclined to move Probability/Statistics to a "field" along with algebra, analysis, etc. Please add a nice problem or theorem if you have any in mind! --[[User:MarkGall|MarkGall]] 23:24, 4 October 2009 (EDT)

Terrific analysis on what college mathematics is not. That should be required reading for many seeking to major in math!--[[User:Aschlafly|Andy Schlafly]] 22:30, 15 October 2009 (EDT)

Why is there no mention of the bible or theology in this article? It should be mentioned, as it is in [[Axiom_of_Infinity]], that the notion of an infinite set is somewhat blasphemous. [[User:Tomkup32|Tomkup32]] 10:58, 9 December 2009 (EST)

For Bezout's theorem, you have some inaccurate claims: the line x+y=0 and x+y=1 never interset. We need to move to projective space for the degree of the intersection to be exactly mn.

== Liberal bias ==

How can there be liberal bias in math? Does saying 1+1 = 2 have a motive?[[User:SusanP|SusanP]] 23:29, 9 February 2012 (EST)

:College math is not completely immune to liberal influences that have destroyed other subjects like physics.--[[User:Aschlafly|Andy Schlafly]] 23:37, 9 February 2012 (EST)

:Can you give an example of liberal bias in math? --[[User:Bogart12|Bogart12]]
:Possible liberal bias--the study of so-called "homomorphisms" in modern liberal algebra could be part of the gay agenda?--[[User:Bogart12|Bogart12]]
::No, sorry, that's absurd and I think you know it. "Homo" simply means same and is used in a wide variety of contexts that have nothing to do with liberal bias. Is homogenized milk liberal bias? Or homonyms? Homophones? I've already reverted your addition to the article once, so I won't do it again just yet, but please consider removing or modifying it yourself.--[[User:JustinD|JustinD]] 19:32, 24 February 2012 (EST)
::There is a crucial difference between your examples and my claim. A homophone describes two words sounding the same but being different. Bat is not a homophone with bat, that doesn't make sense. Saying wind and wind are homophones acknowledges that they sound the same but are different words. A homomorphism allows groups that are different, like Z_2xZ_2 and the Klein four group, to be treated as equal. Additionally the global warming obsession is prolific. I didn't mean my writing to sound flippant, and perhaps its tone can be improved, but it was certainly not meant as a joke.
:::I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs. --[[User:JustinD|JustinD]] 01:23, 26 February 2012 (EST)
::::Haha you are absolutely right, my apologies. I thought I had picked a word specifically with no homophones. Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine. But consider a statement like "there is only one group of order 3." There are clearly many, because you can define one on any set with 3 elements. Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms. Compare this with the professor value of refusing to distinguish between men and women. To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even. To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same. I hope that clarifies what I was struggling to say before. --[[User:Bogart12|Bogart12]]
:::::They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between male and female. So yes, in many situations, women and men are essentially the same.[[User:KenShomer|KenShomer]] 15:15, 26 February 2012 (EST)

::::::If that statement were true, then why are the top achievers on difficult math contests (such as the Putnam exam) more than 90% male, and less than 10% female?--[[User:Aschlafly|Andy Schlafly]] 16:32, 26 February 2012 (EST)\
::::::: I can't vouch for this on a national level, but when I took the Putnam at UConn last year, about 90% of the participants were male. If that's true at a national level (and I don't know if it is) then it stands to reason. [[User:Gregkochuconn|Gregkochuconn]] 21:28, 26 February 2012 (EST)
::::::: It's gotten so bad that now they make women put red stickers on the exams so they can graded differently! Women often have separate prizes too.--Bogart12
:::::I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms.
:::::This is getting a bit off topic, but if Andy and you are right and (liberal?) universities improperly equate the aptitude of men and women (by analogy, posit a homomorphism between men and women), we shouldn't conclude that the positing of all equivalences is liberal bias (by analogy, that homomorphisms are the result of liberal bias), but instead should conclude that universities are mistaken and that no such equivalence exists in this case (by analogy, there is no homomorphism between a group of order 3 and a group of order 4, say).--[[User:JustinD|JustinD]] 17:01, 26 February 2012 (EST)
:::::Again though, the university claims more than "these sets have similar group structures on them," and goes so far as to insist that there is no reason to distinguish between them. [[User:Bogart12|Bogart12]]
::::::Okay, so then universities are wrong to equate men and women in this way. What does that have to do with homomorphisms? Are we still disagreeing whether they serve a legitimate mathematical purpose or are instead the product of improper liberal bias?--[[User:JustinD|JustinD]] 21:54, 26 February 2012 (EST)
:::::::It's central to liberal ideology to view these blasphemous notions as "useful." Next, you'll be defending relativity as useful, and that is a slippery slope my friend. We draw the line here at Conservapedia where ideas that are wrong are rejected, regardless of how useful we have been told they are.[[User:Bogart12|Bogart12]]

== Examples of Liberal Math

The purported proof of [[Fermat's Last Theorem]] would be an example of liberal math.--[[User:Aschlafly|Andy Schlafly]] 16:48, 26 February 2012 (EST)
:This may quickly move outside my area of understanding, but could you clarify this at all? Is the concern the use of the [[axiom of choice]] and/or non-[[ZF]] axioms? I've read our article and vaguely remember a book I read in high school, but other than the use of some non-standard techniques, I wasn't aware there was any serious doubt as to the validity of the proof. --[[User:JustinD|JustinD]] 17:10, 26 February 2012 (EST)
:: What would be an example of Conservative Math? --[[User:BradleyS|BradleyS]] 17:13, 26 February 2012 (EST)

:::[[Godel's Incompleteness Theorems]], and [[liberals]] ostracized [[Kurt Godel]] for it.--[[User:Aschlafly|Andy Schlafly]] 17:41, 26 February 2012 (EST)
:::: What is there that evidence that liberals ostracized Gödel? And what makes the Incompleteness Theorem conservative? --[[User:BradleyS|BradleyS]] 19:12, 26 February 2012 (EST)

:::::Liberals kept Godel from obtaining tenure at most university math departments, and ostracized him in other ways. [[Bertrand Russell]], a leading leftist of that time, was humiliated by Godel's insight, which was conservative in how it debunked intellectual arrogance.--[[User:Aschlafly|Andy Schlafly]] 19:33, 26 February 2012 (EST)

:::::Exactly Andy, Whitehead and Russell were both in the middle of trying to "prove" everything when Godel administered a much-needed dose of humility. [[User:Bogart12|Bogart12]]

::::::Right. A liberal claims to know almost everything. A conservative recognizes that the liberal actually knows almost nothing of value.--[[User:Aschlafly|Andy Schlafly]] 22:39, 26 February 2012 (EST)

===Carbon Dating===
Using the most advanced scientific & mathematical calculations, the dating process is still prone to error. The [[Shroud of Turin]] is claimed as fabrication by the scientific community but the liberals fail to grasp their errors in calculating exposure to contamination, such as soot. --[[User:Jpatt|Jpatt]] 19:37, 26 February 2012 (EST)
:That's not necessarily mathematics, but, archaeology + ''applied'' mathematics.[[User:JonM|JonM]] 19:50, 26 February 2012 (EST)

::Good point, but applied math is still math, and the example illustrates liberal use of math to convey an unjustified claim of "proof".--[[User:Aschlafly|Andy Schlafly]] 20:10, 26 February 2012 (EST)
:::Hammers have been used throughout history for the construction of buildings intended to promote both liberal and conservative ideals. The hammer has no inherent political philosophy. The hammer is a tool, and though it can be used for liberal or conservative purposes, it is inherently a neutral party. Math is the same way. While math can be used to promote liberal ideals, and is often studied by liberals, it is not liberal or conservative. Math is a tool.[[User:KenShomer|KenShomer]] 22:11, 26 February 2012 (EST)

::::But hammers are not courses of study or an ideology. Math is. And all courses of study and ideologies are susceptible to liberal bias. Engineering, with its grounding in what works, is probably the most immune to [[liberal bias]]. Women's studies and English literature are probably the most susceptible to liberal bias.--[[User:Aschlafly|Andy Schlafly]] 22:37, 26 February 2012 (EST)

== atheist and liberal idiocy extends to math: 2+2=5? (Lawrence Krauss vs William Lane Craig) ==

[http://www.youtube.com/watch?v=NOrlIOm6eGM 2+2=5? (Lawrence Krauss vs William Lane Craig)] [[User:Conservative|Conservative]] 20:33, 26 February 2012 (EST)

Talk:Majoring in Mathematics

2012-02-27T05:03:31Z

Bogart12:

This is an extremely rough outline for this new article. I will continue to expand it over the next few weeks based on feedback about the appropriateness of the problems and other suggestions for improvements. Please let me know what you think! --[[User:MarkGall|MarkGall]] 23:12, 4 October 2009 (EDT)
::well I was a math major in college many years ago (before Rubic's cube!) Suggest adding statistics.
:::Ah, good idea. At my undergrad school mathematics and statistics were separate programs, but I guess this isn't typical. I'll throw in a new section. I'm not much for statistics -- can anyone suggest some good problems? --[[User:MarkGall|MarkGall]] 23:20, 4 October 2009 (EDT)

Tremendous work, Mark. I'll try to add something for probability or statistics, which I studied.--[[User:Aschlafly|Andy Schlafly]] 23:22, 4 October 2009 (EDT)
:Great, thanks. These are subjects in which I'm inexpert. Now I'm inclined to move Probability/Statistics to a "field" along with algebra, analysis, etc. Please add a nice problem or theorem if you have any in mind! --[[User:MarkGall|MarkGall]] 23:24, 4 October 2009 (EDT)

Terrific analysis on what college mathematics is not. That should be required reading for many seeking to major in math!--[[User:Aschlafly|Andy Schlafly]] 22:30, 15 October 2009 (EDT)

Why is there no mention of the bible or theology in this article? It should be mentioned, as it is in [[Axiom_of_Infinity]], that the notion of an infinite set is somewhat blasphemous. [[User:Tomkup32|Tomkup32]] 10:58, 9 December 2009 (EST)

For Bezout's theorem, you have some inaccurate claims: the line x+y=0 and x+y=1 never interset. We need to move to projective space for the degree of the intersection to be exactly mn.

== Liberal bias ==

How can there be liberal bias in math? Does saying 1+1 = 2 have a motive?[[User:SusanP|SusanP]] 23:29, 9 February 2012 (EST)

:College math is not completely immune to liberal influences that have destroyed other subjects like physics.--[[User:Aschlafly|Andy Schlafly]] 23:37, 9 February 2012 (EST)

:Can you give an example of liberal bias in math? --[[User:Bogart12|Bogart12]]
:Possible liberal bias--the study of so-called "homomorphisms" in modern liberal algebra could be part of the gay agenda?--[[User:Bogart12|Bogart12]]
::No, sorry, that's absurd and I think you know it. "Homo" simply means same and is used in a wide variety of contexts that have nothing to do with liberal bias. Is homogenized milk liberal bias? Or homonyms? Homophones? I've already reverted your addition to the article once, so I won't do it again just yet, but please consider removing or modifying it yourself.--[[User:JustinD|JustinD]] 19:32, 24 February 2012 (EST)
::There is a crucial difference between your examples and my claim. A homophone describes two words sounding the same but being different. Bat is not a homophone with bat, that doesn't make sense. Saying wind and wind are homophones acknowledges that they sound the same but are different words. A homomorphism allows groups that are different, like Z_2xZ_2 and the Klein four group, to be treated as equal. Additionally the global warming obsession is prolific. I didn't mean my writing to sound flippant, and perhaps its tone can be improved, but it was certainly not meant as a joke.
:::I'm not sure I see the "crucial difference" you're seeing. I don't know what you mean by saying that homomorphisms "allow[] groups that are different . . . to be treated as equal." What do you mean by "treated as equal"? Obviously, if a homomorphism exists between two groups it shows that there are certain structural similarities between the two groups, but this hardly means that they are equal. The fact that 124 and 490 are both even shows that there are certain similarities between them (namely that each includes 2 in its prime factorization), but that doesn't mean we treat them as equal and it certainly isn't evidence that evenness is the result of some sort of liberal bias. Also, I think you have your examples backwards. Bat (animal) is a homophone with bat (sports) because both are pronounced the same but have different meanings. Wind (air flow) is not a homophone with wind (watches) because the pronunciation differs. They are, however, homographs. --[[User:JustinD|JustinD]] 01:23, 26 February 2012 (EST)
::::Haha you are absolutely right, my apologies. I thought I had picked a word specifically with no homophones. Allow me to elaborate: saying that 124 and 490 are both even emphasizes similarities which is fine. But consider a statement like "there is only one group of order 3." There are clearly many, because you can define one on any set with 3 elements. Nevertheless, you will never hear discussion of the many different groups of order 3, they are all lumped together because of homomorphisms. Compare this with the professor value of refusing to distinguish between men and women. To say men and women are both children of God is to discuss similarities while acknowledging differences, as in saying 124 and 490 are both even. To say men and women are basically the same, as universities today do, is consistent with saying that groups are essentially the same. I hope that clarifies what I was struggling to say before. --[[User:Bogart12|Bogart12]]
:::::They key point you are missing, however, is that in many, many subjects, such as in mathematical aptitude, there is no functional difference between male and female. So yes, in many situations, women and men are essentially the same.[[User:KenShomer|KenShomer]] 15:15, 26 February 2012 (EST)

::::::If that statement were true, then why are the top achievers on difficult math contests (such as the Putnam exam) more than 90% male, and less than 10% female?--[[User:Aschlafly|Andy Schlafly]] 16:32, 26 February 2012 (EST)\
::::::: I can't vouch for this on a national level, but when I took the Putnam at UConn last year, about 90% of the participants were male. If that's true at a national level (and I don't know if it is) then it stands to reason. [[User:Gregkochuconn|Gregkochuconn]] 21:28, 26 February 2012 (EST)
::::::: It's gotten so bad that now they make women put red stickers on the exams so they can graded differently! Women often have separate prizes too.
:::::I think the problem is a lack of imprecision when using words like "same" or "equal". In mathematics such terms have very precisely defined meanings and so to say that all groups of order three are the same or are equal (or, equivalently, to say that "there is only one group of order 3") is not to say that all such groups are the same in all respects (obviously, this isn't true or they would all have the same name/description and we wouldn't even doubt there were more than one such group), but instead only says that all such groups behave similarly in all the ways that are (currently) important to mathematicians. When dealing with real world situations like mathematical aptitude and gender, it's much easier to speak imprecisely (either mistakenly or maliciously) and thus much more plausible that some suggested equivalences are the result of liberal bias and not some underlying similarities. I just don't see how that is possible, however, in the realm of mathematics, at least with respect to homomorphisms.
:::::This is getting a bit off topic, but if Andy and you are right and (liberal?) universities improperly equate the aptitude of men and women (by analogy, posit a homomorphism between men and women), we shouldn't conclude that the positing of all equivalences is liberal bias (by analogy, that homomorphisms are the result of liberal bias), but instead should conclude that universities are mistaken and that no such equivalence exists in this case (by analogy, there is no homomorphism between a group of order 3 and a group of order 4, say).--[[User:JustinD|JustinD]] 17:01, 26 February 2012 (EST)
:::::Again though, the university claims more than "these sets have similar group structures on them," and goes so far as to insist that there is no reason to distinguish between them. [[User:Bogart12|Bogart12]]
::::::Okay, so then universities are wrong to equate men and women in this way. What does that have to do with homomorphisms? Are we still disagreeing whether they serve a legitimate mathematical purpose or are instead the product of improper liberal bias?--[[User:JustinD|JustinD]] 21:54, 26 February 2012 (EST)
:::::::It's central to liberal ideology to view these blasphemous notions as "useful." Next, you'll be defending relativity as useful, and that is a slippery slope my friend. We draw the line here at Conservapedia where ideas that are wrong are rejected, regardless of how useful we have been told they are.[[User:Bogart12|Bogart12]]

== Examples of Liberal Math

The purported proof of [[Fermat's Last Theorem]] would be an example of liberal math.--[[User:Aschlafly|Andy Schlafly]] 16:48, 26 February 2012 (EST)
:This may quickly move outside my area of understanding, but could you clarify this at all? Is the concern the use of the [[axiom of choice]] and/or non-[[ZF]] axioms? I've read our article and vaguely remember a book I read in high school, but other than the use of some non-standard techniques, I wasn't aware there was any serious doubt as to the validity of the proof. --[[User:JustinD|JustinD]] 17:10, 26 February 2012 (EST)
:: What would be an example of Conservative Math? --[[User:BradleyS|BradleyS]] 17:13, 26 February 2012 (EST)

:::[[Godel's Incompleteness Theorems]], and [[liberals]] ostracized [[Kurt Godel]] for it.--[[User:Aschlafly|Andy Schlafly]] 17:41, 26 February 2012 (EST)
:::: What is there that evidence that liberals ostracized Gödel? And what makes the Incompleteness Theorem conservative? --[[User:BradleyS|BradleyS]] 19:12, 26 February 2012 (EST)

:::::Liberals kept Godel from obtaining tenure at most university math departments, and ostracized him in other ways. [[Bertrand Russell]], a leading leftist of that time, was humiliated by Godel's insight, which was conservative in how it debunked intellectual arrogance.--[[User:Aschlafly|Andy Schlafly]] 19:33, 26 February 2012 (EST)

:::::Exactly Andy, Whitehead and Russell were both in the middle of trying to "prove" everything when Godel administered a much-needed dose of humility. [[User:Bogart12|Bogart12]]

::::::Right. A liberal claims to know almost everything. A conservative recognizes that the liberal actually knows almost nothing of value.--[[User:Aschlafly|Andy Schlafly]] 22:39, 26 February 2012 (EST)

===Carbon Dating===
Using the most advanced scientific & mathematical calculations, the dating process is still prone to error. The [[Shroud of Turin]] is claimed as fabrication by the scientific community but the liberals fail to grasp their errors in calculating exposure to contamination, such as soot. --[[User:Jpatt|Jpatt]] 19:37, 26 February 2012 (EST)
:That's not necessarily mathematics, but, archaeology + ''applied'' mathematics.[[User:JonM|JonM]] 19:50, 26 February 2012 (EST)

::Good point, but applied math is still math, and the example illustrates liberal use of math to convey an unjustified claim of "proof".--[[User:Aschlafly|Andy Schlafly]] 20:10, 26 February 2012 (EST)
:::Hammers have been used throughout history for the construction of buildings intended to promote both liberal and conservative ideals. The hammer has no inherent political philosophy. The hammer is a tool, and though it can be used for liberal or conservative purposes, it is inherently a neutral party. Math is the same way. While math can be used to promote liberal ideals, and is often studied by liberals, it is not liberal or conservative. Math is a tool.[[User:KenShomer|KenShomer]] 22:11, 26 February 2012 (EST)

::::But hammers are not courses of study or an ideology. Math is. And all courses of study and ideologies are susceptible to liberal bias. Engineering, with its grounding in what works, is probably the most immune to [[liberal bias]]. Women's studies and English literature are probably the most susceptible to liberal bias.--[[User:Aschlafly|Andy Schlafly]] 22:37, 26 February 2012 (EST)

== atheist and liberal idiocy extends to math: 2+2=5? (Lawrence Krauss vs William Lane Craig) ==

[http://www.youtube.com/watch?v=NOrlIOm6eGM 2+2=5? (Lawrence Krauss vs William Lane Craig)] [[User:Conservative|Conservative]] 20:33, 26 February 2012 (EST)

Talk:Majoring in Mathematics

2012-02-27T02:23:05Z

Bogart12:

Satan

2012-02-26T20:05:03Z

Bogart12: /* Liberal Protestant views */

[[Image:GustaveDoreParadiseLostSatanProfile.jpg|right|thumb|Gustave Doré's depiction of Satan from John Milton's Paradise Lost.]]

'''Satan''' or the '''Devil''' is the embodiment of evil, and plays a major role in Christian theology and literature, as well as in many other religions. He is the tempter and spiritual enemy of mankind. He is the adversary of God, although subordinate to him and able to act only by his sufferance, and is represented frequently as the leader or prince of all apostate angels and as ruler of [[hell]].
"Satan is the force that loves to find the guilt and weakness in people, to humiliate them with it, to convince them that, because they are not good, God cannot love them."<ref> [http://www.nationalreview.com/corner/258360/iritei-stuff-satan-prosecutor-mike-potemra The Rite Stuff: Satan as Prosecutor] - Mike Potemra</ref>

==Old Testament==
Satan was once a member of the divine council of God referenced in the [[Old Testament]]. He is referenced 11 times in [[Job]] and 4 other times in the Old Testament. The [[New Testament]] mentions Satan 34 times in all, starting with the first book [[Matthew]] and ending with the last [[Revelation]]. In the Christian tradition he rebelled against God and is now the enemy of God and man alike. He is the father of lies and no good is found in him. He leads a host of fallen angels (or [[demon]]s) who know their days are numbered before they will be cast in the lake of fire and they seek to take as many humans as possible with them.

== New Testament==
In the [[New Testament]], Satan tries to tempt [[Jesus]] in the desert, and fails. Jesus warns extensively to beware of Satan as does [[Paul]].

In Christian theology Satan's goal is to lead people away from the love of God, by tempting or tricking them. The only sources of supernatural power in the world are from either God (good) or Satan (evil). In the book of [[Genesis]], Satan takes the form of a snake and tempts Eve with fruit from a tree. This causes sin to come into the world. Kelly (2006) demonstrates how assumptions--such as the identification of the Eden serpent with Satan, probably first made by Justin Martyr in the second century--have hardened into fact.

Satan, in the Book of Job, listens to God speak highly of Job and accuses Job to God before the host of angels that Job praises God only because he is blessed and would curse God if he was forced to suffer. God allows Satan to do what he will except to spare his life, and Satan causes Job to suffer immensely. (Job remained true to God through his hardships; Satan accused him further and punished him further, but could not get Job to break).
==Possession==
[[Jesus]] makes references to demonic possession on multiple occasions that He then casts out. Some believe that Satan is able to possess and control living humans on Earth even today. Even more, some others believe that Satan actually has done this in the past as well. The Catholic church believes that priests (and sometimes only bishops) are able to [[exorcise]] this possession through Jesus.

==Terms==
The word ''Satan'' derives from the Hebrew "ha-satan", meaning the "accuser", "tempter", "persecutor", "calumniator", or "adversary". He "was a liar and a murderer from the beginning" (John 8:44) Synonyms include '''Lucifer, demon, Mephistopholes, Mephisto, Beelzebub, the Evil One, the Tempter,''' and '''The Prince of Darkness.''' Only "devil" is used as an epithet for a profoundly evil person.

The adjectives include "devilish," "demonic", and "diabolic". Those who worship Satan are called [[satanism | Satanists]], Satan-worshippers, or demonists.
=== Lucifer ===
'''Lucifer''' is a name literally meaning "Son of the Morning" (or "Light-Bearer"), and is mentioned in the Bible only in the [[book of Isaiah]] (Isaiah 14:12). Though in Christian tradition Lucifer is equated with Satan, the immediate context of the passage is Isaiah's prophecy against the king of Babylon, and the name "Lucifer" was not present at all in the original manuscripts (in the Latin Vulgate, the phrase "Son of the Morning" was transliterated as a proper name).

Whomever Lucifer may be, the Isaiah makes strong prophecy against him, condemning him for 5 pronouncements:

* I will ascend into [[heaven]]
* I will exalt my throne above the stars of God
* I will sit also upon the mount of the congregation, in the sides of the north
* I will ascend above the heights of the clouds
* I will be like the most High

Those who take this passage to be a reference to Satan believe that it gives more history of what caused his downfall, that he was created by God as one of His most powerful angels (possibly a [[Seraphim | Seraph]]), but that he fell from grace after he in his pride rebelled against his Creator. Some, however, believe that there is no grounding to interpret the passage as a history of Satan, citing that the passage uses highly figurative and poetic language that was meant as a prophecy against Babylon and nothing more.

[[Image:Paradise Lost 12.jpg|right|thumb|''The fall of Lucifer'' by Gustave Doré.]]

== Jewish Views ==
In the Jewish tradition, Satan is an angel who faithfully serves God as a prosecuting attorney - one who accuses men of wickedness and impiety. At the direction of God, Satan may be permitted to test these accusations, such as in Job. In this view, Satan's goal is not to lead men away from their faithfulness to God, but merely to reveal the true depths of their devotion, although in [[I Chronicles]] 21:1 Satan provoked [[David]] to take a [[census]] of the people of Israel against the will of God and 70,000 men are slain because of it.

==Jehovah's Witnesses==

[[Jehovah's Witnesses]] believe that Satan was at one time an [[Angel]] who lived among the many millions of Angels that existed before the [[world]] was created. They believe that at some point He developed the desire to be worshiped by [[Humans]] and other Angels and so set himself in Opposition to worship of [[Jehovah]], his [[God]] and Father. This they believe occured in the Garden of Eden, and not prior to the Earths creation. [[Jehovah's Witnesses]] teach that Satan used a serpent as his mouth piece, the same way a vantriloquist uses a dummy, to bring the first [[Human]] couple under his control.

[[Jehovah's Witnesses]] teach that God has allowed Satan to rule mankind for several resons such as:

*Satan has challenged God's Right to rule his creations, not his power....

*Satan accuses God of bribeing Humans for their loyalty with protection and blessings....

*Satan has accused Humans of being loyal to God out of selfish reasons....

*Satan claims that he can rule mankind better then God....

[[Jehovah's Witnesses]] teach also that [[God]] decided that time, rather then a display of force, is needed to settle these issues. This, they believe, has giving Satan thousands of years to prove that Mankind is better off without God, that He (Satan) can rule Mankind sucessfully, and that the Humans that Do serve God do so only out of selfish reasons.

[[Jehovah's Witnesses]] teach that Satan does not live in any kind of [[Hell]] or world of the dead, but on the [[Earth]] as it's current ruler, along with as many as a third of the Angels of [[Heaven]]. They teach that Satan had lived in Heaven up until 1914, when Jesus and his Angels cast him out of Heaven, bringing woe to the Earth. this is their reasoning on Why the world has experienced two World wars, increasing lawlessness, an increase in disease and polution, and the overall conditions on earth today.

[[Jehovah's Witnesses]] believe that Satan delegates authority to each Demon as he see's fit, and over what he see's fit, sometimes including whole Nations and kingdoms. They believe that Satan and his demons are in every way the enemy of God, rather then working along side him. They teach that Satan will continue to rule the world until [[Armageddon]], when Jesus Christ and his heavenly Angels come to earth and bind him, eventually killing him, freeing the world of all opposition towards True worship.

==Defenses==
The three classic defenses against Satan are:

* mockery, which Satan cannot withstand due to his pride
* sunlight or exposure, from which Satan hides
* the [[Holy Spirit]], meaning "The Advocate" (i.e., defense lawyer), or the ''Armor of God''<ref>Ephesians 6:1-17</ref>.

Note that Satan lacks self-restraint, which often leads him to failure. In addition, Satan delights in [[deceit]], even to the point of causing his downfall.

==Dante and Milton==
The classic literary depictions of Satan appear in Dante's Italian poem, "Inferno," and in [[John Milton]]'s English poem, "Paradise Lost." These are considered the two greatest poems in Italian and English literature.

==Liberal Protestant views==
Like [[Santa Claus]], Satan is not considered a real person but is the embodiment or epitome of evil, in a watering-down typical of [[cafeteria Christianity]].

In western art and popular culture the devil is used to represent evil influences or motivations.

==See also==
* [[Devil]]
*[[Atheism and satanic deception]]
* [[Salem Witch Trials]]

==Further reading==
* Caldwell, William. "The Doctrine of Satan: I. In the Old Testament," ''The Biblical World,'' Vol. 41, No. 1 (Jan., 1913), pp. 29-33 [http://www.jstor.org/stable/3142352 in JSTOR]
* Caldwell, William. "The Doctrine of Satan: II. Satan in Extra-Biblical Apocalyptical Literature," ''The Biblical World,'' Vol. 41, No. 2 (Feb., 1913), pp. 98-102 [http://www.jstor.org/stable/3142425 in JSTOR]
* Caldwell, William. "The Doctrine of Satan: III. In the New Testament," ''The Biblical World,'' Vol. 41, No. 3 (Mar., 1913), pp. 167-172 [http://www.jstor.org/stable/3142755 in JSTOR]
* Empson, William. ''Milton's God'' (1966)
* Jacobs, Joseph, and Ludwig Blau. "Satan," ''The Jewish Encyclopedia'' (1906) [http://www.jewishencyclopedia.com/view.jsp?artid=270&letter=S&search=Satan#ixzz0UQlw0zPS online] pp 68-71
* Kelly, Henry Ansgar. ''Satan: A Biography.'' (2006). 360 pp. [http://books.google.com/books?id=gPIpQg0lRbMC&pg=PA12&dq=intitle:satan+inauthor:kelly&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&num=30&as_brr=3#v=onepage&q=&f=false excerpt and text search]ISBN 0-521-60402-8, a study of the Bible and Western literature
* Kent, William. "Devil." ''The Catholic Encyclopedia'' (1908) Vol. 4. [http://www.newadvent.org/cathen/04764a.htm online older article]
* Osborne, B. A. E. "Peter: Stumbling-Block and Satan," ''Novum Testamentum,'' Vol. 15, Fasc. 3 (Jul., 1973), pp. 187-190 [http://www.jstor.org/stable/1560340 in JSTOR] on "Get thee behind me, Satan!"
* Rebhorn Wayne A. "The Humanist Tradition and Milton's Satan: The Conservative as Revolutionary," ''Studies in English Literature, 1500-1900,'' Vol. 13, No. 1, The English Renaissance (Winter, 1973), pp. 81-93 [http://www.jstor.org/stable/449871 in JSTOR]
* Russell, Jeffrey Burton. ''The Devil: Perceptions of Evil from Antiquity to Primitive Christianity'' (1987) [http://www.amazon.com/Devil-Perceptions-Antiquity-Christianity-Paperbacks/dp/0801494095/ref=pd_sim_b_1 excerpt and text search]
* Russell, Jeffrey Burton. ''Satan: The Early Christian Tradition'' (1987) [http://www.amazon.com/Satan-Christian-Jeffrey-Burton-Russell/dp/0801494133/ref=pd_bxgy_b_text_c excerpt and text search]
* Russell, Jeffrey Burton. ''Lucifer: The Devil in the Middle Ages'' (1986) [http://www.amazon.com/Lucifer-Devil-Middle-Cornell-Paperbacks/dp/080149429X/ref=pd_sim_b_1 excerpt and text search]
* Russell, Jeffrey Burton. ''Mephistopheles: The Devil in the Modern World'' (1990) [http://www.amazon.com/Mephistopheles-Modern-Jeffrey-Burton-Russell/dp/0801497183/ref=pd_bxgy_b_text_c excerpt and text search]
* Russell, Jeffrey Burton. ''The Prince of Darkness: Radical Evil and the Power of Good in History'' (1992) [http://www.amazon.com/Prince-Darkness-Radical-Power-History/dp/0801480566/ref=sr_1_1?ie=UTF8&s=books&qid=1255995689&sr=1-1 excerpt and text search]
* Schaff, D. S. "Devil" in ''New Schaff-Herzog Encyclopedia of Religious Knowledge'' (1911), [[Mainline]] Protestant; vol 3 pp 414-417 [http://www.ccel.org/ccel/schaff/encyc03.d.iii.html online]
* Scott, Miriam Van. ''The Encyclopedia of Hell'' (1999) [http://www.amazon.com/Encyclopedia-Hell-Miriam-Van-Scott/dp/0312244428/ref=pd_bxgy_b_text_b excerpt and text search] comparative religions; also popular culture
* Wray, T. J. and Gregory Mobley. ''The Birth of Satan: Tracing the Devil's Biblical Roots'' (2005) [http://www.amazon.com/Birth-Satan-Tracing-Devils-Biblical/dp/1403969337/ref=pd_sim_b_1 excerpt and text search]

== Notes ==
<references/>

== External links ==

*[http://www.1timothy4-13.com/files/teach/accuser.html The accuser of the brethren - commentary on Revelation 12:7-12] - Dr. J.B. Buffington
[[category:Abrahamic Religions]]
{{DivineComedy}}

Talk:Majoring in Mathematics

2012-02-26T19:52:30Z

Bogart12:

Talk:Majoring in Mathematics

2012-02-26T00:28:42Z

Bogart12: /* Liberal bias */

Majoring in Mathematics

2012-02-24T15:06:14Z

Bogart12: Undo revision 963541 by JustinD (talk)

This article is intended to provide a brief introduction to what college mathematics is all about. It is aimed at high school students who have enjoyed mathematics in high school, and are starting to think about what to study in college. This article is a work in progress -- please expand and leave suggestions at the talk page. The theorems and ideas mentioned here aren't all things that you'll necessarily encounter in classes; indeed, most of them you probably won't. Instead, they are presented to indicate the sorts of thinking and methods that go into mathematics, and the sorts of problems that mathematicians work on today.

Mathematics is a strong and marketable major for students, relatively (but not completely) free of [[liberal bias]].

Here is an outline of what I hope to write.

== What College Mathematics is Not ==
Before we look at the sorts of problems that actually ''are'' dealt with by mathematics in college, let's look at some that are not. Rest assured, many of the most painful aspects of math classes you've taken before aren't so bad in college!
# Simply learning more advanced versions of mathematical ideas from high school. Tired of learning tricks for integration? Majoring in math won't just teach you new methods to integrate functions -- if you've taken an introductory calculus class, chances are you already know the important ones! What it will do is force you to think carefully about basic questions about what an integral is. Given some subset of space, what does it really mean to find its volume?
# Doing lots of computations. Chances are you'll have to do a few, but most mathematics in college is based around "proofs" -- very careful and rigorous arguments which show that mathematical statements are true. Many proofs won't involve any computations at all!
# Learning a bag of tricks to do Olympiad-type problems. If you've ever taken the AMC, Math League, or other similar competition tests, and not done well, don't worry! Much of these tests check nothing more than whether you're familiar with some collection of techniques for solving special problems. One math professor at Harvard keeps in his desk a copy of a math competition on which he scored a perfect 0/120. Mathematical theory goes far beyond these problems.

Instead, college mathematics is about developing new ways to rigorously approach a wide array of problems. More than aiming to find tricky techniques to solve certain problems, it is about building powerful approaches that solve many problems, and learning to think rigorously about them.

== Liberal Bias ==
It is important to be aware that like many college degrees, mathematics has been subject to [[liberal bias]].
Examples include the study of "homo-morphisms," which encourage treating mathematical objects that are different as the same, in accordance with the liberal agenda, and widespread support of the [[global warming hoax]].
Fortunately, more [[conservative]] fields such as real analysis and differential geometry are perfectly viable paths for a student to take.

== Major Topics of Study ==
Given that a math major won't just be getting more practice at the sorts of math encountered in high school, what is it about? Here's a list of some of the major fields that are the foundation of a mathematics education.

For each field, I plan to give a very general description and to describe a few problems/theorems that are nice results and capture some of the essence of a subject. I'll aim for a few paragraphs about each one. Then I will give a problem or two that is a much more open-ended question that has motivated the development of large amounts of theory. For now I have no written about any of these -- please leave feedback and suggestions on the talk page and I will try to arrive at the best set of motivating problems!

=== Algebra ===
# How many positions are there for a Rubik's cube. Brief discussion of group theory, and how a group acts on the Rubik's cube.

==== Bezout's theorem ====
It's a very basic fact that two lines intersect at exactly one point. But we can ask a similar question about other shapes. At how many points do two parabolas intersect? A circle and a line? The graphs of two cubics? A circle and a line may intersect at either 0 points (for example, the unit circle <math>x^2+y^2=0</math> and the line <math>y=2</math>), 1 point (if the line is tangent to the circle), or 2 points. It's easy to see that we can arrange for two parabolas to intersect at four points: just consider the examples <math>y=x^2-10</math> and <math>x=y^2-10</math>. Similarly, we can up with two cubics that intersect at nine points. You might be noticing a pattern here: a parabola is defined as the set of solutions to a polynomial equation in two variables, whose biggest exponent is 2: we say that a parabola has degree 2. For the same reasons, we say that a line has degree 1, and a cubic as degree 3. Bezout's theorem then gives a very rough answer to our question: a curve of degree m and a curve of degree n intersect in at most mn points.

We have seen that sometimes the number of intersections is less than this, but Bezout's theorem, properly generalized, says that the number of intersections is in fact ''equal'' to mn: in the case of the circle and the line given earlier, there are exactly two solutions as predicted, if we allow <math>x</math> and <math>y</math> to be complex numbers. Similarly, a point of tangency is in some sense a "double intersection", and should count twice: if we nudged the line just a little bit, the point of intersection would turn into two distinct points. After we make these adjustments (counting complex solutions, changing the setting to projective space, and counting points of tangency multiple times), Bezout's theorem provides a simple and elegant answer to our original motivating question: curves of degree m and degree n intersect at exactly mn points!

# Is the quintic solvable in radicals? And what in the world does this problem have to do with group theory?
# The ancient Greeks were fascinated by geometric constructions with straightedge and compass. They could bisect angles and take square roots, but they couldn't trisect angles or take cube roots. Why not?

==== Algebra and Number Theory ====
The development of the modern field of algebra has been deeply influenced by research in number theory. An example of a problem from number theory that has provided far-reaching motivation for work in pure algebra has been the question of unique factorization.

It's a well-known fact, the [[fundamental theorem of arithmetic]], that every integer can be factored in a unique way as the product of prime numbers. It's natural to wonder whether this unique factorization holds in other simple rings, for example, the set of complex numbers whose real and complex parts are both integers (for example, <math>3+7i</math>). These are the so-called Gaussian integers, and there is a good notion of "prime", and that every Gaussian integer can be uniquely factored into primes! For example, 7+0i is a Gaussian prime, while 5+0i is not: <math>5+0i</math> factors as <math>(2+i)(2-i)<math>, and both <math>2-i</math> and <math>2+i</math> are prime. In general, it turns out that
a Gaussian integer <math>a+bi</math> is prime if either one of <math>a</math> or <math>b</math> is zero, and the other is a prime congruent to three mod 4, or if <math>a</math> and <math>b</math> are nonzero, and <math>a^2+b^2</math> is a prime (in the usual sense).

So unique factorization works well for the Gaussian integers, but what about other settings? An example similar to the Gaussian integers is the set of real numbers of the form <math>a+b\sqrt{7}</math>: note that <math>(a+b\sqrt{7})(c+d\sqrt{7}) = (ac+7bd)+(ad+bc)\sqrt{7}</math>, so the numbers of this form are closed under multiplication. Here too, and in many other cases, there is a good notion of unique factorization. It was formerly assumed that <math>\mathbb Z[\sqrt{d}]</math> would have unique factorization, but this turns out not to be the case. Consider the ring of complex numbers of the form <math>a+b\sqrt{-5}</math>. We can write <math>6 = 2 \cdot 3 = (1-\sqrt{-5})(1+\sqrt{5})</math>. A bit more work shows that both of these are prime factorizations, and they're not equivalent! This discovery necessitated the careful investigation of unique factorization, a purely algebraic notion that had not been seriously considered. Ernst Kummer proposed a proof of [[Fermat's Last Theorem]] which failed only because it assumed some properties of unique factorization, but further consideration of this problem led to a revolution in algebra.

=== Linear Algebra ===
If you throw a beach ball into the air, letting it spin in any way whatsoever, and then catch it, all of its rotations will comprise one rotation about some axis. That is, there will be two "poles" that will end exactly where they started, and all other points will just have rotated around them. What does this have to do with orthogonal operators? What does it have to do with the fact that every cubic equation has at least one real root?

If you do the same with a ring (e.g. a Hula Hoop), spinning it and letting it fall on its original "footprint", there will be no points that land exactly on their original position (except in the case in which it didn't move at all.) What does this have to do with the fact that quadratic equations are ''not'' guaranteed to have any real roots?

(Something about eigenvectors of distinct eigenvalues of an orthogonal/Hermitian matrix being orthogonal, can't think of a cute example just now.)

=== Geometry ===

In college math, "geometry" does not refer to more work on Euclidean high school geometry. Instead, college geometry includes a challenging field known as "differential geometry." This includes Tensor Calculus, Riemannian Geometry,
Covariant Vector Fields, Minkowskian Manifolds, and General Relativity.

Some problems include:

# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?

==== The Double Bubble Conjecture ====
You've probably noticed that when you blow a soap bubble, it quickly stretches into a nearly spherical shape. But why should a bubble tend towards a spherical conformation, instead of a cube or an icosahedron? According to physics, the bubble will tend toward a shape with the lowest energy, and the physical effect of surface tension is that this lowest energy is achieved when the bubble is in the shape with the least possible surface area enclosing a given volume. For example, if we want to enclose one cubic inch of air, the smallest surface that could contain it is a perfect sphere. The proof of this case, for a simple bubble, involves techniques from the mathematical study of [[differential geometry]], but turns out not to be too difficult. Related problems in finding minimal surfaces, however, turn out to be quite fiendish, and involve computations of "mean curvature" related to the notions of curvature defined above. The double bubble conjecture is one such.

*insert a picture here!

What is the smallest possible surface area for two bubbles joined stuck together, each enclosing some fixed volume? Thinking back to childhood experience, we know such bubbles end up as two partial spheres, connected together at a perfectly flat surface. But there are many other possibilities: why couldn't it be two tetrahedra, connected along some wavy surface? Quite sophisticated mathematical techniques are needed to prove this seemingly obvious result. The proof was not completed until 2000, by a team of mathematicians including [[User:RSchlafly|Roger Schlafly]].

=== Topology ===
==== The Bridges of Konigsberg ====
The earliest roots of the modern study of topology (and [[graph theory]]) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.

[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]

Euler proved that no such path existed, with the following simple and elegant argument: observe that the path one takes while on the islands is irrelevant to the problem at hand, and that all that matters is the order in which the bridges are traversed. Every time one enters one landmass by means of a bridge, he leaves it by means of another. This means that the number of bridges entering and exiting each landmass must be even, except possibly the landmass in which he starts and the one in which he ends (since he does not both enter and exit these). However, in Konigsberg, each of the four landmasses is served by an odd number of bridges! This means that no tour of the sort desired is possible.

This argument is fundamentally a "topological" one because of the recognition that the rigid shapes and geometry of the problem make no difference. If the shape of the islands were changed, or a bridge were moved but stayed between the same two islands, the solution of the problem would not be affected. The only thing that matters is the number of islands and which islands are connected by bridges. The modern field of topology is at its heart the study of geometric objects whose rigid shape is not important.

# Connection between topological spaces and algebraic groups
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.

==== How can we tell the difference between a sphere and a torus? ====
This is the sort of question that motivated the development of the field of topology for many years. Recall that a [[torus]] is the shape of an inner tube, or the surface of a donut: it is a two-dimensional surface with one hole. If a torus were made out of clay, one could stretch and squish it, but it is intuitively clear that no amount of stretching could possibly deform in into a sphere: it's simply impossible to get rid of the hole! Similarly, a sphere made out of clay can't be deformed into a torus without ripping it. The question of why the two shapes are not the same is fundamentally a topological one: we are interested in some intrinsic geometric properties of these objects, but not their specific rigid shapes.

It turns out that methods from [[algebra]] provide the easiest way to prove that it is impossible to deform a sphere into a donut. Observe that a sphere has the following property: given any loop drawn on the sphere (say, a rubber band stretched around it somehow), it is possible to "contract" that loop to a point (i.e., to scrunch up the whole rubber band at one place). On the other hand, if a rubber band is placed on a donut in such a way that it loops around the central whole, there is no way to contract it to a single point. A crucial observation in the field of algebraic topology is that if a space can be obtained by squeezing and stretching a sphere, then it will still have the property that every loop is contractible. Since a torus doesn't, we conclude that it must be fundamentally different from a sphere. Arguments like this are the basis for the field of [[algebraic topology]], and this problem of contracting loops in a space is studied using the [[fundamental group]].

=== Analysis ===
# Riemann mapping theorem. State this in terms of conformal mappings of the unit disk and draw lots of pictures!

==== Fixed points ====
Often in mathematics or physics, it is interesting to think about what happens when we apply the same function repeatedly. For example, one might take a calculator, punch in a random number, and then hit the button "[[cosine|cos]]" repeatedly. What happens when we do this? If you try it, you might see something that looks like this:1.3, 0.267499, 0.964435, 0.569881, 0.841965, 0.665998, 0.7863, 0.706469, 0.760659, 0.724382, 0.748909, ...

It looks like these are getting closer and closer to some fixed number, and if you hit the button a few more times, you'd discover that indeed these terms approach some constant around C=0.739085. This is the value of C for which cos(C) = C. There's no way to solve for this C algebraically, but we can see from the [[intermediate value theorem]] that there must be some value of C for which this is the case, since cos(0) > 0 but cos(1) < 1.
Generally, a value x is called a '''fixed point''' of a function f if f(x)=x, and it is interesting to study when a function must have a fixed point. Although many functions have no fixed points, there are theorems that give certain conditions under which any function must have a fixed point.

One of the most famous such theorems is the Brouwer fixed-point theorem, which says in its simplest form that any continuous function <math>f: D^2 \to D^2</math> has a fixed point. This fact has a very intuitive description: if we take a sheet of graph paper (so we can label each point with coordinates), crumple it up, and set it on top of another sheet of graph paper, then there is some point on the crumpled up sheet which is directly above the corresponding point on the second sheet! While this sounds like a simple fact, proving it rigorously relies on the techniques of [[algebraic topology]].

Another celebrated example of a fixed point theorem is known as Sharkovsky's theorem. In addition to fixed points, some functions have points for which repeating the function several times yields the same result: for example, a value of x for which cos(cos(cos(x))) = x is called a 3-periodic point of the function cosine. Sharkovsky's theorem is the surprising result that if a continuous function f has points of period 3, then it has points of all other periods! For example, consider the quadratic <math>f(x) = -\frac{5}{2} x^2 + \frac{7}{2} +1</math> has f(0) = 1, f(f(0)) = f(1) = 2, f(f(f(0))) = f(f(1))=f(2) = 0. So 0 is a point of period 3 of f(x). Sharkovsky's theorem implies that there are points of every other period. For example, there is some x such that f(f(f(f(f(f(f(f(x)))))))=x! Solving this explicitly would involve solving a polynomial of degree 14, an impossible task. But Sharkovsky's theorem guarantees that there is '''some''' value of x satisfying this.

==== Mathematical Billiards ====
Imagine that you're playing a game of pool on a standard rectangular table, but with a twist: there's no friction, so after you hit the ball, it continues along its trajectory forever. Obviously if you hit the ball so that its path is perpendicular to one of the walls of the table, it will bounce straight back, then off the opposite wall, straight back again, etc.: the ball will follow a repeating pattern of bouncing between the two walls forever. Similarly, if you aim just right, you can hit the ball so that it moves in a diamond-shaped path forever, bouncing off the middle of the sides of the walls repeatedly. A trajectory of the cue ball is called "periodic" if it's like one of these, in that the ball eventually ends up back where it started, and moving in the same direction. A trajectory is said to have "period p" if it hits the wall exactly <math>p</math> times in the course of this repeating cycle. The two examples given above have periods of two and four, respectively. One question we might ask is whether there is an orbit of period <math>p</math> for every possible choice of p. Can you come up with a path on the standard billiards table that has period 3? If not, can you prove that one doesn't exist?

As is often the case is mathematics, we attempt to generalize these results on periodic orbits to other situations. What if the billiards table is not rectangular, but triangular? It's true, but extremely difficult to prove, that given any triangular billiards table, there exists a periodic orbit of '''some''' period. The existence of periodic orbits is an extremely subtle question. This can be generalized even further, to ask whether all polygons admit periodic orbits. What about polyhedra? Can you imagine some periodic billiards orbits on a cube-shaped "table" (no gravity! think billiards in space).

The orbits that aren't periodic turn out to be just as interesting as those that are. Imagine that you place the cue ball at random on your billiards table, and smack it in some random direction. Chances are it won't end up in a periodic orbit -- putting the ball in a periodic orbit requires a very careful shot. So the ball will bounce around forever without retracing its path. But will it ever come back to the point where it started, perhaps moving in a different direction? The answer to this question is "no", but the Poincare Recurrence Theorem gives a somewhat satisfactory replacement: given any distance (e.g., an eighth of an inch), and any angle (e.g. two degrees), after some amount of time, the ball will be within that distance of its starting point, and directed within that angle of its initial path! This is a very suprising fact.

While this problem seems extremely elementary, sophisticated mathematical techiques from a range of fields of geometry and analysis have been brought to bear on it. Even so, many easily-stated questions remain open.

# Periodic orbits in billiards in polyhedra. I think it should be possible to say some interesting things about this but with some real content. Possibly there's a better idea.

Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.

=== Probability and Statistics ===
# Discussion of Benford's law, application to recognizing fraud.
# Understanding the concept of the "random variable"
# Proving the Central Limit Theorem

Motivating problem: Deriving conclusions from rarely occurring events, such as multiple no-hitters by the same pitcher. Specifically, how many no-hitters must a pitcher toss before one can conclude from that evidence alone that he is a great pitcher?

===Partial Differential Equations===
If you take a uniform circular metal disk and hold the temperatures at the periphery to some fixed pattern (say, lighting fires at some places and applying ice at others), and give it plenty of time to reach equilibrium, can you calculate the final temperature at every point inside? What does this have to do with Fourier series? (Hint: It has '''everything''' to do with Fourier series. This is the problem that Joseph Fourier was studying when he invented the series.)

=== Other fields ===
# Logic: still need a good problem
# Number theory: connected to the other fields above in many ways. Prime number theorem?
# Set theory: some discussion of axioms, maybe talk about AoC.
# applied mathematics, emphasizing the solution of partial differential equations which are essential to mechanical engineering

=== Related fields ===
Many other subjects are often considered parts of mathematics as well. Depending on specific undergraduate programs, a math major may or may not be required to take courses in these areas, but many of the same ideas are used in these subjects as in the others.
# Computer science: something about algorithmic complexity: maybe the fact that primality testing may be done in polynomial time?
# Computer science: How can Fourier transforms be used to multiply enormous integers much faster than normal methods?
...

=== Interplay ===
None of these fields exists in a vacuum, and there is rich interplay between them. If you insert "algebraic" or "differential" before the name of just about any branch of math, you get a more specialized, but important field. Motivate some of these connections:
# Algebra+topology: discussion of fundamental group.
# Analysis+topology: discuss conservative fields, and hint at de Rham cohomology without actually saying those words.
# Algebra+analysis: The set of derivations on the tangent bundle of a smooth manifold form a Lie algebra, connecting solutions to partial differential equations and algebra.

== So What? ==
After finishing a major in mathematics, most people don't keep working in pure math. But the ways of thinking and skills that the study of mathematics provide make available a wide range of career opportunities.

Specifically, mathematicians seeking to remain connected to their field pursue career opportunities in:
*actuary or insurance work
*defense-related work
*market trading analysis for investment banks
*mathematical modeling

Less-related fields that are also of some interest to mathematicians are:
*computer programming
*accounting
*K-12 teaching

Some mathematicians enter entirely unrelated fields. Math majors have the highest average scores of students in any field on the LSAT and GMAT, the tests required for entrance into law school and business school <ref>http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1430654</ref>: the skills acquired in studying mathematics in invaluable in the logic section of the LSAT and for subsequent careers in law.

== Further Reading ==
Numerous expository books cover the topics mentioned on this page, along with many others, in a very accessible way. Below are a few recommended books whose content is comparable to that of this article.
# ''Mathematics: The New Golden Age'', by Keith Devlin. Accessible discussions of many important ideas.
# ''Professor Stewart's Cabinet of Mathematical Curiosities'', by Ian Stewart. A similar book covering the exciting side of mathematics and requiring little background.
# ''Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics'', by John Derbyshire. Focuses on the famous [[Riemann hypothesis]] and related material.
# ''Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games''. A collection of articles by one of mathematics' foremost expositors.
[[Category:Mathematics]]
[[Category:Higher Education]]

==References==
{{reflist}}

Talk:2012 Republican Primary

2012-02-23T21:34:20Z

Bogart12: Created page with "Can we add some references here? How many is "many," for instance. --Bogart12"

Can we add some references here? How many is "many," for instance. --[[User:Bogart12|Bogart12]]

Ring (mathematics)

2012-02-23T21:28:25Z

Bogart12: /* Remarks */

A '''ring''' in [[mathematics]] is a set ''R'' equipped with two [[binary]] [[operation]]s, usually called addition and multiplication, that is a [[group]] under the operation of addition and a monoid (no inverses) under the operation of multiplication.

==Examples==
*<math>(\mathbb{Z},+, \cdot)</math> - the set of the [[integers]] - together with the usual [[addition]] and [[multiplication]] is a ring.
*For any ring <math>R</math> the polynomial ring <math>R[x]</math> consisting of elements of the form <math>b_0 +b_1x+...+b_mx^m</math> where <math>b_i \in R</math> is a ring as well. All polynomials with integer coefficients form the ring <math>Z[x]</math>.
*<math>(\mathbb{Z} / 6\mathbb{Z},+, \cdot)</math> : this is the ring of six elements {0,1,2,3,4,5} and the usual addition and multiplication [[modulo]] six. So, here 1+3= 4, but 4+5 = 3. Interestingly, <math>2 \cdot 3 = 0 </math>, so, you can multiply two elements, neither of which is zero, and get zero as the result! This means that this ring is not an [[domain]].
*<math>M^{n \times n}(\mathbb R)</math>, the set of <math>n \times n</math> real matrices, with operations of matrix addition and multiplication, is a ring.

==Axioms==

Explicitly, a ring <math> R</math> is a set, with two binary operations usually labeled <math>*</math> and <math>+</math> that satisfy the following axioms.

'''Axioms of Addition'''
 
1. '''Identity''' - there exists an element (usually labeled <math> 0</math> ) such that <math> 0+x = x+0 = x \ \forall x \in R </math>
 
2. '''Associativity''' - for any three elements <math>a,b,c\in R\ ,(a+b)+c = a+(b+c)</math>
 
3. '''Inverses''' - for any element <math>a \in R</math> there exists an element (usually labeled as <math>-a</math> such that <math>a+(-a) = (-a)+a = 0</math>
 
4. ''''Commutativity''' - for any two elements <math>a,b \in R\ ,a+b = b+a</math>

'''Axioms of Multiplication'''
 
1. '''Identity*''' - there exists an element (usually labeled <math>1</math> ) such that <math> 1*x = x*1 = x \ \forall x \in R</math>
 
2. '''Associativity''' - for any three elements <math>a,b,c\in R\ ,(a*b)*c = a*(b*c)</math>

'''Distributive Property'''
 
1. For three elements <math>a,b,c \in R\ , a*(b+c) = a*b =a*c</math>

'''*''' - Some texts define a ring without a multiplicative identity. See [[ring (mathematics)#Remarks|rng]]

==Elements==
An element of a ring <math> a \in R</math> is a '''unit''' if it has a multiplicative inverse. The numbers <math>\pm 1 \in \mathbb{Z}</math> are the only units in the Integers

An element of a <math> x \in R </math> is a '''zero divisor''' if there is another element <math> y\in R \ ,\ y \neq 0\mbox{ such that } xy = 0 \mbox{ or } yx = 0 </math> . In the third example above, 2 and 3 are zero divisors. In fact, for any ring of Integers modulo m, all prime factors of m and their producs are zero divisors.

The '''multiplicative identity''' (usually denoted as <math> 1 \in R</math> ) is the unique element of the ring that <math> 1x = x1 = x \ \forall x \in R</math>

The '''additive Identity''' (usually denoted as <math> 0 \in R </math> ) is the unique element of the ring that <math> 0+x = x+0 = x \ \forall x \in R </math>

A '''prime element''' (or prime) is an element of a ''commutative'' ring s.t. a non-unit <math> p \in R</math> is prime if and only if <math>p|ab \rightarrow p|a \mbox{ or } p|b</math> (note that this differs from the definition of a [[prime]] that is more commonly presented in grade school).

An '''irreducible element''' is an element of an [[integral domain]] (a special type of ring) such that <math>a\in R</math> is irreducible if it cannot be written as a product of two non-units. When applied to the integers (which is an integral domain) this means that an irreducible element is any element that only has itself and 1 as prime factors (1 is unit, so we satisfy the definition), this is the common way to define [[prime|prime numbers]]. Note that every ''prime element'' is necessarily irreducible, but not every irreducible element is necessarily a prime element (this motivates us to exclude 1 from the list of prime numbers)
==Remarks==
A '''rng''' (pronounced "rung") is an a ring without a multiplicative identity. In some texts, a ring is defined as rng, it turns out that many of the most elementary theorems (the ones that apply to arbitrary rings) do not require an identity, this ambiguity causes the confusion.

In texts where a ring is defined as a rng - a '''ring with unity''' is a rng with a multiplicative identity (our definition of a ring)

A '''commutative ring''' is a ring in which multiplication is commutative. The first three examples of rings given above are commutative rings: the last is not, since matrix multiplication is not in general commutative. The study of the properties of commutative rings is usually called '''commutative algebra'''.

An '''entire ring''' is a ring that has no zero divisors.

An '''integral domain''' is a commutative entire ring.

A '''Unique Factorization Domain (UFD)''' is an integral domain in which every element that is not 0 or a unit can be written as a product of irreducible elements. i.e. every element can be factored into a product of primes, analogous to the integers (In a related theorem, every irreducible element of a UFD is prime)

A [[Field]] is a commutative ring where every element except 0 is a unit (is invertible). In other words, a field is a ring that is an [[abelian group]] over both addition and multiplication on the non-zero elements.

A '''division ring''' (also known as a skew field) is a ring that is a [[group]] over multiplication (every non-zero element has an inverse, but not necessarily commutative). A division ring can also be thought of as a [[field]] that is not commutative.

[[Category:Algebra]]

Majoring in Mathematics

2012-02-23T21:12:49Z

Bogart12: Added a section elaborating on liberal bias

Talk:Majoring in Mathematics

2012-02-21T02:38:12Z

Bogart12:

Talk:Majoring in Mathematics

2012-02-21T02:37:48Z

Bogart12: I removed the RJJensen tag because the site said the spam filter was blocking it?

Talk:Complex number

2012-02-12T01:32:03Z

Bogart12:

Dose anyone have a cite for what the Pope said about Complex numbers? --[[User:StevenM|Ṣ₮ёVeN]] 10:15, 6 June 2008 (EDT)

It would be more accurate to describe the complex numbers as an R-algebra; they have more structure than a 2-dimensional vector space. -- [[User:Bogart12|Bogart12]]

Majoring in Mathematics

2012-02-11T20:22:33Z

Bogart12: /* Interplay */

This article is intended to provide a brief introduction to what college mathematics is all about. It is aimed at high school students who have enjoyed mathematics in high school, and are starting to think about what to study in college. This article is a work in progress -- please expand and leave suggestions at the talk page. The theorems and ideas mentioned here aren't all things that you'll necessarily encounter in classes; indeed, most of them you probably won't. Instead, they are presented to indicate the sorts of thinking and methods that go into mathematics, and the sorts of problems that mathematicians work on today.

Mathematics is a strong and marketable major for students, relatively (but not completely) free of [[liberal bias]].

Here is an outline of what I hope to write.

== What College Mathematics is Not ==
Before we look at the sorts of problems that actually ''are'' dealt with by mathematics in college, let's look at some that are not. Rest assured, many of the most painful aspects of math classes you've taken before aren't so bad in college!
# Simply learning more advanced versions of mathematical ideas from high school. Tired of learning tricks for integration? Majoring in math won't just teach you new methods to integrate functions -- if you've taken an introductory calculus class, chances are you already know the important ones! What it will do is force you to think carefully about basic questions about what an integral is. Given some subset of space, what does it really mean to find its volume?
# Doing lots of computations. Chances are you'll have to do a few, but most mathematics in college is based around "proofs" -- very careful and rigorous arguments which show that mathematical statements are true. Many proofs won't involve any computations at all!
# Learning a bag of tricks to do Olympiad-type problems. If you've ever taken the AMC, Math League, or other similar competition tests, and not done well, don't worry! Much of these tests check nothing more than whether you're familiar with some collection of techniques for solving special problems. One math professor at Harvard keeps in his desk a copy of a math competition on which he scored a perfect 0/120. Mathematical theory goes far beyond these problems.

Instead, college mathematics is about developing new ways to rigorously approach a wide array of problems. More than aiming to find tricky techniques to solve certain problems, it is about building powerful approaches that solve many problems, and learning to think rigorously about them.

== Major Topics of Study ==
Given that a math major won't just be getting more practice at the sorts of math encountered in high school, what is it about? Here's a list of some of the major fields that are the foundation of a mathematics education.

For each field, I plan to give a very general description and to describe a few problems/theorems that are nice results and capture some of the essence of a subject. I'll aim for a few paragraphs about each one. Then I will give a problem or two that is a much more open-ended question that has motivated the development of large amounts of theory. For now I have no written about any of these -- please leave feedback and suggestions on the talk page and I will try to arrive at the best set of motivating problems!

=== Algebra ===
# How many positions are there for a Rubik's cube. Brief discussion of group theory, and how a group acts on the Rubik's cube.

==== Bezout's theorem ====
It's a very basic fact that two lines intersect at exactly one point. But we can ask a similar question about other shapes. At how many points do two parabolas intersect? A circle and a line? The graphs of two cubics? A circle and a line may intersect at either 0 points (for example, the unit circle <math>x^2+y^2=0</math> and the line <math>y=2</math>), 1 point (if the line is tangent to the circle), or 2 points. It's easy to see that we can arrange for two parabolas to intersect at four points: just consider the examples <math>y=x^2-10</math> and <math>x=y^2-10</math>. Similarly, we can up with two cubics that intersect at nine points. You might be noticing a pattern here: a parabola is defined as the set of solutions to a polynomial equation in two variables, whose biggest exponent is 2: we say that a parabola has degree 2. For the same reasons, we say that a line has degree 1, and a cubic as degree 3. Bezout's theorem then gives a very rough answer to our question: a curve of degree m and a curve of degree n intersect in at most mn points.

We have seen that sometimes the number of intersections is less than this, but Bezout's theorem, properly generalized, says that the number of intersections is in fact ''equal'' to mn: in the case of the circle and the line given earlier, there are exactly two solutions as predicted, if we allow <math>x</math> and <math>y</math> to be complex numbers. Similarly, a point of tangency is in some sense a "double intersection", and should count twice: if we nudged the line just a little bit, the point of intersection would turn into two distinct points. After we make these adjustments (counting complex solutions, changing the setting to projective space, and counting points of tangency multiple times), Bezout's theorem provides a simple and elegant answer to our original motivating question: curves of degree m and degree n intersect at exactly mn points!

# Is the quintic solvable in radicals? And what in the world does this problem have to do with group theory?
# The ancient Greeks were fascinated by geometric constructions with straightedge and compass. They could bisect angles and take square roots, but they couldn't trisect angles or take cube roots. Why not?

==== Algebra and Number Theory ====
The development of the modern field of algebra has been deeply influenced by research in number theory. An example of a problem from number theory that has provided far-reaching motivation for work in pure algebra has been the question of unique factorization.

It's a well-known fact, the [[fundamental theorem of arithmetic]], that every integer can be factored in a unique way as the product of prime numbers. It's natural to wonder whether this unique factorization holds in other simple rings, for example, the set of complex numbers whose real and complex parts are both integers (for example, <math>3+7i</math>). These are the so-called Gaussian integers, and there is a good notion of "prime", and that every Gaussian integer can be uniquely factored into primes! For example, 7+0i is a Gaussian prime, while 5+0i is not: <math>5+0i</math> factors as <math>(2+i)(2-i)<math>, and both <math>2-i</math> and <math>2+i</math> are prime. In general, it turns out that
a Gaussian integer <math>a+bi</math> is prime if either one of <math>a</math> or <math>b</math> is zero, and the other is a prime congruent to three mod 4, or if <math>a</math> and <math>b</math> are nonzero, and <math>a^2+b^2</math> is a prime (in the usual sense).

So unique factorization works well for the Gaussian integers, but what about other settings? An example similar to the Gaussian integers is the set of real numbers of the form <math>a+b\sqrt{7}</math>: note that <math>(a+b\sqrt{7})(c+d\sqrt{7}) = (ac+7bd)+(ad+bc)\sqrt{7}</math>, so the numbers of this form are closed under multiplication. Here too, and in many other cases, there is a good notion of unique factorization. It was formerly assumed that <math>\mathbb Z[\sqrt{d}]</math> would have unique factorization, but this turns out not to be the case. Consider the ring of complex numbers of the form <math>a+b\sqrt{-5}</math>. We can write <math>6 = 2 \cdot 3 = (1-\sqrt{-5})(1+\sqrt{5})</math>. A bit more work shows that both of these are prime factorizations, and they're not equivalent! This discovery necessitated the careful investigation of unique factorization, a purely algebraic notion that had not been seriously considered. Ernst Kummer proposed a proof of [[Fermat's Last Theorem]] which failed only because it assumed some properties of unique factorization, but further consideration of this problem led to a revolution in algebra.

=== Linear Algebra ===
If you throw a beach ball into the air, letting it spin in any way whatsoever, and then catch it, all of its rotations will comprise one rotation about some axis. That is, there will be two "poles" that will end exactly where they started, and all other points will just have rotated around them. What does this have to do with orthogonal operators? What does it have to do with the fact that every cubic equation has at least one real root?

If you do the same with a ring (e.g. a Hula Hoop), spinning it and letting it fall on its original "footprint", there will be no points that land exactly on their original position (except in the case in which it didn't move at all.) What does this have to do with the fact that quadratic equations are ''not'' guaranteed to have any real roots?

(Something about eigenvectors of distinct eigenvalues of an orthogonal/Hermitian matrix being orthogonal, can't think of a cute example just now.)

=== Geometry ===

In college math, "geometry" does not refer to more work on Euclidean high school geometry. Instead, college geometry includes a challenging field known as "differential geometry." This includes Tensor Calculus, Riemannian Geometry,
Covariant Vector Fields, Minkowskian Manifolds, and General Relativity.

Some problems include:

# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?

==== The Double Bubble Conjecture ====
You've probably noticed that when you blow a soap bubble, it quickly stretches into a nearly spherical shape. But why should a bubble tend towards a spherical conformation, instead of a cube or an icosahedron? According to physics, the bubble will tend toward a shape with the lowest energy, and the physical effect of surface tension is that this lowest energy is achieved when the bubble is in the shape with the least possible surface area enclosing a given volume. For example, if we want to enclose one cubic inch of air, the smallest surface that could contain it is a perfect sphere. The proof of this case, for a simple bubble, involves techniques from the mathematical study of [[differential geometry]], but turns out not to be too difficult. Related problems in finding minimal surfaces, however, turn out to be quite fiendish, and involve computations of "mean curvature" related to the notions of curvature defined above. The double bubble conjecture is one such.

*insert a picture here!

What is the smallest possible surface area for two bubbles joined stuck together, each enclosing some fixed volume? Thinking back to childhood experience, we know such bubbles end up as two partial spheres, connected together at a perfectly flat surface. But there are many other possibilities: why couldn't it be two tetrahedra, connected along some wavy surface? Quite sophisticated mathematical techniques are needed to prove this seemingly obvious result. The proof was not completed until 2000, by a team of mathematicians including [[User:RSchlafly|Roger Schlafly]].

=== Topology ===
==== The Bridges of Konigsberg ====
The earliest roots of the modern study of topology (and [[graph theory]]) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.

[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]

Euler proved that no such path existed, with the following simple and elegant argument: observe that the path one takes while on the islands is irrelevant to the problem at hand, and that all that matters is the order in which the bridges are traversed. Every time one enters one landmass by means of a bridge, he leaves it by means of another. This means that the number of bridges entering and exiting each landmass must be even, except possibly the landmass in which he starts and the one in which he ends (since he does not both enter and exit these). However, in Konigsberg, each of the four landmasses is served by an odd number of bridges! This means that no tour of the sort desired is possible.

This argument is fundamentally a "topological" one because of the recognition that the rigid shapes and geometry of the problem make no difference. If the shape of the islands were changed, or a bridge were moved but stayed between the same two islands, the solution of the problem would not be affected. The only thing that matters is the number of islands and which islands are connected by bridges. The modern field of topology is at its heart the study of geometric objects whose rigid shape is not important.

# Connection between topological spaces and algebraic groups
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.

==== How can we tell the difference between a sphere and a torus? ====
This is the sort of question that motivated the development of the field of topology for many years. Recall that a [[torus]] is the shape of an inner tube, or the surface of a donut: it is a two-dimensional surface with one whole. If a torus were made out of clay, one could stretch and squish it, but it is intuitively clear that no amount of stretching could possibly deform in into a sphere: it's simply impossible to get rid of the hole! Similarly, a sphere made out of clay can't be deformed into a torus without ripping it. The question of why the two shapes are not the same is fundamentally a topological one: we are interested in some intrinsic geometric properties of these objects, but not their specific rigid shapes.

It turns out that methods from [[algebra]] provide the easiest way to prove that it is impossible to deform a sphere into a donut. Observe that a sphere has the following property: given any loop drawn on the sphere (say, a rubber band stretched around it somehow), it is possible to "contract" that loop to a point (i.e., to scrunch up the whole rubber band at one place). On the other hand, if a rubber band is placed on a donut in such a way that it loops around the central whole, there is no way to contract it to a single point. A crucial observation in the field of algebraic topology is that if a space can be obtained by squeezing and stretching a sphere, then it will still have the property that every loop is contractible. Since a torus doesn't, we conclude that it must be fundamentally different from a sphere. Arguments like this are the basis for the field of [[algebraic topology]], and this problem of contracting loops in a space is studied using the [[fundamental group]].

=== Analysis ===
# Riemann mapping theorem. State this in terms of conformal mappings of the unit disk and draw lots of pictures!

==== Fixed points ====
Often in mathematics or physics, it is interesting to think about what happens when we apply the same function repeatedly. For example, one might take a calculator, punch in a random number, and then hit the button "[[cosine|cos]]" repeatedly. What happens when we do this? If you try it, you might see something that looks like this:1.3, 0.267499, 0.964435, 0.569881, 0.841965, 0.665998, 0.7863, 0.706469, 0.760659, 0.724382, 0.748909, ...

It looks like these are getting closer and closer to some fixed number, and if you hit the button a few more times, you'd discover that indeed these terms approach some constant around C=0.739085. This is the value of C for which cos(C) = C. There's no way to solve for this C algebraically, but we can see from the [[intermediate value theorem]] that there must be some value of C for which this is the case, since cos(0) > 0 but cos(1) < 1.
Generally, a value x is called a '''fixed point''' of a function f if f(x)=x, and it is interesting to study when a function must have a fixed point. Although many functions have no fixed points, there are theorems that give certain conditions under which any function must have a fixed point.

One of the most famous such theorems is the Brouwer fixed-point theorem, which says in its simplest form that any continuous function <math>f: D^2 \to D^2</math> has a fixed point. This fact has a very intuitive description: if we take a sheet of graph paper (so we can label each point with coordinates), crumple it up, and set it on top of another sheet of graph paper, then there is some point on the crumpled up sheet which is directly above the corresponding point on the second sheet! While this sounds like a simple fact, proving it rigorously relies on the techniques of [[algebraic topology]].

Another celebrated example of a fixed point theorem is known as Sharkovsky's theorem. In addition to fixed points, some functions have points for which repeating the function several times yields the same result: for example, a value of x for which cos(cos(cos(x))) = x is called a 3-periodic point of the function cosine. Sharkovsky's theorem is the surprising result that if a continuous function f has points of period 3, then it has points of all other periods! For example, consider the quadratic <math>f(x) = -\frac{5}{2} x^2 + \frac{7}{2} +1</math> has f(0) = 1, f(f(0)) = f(1) = 2, f(f(f(0))) = f(f(1))=f(2) = 0. So 0 is a point of period 3 of f(x). Sharkovsky's theorem implies that there are points of every other period. For example, there is some x such that f(f(f(f(f(f(f(f(x)))))))=x! Solving this explicitly would involve solving a polynomial of degree 14, an impossible task. But Sharkovsky's theorem guarantees that there is '''some''' value of x satisfying this.

==== Mathematical Billiards ====
Imagine that you're playing a game of pool on a standard rectangular table, but with a twist: there's no friction, so after you hit the ball, it continues along its trajectory forever. Obviously if you hit the ball so that its path is perpendicular to one of the walls of the table, it will bounce straight back, then off the opposite wall, straight back again, etc.: the ball will follow a repeating pattern of bouncing between the two walls forever. Similarly, if you aim just right, you can hit the ball so that it moves in a diamond-shaped path forever, bouncing off the middle of the sides of the walls repeatedly. A trajectory of the cue ball is called "periodic" if it's like one of these, in that the ball eventually ends up back where it started, and moving in the same direction. A trajectory is said to have "period p" if it hits the wall exactly <math>p</math> times in the course of this repeating cycle. The two examples given above have periods of two and four, respectively. One question we might ask is whether there is an orbit of period <math>p</math> for every possible choice of p. Can you come up with a path on the standard billiards table that has period 3? If not, can you prove that one doesn't exist?

As is often the case is mathematics, we attempt to generalize these results on periodic orbits to other situations. What if the billiards table is not rectangular, but triangular? It's true, but extremely difficult to prove, that given any triangular billiards table, there exists a periodic orbit of '''some''' period. The existence of periodic orbits is an extremely subtle question. This can be generalized even further, to ask whether all polygons admit periodic orbits. What about polyhedra? Can you imagine some periodic billiards orbits on a cube-shaped "table" (no gravity! think billiards in space).

The orbits that aren't periodic turn out to be just as interesting as those that are. Imagine that you place the cue ball at random on your billiards table, and smack it in some random direction. Chances are it won't end up in a periodic orbit -- putting the ball in a periodic orbit requires a very careful shot. So the ball will bounce around forever without retracing its path. But will it ever come back to the point where it started, perhaps moving in a different direction? The answer to this question is "no", but the Poincare Recurrence Theorem gives a somewhat satisfactory replacement: given any distance (e.g., an eighth of an inch), and any angle (e.g. two degrees), after some amount of time, the ball will be within that distance of its starting point, and directed within that angle of its initial path! This is a very suprising fact.

While this problem seems extremely elementary, sophisticated mathematical techiques from a range of fields of geometry and analysis have been brought to bear on it. Even so, many easily-stated questions remain open.

# Periodic orbits in billiards in polyhedra. I think it should be possible to say some interesting things about this but with some real content. Possibly there's a better idea.

Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.

=== Probability and Statistics ===
# Discussion of Benford's law, application to recognizing fraud.
# Understanding the concept of the "random variable"
# Proving the Central Limit Theorem

Motivating problem: Deriving conclusions from rarely occurring events, such as multiple no-hitters by the same pitcher. Specifically, how many no-hitters must a pitcher toss before one can conclude from that evidence alone that he is a great pitcher?

===Partial Differential Equations===
If you take a uniform circular metal disk and hold the temperatures at the periphery to some fixed pattern (say, lighting fires at some places and applying ice at others), and give it plenty of time to reach equilibrium, can you calculate the final temperature at every point inside? What does this have to do with Fourier series? (Hint: It has '''everything''' to do with Fourier series. This is the problem that Joseph Fourier was studying when he invented the series.)

=== Other fields ===
# Logic: still need a good problem
# Number theory: connected to the other fields above in many ways. Prime number theorem?
# Set theory: some discussion of axioms, maybe talk about AoC.
# applied mathematics, emphasizing the solution of partial differential equations which are essential to mechanical engineering

=== Related fields ===
Many other subjects are often considered parts of mathematics as well. Depending on specific undergraduate programs, a math major may or may not be required to take courses in these areas, but many of the same ideas are used in these subjects as in the others.
# Computer science: something about algorithmic complexity: maybe the fact that primality testing may be done in polynomial time?
# Computer science: How can Fourier transforms be used to multiply enormous integers much faster than normal methods?
...

=== Interplay ===
None of these fields exists in a vacuum, and there is rich interplay between them. If you insert "algebraic" or "differential" before the name of just about any branch of math, you get a more specialized, but important field. Motivate some of these connections:
# Algebra+topology: discussion of fundamental group.
# Analysis+topology: discuss conservative fields, and hint at de Rham cohomology without actually saying those words.
# Algebra+analysis: The set of derivations on the tangent bundle of a smooth manifold form a Lie algebra, connecting solutions to partial differential equations and algebra.

== So What? ==
After finishing a major in mathematics, most people don't keep working in pure math. But the ways of thinking and skills that the study of mathematics provide make available a wide range of career opportunities.

Specifically, mathematicians seeking to remain connected to their field pursue career opportunities in:
*actuary or insurance work
*defense-related work
*market trading analysis for investment banks
*mathematical modeling

Less-related fields that are also of some interest to mathematicians are:
*computer programming
*accounting
*K-12 teaching

Some mathematicians enter entirely unrelated fields. Math majors have the highest average scores of students in any field on the LSAT and GMAT, the tests required for entrance into law school and business school <ref>http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1430654</ref>: the skills acquired in studying mathematics in invaluable in the logic section of the LSAT and for subsequent careers in law.

== Further Reading ==
Numerous expository books cover the topics mentioned on this page, along with many others, in a very accessible way. Below are a few recommended books whose content is comparable to that of this article.
# ''Mathematics: The New Golden Age'', by Keith Devlin. Accessible discussions of many important ideas.
# ''Professor Stewart's Cabinet of Mathematical Curiosities'', by Ian Stewart. A similar book covering the exciting side of mathematics and requiring little background.
# ''Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics'', by John Derbyshire. Focuses on the famous [[Riemann hypothesis]] and related material.
# ''Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games''. A collection of articles by one of mathematics' foremost expositors.
[[Category:Mathematics]]
[[Category:Higher Education]]

==References==
{{reflist}}

Talk:Majoring in Mathematics

2012-02-11T20:15:07Z

Bogart12:

Talk:Majoring in Mathematics

2012-02-11T20:13:38Z

Bogart12:

Talk:Idolatry

2012-02-11T20:10:08Z

Bogart12:

{{Wikiproject Religion}}
== "Modern secularism is considered to be a form of idolatry." ==

By whom? More importantly, secularism implies a total lack of worship, be it of idols or otherwise. [[User:PFoster|PFoster]] 20:28, 16 July 2007 (EDT)

Idolotry is classified as the worship of anything that is not God. If modern secularists means humanists, they, by definition, worship themselves; not God. So, even if it's not the commonly accepted definition of bowing down in a temple to a statue, its still idolatry. [[User:StevenM]]

Idolatry is defined as the worship of idols (google it); what idol do secularists worship? [[User:Bogart12]]

Global warming

2012-02-11T20:06:02Z

Bogart12: Undo revision 960370 by Aschlafly (talk)

[[Image:NASA-1024x933.jpg|thumb|right|250px|A composite map of [[Antarctica]] showing areas of greatest warming in red. The Wilkins Ice Shelf lies off the peninsula in the top left corner, and shows extensive warming. Overall, Antarctica shows little warming, and many areas to the East (right) are cooling<ref>Roberts, Greg. "Antarctic Ice is Growing, Not Melting Away." April 18, 2009. http://www.news.com.au/antarctic-ice-is-growing-not-melting-away/story-0-1225700043191</ref>.]]
'''Global warming''' is the theory that the world is becoming dangerously warmer, and that government needs to assert more controls over energy production and use to try to stop it. Put another way, [[liberals]] concocted a theory of [[Global warming theory|man-made global warming]] to justify demands for a more powerful government. As temperatures have cooled in many areas, liberals have switched their theory to one of [[climate change]]. [[Global cooling]], a liberal theory that predates global warming, obviously occurs naturally many times throughout [[Earth|Earth's]] geological history.<ref>"After any given warming phase begins, thousands of years later the cyclical [[Milankovitch]] decrease in the sun's heat kicks in. The warming stops, reverses and an [[ice age]] ensues." [http://www.counterpunch.org/cockburn06092007.html Counterpunch], June 2007</ref> The ease of refutation of global cooling claims foretells the eventual fate of the current global warming hysteria.

[[Liberal]] claims of global warming led to the resignation in October 2010 by Professor Hal Lewis from The American Physical Society because of "the [[global warming]] scam, with the (literally) trillions of dollars driving it, that has corrupted so many scientists, and has carried APS before it like a rogue wave. '''It is the greatest and most successful pseudoscientific fraud I have seen in my long life as a physicist'''."<ref>http://thegwpf.org/ipcc-news/1670-hal-lewis-my-resignation-from-the-american-physical-society.html</ref>

Many political activists use the term '''"global warming"''' to refer the [[anthropogenic global warming theory]] (AGW), which asserts that human activity such as spewing "[[greenhouse gases]]" is causing more temperature increase than all natural causes combined. The AGW theory is supported by left-leaning political parties, as well as a majority of sovereign states, national agencies, and an intergovernmental panel (see [[IPCC]]). The reality is that there is no global crisis, despite dire warning by the UN's [[Intergovernmental Panel on Climate Change]] (IPCC). Predictions made by [[climate model]]s publicized by the IPCC have not come to pass.

In November 2009, emails were disclosed that demonstrated wrongful manipulation and concealment of data by scientists who have insisted that there is dangerous man-made global warming. Prior to [[ClimateGate]], both the Republican and Democratic party Platforms in 2008 suggested that global warming is happening, that it is caused by human activity, and that it should be counteracted. For example, in 2007, the Republican presidential candidate Senator [[John McCain]] called global warming "an issue we can no longer afford to ignore".<ref>[http://www.ontheissues.org/domestic/John_McCain_Environment.htm]</ref>

The idea of dangerous anthropogenic (man-made) global warming (AGW) is promoted by liberals and socialists seeking greater government control over the production and use of energy, which is a substantial percentage of the economy. In economic terms, they would like to 'internalize' the 'externality,' which is to say that they think that producers of emissions should be directly connected to the consequences of those emissions, leading syndicated columnist Charles Krauthammer to warn of an impending ''Environmental Shakedown''.<ref>http://www.realclearpolitics.com/printpage/?url=http://www.realclearpolitics.com/articles/2009/12/11/copenhagen_shakedown.html</ref> The unsuccessful Democratic candidate for President in 2000, [[Al Gore]], won a [[Nobel Prize]] in 2007 for claiming that there is a dangerous man-made global warming that threatens the world. However, it has since been revealed that he convinced many people through inaccurate information in his "documentary," i.e., he only won the Nobel Prize by lying.<ref>Citation needed</ref>

Although 2005 and 2010 are the warmest years on record,<ref>[http://www.nasa.gov/topics/earth/features/2010-warmest-year.html NASA Research Finds 2010 Tied for Warmest Year on Record, Jan. 12 2011, NASA]</ref> historically, natural periods of global warming and global cooling have alternated, and not long ago liberals were demanding more government control to combat an alleged cooling in temperatures, with some scientists warning of a possible ice age.<ref>''Science: Another Ice Age?'' Time magazine, Monday, Jun. 24, 1974</ref>

In 2008 86 evangelical pastors, including Rev. Dr.[[Rick Warren]] signed a statement titled "Climate Change: An Evangelical Call to Action", which called on Christians to acknowledge the moral importance of action to counteract man-made climate change. the statement includes specific support for market-based CO2 reductions such as a cap-and-trade program.<ref>[http://christiansandclimate.org/]</ref> In contrast, a group of evangelical scholars, comprised of scientists, economists and theologians, contend that the liberal view of pending catastrophe caused by climate change is misleading and/or exaggerated.<ref>[http://www.christianpost.com/article/20091204/evangelicals-push-back-against-climate-change-hoax/pageall.html ''Evangelicals Push Back Against Global Warming Doom'', Dec. 04 2009, christianpost.com]</ref>

==Science of Global Warming==
===Presence of CO2===

One of the primary concerns of Global Warming research is the increased presence of carbon dioxide in the atmosphere. Original claims stated that the increase in carbon dioxide - which is a greenhouse gas - were caused primarily through the burning of [[fossil fuels]], and that such increases were the foremost cause of global temperatures rising. Historically, Global temperature changes precede changes in carbon dioxide in the atmosphere.<ref> [http://www.skepticalscience.com/co2-lags-temperature.htm]</ref>

The most obvious way that this would occur would be through the evaporation of ocean water. The oceans are the single largest storage unit for carbon dioxide gas on the planet, containing about 93% of the Earth's carbon dioxide. <ref> [http://www.waterencyclopedia.com/Bi-Ca/Carbon-Dioxide-in-the-Ocean-and-Atmosphere.html] </ref> As temperatures rise, ocean water evaporates, causing the dissolved carbon dioxide gas to enter the atmosphere, and begin trapping radiation from the sun. Scientists now believe that this cycle causes a sort of chain effect, where increased temperature causes more carbon dioxide to enter the atmosphere, which in turn causes more temperature rise.

It is also noteworthy to point out that carbon dioxide, while not as abundant in the atmosphere, has a more significant effect on global warming than water vapor does. Carbon dioxide cannot form clouds, as water vapor does. When water vapor forms clouds, those clouds actually block some of the sun's radiation from reaching the Earth, causing water vapor to both contribute positively and negatively to global temperature rise. Carbon dioxide can only act as a greenhouse gas, causing the above mentioned cyclic effect. The current concentration of carbon dioxide in the Earth's atmosphere is about 392 ppm, which is the highest it has been in at least 800,000 years.<ref>"Trends in Atmospheric Carbon Dioxide" [http://www.esrl.noaa.gov/gmd/ccgg/trends/mlo.html NOAA], December 2011</ref>

===The Modern Warm Period===

The Average [[Earth]] surface air temperature has risen about 1° F since 1970.
<ref>Hansen's group at the Goddard Institute wrote, "Global warming is now 0.6 °C [1.0 °F] in the past three decades and 0.8 °C [1.4 °F] in the past century." http://data.giss.nasa.gov/gistemp/2005/</ref> Studies have ruled out the possibility that errors in the measurements and sampling significantly affect the temperature trends detected over the past century. This accounts for spatial errors in the sampling and thus also incorporates errors associated with the urban-heating effect. According to Karl et al. (1993) ''"Results imply that the errors associated with century-scale trends of temperature are probably an order of magnitude smaller than the observed global warming of nearly 0.5°C per 100 years since the late nineteenth century"'' <ref>http://adsabs.harvard.edu/abs/1994JCli....7.1144K Karl et al. (1993) 'Global and Hemispheric Temperature Trends: Uncertainties Related to Inadequate Spatial Sampling' in Journal of Climate, 7(7); 1144 - 1168</ref>

According to temperature reconstruction made within an [[Old Earth]] paradigm, there have been many cycles of naturally-caused global warming and cooling over many millions of years (see [[climate cycles]]). Some scientists, including [[Richard Lindzen]] of [[MIT]], [[Sallie Baliunas]] of [[Harvard]] and [[Fred Singer]] (independent), say that the recent warming could be part of another natural cycle or random fluctuations in the atmosphere. However, many scientists also think that human activities were most likely the cause of the the planet's recent warming.

Recent studies of the Milankovitch Cycles, which predict Earth's climate by studying changes in its orbit and axial tilt, suggest that we are currently 18,000 years into a 150,000 year period between ice ages. This would imply that we should expect the temperature to be rising anyway. A 2002 study by Berger and Loutre suggests 50,000 years of warmer weather before Earth begins to cool again, but that model incorroprated anthropogenic forces and concluded:
<blockquote>While combinations of natural forcings produce a gradual warming up to about 1960, none of them leads to a warming over the last 30 years (this period containing three major volcanic eruptions). In contrast, simulations incorporating only anthropogenic forcings reproduce the warming over the last three decades at a rate consistent with that observed, but underestimate the early 20th century warming. As a consequence, only the use of both natural and anthropogenic forcings allows to reproduce much of the observed decadal scale variations of the annual mean hemispheric temperature over the last 150 years.<ref>[http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0870.2002.00287.x/full] Climate of the last millennium: a sensitivity study, May 2002</ref></blockquote>

It should be noted, however, that computer simulated climate models are often tweaked so they agree with the historical temperature record. There is no way to completely simulate all of the Earth's climate with a computer program.

===Sun Spots===
Sunspot activity is a factor in climate fluctuations, however, little details were known about how much of an impact these fluctuations had on the Earth's climate. During the deepest solar minimum ever recorded, from 2005 to 2010, NASA measured the Earth's energy balance, i.e. the amount of energy absorbed by the sun subtract the amount of energy lost to radiation into space. They concluded:
<blockquote>If the Sun were the only climate forcing or the dominant climate forcing, then the planet would gain energy during the solar maxima, but lose energy during solar minima. The fact that Earth gained energy at a rate 0.58 W/m2 during a deep prolonged solar minimum reveals that there is a strong positive forcing overwhelming the negative forcing by below-average solar irradiance. That result is not a surprise, given knowledge of other forcings, but it provides unequivocal refutation of assertions that the Sun is the dominant climate forcing. <ref>[http://www.giss.nasa.gov/research/briefs/hansen_16/ NASA: Earth's Energy Imbalance] nasa.gov, January, 2012</ref></blockquote>
However, just because the sun isn't the dominate force, doesn't mean that it doesn't nonetheless have a significant impact upon the Earth's climate.

==Global Warming in Politics==
===Politicization of the Issue===

Environmentalists and their political allies have presented a one-sided, anti-scientific account of global warming. They have ignored natural warming cycles and suppressed evidence which contradicts their theories. They have viciously attacked the credibility of any scientist daring to contradict them, creating a climate of fear where only a tiny handful of scientists dare speak out.

Bill Gray wrote:
* The contrary views of the many warming skeptics have been largely ignored and their motives denigrated.
* The normal scientific process of objectively studying both sides of the question has not yet occurred.<ref> [http://www.cgd.ucar.edu/cas/Trenberth/XchangeGray_FtCollinsFeb08.pdf Area Experts Debate Global Warming]</ref>

Journalists in the West, dominated by liberal viewpoints, have painted a misleading picture of the science. They have publicized liberal slanders against scientists who dare to speak up against the fake "consensus"

Even organizations that are not normally biased towards leftist ideas have publicly supported the global warming theory. The oil company Exxon/Mobil official policy is that CO2 emissions pose risks to society and ecosystems. Exxon/Mobil has also committed to reducing their own CO2 emissions, and invested $600 million in algae based fuels.<ref> [http://www.exxonmobil.com/Corporate/energy_climate_views.aspx]</ref>

Agencies of the United States Government such as NASA, EPA & NOAA give selected information that strongly supports the global warming theory. At the same time, they reject freedom of information requests to see the raw data. <ref>[http://www.cnsnews.com/news/article/58087 Vitter, Inhofe Ask NASA Inspector General to Probe Possible Obstruction of FOIA Requests Seeking Climate Change Records, CNSNews.com, December 04, 2009]</ref> The National Oceanic and Atmospheric Administration (NOAA), for one example, states that CO2 levels in the atmosphere are rising due to human activity, and that the surface of the Earth has warmed, on average, quickly over the last 50 years, even though North America cooled slightly.<ref> [http://www.ncdc.noaa.gov/oa/climate/globalwarming.html#q2]</ref> In 2008 The Bush Administration requested $4.1 billion dollars of taxpayer money from Congress to fund NOAA, a 7.7 percent increase from 2008.<ref> [http://www.noaa.gov/budget/] </ref>

The 2008 Democratic National Committee Platform states;<ref>[states;http://www.democrats.org/a/party/platform.html]</ref>

"We must end the tyranny of oil in our time. This immediate danger is eclipsed only by the longer - term threat from climate change"

and

"...climate change is not just an economic issue or an environmental concern - this is a national security crisis."

The 2008 Republican National Committee Platform states; <ref>[http://www.gop.com/2008Platform/Environment.htm]</ref>

"The same human economic activity that has brought freedom and opportunity to billions has also increased the amount of carbon in the atmosphere. While the scope and long-term consequences of this are the subject of ongoing scientific research, common sense dictates that the United States should take measured and reasonable steps today to reduce any impact on the environment."

There have also been some Conservatives, such as John Bliese, Ph.D., who at one point believed that global warming is a critical problem, and that [[Conservatism]] and environmental conservation are fully compatible. Speaking to those who are skeptical of global warming, in the [[Summer]] of 2001, he wrote, "[T]here is nothing conservative about denying scientific evidence."<ref>[http://www.rep.org/news/GEvol5/ge5.1_globalwarming.html]</ref>

On October 10, 2009, Republican Senator Lindsey Graham coauthored (with Democrat Senator John Kerry) an op ed piece in the New York Times which stated "Even climate change skeptics should recognize that reducing our dependence on foreign oil and increasing our energy efficiency strengthens our national security. Both of us served in the military. We know that sending nearly $800 million a day to sometimes-hostile oil-producing countries threatens our security. In the same way, many scientists warn that failing to reduce greenhouse gas emissions will lead to global instability and poverty that could put our nation at risk."
<ref>[http://www.nytimes.com/2009/10/11/opinion/11kerrygraham.html?pagewanted=1]</ref>

in 2008 the Center for Naval Analyses empaneled eleven retired generals and admirals to prepare a paper titled "National Security and the Threat of Climate Change". They concluded that Global climate change presents a serious national security threat which could impact Americans at home, impact United States military operations and heighten global tensions.<ref>[http://securityandclimate.cna.org/]</ref>

The Central Intelligence Agency has opened The Center on Climate Change and National Security to study the impact of climate change on US national security.<ref>[https://www.cia.gov/news-information/press-releases-statements/center-on-climate-change-and-national-security.html CIA Opens Center on Climate Change and National Security], Central Intelligence Agency, September 25, 2009.</ref>

Conservative activist and former House Speaker Newt Gingrich has called for a Conservative Environmentalism to find solutions to global warming by free market mechanisms.<ref>http://newt.org/EditNewt/FeaturedBloggersDB/tabid/193/articleType/ArticleView/articleId/3392/Default.aspx</ref>

===Climate Change As A Cult===
The zeal of climate-change advocates and lack of objectivity has led some observers to see it as a core belief in a new eco-theology, using themes of traditional Judeo-Christian beliefs. columnist Deon Feder warns, that following other attempts such as Marxism, overpopulation, ''Silent Spring'',
<blockquote>now we have the Church of Global Warming, under the leadership of Pope Albert I and his college of cardinals (the [[Natural Resources Defense Council]], Sierra Club and editorial board of The New York Times).

Its Office for the Propagation of the Faith works overtime, churning out books, movies (from the fictional “The Day After Tomorrow” to the fictional “An Inconvenient Truth”), textbooks, concerts, congressional hearings, media pleading and inquisitions.<ref>Don Feder, ''The Cult of Global Warming'', GrassTopsUSA.com 7/31/2007</ref> </blockquote>

Commenting on the tendency to hastily issue dire warnings of Climate Change, seen in the coming [[Ice Age]] scare of the 70's, Maurizio Morabito asked, “Is the problem with the general public, who cannot talk about climate except in doom-laden terms, and for whom the sky is the last animist god?" <ref>Maurizio Morabito, ''The CIA’s ‘global cooling’ files'', The Spectator December 5 2009</ref>

Mark Steyn writes in Macleans,
<blockquote>
"Forty years ago conventional religious belief was certainly in decline in what we once knew as Christendom, but the hole was not yet ozone-layer sized. Once the sea of faith had receded far from shore, the post-Christian West looked at what remained and found “Gaia.”</blockquote>

And while, "When man was made in the image of God, he was fallen but redeemable", among these devotees of [[Gaia]],
<blockquote>Anti-humanism is everywhere, not least in the barely concealed admiration for China’s (demographically disastrous) “One Child” policy advanced by everyone from the National Post’s Diane Francis to Sir David Attenborough, the world’s leading telly naturalist but also a BBC exec who once long ago commissioned the great series The Ascent of Man. If Sir David’s any guide, the great thing about man’s ascent is it gives him a higher cliff to nosedive off.<ref>Mark Steyn, ''Why climate change is hot hot hot'' Macleans, December 24, 2009</ref></blockquote>

===Politics of Global Warming and Dissent===
{{main|Politics of global warming}}

Christine Stewart- Canadian Environment Ministry, "'''No matter if the science is all phony''', there are collateral environmental benefits . . . Climate change provides the greatest chance to bring about justice and equality in the world.” <ref>[http://www.aim.org/wls/use-environmentalism-to-change-the-world/ Christine Stewart] Accuracy in Media</ref>

'Global Warming Now World's Most Boring Topic’ <ref>http://newsbusters.org/node/14167</ref>

The need to fight "global warming" has become part of the dogma of the liberal conscience. <ref name="cato" />

Clearly, "global warming" is a tempting issue for many very important groups to exploit.
... dealing with the threat of warming fits in with a great variety of preexisting agendas [like] dissatisfaction with industrial society (neopastoralism), ... governmental desires for enhanced revenues (carbon taxes), and bureaucratic desires for enhanced power. <ref name="cato" />

Mark Steyn writes in "Why climate change is hot hot hot",
<blockquote>
What’s also changed since the seventies is the nature of the UN and the transnational bureaucracies...“Aid” is a discredited word these days and comes with too many strings attached. But eco-credits sluiced through an oil-for-food program on steroids offers splendid new opportunities for bulking up an ambitious dictator’s Swiss bank accounts.<ref>http://www2.macleans.ca/2009/12/24/why-climate-change-is-hot-hot-hot/2/</ref></blockquote>

The IPCC is desperate to claim the 20th century-- the warmest on record. Thus, tying the progress of modern mankind to our supposed planet imbalance problem. Unfortunately for the IPCC, that point is disputed as well. In 2008, it was discovered that tree rings in Finland were more accurate record of the warmest century. The current era was not the warmest period-- it was the period between 931 and 1180. <ref>[http://tbirdnow.mee.nu/archive/2008/6?page=2 The Trees of Finland; Temperature Readings and Historical Reconstruction] Tbirdnow.mee.nu Blog (with links to actual data sources), June 24, 2008</ref>

Assessments of climate science by the [[United Nations]] (see [[IPCC]] - ''Intergovernmental Panel on Climate Change'')
have claimed that scientists are 90% sure that over 50% of the observed global warming in recent decades is human-caused, and that continued global warming should be expected over at least the next century.

Several prominent scientists have pointed out the [[politicized science]] of the UN's assessment methods. The scientific reports are submitted to a panel of representatives appointed by each country in the IPCC. Several scientists whose research demonstrates that climate change is taking place have complained about their work being misrepresented by the U.N.

In addition, a number of the participants have testified to the pressures placed on them to emphasize results supportive of the current scenario and to suppress other results. That pressure has frequently been effective, and a survey of participants reveals substantial disagreement with the final report. <ref name="cato" />

Richard Lindzen wrote:
:Perhaps more important are the pressures being brought to bear on scientists to get the "right" results. Such pressures are inevitable, given how far out on a limb much of the scientific community has gone. The situation is compounded by the fact that some of the strongest proponents of "global warming" in Congress are also among the major supporters of science (Sen. Gore is notable among those). <ref name="cato" />

Christopher Monckton wrote an article titled Climate Sensitivity Reconsidered.
:States that Intergovernmental Panel on Climate Change studies are flawed. The present analysis suggests the models failure to predict other climatic phenomena arises from defects in its evaluation of radioactive forcing, no-feedbacks climate sensitivity parameter and feedback multiplier. In conclusion, that there may be no "Climate Crisis" and for governments to reduce emissions may be pointless or even harmful. <ref>http://www.aps.org/units/fps/newsletters/200807/monckton.cfm , Climate Sensitivity Reconsidered, July 2008</ref> This was published on a forum of the American Physical Society with the following disclaimer "The article has not undergone any scientific peer review" and "the APS disagrees with the articles conclusions" In fact, the APS disagrees with the article without ever reviewing it.

Ryan N. Maue:
:A doctoral student at the Department of Meteorology at Florida State University did a study of global tropical cyclone activity. Its conclusions state that global warming might be greatly overblown. <ref>[http://www.pittsburghlive.com/x/pittsburghtrib/opinion/s_617111.html# Global warming? More doubts] Pittsburgh Tribune, March 21, 2009</ref> Mr. Maue found that tropical cyclone activity worldwide "has completely and utterly collapsed" during the past two to three years with energy levels sinking to those of the late 1970s.

Dr. Vincent Gray:
:A member of the IPCC’s expert reviewers’ panel asserts, “There is no relationship between warming and the level of gases in the atmosphere,” and "there is no serious threat to the climate" <ref>[http://americanfreedomnow.com/2009/06/04/the-panic-over-global-warming-is-totally-unjustified-says-vice-chair-ipcc/ “THE PANIC OVER GLOBAL WARMING IS TOTALLY UNJUSTIFIED” says Vice Chair, IPCC] Americanfreedomnow.com, June 4th, 2009</ref>

Joe D’Aleo: Climatologist
:The International Climate and Environmental Change Assessment Project says new data "show that in five of the last seven decades since World War II, including this one, global temperatures have cooled while carbon dioxide has continued to rise," and "'''The data suggest cooling''', not warming, in Earth's future." <ref>[http://www.wnd.com/index.php?fa=PAGE.view&pageId=92557 Shocker: 'Global warming' simply no longer happening] Worldnetdaily, March 22, 2009</ref>

Dr. John S. Theon:
:Retired senior NASA atmospheric [[scientist]], Dr. John S. Theon, the former boss of global warming alarmist James Hansen of [[NASA]], rebukes him declaring “climate models are useless.” “My own belief concerning anthropogenic climate change is that the models do not realistically simulate the climate system because there are many very important sub-grid scale processes that the models either replicate poorly or completely omit,” “Furthermore, some scientists have manipulated the observed data to justify their model results." <ref>[http://newsbusters.org/blogs/tom-blumer/2009/01/28/former-boss-rebukes-nasa-global-warming-alarmist-hansen-agw-skeptic Former Boss Rebukes NASA Global Warming Alarmist Hansen, Is AGW Skeptic] NewsBusters.org, January 28, 2009 </ref>

Sammy Wilson -Ireland's environment minister
:He argues that global weather patterns are naturally cooling, not warming. He calls television ads that promote global warming as "an insidious propaganda campaign" peddling "patent nonsense." <ref>[http://www.cnsnews.com/public/content/article.aspx?RsrcID=43255 Belfast Environment Chief Bans Climate Change Ads] AP, February 09, 2009</ref>

After the broadcast of his movie '[[The Great Global Warming Swindle]]', filmmaker Martin Durkin's statements read <ref>[http://www.cnsnews.com/public/content/article.aspx?RsrcID=32796 UK Broadcaster Scolded for Film on Global Warming] CNSNEWS July 22, 2008</ref>

*“Everywhere you are told that man-made [[climate change]] is proved beyond doubt,” “But you are being told lies.”
*“This is a story of how a theory about climate turned into a political [[ideology]] ... it is the story of the distortion of a whole area of [[science]].”
*“as the frenzy over man-made [[global warming]] grows shriller, many senior scientists say the actual scientific basis for the [[theory]] is crumbling.”

In late 2008, the [[AP]] published an article by its Science Writer Seth Borenstein, which is seen by skeptics as another example of one-sided, uncritical reporting on the issue by [[liberal media]]. The report stated that global warming was "a ticking time bomb that President-elect Barack Obama can't avoid", and that "We're out of time", with Al Gore calling the situation "the equivalent of a five-alarm fire that has to be addressed immediately."<ref>http://www.breitbart.com/article.php?id=D952LKOO1&show_article=1</ref> In response, Fox News (December 16, 2008) reported that scientists skeptical of anthropogenic global warming criticized the report as "irrational hysteria," "horrifically bad" and "incredibly biased", containing sweeping scientific errors and being a one-sided portrayal of a complicated issue. Geology professor [[David Deming]] stated, "If the issues weren't so serious and the ramifications so profound, I would have to laugh at it", and accused Borenstein of "writing a polemic and reporting it as fact." Deming noted that "the mean global temperature, at least as measured by satellite, is now the same as it was in the year 1980. In the last couple of years sea level has stopped rising. Hurricane and cyclone activity in the northern hemisphere is at a 24-year low and sea ice globally is also the same as it was in 1980." The AP responded to criticism by stating that, "It’s a news story, based on fact and the clearly expressed views of President-elect Barack Obama and others."<ref>[http://www.foxnews.com/story/0,2933,468084,00.html Scientists Call AP Report on Global Warming 'Hysteria'] Fox News, December 16, 2008</ref>

Also in the discussion of the biased AP report, Michael R. Fox, a retired nuclear scientist and chemistry professor from the University of Idaho stated, "There is little evidence to believe that man-made carbon dioxide is causing temperature fluctuation. Other factors, including sun spots, solar winds, variations in the solar magnetic field and solar irradiation, could all be affecting temperature changes."

The year 2008 turned out to be the coolest year since 2000, yet the seventh to tenth warmest year on record, according to the NASA Goddard Institute for Space Studies.<ref>http://news.eoportal.org/research/090127_res3.html</ref> According to a preliminary analysis by NOAA’s National Climatic Data Center, the average June-August 2009 summer temperature for the contiguous United States was below average – the 34th coolest on record.<ref>[http://www.noaanews.noaa.gov/stories2009/20090910_summerstats.html NOAA: Summer Temperature Below Average for U.S.]</ref>

Richard S. Courtney, a U.N. Intergovernmental Panel on Climate Change (IPCC) expert reviewer and a U.K.-based climate and atmospheric science consultant says "Rubbish! Global warming is not 'accelerating," and "...that anybody who proclaims that 'Global warming is accelerating' is a liar, a fool, or both." <ref>[http://www.newsmax.com/brennan/global_warming_debunked/2008/12/16/162489.html Global Warming’s Last Gasp] NewsMax, December 17, 2008</ref>

Don J. Easterbrook, Ph.D., emeritus professor of geology at Western Washington University, asked, "What does it take to ignore 10 years of global cooling....? The answer is really quite simple — just follow the money!"

===2008 Presidential candidates on climate Change===

[[Bob Barr]] is the only major 2008 Presidential Candidate who has not adopted wholesale the theory of human-caused global warming.

According to his website,<ref>[http://www.johnmccain.com/Informing/News/PressReleases/BA6709C3-B27D-4EF9-81E6-2BA9D6F8AB20.htm John McCain on Global warming.]</ref> [[Republican]] Presidential candidate [[John McCain]] will take a more "aggressive approach" to global warming which he has declared as "undeniable and urgent." He was supported in this in June 2008 by Republican governor [[Arnold Schwarzenegger]] who said McCain was the "real deal on the environment".<ref>[http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2008/06/30/MNDB11H66C.DTL&type=politics Schwarzenegger backs McCain on climate Change]</ref>.

In his own words, McCain says "the overwhelming majority of scientific opinion in America today, and in the world, is that climate change is real. The fact is that it ''is'' real. The fact is that the solution to it is the development of technologies.... and a [[cap and trade]] proposal.... the debate is over."[http://www.youtube.com/watch?v=gQMxIwpK_es] Unless McCain believes that Global Warming is entirely or largely man-made, there would be no sense in supporting a cap and trade solution.

[[Barack Obama]] believes "that global warming is not just the greatest [[environmental]] [[challenge]] facing our planet—it is one of our greatest challenges of any kind." During his first 100 days in office, he would enact a giant and far-reaching [[tax]] "an economy-wide cap on U.S. carbon emissions that will reduce U.S. emissions by the amount scientists agree is necessary (80% by 2050). With worldwide cuts in emissions estimated to cost '''$45 Trillion dollars''' overall. <ref>[http://business.timesonline.co.uk/tol/business/industry_sectors/natural_resources/article4079036.ece World needs $45 trillion energy revolution] Timesonline.uk, June 6, 2008</ref> He comments "Putting a price on carbon is the most important step we can to take to reduce emissions."<ref>[http://presidentialprofiles2008.org/Obama/tab1.html League of Conservation Voters] presidentialprofiles2008.org</ref>

==Inaccuracies of Global Warming evidence==
===Climate "Science" Fraud===
{{main|Climategate}}

The [[Climategate#Climategate_scandal|Climategate scandal]] revealed how liberal scientists appeared to be deceiving the public with the use of fraudulent data for use as climate science. The [[Liberal media|liberal media]] has attempted to bury the story and discount it as the work of computer hackers illegally stealing data, however, [[FOIA|Freedom of Information]] requests is likely what led to the data being leaked — intentionally.<ref>http://www.junkscience.com/</ref> Dr. Willie Soon, a [[Physicist|physicist]], [[Astronomer|astronomer]] and climate researcher at the solar and stellar physics division of the [[Harvard University]]-Smithsonian Center for Astrophysics, said in an interview, "[The Climatic Research Unit climate scientists] are making scientific progress more difficult now. This is a shameful, dark day for science." Dr. Soon also suggested that there has been systemic suppression of dissenting opinion among scientists in the climate change community, ranging from social snubs to e-mail stalking and even threats of harm.<ref>Gene J. Koprowski. [http://www.foxnews.com/story/0,2933,578368,00.html Global Warming Scandal Makes Scientific Progress More Difficult, Experts Say], ''[[Fox News]]'', December 01, 2009.</ref>

[[Image:GoreFireBreathing.jpg|thumb|left|250px|Al Gore's [[Schlockumentary]] under fire; [[An Inconvenient Truth]] found to be an inconvenient [[lie]] based on [[junk science]] and digitally enhanced, totally faked scenes of polar icecaps melting.]]

===Liberal claims of "Consensus"===
Reports of a scientific "consensus" among scientists allege that the Earth is warming overall, and that this warming, as well as other changes in climate patterns, is largely caused by human activities.<ref>Anderegg, Prall, Harold, and Schneider. "Expert credibility in climate change." April 9, 2010. Proceedings of the National Academy of Sciences. http://www.pnas.org/content/early/2010/06/04/1003187107.full.pdf+html</ref><ref>From "IPCC Fourth Assessment Report: Climate Change 2007." Intergovernmental Panel on Climate Change. http://www.ipcc.ch/publications_and_data/ar4/wg1/en/spmsspm-understanding-and.html</ref> These allegations do not necessarily make the consensus true, as discussed throughout the referenced citation. Numerous scientists, especially those outside of university faculties, have been critical of anthropogenic global warming. However, according to some researchers, scientists who do not support the anthropogenic global warming theory offer a general lack of comparative credentials; proponents of man-made global warming argue that this has led to agreement that, among authorities in scientific disciplines, there is a "[[scientific consensus]]" supporting the theory for greater government control. Scientists skeptical of the theory question whether there is a financial incentive for supporting research.<ref>[http://www.seattlepi.com/printer2/index.asp?ploc=t&refer=http://www.seattlepi.com/opinion/336889_climatepolicy26.html Pual Chesser,
''Be wary of climate policy development'', Seattle Post-Intelligencer, Act. 25, 2007]</ref> It has also been documented that on most college campuses criticism of the global warming theory is silenced or censored; evidence shows that scientists skeptical of AGW are being supressed.<ref>http://www.spiked-online.com/index.php?/site/article/1782/</ref><ref>http://www.wnd.com/index.php?fa=PAGE.view&pageId=102031</ref>

It is well understood that most media companies do not offer balanced reporting. Many politicians have bought into the liberal claim of consensus, for example Barack Obama's views, "Few challenges facing America and the world are more urgent than fighting climate change. The science is beyond dispute and the facts are clear." <ref>[http://cato.org/special/climatechange/ Climate Change Reality] Cato Institute</ref> In fact, many scientists disagree with the "facts," their certainty, and their interpretation. Over 100 of them have signed the statement that appears in the Cato Institute's newspaper ad. Liberals have failed to back up their claims with any scientific facts.

[[File:ad.jpg|center]]

===Past Speculation===

Speculation and warnings of catastrophic climate change are not unprecedented. In 2001 the ''Guardian'' noted that some 70s headlines shouted, "Brace yourself for another ice age". In 1971 the journal ''Science'' reported that the subsequent cooling effect resulting from a possible eightfold increased from atmospheric aerosol concentrations, "if sustained over a period of several years - is believed to be sufficient to trigger an ice age." <ref>Reported by Alison George in ''Breaking the ice'', The Guardian, Thursday 28 June 2001</ref>

[[Richard Lindzen]] wrote in 1992 on the doubtfulness of man-caused warming on Earth.

{{Cquote|Indeed, a recent Gallup poll of climate scientists in the American Meteorological Society and in the American Geophysical Union shows that a vast majority doubts that there has been any identifiable man-caused warming to date (49 percent asserted no, 33 percent did not know, 18 percent thought some has occurred; however, among those actively involved in research and publishing frequently in peer-reviewed research journals, none believes that any man-caused global warming has been identified so far). <ref name="cato">http://www.cato.org/pubs/regulation/regv15n2/reg15n2g.html</ref>}}

Oddly enough, even though 82% of US climate scientists refused to support the global warming theory then, [[liberal]] activists were already claiming a scientific consensus for [[anthropogenic global warming]]. (It's hard to understand how 18 percent credence in ''any'' global warming translates into "consensus" support for ''human-caused'' global warming.)

The campaign to convince the public (and their elected representatives) that the "science is settled" began in 1988 or 1989.

By the 2008 elections both candidates for the Presidency of the United States were proposing plans to mitigate climate change.

Over 31,000 American scientists have signed the petition rejecting global warming. <ref>[http://www.petitionproject.org/</ref>

[[Image:Teller_Card_100dpi.jpg|600px|center|thumb| Global Warming Petition]]

In June, 1974, ''[[Time]]'' magazine published its front page article, ''Science: Another Ice Age?'',<ref>''Science: Another Ice Age?'' Time magazine, Monday, Jun. 24, 1974</ref> while a report by the [[CIA]] in the same year stated that, "The world's leading climatologists have confirmed recent reports of a detrimental global climatic change”, noting such things as that the "world's snow and ice cover had increased by at least 10 to 15 percent", and "the Canadian area of [[Arctic]] Greenland suffered below normal temperatures for 19 consecutive months", which was unique during the last 100 years. A "major climatic shift" was speculated, which would threaten the "the stability of most nations.” It further warned that "Scientists are confident that unless man is able to modify the climate, the northern regions, such as Canada" to "major areas in northern China will again be covered with 100 to 200 feet of ice and snow", within the next 2500 years - or sooner.<ref>[http://www.climatemonitor.it/wp-content/uploads/2009/12/1974.pdf ''A study of climatological research as it pertains to intelligence problems'', August 1974]</ref>

Also in 1974, Nigel Calder, former editor of ''New Scientist'' and atmospheric researcher wrote in his book ''The Weather Machine'', "One might argue that there is a virtual certainty of the next ice age starting some time in the next 2000 years. Then the odds are only about 20-to-1 against it beginning in the next 100 years."

In 1975 the liberal magazine ''[[Newsweek]]'' reported that "Meteorologists disagree about the cause and extent of the cooling trend,...but they are almost unanimous in the view that the trend will reduce agricultural productivity for the rest of the century." These authorities were skeptical that political leaders would take any positive action to compensate for the [[climate change]], and they conceded that the more dramatic solutions, such as melting the arctic ice cap, might create worse problems than that which they were designed to solve.<ref>http://denisdutton.com/newsweek_coolingworld.pdf</ref>

===Natural Variability of the Climate System===
It is virtually universally accepted amongst secular climatologists that the earth has experienced numerous [[Ice Age|ice age]]s over two million years, during which global temperatures fluctuated created glacial and inter-glacial periods. The frigid temperatures allowed ice sheets to expand southward, covering much of [[Asia]], [[Europe]], and [[North America]]. The cooling associated with ice ages is gradual, while the terminations are relatively rapid. However, even the rapid terminations of ice ages take centuries to millennia.

===Natural Climate Change on Other Planets===

Since the [[Viking spacecraft]] reached [[Mars]] in the 1970s until recent readings were taken, the average temperature on Mars has risen {{temperature|0.6|1.1}} just as the average temperature on the earth has risen. Since human industrialization is clearly not to blame for the change on Mars, other causes are being considered. One possibility is that dust storms are changing the albedo of the planet, allowing it to warm, while another possibility is that solar variations from the sun are causing the warming.<ref>http://www.space.com/scienceastronomy/070404_gw_mars.html</ref><ref>http://www.heartland.org/Article.cfm?artId=17977</ref>

Recently, it has also been found that similar to the Earth and Mars, [[Neptune]] is also undergoing global warming. Measurements taken at the Lowell observatory in [[Arizona]] have shown an increase in Neptune's brightness and temperature since 1980 following the same pattern seen on Earth and Mars. The researchers who discovered this warming suggest there may be a correlation between the warming and solar variations.<ref>http://www.agu.org/pubs/crossref/2007.../2006GL028764.shtml</ref>

[[Pluto]] has also been found to be undergoing global warming. The overall temperature increase on Pluto has been greater than that on the earth.<ref>http://www.space.com/scienceastronomy/pluto_warming_021009.html</ref>

On the other hand [[Uranus]] has had no net change in temperature since 1977. A rapid increase in temperature reversed itself. The reasons for this are not understood.<ref>http://www.boulder.swri.edu/~layoung/eprint/ur149/Young2001Uranus.pdf</ref>

Global temperatures change on other planets even when there is no life, something which strongly supports the idea that humans are not necessarily the cause of earth's global warming. Moreover, the temperature on Uranus has fluctuated back and forth. There is no reason that fluctuations cannot occur on earth, too.

Although measurements have been made of the temperatures of other planets these are by no means thorough or comparable with the measurements used for earth. The short space of time over which measurements have been taken and the very limited spatial coverage means that reliable average figures have not been obtained. They have certainly not been taken extensively enough to produce a five year average temperature, which is the standard when determining temperature trends on earth.

However, if accurate measurements could be made, and their accuracy and reliability is improving over time, then they may prove useful to climate science. Their different atmospheres and distances from the sun provide natural laboratories to study climatic changes without human influences. Though of course they will not be directly comparable due to the vast differences.

===Al Gore's Claims===
[[File:Gore GlobalWarming.jpg|right|200px]]
The decision by the government to distribute Al Gore's film, ''An Inconvenient Truth'', became the subject of a legal challenge by [[New Party]] member Stewart Dimmock. A school governor from Dover and father of two, Dimmock charged the Government with brainwashing children with propaganda by presenting Gore’s sci-fi film as science. In October 2007, Mr Justice Burton of London's High Court found that while the film was "broadly accurate", it contained nine significant errors,“in which statements were made that were not supported by the current mainstream scientific consensus”, some of which had arisen in “the context of alarmism and exaggeration”. He also found the Guidance Notes drafted by the Education Secretary’s advisers only worked to exacerbate the political propaganda in the film.<ref>[http://www.americanthinker.com/blog/2009/07/clearly_its_al_gore_whos_in_de.html American Thinker; ''Clearly It's Al Gore Who's In Denial'']</ref><ref>Times online, October 11, 2007 ''Al Gore’s inconvenient judgment''</ref>

Taken from the official transcript,<ref>[http://noteviljustwrong.com/images/nejw/docs/22161.pdf Stuart Dimmock and Secretary of State for Education and Skills]</ref> the nine errors the judge found were:

*1. Sea level rise of up to 20 feet (7 metres) will be caused by melting of either West Antarctica or Greenland in the near future. This is distinctly alarmist, and part of Mr Gore's 'wake-up call'. It is common ground that if indeed Greenland melted, it would release this amount of water, but only after, and over, millennia, so that the Armageddon scenario he predicts, insofar as it suggests that sea level rises of 7 metres might occur in the immediate future, is not in line with the scientific consensus.

*2. Low lying inhabited Pacific atolls are being inundated because of anthropogenic global warming. In scene 20, Mr Gore states "that's why the citizens of these Pacific nations have all had to evacuate to New Zealand". There is no evidence of any such evacuation having yet happened.

*3. Shutting down of the "Ocean Conveyor". According to the IPCC, it is very unlikely that the Ocean Conveyor (known technically as the Meridional Overturning Circulation or thermohaline circulation) will shut down in the future, though it is considered likely that thermohaline circulation may slow down.

*4. Direct coincidence between rise in CO2 in the atmosphere and in temperature, by reference to two graphs. In scenes 8 and 9, Mr Gore shows two graphs relating to a period of 650,000 years, one showing rise in CO2 and one showing rise in temperature, and asserts (by ridiculing the opposite view) that they show an exact fit. Although there is general scientific agreement that there is a connection, the two graphs do not establish what Mr Gore asserts.

*5. The snows of Kilimanjaro. The film asserted that melting snows on Mount Kilimanjaro evidenced global warming. The Government's expert was had to admit that this is not correct. Mr Gore asserts in scene 7 that the disappearance of snow on Mt Kilimanjaro is expressly attributable to global warming. It is noteworthy that this is a point that specifically impressed Mr Milliband (see the press release quoted at paragraph 6 above). However, it is common ground that, the scientific consensus is that it cannot be established that the recession of snows on Mt Kilimanjaro is mainly attributable to human-induced climate change.

*6. Lake Chad etc. The drying up of Lake Chad is used as a prime example of a catastrophic result of global warming. However, it is generally accepted that the evidence remains insufficient to establish such an attribution. It is apparently considered to be far more likely to result from other factors, such as population increase and over-grazing, and regional climate variability.

*7. Hurricane Katrina. In scene 12 Hurricane Katrina and the consequent devastation in New Orleans is ascribed to global warming. It is common ground that there is insufficient evidence to show that.

*8. Death of polar bears. In scene 16, by reference to a dramatic graphic of a polar bear desperately swimming through the water looking for ice, Mr Gore says: "A new scientific study shows that for the first time they are finding polar bears that have actually drowned swimming long distances up to 60 miles to find the ice. They did not find that before." The only scientific study that either side before me can find is one which indicates that four polar bears have recently been found drowned because of a storm.

*9. Coral reefs. In scene 19, Mr Gore says: "Coral reefs all over the world because of global warming and other factors are bleaching and they end up like this. All the fish species that depend on the coral reef are also in jeopardy as a result. Overall specie loss is now occurring at a rate 1000 times greater than the natural background rate." The actual scientific view, as recorded in the IPCC report, is that, if the temperature were to rise by 1-3 degrees Centigrade, there would be increased coral bleaching and widespread coral mortality, unless corals could adapt or climatize, but that separating the impacts of climate change-related stresses from other stresses, such as over-fishing and polluting, is difficult.

Dimmock's lawyer, Mr. Downes, argued that by schools making available such film to its teachers, and if teachers then showed such film to their pupils, then this would inevitably result "in the promotion of partisan political views in the teaching of any subject in the school, which is thus not only not being forbidden by the local education authority (and the DES), but being positively facilitated by them."

Mr Justice Barton stressed that the “apocalyptic vision” presented in the film was politically partisan and not an impartial analysis of the science of climate change. “It is now common ground that it is not simply a science film – although it is clear that it is based substantially on scientific research and opinion – but that it is a political film.

Justice Barton also stated that, “I conclude that the claimant substantially won this case by virtue of my finding that, but for the new guidance note, the film would have been distributed in breach of sections 406 and 407 of the 1996 Education Act.”<ref> BBC news, Thursday, 11 October 2007</ref>

In order for the film to be shown, the Government must first amend their Guidance Notes to Teachers to make clear that

*1. The Film is a political work and promotes only one side of the argument.

*2. If teachers present the Film without making this plain they may be in breach of section 406 of the Education Act 1996 and guilty of political indoctrination.

*3. Nine inaccuracies have to be specifically drawn to the attention of school children.<ref>http://www.newparty.co.uk/articles/inaccuracies-gore.html</ref>

Science and Public Policy took issue with the response to the ruling by Al Gore’s spokesman and environment adviser, and asserted that his film contains ''35 Inconvenient Truths''.<ref>[http://scienceandpublicpolicy.org/monckton/goreerrors.html 35 Inconvenient Truths]</ref>

Regarding his claims that the snow cap atop Africa's Mt. Kilimanjaro is shrinking and that global warming is to blame, the November 23, 2003, issue of Nature magazine stated,

:Although it's tempting to blame the ice loss on global warming, researchers think that deforestation of the mountain's foothills is the more likely culprit. Without the forests' humidity, previously moisture-laden winds blew dry. No longer replenished with water, the ice is evaporating in the strong equatorial sunshine." <ref name="sun" />

Many conservatives see Al Gore as an example of [[liberals]] using [[deceit]]ful tactics in important debates, in order to make a position seem more solid than it is.

===Scientists===

[[Image:Rogerrevelle.jpg|thumb|right|200px|Roger Revelle]]

{|
| valign="top" width="35%"|
* [[Roger Revelle]]
* [[Achim Steiner]]
* [[Fred Singer]]
* [[Richard Lindzen]]
* [[Sallie Baliunas]]
* [[Lonnie Thompson]]
| valign="top" width="33%"|
* [[James E. Hansen]]
* [[Michael Mann]]
* [[Charles Keeling]]
* [[Edwin A. Hernández-Delgado]]
|}

===Critique of the Hockey Stick Reconstruction===
::''See also : [[Climategate#Hockey_Stick_Graph|Climategate: hockey stick graph]]''

*[http://climateaudit.files.wordpress.com/2005/09/mcintyre.mckitrick.2003.pdf Corrections To The Mann et. al. (1998) Proxy Data Base And Northern Hemispheric Average Temperature Series] by Stephen McIntyre and Ross McKitrick, ''Energy & Enviornment'' volume 14, 2003.
*[http://blogs.nature.com/climatefeedback/2007/05/the_decay_of_the_hockey_stick.html The Decay of the Hockey Stick by Von Storch] published on the journal ''Nature'''s blog, May 3, 2007.
*[http://www.technologyreview.com/Energy/13830/ A Global Warming Bombshell] by Richard A. Muller, ''Technology Review'' , Oct. 2004; calls into question famous graph by Michael Mann.
*[http://www.sciencemag.org/cgi/content/abstract/306/5696/679 Reconstructing Past Climate from Noisy Data] by Hans von Storch, Eduardo Zorita, Julie M. Jones, Yegor Dimitriev, Fidel González-Rouco, Simon F. B. Tett, ''Science'' magazine, 22 October 2004.
*[http://www.image.ucar.edu/~boli/manuscripts/2007-LNA-TeA.pdf The ‘hockey stick’ and the 1990s: a statistical perspective on reconstructing hemispheric temperatures] by Bo Li, Douglas W. Nychka and Casper M. Ammann, ''Institute for Mathmatics Applied to Geosciences''; (Manuscript received 22 March 2007; in final form 28 June 2007).
*[http://www.21stcenturysciencetech.com/2006_articles/IceCoreSprg97.pdf Ice Core Data Show No Carbon Dioxide Increase] by Zbigniew Jaworowski, Ph.D., Spring 1997; this article examines one of the main pillars of the global warming thesis.
*[http://climateaudit.files.wordpress.com/2005/09/mcintyre.ee.2005.pdf The M&M Critique of the MBH98 Northern Hemisphere Climate Index: Update and Implications] (''Energy & Environment'', vol. 16, no. 1, pp. 69-100, January 2005) - Stephen McIntyre, Ross McKitrick
*[http://climateaudit.files.wordpress.com/2005/09/mcintyre.grl.2005.pdf Hockey sticks, principal components, and spurious significance] (''Geophysical Research Letters'', vol. 32, February 2005) - Stephen McIntyre, Ross McKitrick


==Effects of Global Warming==
===Beneficial effects of Global Warming===
[[File:Autumn foliage.jpg|thumb|Canoing on a Colorful Day, (NY).]]
Some researchers point out that benefits of health global warming have been overlooked, or minimized. As far back as 1996, Thomas Gale Moore, Senior Fellow at Hoover Institution (Stanford University) contended that positive health and amenity effects would be a result of projected increases in temperature. <ref>[http://www.stanford.edu/~moore/health.html Health and Amenity Effects of Global Warming]</ref>

Another source notes,

In areas that see extreme cold temperatures, deaths related to colder weather would drop significantly, leading to decreased health care costs. Warmer temperatures would also mean less energy use to heat homes and buildings, helping to conserve energy. With the changes brought about by global warming more land would become available for uses like farming and living. Forests and plants would grow stronger, healthier, and more abundant because of the warmer weather, and this would mean more oxygen being released into the atmosphere.<ref>http://www.bionomicfuel.com/what-are-the-benefits-of-global-warming/</ref>

===Reported effects of Climate Change===

Besides Global Warming, reported past or expected/possible future environmental and societal consequences of Climate Change include,

*Global cooling.<ref>http://www.nowpublic.com/environment/global-warming-causing-global-cooling</ref>

* Decreased food production.<ref> Fred Pearce, ''Climate change warning over food production,'' Newscientist.com, April 26, 2005</ref>

* Increased food production. <ref>[http://www.encyclopedia.com/doc/1P2-1127111.html] William Booth, ''Global Heating Could Benefit U.S. Farmers; Prices Seen Rising As Production Falls'' The Washington Post, May 17, 1990</ref>

* Shrinking forests.<ref>[http://www.guardian.co.uk/environment/2009/mar/11/amazon-global-warming-trees/print David Adam, ''Amazon could shrink by 85% due to climate change''] March 11, 2009, guardian.co.uk</ref>

* Increased tree foliage.<ref>http://www.greenfingers.com/articledisplay.asp?id=1734</ref>

* Increased productivity of high-elevation forests.'<ref>'Global Warming May Spur Increased Growth In Pacific Northwest'' Oct. 20, 2009, Forests Science Daily</ref>

* Melting glaciers.<ref>Global warming causing hundreds of Antarctic Peninsula glaciers to melt,''
June 6, 2007, The Hindustan Times</ref>

* Growing glaciers.<ref>http://www.freerepublic.com/focus/news/2043047/posts?page=51</ref>

* Increasing landmass in Antarctica.<ref>http://www.worldclimatereport.com/index.php/2005/05/27/antarctic-ice-a-global-warming-snow-job/</ref>

* Colder winters <ref>''Climate change could bring colder winters,'' March 13, 2003, Canadian Broadcasting Centre</ref>

* A new ice age.<ref>[http://www.guardian.co.uk/environment/2003/nov/13/comment.research/print Bill McGuire, The Guardian, November 13, 2003]</ref>

* Prevention of an ice age.<ref>[http://www.foxnews.com/printer_friendly_story/0,3566,296060,00.html Andrea Thompson, ''Global Warming May Cancel Next Ice Age''], Monday, September 10, 2007</ref>

* Taller mountains.<ref>Ker Than, ''Taller Mountains Blamed on Global Warming, Too'', August 4, 2006, LiveScience</ref>

* A lop-sided planet.<ref>Robert Roy Britt, June 29,2005 LiveScience.com</ref>

* Stronger hurricanes.<ref>''Global Warming: Warmer Seas Linked To Strengthening Hurricanes,'' Sep. 4, 2008, ScienceDaily</ref>

* Weaker Hurricanes.<ref>Randolph E. Schmid, AP Science Writer, ''Global warming may diminish Atlantic hurricane activity'', 04-17-2007, USA Today</ref>

* Shorter days.<ref>[http://www.itwire.com/content/view/11220/1066/ William Atkins, ''Researchers say global warming should cause shorter days''], ITWire, April 11, 2007</ref>

* Earthquakes and volcanoes, and other geological disasters. Attempts to prevent climate change may do the same.<ref>Richard Fisher, ''Climate change may trigger earthquakes and volcanoes,'' September 23 2009 Newscientist.com</ref>

* Shrinking brains.<ref>Gordon G. Gallup Jr., Human Nature (Vol. 18, Issue 2, 2007U)</ref>

* Shrinking sheep.<ref> Steve Connor, Science Editor, ''How global warming shrank St Kilda's sheep,''
Independent.co.uk, 3 July 2009</ref>

* Tiger Attacks.<ref>''Global Warming Linked to Indian Tiger Attacks'', Reuters, Mon Oct 20, 2008</ref>

* Shark attacks.<ref>[http://www.junkscience.com/news3/shark.htmlBruce Johnston, ''Shark attack on boat result of global warming''] Augsut 31, 1998, Electronic Telegraph (U.K.)</ref>

* Walrus stampede deaths.<ref>http://www.freerepublic.com/focus/f-news/1939754/posts ''Global warming is blamed for walrus stampede deaths'', Associated Press - December 14, 2007</ref>

* Imminent cannibalism.<ref>Ted Turner, April 1, 2008, Charlie Rose PBS show</ref>

* The need for a drastic reduction of the earth’s population.<ref>http://thisistheendoftheworldasweknowit.com/archives/one-less-child-environmental-extremists-warn-that-overpopulation-is-causing-climate-change-and-will-ultimately-destroy-the-earth</ref>

* A strong increase in people dying of [[AIDS]]<ref>Daniel Tarantola, University of NSW, Australia</ref> <ref>http://www.skepticsglobalwarming.com/?p=608</ref>

* Increased risk of civil war in Africa.<ref>[http://news.stanford.edu/news/2009/november23/climate-civil-wars-112309.html?view=print ''Global warming increases risk of civil war in Africa,''] Stanford Report, November 23, 2009</ref>

* Child ''climate cops''.<ref>http://www.wnd.com/index.php?fa=PAGE.view&pageId=70811</ref>

*Increase in depression.<ref>Emily Sohn Thurs., Discovery Channel, Dec . 10, 2009</ref>

* Increase in psychiatric illness.<ref>World Health Organisation</ref> <ref>''Climate change leads to psychiatric illness'' 04-08, 2008, Sify.com</ref>

* Increased anxiety and loss of sleep among many children.<ref>Alan Jones, The Scotsman, February 22, 2007</ref>

{{liberalism}}
{{Climategate scandal}}

==References==
{{reflist|2}}

== See Also ==
*''[[Massachusetts v. EPA]]''
*[[Liberal_hysteria#Global_Warming_Derangement_Syndrome|Global Warming Derangement Syndrome]]
*[[Socialist Environmental Disasters]]
*[[Counterexamples to Global Warming]]

==External Links==
*[http://www.aim.org/wls/category/global-warming/ What Liberals Say - Category: Global Warming], [[Accuracy In Media]]
*[http://global-warming.accuweather.com/2007/12/attempting_to_stop_global_warm_1.html Attempting to Stop Global Warming is Futile and a Mistake, says letter to the UN]
*[http://www.nationalpost.com/news/story.html?id=164004 Signatories of an open letter on the UN climate-conference]
*[http://schwinger.harvard.edu/~motl/global-temperature-not-exist.pdf Does a global temperature exist?], ''Journal of Non-Equilibrium Thermodynamics'', June 2007.
*[http://environment.guardian.co.uk/climatechange/story/0,,2032821,00.html The appliance of science] by Mike Hulme.
*[http://www.climatecrisis.net/ ''An Inconvenient Truth''], Film by [[Al Gore]]
*[http://video.google.com/videoplay?docid=2332531355859226455&q=great+global+warming+swindle ''The Great Global Warming Swindle'' - Documentary Film]
*[http://www.physics.harvard.edu/~motl/iris-effect.pdf Climate Sensitivity and Observed Negative Feedbacks], lecture by Richard Lindzen and Roberto Rondanelli.
*[http://www.physics.harvard.edu/~motl/lindzen-nature-of-arguments.pdf Nature of Arguments for Anthropogenic Global Warming], by Richard Lindzen
*[http://www.independent.org/store/book_detail.asp?bookID=42 ''Hot Talk, Cold Science: Global Warmings's Unfinished Debate'', by S. Fred Singer]
*[http://www.cato.org/pubs/regulation/regv15n2/reg15n2g.html Global Warming: The Origin and Nature of the Alleged Scientific Consensus] - [[Richard S. Lindzen]], Alfred P. Sloan Professor of Meteorology at the [[Massachusetts Institute of Technology]]
*[http://www.independent.org/publications/tir/article.asp?issueID=47&articleID=604 "Should We Have Acted Thirty Years Ago to Prevent Climate Change?", by Randall G. Holcombe].
*[http://www.independent.org/publications/tir/article.asp?issueID=25&articleID=296 "After Kyoto: A Global Scramble for Advantage," by Bruce Yandle].
*[http://www.ncpa.org/sub/dpd/index.php?Article_ID=2319 The physical evidence of earth's unstoppable 1,500-year climate cycle]
*[http://www.independent.org/publications/article.asp?id=1714 "Is There a Basis for Global Warming Alarm?", by Richard Lindzen]
*[http://www.independent.org/publications/policy_reports/detail.asp?type=full&id=5 "New Perspectives in Climate Change: What the EPA Isn’t Telling Us"]
*[http://www.heartland.org/Article.cfm?artId=17181 Survey Shows Climatologists Are Split on Global Warming]
*[http://www.magma.ca/~hurleyp/FightingTheHoax.htm Fighting the Hoax]
*[http://www.globalwarminghoax.com/news.php Refuting the Myth of Man-made Global Warming]
*[http://www.climateaudit.org Climate Audit], Steve McIntyre's blog
*[http://www.realclimate.org Real Climate], blog by a group of climatologists including Michael Mann
*[http://www.americanthinker.com/2009/01/co2_fairytales_in_global_warmi.html "CO2 Fairytales in Global Warming"]
*[http://www.numberwatch.co.uk/warmlist.htm A complete list of things caused by global warming]
*[http://globaleconomicanalysis.blogspot.com/2009/11/hackers-prove-global-warming-is-scam.html Hackers Prove Global Warming Is A Scam]

[[Category:Earth Sciences]]
[[Category:Environmentalism]]
[[Category:Liberal Bias]]
[[Category:Liberal Falsehoods]]
[[Category:Featured articles]]

Global warming

2012-02-09T19:32:57Z

Bogart12:

Stolen concept

2012-02-09T05:48:56Z

Bogart12: A more accurate statement would be that socialists claim private property is theft from the community; there is no contradiction

The fallacy of the '''stolen concept''', also known as the fallacy of the '''self-negating statement''', is the [[logical fallacy]] of implicitly affirming what one wants to disprove or, alternatively, implicitly denying what one wants to prove. That is, the [[conclusion]] [[contradiction|contradicts]] one of the [[premise]]s. The term "stolen concept" referst to a concept that is "stolen" from the [[out of context|context]] that gives that concept meaning.
==Examples==
*[[postmodernism|Postmodernists]] claim to know objectively that objective knowledge is impossible.
*[[Liberal Christianity|Liberal Christians]] claim that the [[Bible]], when [[Cafeteria Christianity|"rightly" divided]] and [[allegorical interpretation|"correctly" interpreted]], is the ultimate authority on [[faith]]. However, for that to work, the truly ultimate authority on faith would be the standard used for choosing which Bible verses to follow and for interpreting them, not the Bible itself.
*[[Liberal]] [[collectivist]]s want greater [[government]] intrusion into our lives to protect [[freedom]].
*[[Pro-abortion]] activists argue that since there are no such things as [[unalienable rights]], there is no [[right to life]], so that there is an unalienable right to [[abortion]].
*Liberal [[nanny state|nanny statists]] argue that some acts are contrary to universally accepted standards and that if they are not prevented, everyone will want to do them.
*Liberals justify [[special rights]] as furthering [[equality]] and oppose genuine equality as a special right.
*Liberals argue that the [[Equal Protection Clause]] was meant only to protect certain politically favored groups. That interpretation defeats the whole point of that clause.
*Liberals argue that the debt ceiling should be raised whenever reached. This argument makes the entire ceiling worthless in preventing excessive spending.
*[[Evolutionists]] use the [[argument from poor design]] to attempt to disprove [[creationism]]; however, according to evolutionism, natural selection should have selected out all suboptimal designs.

==See also==
*[[Reductio Ad Absurdum]], a form of argument that can be used to expose a stolen concept

==References==
*[http://www.goodart.org/stolen.htm Stolen Concept]
[[Category:Logical Fallacies]]

Reductio Ad Absurdum

2012-02-09T05:46:00Z

Bogart12: There is no controversy over this

'''''Reducto ad absurdum''''' is [[Latin]] for "reduction to the absurd." It is a form of argument that seeks to disprove a proposition by showing that that proposition inevitably leads to an absurdity, or of proving a proposition by assuming its negation and then showing that that assumption inevitably leads to an absurdity.<ref>[http://www.thefreedictionary.com/reductio+ad+absurdum Reductio ad absurdum]</ref> One use is in [[mathematics]], as will be described in greater detail below. ''Reductio ad absurdum'' should not be confused with the [[straw man fallacy]] or the [[slippery slope]] fallacy.

==In Mathematics==
''Reductio ad absurdum,'' also called "proof by contradiction" or "proof by assuming the opposite," is a method of [[mathematical proof]]. It involves assuming the opposite of what one is trying to [[prove]], and showing that this would lead to a [[contradiction]]. It works by the [[law of the excluded middle]]. The proof typically follows this structure:

#Create an initial assumption
#Follow a series of axiomatically valid steps
#Reach a contradiction
#Therefore, the initial assumption is incorrect

===Proof of Proposition ''P'' by Contradiction===
#Suppose ~P.
#...
#Therefore, Q.
#...
#Therefore, ~Q
#Hence, Q and ~Q, a contradiction
#Thus, P

===Example===
An example of this is [[Euclid]]'s proof of the [[infinitude]] of the [[Prime number|primes]]:

#Assume there are finitely many primes
#Take the product of all primes and call it ''N''. Since ''N''+1 is not in our finite set of primes, it must be composite
#By the [[fundamental theorem of arithmetic]], ''N''+1 has a prime factorization. But ''N+1'' is not divisible by any of the previous primes
#Since ''N''+1 is composite, there must be a prime missing from our set of primes. But this set contains all primes
#Therefore, our initial assumption ("there are finitely many primes") is invalid

==See also==
*[[Stolen concept]], a fallacy that can be exposed using a ''reductio ad absurdum''

==References==
<references/>
[[Category:Mathematics]]
[[Category:Logic]]

Environmentalist

2012-02-09T05:42:26Z

Bogart12:

{| align=right border=3 cellspacing=0 style="border-width: 5px; border-color: #c0c0c0; background: #e0e0e0; margin: 2em;"
| style="text-align: center; padding: 10px 40px 10px 40px;" | [[Previous_Breaking_News/Environmentalist | Previous Breaking News: Environmentalist]]
|}

'''Environmentalists''' are concerned with protecting the environment instead of letting human beings take dominion over it. Going way beyond [[conservationism]], they seek legal limitations on human use of the Earth's natural environment and resources. Media reporting usually blurs the distinction between "no-use" environmentalism and "wise-use" conservation.

[[David Gelernter]] wrote:
*Passionate environmentalists reject the proposition that love of nature is ennobling because loving nature is good for human dignity and happiness. They flirt instead with a worldview in which human beings are a species on a par with every other, and nature is to be protected not because you damage other people’s happiness when you destroy it wantonly but because nature itself has rights to assert against man. The Smithsonian, for example, posted a label in its Museum of Natural History apologizing for a display in which “humans are treated as more important than other mammals.” [http://www.city-journal.org/html/6_4_the_immorality.html]

==Forest fires and "saving" trees==

In June 2007 residents of Lake Tahoe California were furious at environmentalists and the grip they hold on government regulators who refused to allow the clearing of dead trees. 1,300 homes sustained damage, and the newly homeless victims blamed the special interest environmentalists for their woes.

The amount of fuel in the Tahoe Basin reached critical levels after years of discord among environmentalists and government agencies over how to thin forests and reduce the fire threat. And it has led to predictions of a devastating wildfire because the basin is one of the areas with the most fire starts in the Sierra Nevada. <ref>[http://www.latimes.com/news/local/la-me-clearance26jun26,0,2914697.story?coll=la-home-center Crowd aims fury at regional panel], Land use agency is criticized for failing to allow adequate clearing of combustible materials. By Eric Bailey and J. Michael Kennedy, ''Los Angelas Times'', June 26, 2007.</ref>

==Animal rights and vegetarians==

Citing a heretofore unknown connection between the environment, [[animal rights]], and [[vegetarianism]] movements, [[People for the Ethical Treatment of Animals]] (PETA) requested of [[Democratic]] Speaker of the U.S. House of Representatives [[Nancy Pelosi]] and Senate Majority Leader [[Harry Reid]] special treatment in administration of tax laws used to support ecological sustainability. PETA President Ingrid Newkirk alleges, "[V]egetarians are responsible for far fewer [[greenhouse-gas]] emissions and other kinds of environmental degradation than meat-eaters," and that vegetarians should receive a tax break "just as people who purchase a hybrid vehicle enjoy a tax break."

Asked how would the government certify the special interest tax break would go to vegetarians only, PETA spokesman Matt Prescott said, "I imagine that a system could be adopted whereby taxpayers could show receipts for food purchases and/or sign an affidavit attesting … that they are vegetarian." <ref>[http://thehill.com/leading-the-news/peta-seeks-tax-breaks-for-vegetarians-2007-05-31.html PETA seeks tax breaks for vegetarians], By Ilan Wurman, ''The Hill'', May 31, 2007.</ref>

==Worship of Gaia==
The environmentalist movement has taken on a new age religious philosophy, and this belief system is considered to be the religion of choice for urban [[Atheism|atheists]] and is one of the most powerful religions in the Western World:
{{Cquote|The religion of environmentalism is a perfect 21st century remapping of traditional [[Judeo-Christian]] beliefs and myths. There's an initial Eden, a paradise, a state of grace and unity with nature, there's a fall from grace into a state of pollution as a result of eating from the tree of knowledge, and as a result of our actions there is a judgment day coming for us all. We are all energy sinners, doomed to die, unless we seek salvation, which is now called sustainability. Sustainability is salvation in the church of the environment. Just as organic food is its communion, that pesticide-free wafer that the right people with the right beliefs, imbibe.

Eden, the fall of man, the loss of grace, the coming doomsday---these are deeply held mythic structures. They are profoundly conservative religious beliefs. These are not facts that can be argued. These are issues of faith. Facts aren't necessary, because the tenets of environmentalism are all about belief. It's about whether you are going to be a sinner, or saved. Whether you are going to be one of the people on the side of salvation, or on the side of doom. Whether you are going to be one of us, or one of them. <ref>[[Michael Crichton]], [http://www.crichton-official.com/speeches/speeches_quote05.html Environmentalism as Religion]," Commonwealth Club, San Francisco, CA, September 15, 2003. </ref>}}

Former U.S. Vice President [[Al Gore]] sees a "spiritual crisis" in [[global warming]]. <ref>[http://www.mysanantonio.com/news/metro/stories/MYSA050607.01B.gore.35aecd4.html Gore sees 'spiritual crisis' in warming], Anton Caputo, ''San Antonio Express News'', 05/05/2007. </ref> He also believes that [[goddess]] worship is a better and more legitimate spiritual belief than [[Christianity]] and that the life of human beings is comparable to that of trees.<ref>http://worldnetdaily.com/news/article.asp?ARTICLE_ID=45581</ref> British biologist James Lovelock <ref>*James Lovelock, [http://books.guardian.co.uk/extracts/story/0,,1738945,00.html ''Revenge of Gaia''], Publisher: Allen Lane, 02/02/2006. ISBN13: 9780713999143 </ref> first publicly explained the Gaia theory - that the earth as a whole is a living, conscious organism. <ref>[http://www.tcrnews2.com/gennewage.html Eco-spirituality, eco-feminism, global spirituality, ecological theology, creation spirituality, the new cosmology] </ref> Rep. Helen Chenoweth (R-Idaho) has described this phenomenon as "environmental religion" and says that it has "profound constitutional implications" because of the First Amendment prohibition on government establishment of religion. <ref>Cliff Kincaid, [http://www.usasurvival.org/cultofgaia.html ''Al Gore, the United Nations, and the Cult of Gaia''], (1999). </ref>

[[Reid Bryson|Dr. Reid Bryson]], founding chairman of the department of meteorology at the [[University of Wisconsin-Madison]] and of the Institute for Environmental Studies, now known as the [[Gaylord Nelson]] Institute for Environmental Studies and is known as the father of scientific climatology says of global warming:
{{Cquote|It's almost a religion. Where you have to believe in anthropogenic (or man-made) global warming or else you are nuts. <ref>[http://www.madison.com/tct/mad/topstories/197613 Local scientist calls global warming theory hooey], Samara Kalk Derby, ''The Capital Times'', 6/18/2007. </ref>}}

Environmentalism has been called "school prayer for liberals", in the sense that it functions as a substitute spiritual experience for them, since they lack a true spiritual connection to God. This allows them to feel good about themselves, if only temporarily. <ref>http://pajamasmedia.com/eddriscoll/2009/07/01/environmentalism-is-school-prayer-for-liberals/?email=1</ref>

==The Bible and Environmentalism==
{{Cquote|And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth. Genesis 1:28}}

Many Christians have looked to this passage to justify their use of the gifts God has left us in and on the Earth. [[Farming]], [[fishing]], [[mining]], [[oil drilling]], [[hunting]], [[industry]], and the like are all examples of human beings making the most of our dominion, converting it into glorious products that help our fellow man. Products like [[medicine]], [[shelter]], and [[food]] satisfy the basic needs of mankind, while other products make a life serving God easier and more effective.

However, other Christians interpret this as [[stewardship]], the belief that human beings are "caretakers" of the Earth.

== Deep Ecology ==
Deep ecology is an environmental movement that rejects [[modern]] culture and seeks to include non-human life in the moral circle. They find the cause of the current ecological crisis in the modern attitude towards the environment. The theory can be defined as the following principles;
1. The well-being and flourishing of human and non-human life on Earth have value in themselves. These values are independent of the usefulness of the non-human world for human purposes.
2. Richness and diversity of life forms contribute to the realization of these values and are also values in themselves.
3. Humans have no right to reduce this richness and diversity except to satisfy vital needs.
4. The flourishing of human life and cultures is compatible with a substantial decrease of the human population. The flourishing of non-human life requires such a decrease.
5. Present human interference with the non-human world is excessive, and the situation is rapidly worsening.
6. Policies must therefore be changed. The changes in policies affect basic economic, technological, and ideological structures. The resulting state of affairs will be deeply different from the present.
7. The ideological change is mainly that of appreciating quality (dwelling in situations of inherent worth) rather than adhering to an increasingly higher standard of living. There will be a profound awareness of the difference between big and great.
8. Those who subscribe to the foregoing points have an obligation directly or indirectly to participate in the attempt to implement the necessary changes.

Issues that arise from the practise of this theory is where one life form needs another life form as food. Such an example may include humans needing to eat a cow, how would a deep ecologist jusitify this?

== The Concept of Sustainability ==
According to the U.S. [[EPA]], "sustainability creates and maintains the conditions under which humans and nature can exist in productive harmony, that permit fulfilling the social, economic and other requirements of present and future generations."<ref>United States Environmental Protection Agency http://www.epa.gov/sustainability/basicinfo.htm</ref> There are two things wrong with this liberal concept of sustainability. The first is that it directly contradicts the word of God (as described above), since living in productive harmony is not the same as humans having domion over nature. The other important point is that the EPA's definition does not take into account rapidly changing social and economic conditions. There are numerous examples of economically<ref>Wellington, Beth. "The Myth of Mountaintop Removal Mining." August 19, 2011. http://www.guardian.co.uk/commentisfree/cifamerica/2011/aug/19/mountaintop-removal-mining</ref> or socially<ref>Stromberg, Per. "The Mexican Maquila Industry and the Environment; An Overview of the Issues." http://www.eclac.org/publicaciones/xml/2/11862/lcmexl548eDocumento%20Completo.pdf</ref> valuable activities that are not regarded as "sustainable."

== Wilderness ==
See [[wilderness]]

==See Also==
*[[Conservation and environmentalism]]
*[[Essay: Real Environmentalism]]
*[[Socialist Environmental Disasters]]
*[[Van Jones]]
*[[Gulf of Mexico oil spill disaster]]
*[[Previous Breaking News/Environmentalist|Examples of Environmentalism from previous "Breaking News" articles]]

==References==

<references/>
For deep ecology see Environmental Ethics; A Guide. Hammerman and Gass 1993
[[Category:Political Terms]]
[[Category:Environmentalism]]

Talk:Majoring in Mathematics

2012-02-09T05:23:48Z

Bogart12:

Majoring in Mathematics

2012-02-09T05:22:12Z

Bogart12: /* Bezout's theorem */

This article is intended to provide a brief introduction to what college mathematics is all about. It is aimed at high school students who have enjoyed mathematics in high school, and are starting to think about what to study in college. This article is a work in progress -- please expand and leave suggestions at the talk page. The theorems and ideas mentioned here aren't all things that you'll necessarily encounter in classes; indeed, most of them you probably won't. Instead, they are presented to indicate the sorts of thinking and methods that go into mathematics, and the sorts of problems that mathematicians work on today.

Here is an outline of what I hope to write.

== What College Mathematics is Not ==
Before we look at the sorts of problems that actually ''are'' dealt with by mathematics in college, let's look at some that are not. Rest assured, many of the most painful aspects of math classes you've taken before aren't so bad in college!
# Simply learning more advanced versions of mathematical ideas from high school. Tired of learning tricks for integration? Majoring in math won't just teach you new methods to integrate functions -- if you've taken an introductory calculus class, chances are you already know the important ones! What it will do is force you to think carefully about basic questions about what an integral is. Given some subset of space, what does it really mean to find its volume?
# Doing lots of computations. Chances are you'll have to do a few, but most mathematics in college is based around "proofs" -- very careful and rigorous arguments which show that mathematical statements are true. Many proofs won't involve any computations at all!
# Learning a bag of tricks to do Olympiad-type problems. If you've ever taken the AMC, Math League, or other similar competition tests, and not done well, don't worry! Much of these tests check nothing more than whether you're familiar with some collection of techniques for solving special problems. One math professor at Harvard keeps in his desk a copy of a math competition on which he scored a perfect 0/120. Mathematical theory goes far beyond these problems.

Instead, college mathematics is about developing new ways to rigorously approach a wide array of problems. More than aiming to find tricky techniques to solve certain problems, it is about building powerful approaches that solve many problems, and learning to think rigorously about them.

== Major Topics of Study ==
Given that a math major won't just be getting more practice at the sorts of math encountered in high school, what is it about? Here's a list of some of the major fields that are the foundation of a mathematics education.

For each field, I plan to give a very general description and to describe a few problems/theorems that are nice results and capture some of the essence of a subject. I'll aim for a few paragraphs about each one. Then I will give a problem or two that is a much more open-ended question that has motivated the development of large amounts of theory. For now I have no written about any of these -- please leave feedback and suggestions on the talk page and I will try to arrive at the best set of motivating problems!

=== Algebra ===
# How many positions are there for a Rubik's cube. Brief discussion of group theory, and how a group acts on the Rubik's cube.

==== Bezout's theorem ====
It's a very basic fact that two lines intersect at exactly one point. But we can ask a similar question about other shapes. At how many points do two parabolas intersect? A circle and a line? The graphs of two cubics? A circle and a line may intersect at either 0 points (for example, the unit circle <math>x^2+y^2=0</math> and the line <math>y=2</math>), 1 point (if the line is tangent to the circle), or 2 points. It's easy to see that we can arrange for two parabolas to intersect at four points: just consider the examples <math>y=x^2-10</math> and <math>x=y^2-10</math>. Similarly, we can up with two cubics that intersect at nine points. You might be noticing a pattern here: a parabola is defined as the set of solutions to a polynomial equation in two variables, whose biggest exponent is 2: we say that a parabola has degree 2. For the same reasons, we say that a line has degree 1, and a cubic as degree 3. Bezout's theorem then gives a very rough answer to our question: a curve of degree m and a curve of degree n intersect in at most mn points.

We have seen that sometimes the number of intersections is less than this, but Bezout's theorem, properly generalized, says that the number of intersections is in fact ''equal'' to mn: in the case of the circle and the line given earlier, there are exactly two solutions as predicted, if we allow <math>x</math> and <math>y</math> to be complex numbers. Similarly, a point of tangency is in some sense a "double intersection", and should count twice: if we nudged the line just a little bit, the point of intersection would turn into two distinct points. After we make these adjustments (counting complex solutions, changing the setting to projective space, and counting points of tangency multiple times), Bezout's theorem provides a simple and elegant answer to our original motivating question: curves of degree m and degree n intersect at exactly mn points!

# Is the quintic solvable in radicals? And what in the world does this problem have to do with group theory?
# The ancient Greeks were fascinated by geometric constructions with straightedge and compass. They could bisect angles and take square roots, but they couldn't trisect angles or take cube roots. Why not?

==== Algebra and Number Theory ====
The development of the modern field of algebra has been deeply influenced by research in number theory. An example of a problem from number theory that has provided far-reaching motivation for work in pure algebra has been the question of unique factorization.

It's a well-known fact, the [[fundamental theorem of arithmetic]], that every integer can be factored in a unique way as the product of prime numbers. It's natural to wonder whether this unique factorization holds in other simple rings, for example, the set of complex numbers whose real and complex parts are both integers (for example, <math>3+7i</math>). These are the so-called Gaussian integers, and there is a good notion of "prime", and that every Gaussian integer can be uniquely factored into primes! For example, 7+0i is a Gaussian prime, while 5+0i is not: <math>5+0i</math> factors as <math>(2+i)(2-i)<math>, and both <math>2-i</math> and <math>2+i</math> are prime. In general, it turns out that
a Gaussian integer <math>a+bi</math> is prime if either one of <math>a</math> or <math>b</math> is zero, and the other is a prime congruent to three mod 4, or if <math>a</math> and <math>b</math> are nonzero, and <math>a^2+b^2</math> is a prime (in the usual sense).

So unique factorization works well for the Gaussian integers, but what about other settings? An example similar to the Gaussian integers is the set of real numbers of the form <math>a+b\sqrt{7}</math>: note that <math>(a+b\sqrt{7})(c+d\sqrt{7}) = (ac+7bd)+(ad+bc)\sqrt{7}</math>, so the numbers of this form are closed under multiplication. Here too, and in many other cases, there is a good notion of unique factorization. It was formerly assumed that <math>\mathbb Z[\sqrt{d}]</math> would have unique factorization, but this turns out not to be the case. Consider the ring of complex numbers of the form <math>a+b\sqrt{-5}</math>. We can write <math>6 = 2 \cdot 3 = (1-\sqrt{-5})(1+\sqrt{5})</math>. A bit more work shows that both of these are prime factorizations, and they're not equivalent! This discovery necessitated the careful investigation of unique factorization, a purely algebraic notion that had not been seriously considered. Ernst Kummer proposed a proof of [[Fermat's Last Theorem]] which failed only because it assumed some properties of unique factorization, but further consideration of this problem led to a revolution in algebra.

=== Linear Algebra ===
If you throw a beach ball into the air, letting it spin in any way whatsoever, and then catch it, all of its rotations will comprise one rotation about some axis. That is, there will be two "poles" that will end exactly where they started, and all other points will just have rotated around them. What does this have to do with orthogonal operators? What does it have to do with the fact that every cubic equation has at least one real root?

If you do the same with a ring (e.g. a Hula Hoop), spinning it and letting it fall on its original "footprint", there will be no points that land exactly on their original position (except in the case in which it didn't move at all.) What does this have to do with the fact that quadratic equations are ''not'' guaranteed to have any real roots?

(Something about eigenvectors of distinct eigenvalues of an orthogonal/Hermitian matrix being orthogonal, can't think of a cute example just now.)

=== Geometry ===

In college math, "geometry" does not refer to more work on Euclidean high school geometry. Instead, college geometry includes a challenging field known as "differential geometry." This includes Tensor Calculus, Riemannian Geometry,
Covariant Vector Fields, Minkowskian Manifolds, and General Relativity.

Some problems include:

# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?

==== The Double Bubble Conjecture ====
You've probably noticed that when you blow a soap bubble, it quickly stretches into a nearly spherical shape. But why should a bubble tend towards a spherical conformation, instead of a cube or an icosahedron? According to physics, the bubble will tend toward a shape with the lowest energy, and the physical effect of surface tension is that this lowest energy is achieved when the bubble is in the shape with the least possible surface area enclosing a given volume. For example, if we want to enclose one cubic inch of air, the smallest surface that could contain it is a perfect sphere. The proof of this case, for a simple bubble, involves techniques from the mathematical study of [[differential geometry]], but turns out not to be too difficult. Related problems in finding minimal surfaces, however, turn out to be quite fiendish, and involve computations of "mean curvature" related to the notions of curvature defined above. The double bubble conjecture is one such.

*insert a picture here!

What is the smallest possible surface area for two bubbles joined stuck together, each enclosing some fixed volume? Thinking back to childhood experience, we know such bubbles end up as two partial spheres, connected together at a perfectly flat surface. But there are many other possibilities: why couldn't it be two tetrahedra, connected along some wavy surface? Quite sophisticated mathematical techniques are needed to prove this seemingly obvious result. The proof was not completed until 2000, by a team of mathematicians including [[User:RSchlafly|Roger Schlafly]].

=== Topology ===
==== The Bridges of Konigsberg ====
The earliest roots of the modern study of topology (and [[graph theory]]) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.

[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]

Euler proved that no such path existed, with the following simple and elegant argument: observe that the path one takes while on the islands is irrelevant to the problem at hand, and that all that matters is the order in which the bridges are traversed. Every time one enters one landmass by means of a bridge, he leaves it by means of another. This means that the number of bridges entering and exiting each landmass must be even, except possibly the landmass in which he starts and the one in which he ends (since he does not both enter and exit these). However, in Konigsberg, each of the four landmasses is served by an odd number of bridges! This means that no tour of the sort desired is possible.

This argument is fundamentally a "topological" one because of the recognition that the rigid shapes and geometry of the problem make no difference. If the shape of the islands were changed, or a bridge were moved but stayed between the same two islands, the solution of the problem would not be affected. The only thing that matters is the number of islands and which islands are connected by bridges. The modern field of topology is at its heart the study of geometric objects whose rigid shape is not important.

# Connection between topological spaces and algebraic groups
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.

==== How can we tell the difference between a sphere and a torus? ====
This is the sort of question that motivated the development of the field of topology for many years. Recall that a [[torus]] is the shape of an inner tube, or the surface of a donut: it is a two-dimensional surface with one whole. If a torus were made out of clay, one could stretch and squish it, but it is intuitively clear that no amount of stretching could possibly deform in into a sphere: it's simply impossible to get rid of the hole! Similarly, a sphere made out of clay can't be deformed into a torus without ripping it. The question of why the two shapes are not the same is fundamentally a topological one: we are interested in some intrinsic geometric properties of these objects, but not their specific rigid shapes.

It turns out that methods from [[algebra]] provide the easiest way to prove that it is impossible to deform a sphere into a donut. Observe that a sphere has the following property: given any loop drawn on the sphere (say, a rubber band stretched around it somehow), it is possible to "contract" that loop to a point (i.e., to scrunch up the whole rubber band at one place). On the other hand, if a rubber band is placed on a donut in such a way that it loops around the central whole, there is no way to contract it to a single point. A crucial observation in the field of algebraic topology is that if a space can be obtained by squeezing and stretching a sphere, then it will still have the property that every loop is contractible. Since a torus doesn't, we conclude that it must be fundamentally different from a sphere. Arguments like this are the basis for the field of [[algebraic topology]], and this problem of contracting loops in a space is studied using the [[fundamental group]].

=== Analysis ===
# Riemann mapping theorem. State this in terms of conformal mappings of the unit disk and draw lots of pictures!

==== Fixed points ====
Often in mathematics or physics, it is interesting to think about what happens when we apply the same function repeatedly. For example, one might take a calculator, punch in a random number, and then hit the button "[[cosine|cos]]" repeatedly. What happens when we do this? If you try it, you might see something that looks like this:1.3, 0.267499, 0.964435, 0.569881, 0.841965, 0.665998, 0.7863, 0.706469, 0.760659, 0.724382, 0.748909, ...

It looks like these are getting closer and closer to some fixed number, and if you hit the button a few more times, you'd discover that indeed these terms approach some constant around C=0.739085. This is the value of C for which cos(C) = C. There's no way to solve for this C algebraically, but we can see from the [[intermediate value theorem]] that there must be some value of C for which this is the case, since cos(0) > 0 but cos(1) < 1.
Generally, a value x is called a '''fixed point''' of a function f if f(x)=x, and it is interesting to study when a function must have a fixed point. Although many functions have no fixed points, there are theorems that give certain conditions under which any function must have a fixed point.

One of the most famous such theorems is the Brouwer fixed-point theorem, which says in its simplest form that any continuous function <math>f: D^2 \to D^2</math> has a fixed point. This fact has a very intuitive description: if we take a sheet of graph paper (so we can label each point with coordinates), crumple it up, and set it on top of another sheet of graph paper, then there is some point on the crumpled up sheet which is directly above the corresponding point on the second sheet! While this sounds like a simple fact, proving it rigorously relies on the techniques of [[algebraic topology]].

Another celebrated example of a fixed point theorem is known as Sharkovsky's theorem. In addition to fixed points, some functions have points for which repeating the function several times yields the same result: for example, a value of x for which cos(cos(cos(x))) = x is called a 3-periodic point of the function cosine. Sharkovsky's theorem is the surprising result that if a continuous function f has points of period 3, then it has points of all other periods! For example, consider the quadratic <math>f(x) = -\frac{5}{2} x^2 + \frac{7}{2} +1</math> has f(0) = 1, f(f(0)) = f(1) = 2, f(f(f(0))) = f(f(1))=f(2) = 0. So 0 is a point of period 3 of f(x). Sharkovsky's theorem implies that there are points of every other period. For example, there is some x such that f(f(f(f(f(f(f(f(x)))))))=x! Solving this explicitly would involve solving a polynomial of degree 14, an impossible task. But Sharkovsky's theorem guarantees that there is '''some''' value of x satisfying this.

==== Mathematical Billiards ====
Imagine that you're playing a game of pool on a standard rectangular table, but with a twist: there's no friction, so after you hit the ball, it continues along its trajectory forever. Obviously if you hit the ball so that its path is perpendicular to one of the walls of the table, it will bounce straight back, then off the opposite wall, straight back again, etc.: the ball will follow a repeating pattern of bouncing between the two walls forever. Similarly, if you aim just right, you can hit the ball so that it moves in a diamond-shaped path forever, bouncing off the middle of the sides of the walls repeatedly. A trajectory of the cue ball is called "periodic" if it's like one of these, in that the ball eventually ends up back where it started, and moving in the same direction. A trajectory is said to have "period p" if it hits the wall exactly <math>p</math> times in the course of this repeating cycle. The two examples given above have periods of two and four, respectively. One question we might ask is whether there is an orbit of period <math>p</math> for every possible choice of p. Can you come up with a path on the standard billiards table that has period 3? If not, can you prove that one doesn't exist?

As is often the case is mathematics, we attempt to generalize these results on periodic orbits to other situations. What if the billiards table is not rectangular, but triangular? It's true, but extremely difficult to prove, that given any triangular billiards table, there exists a periodic orbit of '''some''' period. The existence of periodic orbits is an extremely subtle question. This can be generalized even further, to ask whether all polygons admit periodic orbits. What about polyhedra? Can you imagine some periodic billiards orbits on a cube-shaped "table" (no gravity! think billiards in space).

The orbits that aren't periodic turn out to be just as interesting as those that are. Imagine that you place the cue ball at random on your billiards table, and smack it in some random direction. Chances are it won't end up in a periodic orbit -- putting the ball in a periodic orbit requires a very careful shot. So the ball will bounce around forever without retracing its path. But will it ever come back to the point where it started, perhaps moving in a different direction? The answer to this question is "no", but the Poincare Recurrence Theorem gives a somewhat satisfactory replacement: given any distance (e.g., an eighth of an inch), and any angle (e.g. two degrees), after some amount of time, the ball will be within that distance of its starting point, and directed within that angle of its initial path! This is a very suprising fact.

While this problem seems extremely elementary, sophisticated mathematical techiques from a range of fields of geometry and analysis have been brought to bear on it. Even so, many easily-stated questions remain open.

# Periodic orbits in billiards in polyhedra. I think it should be possible to say some interesting things about this but with some real content. Possibly there's a better idea.

Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.

=== Probability and Statistics ===
# Discussion of Benford's law, application to recognizing fraud.
# Understanding the concept of the "random variable"
# Proving the Central Limit Theorem

Motivating problem: Deriving conclusions from rarely occurring events, such as multiple no-hitters by the same pitcher. Specifically, how many no-hitters must a pitcher toss before one can conclude from that evidence alone that he is a great pitcher?

===Partial Differential Equations===
If you take a uniform circular metal disk and hold the temperatures at the periphery to some fixed pattern (say, lighting fires at some places and applying ice at others), and give it plenty of time to reach equilibrium, can you calculate the final temperature at every point inside? What does this have to do with Fourier series? (Hint: It has '''everything''' to do with Fourier series. This is the problem that Joseph Fourier was studying when he invented the series.)

=== Other fields ===
# Logic: still need a good problem
# Number theory: connected to the other fields above in many ways. Prime number theorem?
# Set theory: some discussion of axioms, maybe talk about AoC.
# applied mathematics, emphasizing the solution of partial differential equations which are essential to mechanical engineering

=== Related fields ===
Many other subjects are often considered parts of mathematics as well. Depending on specific undergraduate programs, a math major may or may not be required to take courses in these areas, but many of the same ideas are used in these subjects as in the others.
# Computer science: something about algorithmic complexity: maybe the fact that primality testing may be done in polynomial time?
# Computer science: How can Fourier transforms be used to multiply enormous integers much faster than normal methods?
...

=== Interplay ===
None of these fields exists in a vacuum, and there is rich interplay between them. If you insert "algebraic" or "differential" before the name of just about any branch of math, you get a more specialized, but important field. Motivate some of these connections:
# Algebra+topology: discussion of fundamental group.
# Analysis+topology: discuss conservative fields, and hint at de Rham cohomology without actually saying those words.
# Algebra+analysis: find a good simple example of a Lie group showing up in the study of some differential equations.

== So What? ==
After finishing a major in mathematics, most people don't keep working in pure math. But the ways of thinking and skills that the study of mathematics provide make available a wide range of career opportunities.

Specifically, mathematicians seeking to remain connected to their field pursue career opportunities in:
*actuary or insurance work
*defense-related work
*market trading analysis for investment banks
*mathematical modeling

Less-related fields that are also of some interest to mathematicians are:
*computer programming
*accounting
*K-12 teaching

Some mathematicians enter entirely unrelated fields. Math majors have the highest average scores of students in any field on the LSAT and GMAT, the tests required for entrance into law school and business school <ref>http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1430654</ref>: the skills acquired in studying mathematics in invaluable in the logic section of the LSAT and for subsequent careers in law.

== Further Reading ==
Numerous expository books cover the topics mentioned on this page, along with many others, in a very accessible way. Below are a few recommended books whose content is comparable to that of this article.
# ''Mathematics: The New Golden Age'', by Keith Devlin. Accessible discussions of many important ideas.
# ''Professor Stewart's Cabinet of Mathematical Curiosities'', by Ian Stewart. A similar book covering the exciting side of mathematics and requiring little background.
# ''Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics'', by John Derbyshire. Focuses on the famous [[Riemann hypothesis]] and related material.
# ''Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games''. A collection of articles by one of mathematics' foremost expositors.
[[Category:Mathematics]]
[[Category:Higher Education]]

Majoring in Mathematics

2012-02-09T05:20:42Z

Bogart12: /* The Bridges of Konigsberg */ graph theory isn't a subset of topology

This article is intended to provide a brief introduction to what college mathematics is all about. It is aimed at high school students who have enjoyed mathematics in high school, and are starting to think about what to study in college. This article is a work in progress -- please expand and leave suggestions at the talk page. The theorems and ideas mentioned here aren't all things that you'll necessarily encounter in classes; indeed, most of them you probably won't. Instead, they are presented to indicate the sorts of thinking and methods that go into mathematics, and the sorts of problems that mathematicians work on today.

Here is an outline of what I hope to write.

== What College Mathematics is Not ==
Before we look at the sorts of problems that actually ''are'' dealt with by mathematics in college, let's look at some that are not. Rest assured, many of the most painful aspects of math classes you've taken before aren't so bad in college!
# Simply learning more advanced versions of mathematical ideas from high school. Tired of learning tricks for integration? Majoring in math won't just teach you new methods to integrate functions -- if you've taken an introductory calculus class, chances are you already know the important ones! What it will do is force you to think carefully about basic questions about what an integral is. Given some subset of space, what does it really mean to find its volume?
# Doing lots of computations. Chances are you'll have to do a few, but most mathematics in college is based around "proofs" -- very careful and rigorous arguments which show that mathematical statements are true. Many proofs won't involve any computations at all!
# Learning a bag of tricks to do Olympiad-type problems. If you've ever taken the AMC, Math League, or other similar competition tests, and not done well, don't worry! Much of these tests check nothing more than whether you're familiar with some collection of techniques for solving special problems. One math professor at Harvard keeps in his desk a copy of a math competition on which he scored a perfect 0/120. Mathematical theory goes far beyond these problems.

Instead, college mathematics is about developing new ways to rigorously approach a wide array of problems. More than aiming to find tricky techniques to solve certain problems, it is about building powerful approaches that solve many problems, and learning to think rigorously about them.

== Major Topics of Study ==
Given that a math major won't just be getting more practice at the sorts of math encountered in high school, what is it about? Here's a list of some of the major fields that are the foundation of a mathematics education.

For each field, I plan to give a very general description and to describe a few problems/theorems that are nice results and capture some of the essence of a subject. I'll aim for a few paragraphs about each one. Then I will give a problem or two that is a much more open-ended question that has motivated the development of large amounts of theory. For now I have no written about any of these -- please leave feedback and suggestions on the talk page and I will try to arrive at the best set of motivating problems!

=== Algebra ===
# How many positions are there for a Rubik's cube. Brief discussion of group theory, and how a group acts on the Rubik's cube.

==== Bezout's theorem ====
It's a very basic fact that two lines intersect at exactly one point. But we can ask a similar question about other shapes. At how many points do two parabolas intersect? A circle and a line? The graphs of two cubics? A circle and a line may intersect at either 0 points (for example, the unit circle <math>x^2+y^2=0</math> and the line <math>y=2</math>), 1 point (if the line is tangent to the circle), or 2 points. It's easy to see that we can arrange for two parabolas to intersect at four points: just consider the examples <math>y=x^2-10</math> and <math>x=y^2-10</math>. Similarly, we can up with two cubics that intersect at nine points. You might be noticing a pattern here: a parabola is defined as the set of solutions to a polynomial equation in two variables, whose biggest exponent is 2: we say that a parabola has degree 2. For the same reasons, we say that a line has degree 1, and a cubic as degree 3. Bezout's theorem then gives a very rough answer to our question: a curve of degree m and a curve of degree n intersect in at most mn points.

We have seen that sometimes the number of intersections is less than this, but Bezout's theorem, properly generalized, says that the number of intersections is in fact ''equal'' to mn: in the case of the circle and the line given earlier, there are exactly two solutions as predicted, if we allow <math>x</math> and <math>y</math> to be complex numbers. Similarly, a point of tangency is in some sense a "double intersection", and should count twice: if we nudged the line just a little bit, the point of intersection would turn into two distinct points. After we make these adjustments (counting complex solutions, and counting points of tangency multiple times), Bezout's theorem provides a simple and elegant answer to our original motivating question: curves of degree m and degree n intersect at exactly mn points!

# Is the quintic solvable in radicals? And what in the world does this problem have to do with group theory?
# The ancient Greeks were fascinated by geometric constructions with straightedge and compass. They could bisect angles and take square roots, but they couldn't trisect angles or take cube roots. Why not?

==== Algebra and Number Theory ====
The development of the modern field of algebra has been deeply influenced by research in number theory. An example of a problem from number theory that has provided far-reaching motivation for work in pure algebra has been the question of unique factorization.

It's a well-known fact, the [[fundamental theorem of arithmetic]], that every integer can be factored in a unique way as the product of prime numbers. It's natural to wonder whether this unique factorization holds in other simple rings, for example, the set of complex numbers whose real and complex parts are both integers (for example, <math>3+7i</math>). These are the so-called Gaussian integers, and there is a good notion of "prime", and that every Gaussian integer can be uniquely factored into primes! For example, 7+0i is a Gaussian prime, while 5+0i is not: <math>5+0i</math> factors as <math>(2+i)(2-i)<math>, and both <math>2-i</math> and <math>2+i</math> are prime. In general, it turns out that
a Gaussian integer <math>a+bi</math> is prime if either one of <math>a</math> or <math>b</math> is zero, and the other is a prime congruent to three mod 4, or if <math>a</math> and <math>b</math> are nonzero, and <math>a^2+b^2</math> is a prime (in the usual sense).

So unique factorization works well for the Gaussian integers, but what about other settings? An example similar to the Gaussian integers is the set of real numbers of the form <math>a+b\sqrt{7}</math>: note that <math>(a+b\sqrt{7})(c+d\sqrt{7}) = (ac+7bd)+(ad+bc)\sqrt{7}</math>, so the numbers of this form are closed under multiplication. Here too, and in many other cases, there is a good notion of unique factorization. It was formerly assumed that <math>\mathbb Z[\sqrt{d}]</math> would have unique factorization, but this turns out not to be the case. Consider the ring of complex numbers of the form <math>a+b\sqrt{-5}</math>. We can write <math>6 = 2 \cdot 3 = (1-\sqrt{-5})(1+\sqrt{5})</math>. A bit more work shows that both of these are prime factorizations, and they're not equivalent! This discovery necessitated the careful investigation of unique factorization, a purely algebraic notion that had not been seriously considered. Ernst Kummer proposed a proof of [[Fermat's Last Theorem]] which failed only because it assumed some properties of unique factorization, but further consideration of this problem led to a revolution in algebra.

=== Linear Algebra ===
If you throw a beach ball into the air, letting it spin in any way whatsoever, and then catch it, all of its rotations will comprise one rotation about some axis. That is, there will be two "poles" that will end exactly where they started, and all other points will just have rotated around them. What does this have to do with orthogonal operators? What does it have to do with the fact that every cubic equation has at least one real root?

If you do the same with a ring (e.g. a Hula Hoop), spinning it and letting it fall on its original "footprint", there will be no points that land exactly on their original position (except in the case in which it didn't move at all.) What does this have to do with the fact that quadratic equations are ''not'' guaranteed to have any real roots?

(Something about eigenvectors of distinct eigenvalues of an orthogonal/Hermitian matrix being orthogonal, can't think of a cute example just now.)

=== Geometry ===

In college math, "geometry" does not refer to more work on Euclidean high school geometry. Instead, college geometry includes a challenging field known as "differential geometry." This includes Tensor Calculus, Riemannian Geometry,
Covariant Vector Fields, Minkowskian Manifolds, and General Relativity.

Some problems include:

# The Theorema Egregium - that there exists a quality inherent to a surface no matter how it is "bent."
# What happens if we remove some the Euclidean postulates taught in high school? Specifically, the parallel postulate?

==== The Double Bubble Conjecture ====
You've probably noticed that when you blow a soap bubble, it quickly stretches into a nearly spherical shape. But why should a bubble tend towards a spherical conformation, instead of a cube or an icosahedron? According to physics, the bubble will tend toward a shape with the lowest energy, and the physical effect of surface tension is that this lowest energy is achieved when the bubble is in the shape with the least possible surface area enclosing a given volume. For example, if we want to enclose one cubic inch of air, the smallest surface that could contain it is a perfect sphere. The proof of this case, for a simple bubble, involves techniques from the mathematical study of [[differential geometry]], but turns out not to be too difficult. Related problems in finding minimal surfaces, however, turn out to be quite fiendish, and involve computations of "mean curvature" related to the notions of curvature defined above. The double bubble conjecture is one such.

*insert a picture here!

What is the smallest possible surface area for two bubbles joined stuck together, each enclosing some fixed volume? Thinking back to childhood experience, we know such bubbles end up as two partial spheres, connected together at a perfectly flat surface. But there are many other possibilities: why couldn't it be two tetrahedra, connected along some wavy surface? Quite sophisticated mathematical techniques are needed to prove this seemingly obvious result. The proof was not completed until 2000, by a team of mathematicians including [[User:RSchlafly|Roger Schlafly]].

=== Topology ===
==== The Bridges of Konigsberg ====
The earliest roots of the modern study of topology (and [[graph theory]]) lie in [[Leonhard Euler]]'s investigations of a famous puzzle from the 1730s. The town of Konigsberg (now [[Kaliningrad]]) was bisected by a river, which contained two large islands. There were seven bridges connecting the islands, as indicated in the accompanying image. The problem asked for a walk through the town which would cross each bridge exactly once: every bridge must be crossed once, and none more than once.

[[Image:Konigsberg.jpg|center|alt=Layout of Konigsberg|Layout of Euler's Konigsberg]]

Euler proved that no such path existed, with the following simple and elegant argument: observe that the path one takes while on the islands is irrelevant to the problem at hand, and that all that matters is the order in which the bridges are traversed. Every time one enters one landmass by means of a bridge, he leaves it by means of another. This means that the number of bridges entering and exiting each landmass must be even, except possibly the landmass in which he starts and the one in which he ends (since he does not both enter and exit these). However, in Konigsberg, each of the four landmasses is served by an odd number of bridges! This means that no tour of the sort desired is possible.

This argument is fundamentally a "topological" one because of the recognition that the rigid shapes and geometry of the problem make no difference. If the shape of the islands were changed, or a bridge were moved but stayed between the same two islands, the solution of the problem would not be affected. The only thing that matters is the number of islands and which islands are connected by bridges. The modern field of topology is at its heart the study of geometric objects whose rigid shape is not important.

# Connection between topological spaces and algebraic groups
# Ham sandwich theorem (easy to state, harder to motivate solution. Possibly there's something better.

==== How can we tell the difference between a sphere and a torus? ====
This is the sort of question that motivated the development of the field of topology for many years. Recall that a [[torus]] is the shape of an inner tube, or the surface of a donut: it is a two-dimensional surface with one whole. If a torus were made out of clay, one could stretch and squish it, but it is intuitively clear that no amount of stretching could possibly deform in into a sphere: it's simply impossible to get rid of the hole! Similarly, a sphere made out of clay can't be deformed into a torus without ripping it. The question of why the two shapes are not the same is fundamentally a topological one: we are interested in some intrinsic geometric properties of these objects, but not their specific rigid shapes.

It turns out that methods from [[algebra]] provide the easiest way to prove that it is impossible to deform a sphere into a donut. Observe that a sphere has the following property: given any loop drawn on the sphere (say, a rubber band stretched around it somehow), it is possible to "contract" that loop to a point (i.e., to scrunch up the whole rubber band at one place). On the other hand, if a rubber band is placed on a donut in such a way that it loops around the central whole, there is no way to contract it to a single point. A crucial observation in the field of algebraic topology is that if a space can be obtained by squeezing and stretching a sphere, then it will still have the property that every loop is contractible. Since a torus doesn't, we conclude that it must be fundamentally different from a sphere. Arguments like this are the basis for the field of [[algebraic topology]], and this problem of contracting loops in a space is studied using the [[fundamental group]].

=== Analysis ===
# Riemann mapping theorem. State this in terms of conformal mappings of the unit disk and draw lots of pictures!

==== Fixed points ====
Often in mathematics or physics, it is interesting to think about what happens when we apply the same function repeatedly. For example, one might take a calculator, punch in a random number, and then hit the button "[[cosine|cos]]" repeatedly. What happens when we do this? If you try it, you might see something that looks like this:1.3, 0.267499, 0.964435, 0.569881, 0.841965, 0.665998, 0.7863, 0.706469, 0.760659, 0.724382, 0.748909, ...

It looks like these are getting closer and closer to some fixed number, and if you hit the button a few more times, you'd discover that indeed these terms approach some constant around C=0.739085. This is the value of C for which cos(C) = C. There's no way to solve for this C algebraically, but we can see from the [[intermediate value theorem]] that there must be some value of C for which this is the case, since cos(0) > 0 but cos(1) < 1.
Generally, a value x is called a '''fixed point''' of a function f if f(x)=x, and it is interesting to study when a function must have a fixed point. Although many functions have no fixed points, there are theorems that give certain conditions under which any function must have a fixed point.

One of the most famous such theorems is the Brouwer fixed-point theorem, which says in its simplest form that any continuous function <math>f: D^2 \to D^2</math> has a fixed point. This fact has a very intuitive description: if we take a sheet of graph paper (so we can label each point with coordinates), crumple it up, and set it on top of another sheet of graph paper, then there is some point on the crumpled up sheet which is directly above the corresponding point on the second sheet! While this sounds like a simple fact, proving it rigorously relies on the techniques of [[algebraic topology]].

Another celebrated example of a fixed point theorem is known as Sharkovsky's theorem. In addition to fixed points, some functions have points for which repeating the function several times yields the same result: for example, a value of x for which cos(cos(cos(x))) = x is called a 3-periodic point of the function cosine. Sharkovsky's theorem is the surprising result that if a continuous function f has points of period 3, then it has points of all other periods! For example, consider the quadratic <math>f(x) = -\frac{5}{2} x^2 + \frac{7}{2} +1</math> has f(0) = 1, f(f(0)) = f(1) = 2, f(f(f(0))) = f(f(1))=f(2) = 0. So 0 is a point of period 3 of f(x). Sharkovsky's theorem implies that there are points of every other period. For example, there is some x such that f(f(f(f(f(f(f(f(x)))))))=x! Solving this explicitly would involve solving a polynomial of degree 14, an impossible task. But Sharkovsky's theorem guarantees that there is '''some''' value of x satisfying this.

==== Mathematical Billiards ====
Imagine that you're playing a game of pool on a standard rectangular table, but with a twist: there's no friction, so after you hit the ball, it continues along its trajectory forever. Obviously if you hit the ball so that its path is perpendicular to one of the walls of the table, it will bounce straight back, then off the opposite wall, straight back again, etc.: the ball will follow a repeating pattern of bouncing between the two walls forever. Similarly, if you aim just right, you can hit the ball so that it moves in a diamond-shaped path forever, bouncing off the middle of the sides of the walls repeatedly. A trajectory of the cue ball is called "periodic" if it's like one of these, in that the ball eventually ends up back where it started, and moving in the same direction. A trajectory is said to have "period p" if it hits the wall exactly <math>p</math> times in the course of this repeating cycle. The two examples given above have periods of two and four, respectively. One question we might ask is whether there is an orbit of period <math>p</math> for every possible choice of p. Can you come up with a path on the standard billiards table that has period 3? If not, can you prove that one doesn't exist?

As is often the case is mathematics, we attempt to generalize these results on periodic orbits to other situations. What if the billiards table is not rectangular, but triangular? It's true, but extremely difficult to prove, that given any triangular billiards table, there exists a periodic orbit of '''some''' period. The existence of periodic orbits is an extremely subtle question. This can be generalized even further, to ask whether all polygons admit periodic orbits. What about polyhedra? Can you imagine some periodic billiards orbits on a cube-shaped "table" (no gravity! think billiards in space).

The orbits that aren't periodic turn out to be just as interesting as those that are. Imagine that you place the cue ball at random on your billiards table, and smack it in some random direction. Chances are it won't end up in a periodic orbit -- putting the ball in a periodic orbit requires a very careful shot. So the ball will bounce around forever without retracing its path. But will it ever come back to the point where it started, perhaps moving in a different direction? The answer to this question is "no", but the Poincare Recurrence Theorem gives a somewhat satisfactory replacement: given any distance (e.g., an eighth of an inch), and any angle (e.g. two degrees), after some amount of time, the ball will be within that distance of its starting point, and directed within that angle of its initial path! This is a very suprising fact.

While this problem seems extremely elementary, sophisticated mathematical techiques from a range of fields of geometry and analysis have been brought to bear on it. Even so, many easily-stated questions remain open.

# Periodic orbits in billiards in polyhedra. I think it should be possible to say some interesting things about this but with some real content. Possibly there's a better idea.

Hard problem: What does an integral really mean? Babble a bit about integrating the characteristic function of Q.

=== Probability and Statistics ===
# Discussion of Benford's law, application to recognizing fraud.
# Understanding the concept of the "random variable"
# Proving the Central Limit Theorem

Motivating problem: Deriving conclusions from rarely occurring events, such as multiple no-hitters by the same pitcher. Specifically, how many no-hitters must a pitcher toss before one can conclude from that evidence alone that he is a great pitcher?

===Partial Differential Equations===
If you take a uniform circular metal disk and hold the temperatures at the periphery to some fixed pattern (say, lighting fires at some places and applying ice at others), and give it plenty of time to reach equilibrium, can you calculate the final temperature at every point inside? What does this have to do with Fourier series? (Hint: It has '''everything''' to do with Fourier series. This is the problem that Joseph Fourier was studying when he invented the series.)

=== Other fields ===
# Logic: still need a good problem
# Number theory: connected to the other fields above in many ways. Prime number theorem?
# Set theory: some discussion of axioms, maybe talk about AoC.
# applied mathematics, emphasizing the solution of partial differential equations which are essential to mechanical engineering

=== Related fields ===
Many other subjects are often considered parts of mathematics as well. Depending on specific undergraduate programs, a math major may or may not be required to take courses in these areas, but many of the same ideas are used in these subjects as in the others.
# Computer science: something about algorithmic complexity: maybe the fact that primality testing may be done in polynomial time?
# Computer science: How can Fourier transforms be used to multiply enormous integers much faster than normal methods?
...

=== Interplay ===
None of these fields exists in a vacuum, and there is rich interplay between them. If you insert "algebraic" or "differential" before the name of just about any branch of math, you get a more specialized, but important field. Motivate some of these connections:
# Algebra+topology: discussion of fundamental group.
# Analysis+topology: discuss conservative fields, and hint at de Rham cohomology without actually saying those words.
# Algebra+analysis: find a good simple example of a Lie group showing up in the study of some differential equations.

== So What? ==
After finishing a major in mathematics, most people don't keep working in pure math. But the ways of thinking and skills that the study of mathematics provide make available a wide range of career opportunities.

Specifically, mathematicians seeking to remain connected to their field pursue career opportunities in:
*actuary or insurance work
*defense-related work
*market trading analysis for investment banks
*mathematical modeling

Less-related fields that are also of some interest to mathematicians are:
*computer programming
*accounting
*K-12 teaching

Some mathematicians enter entirely unrelated fields. Math majors have the highest average scores of students in any field on the LSAT and GMAT, the tests required for entrance into law school and business school <ref>http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1430654</ref>: the skills acquired in studying mathematics in invaluable in the logic section of the LSAT and for subsequent careers in law.

== Further Reading ==
Numerous expository books cover the topics mentioned on this page, along with many others, in a very accessible way. Below are a few recommended books whose content is comparable to that of this article.
# ''Mathematics: The New Golden Age'', by Keith Devlin. Accessible discussions of many important ideas.
# ''Professor Stewart's Cabinet of Mathematical Curiosities'', by Ian Stewart. A similar book covering the exciting side of mathematics and requiring little background.
# ''Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics'', by John Derbyshire. Focuses on the famous [[Riemann hypothesis]] and related material.
# ''Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner's First Book of Mathematical Puzzles and Games''. A collection of articles by one of mathematics' foremost expositors.
[[Category:Mathematics]]
[[Category:Higher Education]]

Private property

2012-02-09T05:11:25Z

Bogart12:

'''Private property''' is a legal term specifically referring to the coercive enforcement by the government of private ownership of land, houses, chattels, and goods. It is characterized by a single owner with absolute dominion over the property. When two or more owners have a claim or if the ownership is temporary or limited, it is not private property. Private property, in the United States of America, is constitutionally protected by state and federal constitution (see: [[Fifth Amendment]])

== Exposition ==

Property ownership refers to a set of legal rights, held by a person (or persons), relating to a particular thing, which together are recognized as possession of that thing. Ownership consists of possession and control over the item. Although the exact scope of that set of rights can vary depending upon the nature of the thing owned, and from legal system to legal system, certain of those rights represent the core of what is generally understood as “ownership.” Chief amongst these is the right to exclude others from the use or enjoyment of the thing owned.

“Alienability,” or the right to sell (or refuse to sell) is also a core property right. To the typical person, the right to use and enjoy a thing is the most valuable aspect of property rights, but the scope of this aspect of property rights varies greatly from legal system to legal system, and even over time, with changes within a given system.

Estate in property has traditionally been divided into two main types, real property and personal property, or personalty. Real property refers to qualified ownership of land, while personalty constitutes all other types of property. In addition, the law recognizes certain kinds of analogous rights to immaterial assets that are sometimes considered property rights, as well. For example, patents, trademarks, trade secrets, and copyrights are often referred to as “intellectual property,” because they provide the right to exclude others and the right to sell (but, except for trademark, do not necessarily convey an affirmative right for the owner to use). Furthermore, certain legal theorists have posited that certain other legal rights (particularly government entitlement programs) are "new property." In general, "new property" is not property at all; rather, this is a characterization chosen to try to rhetorically convey upon them the constitutional protection for property rights.

== Ownership ==

Ownership can be characterized as either absolute or qualified. Absolute ownership is synonymous with sovereignty or dominion. Only upon one's private property can one pursue happiness without consent of another. Everywhere else, one needs permission (license) from the other owner, landlord or custodian, else he commits a trespass. The sovereignty of the people referred to in the [[republican form of government]] (See: Article 4, Section 4, U.S. Constitution), implicitly recognizes that fact. For sovereignty can only be exercised upon land that one has exclusive and absolute power over. Furthermore, the governments of the U.S.A. also recognize absolute ownership of private property. No state or federal government levies a tax upon private property. And private property cannot be taken for public use without just compensation (See: Fifth amendment, U.S. Constitution).

In contrast, estate (real and personal property) is subject to taxation.

'''PROPERTY TAX''' - "An ad valorem tax, usually levied by a city or county, on the value of real or personal property that the taxpayer owns on a specified date."
<ref> Black's Law dictionary, sixth ed., p.1218</ref>

== Biblical source for absolute ownership ==

In Genesis 1:26-28, man is given dominion over the earth, and all that is upon it. In law, dominion means absolute ownership or sovereignty. Since there can be no collective absolute ownership, the only valid conclusion is that individual men are endowed with the birthright to absolutely own themselves, the fruits of their labor, and that which they harmlessly acquire, including land.

== Common misconceptions ==

It is often assumed that all land is real estate. But estate refers to qualified ownership, and not absolute ownership. Land is one thing, an estate in land is another. Estate is an interest in property that is less than title. Thus a "title deed" to estate is not title, but qualified ownership, a temporary or limited possession of the real estate.

Since absolute ownership is a right, not a privilege, no American government has the delegated power to tax private property.<REF>Example: Georgia Constitution, Art. 7, Sec. 1, Taxing Authority, Paragraph II. Taxing power limited.</REF> All constitutional delegations of taxing authority are limited to real and personal property (i.e., estate).

== Definitions ==

'''PRIVATE PROPERTY''' - As protected from being taken for public uses, is such
property as belongs absolutely to an individual, and of which he has the
exclusive right of disposition. Property of a specific, fixed and tangible
nature, capable of being in possession and transmitted to another, such as
houses, lands, and chattels.
<ref>Black's Law dictionary, sixth ed., p.1217</ref>

'''OWNERSHIP''' - ... Ownership of property is either absolute or qualified. The
ownership of property is absolute when a single person has the absolute dominion
over it... The ownership is qualified when it is shared with one or more
persons, when the time of enjoyment is deferred or limited, or when the use is
restricted.
<ref>Black's Law dictionary, sixth ed., p. 1106</ref>

'''DOMINION''' - Generally accepted definition of "dominion" is perfect control in
right of ownership. The word implies both title and possession and appears to
require a complete retention of control over disposition. -Sovereignty; as the
dominion of the seas or over a territory.
<ref>Black's Law Dictionary, Sixth Ed., p.486</ref>

'''LAND''' - The land is one thing, and the estate in land is another thing, for an estate in land is a time in land or land for a time.
<ref>Black's Law dictionary, sixth ed., p.877</ref>

'''REAL ESTATE''' ".... is synonymous with real property"
<ref>Black's Law dictionary, sixth ed., p.1263</ref>

'''REAL PROPERTY''' ... A general term for lands, tenements, heriditaments; which on the death of the owner intestate, passes to his heir."
<ref>Black's Law dictionary, sixth ed., p.1218</ref>

'''ESTATE''' - The degree, quantity, nature and extent of interest which a person has in real and personal property. An estate in lands, tenements, and hereditaments signifies such interest as the tenant has therein."
<ref>Black's Law dictionary, sixth ed., p.547</ref>

'''INTEREST''' - ...More particularly it means a right to have the advantage of accruing from anything ; any right in the nature of property, but '''less than title'''.
<ref>Black's Law dictionary, sixth ed., p.812</ref>

'''TITLE''' - "The formal right of ownership of property..."
<ref>Black's Law dictionary, sixth ed., p.1485</ref>

'''PROPERTY TAX''' - "An ad valorem tax, usually levied by a city or county, on the value of real or personal property that
the taxpayer owns on a specified date."
<ref>Black's Law dictionary, sixth ed., p.1218</ref>

== References ==
<references/>

==External Links==
*[http://www.aim.org/wls/category/private-property/ What Liberals Say - Category: Private Property], [[Accuracy In Media]]

[[Category:Economics]]
[[Category:Law]]
[[Category:Legal Terms]]

Counterexamples to Relativity

2012-02-09T04:38:48Z

Bogart12: The removed "counterexample" offers no support except vague, invalid reasoning

The [[theory of relativity]] is a mathematical system that allows no exceptions. It is heavily promoted by [[liberals]] who like its encouragement of [[moral relativism|relativism]] and its tendency to mislead people in how they view the world.<ref>See, e.g., historian Paul Johnson's book about the 20th century, and the article written by liberal law professor Laurence Tribe as allegedly assisted by [[Barack Obama]]. Virtually no one who is taught and believes Relativity continues to read the [[Bible]], a book that outsells ''New York Times'' bestsellers by a hundred-fold.</ref> A similar, but less well-known, example of supposedly hard science supporting political dogma comes from the promotion of [http://en.wikipedia.org/wiki/Kaon#Neutral_kaon_mixing neutral kaon mixing] by anti-war anarchists Gell-Mann and Pais. Here is a list of 39 counterexamples: any one of them shows that the theory is incorrect.

#Despite wasting millions of taxpayer dollars searching for gravitational waves predicted by the theory, none has ever been found.<ref>http://arxiv.org/abs/1102.3781</ref> ''Sound like [[global warming]]?''
#The orbital radius of the [[Moon]]'s orbit is increasing, contrary to what Relativity predicts.<ref>http://arxiv.org/abs/1102.0212</ref><ref>creation.com/moon&search=123233422queery=10101001.php</ref>
#Subatomic particles have a speed observed to be faster than the speed of light, which contradicts a fundamental assumption of Relativity.<ref>http://www.hindustantimes.com/Roll-over-Einstein-Law-of-physics-challenged/Article1-749189.aspx - note that a similar observation of faster-than-light speeds was also made in 2007 (with a larger margin of error).</ref> The Italian lab that "shocked the scientific world" has announced more precise results, confirming their previous announcement.<ref>http://www.reuters.com/article/2011/11/18/us-science-neutrinos-light-idUSTRE7AH0T720111118</ref>
#The [[Pioneer anomaly]].
#Anomalies in the locations of spacecraft that have flown by [[Earth]] ("flybys").<ref>http://www.msnbc.msn.com/id/23410705/</ref>
#Spiral galaxies confound Relativity, and unseen "[[dark matter]]" has been invented to try to retrofit observations to the theory.<ref>http://arxiv.org/abs/1105.1873</ref>
#The acceleration in the expansion of the universe confounds Relativity, and unseen "[[dark energy]]" has been invented to try to retrofit observations to the theory.
#Increasingly precise measurements of the advance of the perihelion of Mercury show a shift greater than predicted by Relativity, well beyond the margin of error.<ref>In a complicated or contrived series of calculations that most physics majors cannot duplicate even after learning them, the theory of general relativity's fundamental formula, <math>G_{\mu\nu} = 8 \pi K T_{\mu\nu}\,</math>, was conformed to match Mercury's then-observed precession of 5600.0 arc-seconds per century. Subsequently, however, more sophisticated technology has measured a different value of this precession (5599.7 arc-seconds per century, with a margin of error of only 0.01), and leading promoters of Relativity (such as Professor Clifford Will) have omitted this in listing tests confirming Relativity.</ref>
#The discontinuity in momentum as velocity approaches "c" for infinitesimal mass, compared to the momentum of light.
#The logical problem of a force which is applied at a right angle to the velocity of a relativistic mass - does this act on the rest mass or the relativistic mass?
#The observed lack of curvature in overall space.<ref>If space were curved, one would never expect the universe as a whole to be almost precisely flat. Yet it is.</ref>
#The universe shortly after its creation, when quantum effects dominated and contradicted Relativity.
#The [[action-at-a-distance]] of [[quantum entanglement]].<ref>Quantum entanglement has not yet communicated information faster than the speed of light, but has already exhibited action faster than the speed of light.</ref>
#The [[action-at-a-distance]] by [[Jesus]], described in [[John 1-7 (Translated)|John 4:46-54]], [[Matthew 10-19 (Translated)|Matthew 15:28]], and [[Matthew 20-28 (Translated)|Matthew 27:51]].
#Newly observed data reveal that the fine-structure constant, α (alpha), actually varies throughout the universe, demonstrating that all inertial frames of reference do '''not''' experience identical laws of physics as claimed by Relativity.<ref>For a report on the data, see a paper submitted in 2010 by John Webb and Julian King of the University of new South Wales, Australia, to the ''Physical Review Letters''.</ref>
#The double star "W13" weighs "40 times as much as the sun—more than enough to form a [[black hole]]. So why is it not a black hole? The only explanation [a leading scientist] can think of ... does not make astrophysical sense."<ref>http://www.economist.com/node/17035953</ref>
#The inability of the theory to lead to other insights, contrary to every verified theory of physics.
#The change in mass over time of standard kilograms preserved under ideal conditions.<ref>[[Mystery:Why Is the Kilogram Losing Weight?]]</ref>
#The uniformity in temperature throughout the universe.<ref>http://www.newscientist.com/article/dn6092-speed-of-light-may-have-changed-recently.html ("A varying speed of light contradicts Einstein's theory of relativity, and would undermine much of traditional physics. But some physicists believe it would elegantly explain puzzling cosmological phenomena such as the nearly uniform temperature of the universe.")</ref>
#"According to Einstein’s view on the universe, space-time should be smooth and continuous" but observations instead show "inexplicable static" greater than "all artificial sources of" possible background noise.<ref>[http://www.csmonitor.com/Science/Cool-Astronomy/2010/1025/Is-the-universe-a-big-hologram-This-device-could-find-out. Hunt for gravitational waves discovers unexpected data instead].</ref>
#"The snag is that in quantum mechanics, time retains its Newtonian aloofness, providing the stage against which matter dances but never being affected by its presence. These two [QM and Relativity] conceptions of time don’t gel."<ref>http://www.scientificamerican.com/article.cfm?id=splitting-time-from-space</ref>
#The theory predicts [[wormholes]] just as it predicts [[black holes]], but wormholes violate causality and permit absurd time travel.<ref>http://prola.aps.org/abstract/PRL/v61/i13/p1446_1 . The popular science press promotes black holes to a far greater extent than wormholes.</ref>
#Data from the [[PSR B1913 16|PSR B1913+16]] increasingly diverge from predictions of the [[General Theory of Relativity]] such that, despite a Nobel Prize in Physics being awarded for early work on this pulsar, no data at all have been released about it for over five years.
#The lack of useful devices developed based on any insights provided by the theory; no lives have been saved or helped, and the theory has not led to other useful theories and may have interfered with scientific progress.<ref>Contrary to the claims of Relativists, the GPS system has never been based on Relativity. The Time Service Department, U.S. Navy, observed that "The Operational Control System (OCS) of the Global Positioning System (GPS) does not include the rigorous transformations between coordinate systems that Einstein’s general theory of relativity would seem to require" in part because "the effects of relativity, where they are different from the effects predicted by classical mechanics and electromagnetic theory, are too small to matter – less than one centimeter, for users on or near the earth.”</ref> This stands in stark contrast with every verified theory of science.
#Relativity requires different values for the inertia of a moving object: in its direction of motion, and perpendicular to that direction. This contradicts the logical principle that the laws of physics are the same in all directions.
#Relativity requires that anything traveling at the speed of light must have mass zero, so it must have momentum zero. But the laws of electrodynamics require that light have nonzero momentum.
#Unlike most well-tested fundamental physical theories, the theory of relativity violates conditions of a conservative field. Path independence, for example, is lacking under the theory of relativity, as in the "twin paradox" whereby the age of each twin under the theory is dependent on the path he traveled.<ref>In defense of the theory, it is noted that it mandates conservation of the matter-stress-energy tensor (the only way to get ''real'' conservation, since matter and energy are interchangeable.) This follows from the "contracted Bianchi identity." [http://www.mth.uct.ac.za/omei/gr/chap6/node14.html] Also, the curl of the "gravitational field vector" is exactly zero in the absence of moving sources, due to symmetries of [[Riemann]]'s tensor. It follows, from [[Stokes' Theorem]], that the gravitational field is conservative and has a potential function. Energy is conserved.</ref>
#The Ehrenfest Paradox: Consider a spinning hoop, where the tangential velocity is near the speed of light. In this case, the circumference (<math>2 \pi R</math>) is length-contracted. However, since <math>R</math> is always perpendicular to the motion, it is not contracted. This leads to an apparent paradox: does the radius of the accelerating hoop equal <math>R</math>, or is it less than <math>R</math>?
#Based on Relativity, Einstein predicted in 1905 that clocks at the Earth's equator would be slower than clocks at the North Pole, due to different velocities; in fact, all clocks at sea level measure time at the same rate, and Relativists made new assumptions about the Earth's shape to justify this contradiction of the theory; they also make the implausible claim that relativistic effects from gravitation precisely offset the effects from differences in velocity.<ref>http://www.nature.com/nature/journal/v227/n5255/abs/227270a0.html</ref>
#Based on Relativity, Einstein claimed in 1909 that the [[aether (science)|aether]] does not exist, but in order to make subatomic physics work right, theorists had to introduce the aether-like concept of the Higgs field, which fills all of space and breaks symmetries.
#[[Minkowski space]] is predicated on the idea of four-dimensional vectors of which one component is [[time]]. However, one of the properties of a [[vector space]] is that every vector have an inverse. Time cannot be a vector because it has no inverse.<ref>Time isn't a vector. It is a component of the vector space known as "spacetime".</ref>
#It is impossible to perform an experiment to determine whether Einstein's theory of relativity is correct, or the older Lorentz aether theory is correct. Believing one over the other is a matter of [[faith]].
#Despite a century of wasting billions of dollars in work on the theory, "No one knows how to solve completely the equations of general relativity that describe gravity; they are simply beyond current understanding."<ref>[http://www.mathunion.org/o/General/Prizes/2006/TaoENG.pdf Statement in awarding the coveted Fields Medal] [Dead link]</ref>
#Experiments in electromagnetic induction contradict Relativity: "Einstein’s Relativity ... can not explain the experiment in graph 2, in which moving magnetic field has not produced electric field."<ref>http://www.wbabin.net/weuro/qingping1.pdf</ref><ref>http://arxiv.org/abs/physics/0504223</ref>
#Relativity breaks down if a [[solenoid]] is traveling at or near the speed of light.<ref>http://www.physicsforums.com/showthread.php?p=3244279</ref>

(add to list)

''For a discussion of attempts to rebut some of these counterarguments, see [[Essay:Rebuttal to Counterexamples to Relativity]].''

{{Relativity}}

== See also ==
*[[Counterexamples to Evolution]]
*[[Counterexamples to an Old Earth]]
*[[Counterexamples to the Bible]]

== References ==

<references/>

[[Category:physics]]
[[Category:relativity]]
[[Category:science]]

Talk:Complex analysis

2012-02-09T04:35:59Z

Bogart12: Created page with "It doesn't make sense to say functions supported on the complex numbers; the support of a function is the closure of the set where it is non-zero."

It doesn't make sense to say functions supported on the complex numbers; the support of a function is the closure of the set where it is non-zero.

Talk:Topology

2012-02-09T04:29:55Z

Bogart12: Created page with "It would be more precise to describe a topological space as a set along with some subset of its power set, designated the open sets. The open sets do not generate the topology, ..."

It would be more precise to describe a topological space as a set along with some subset of its power set, designated the open sets. The open sets do not generate the topology, they ARE the topology. A basis for a topology generates the topology. Also, it might be worthwhile to describe what properties the open sets have to satisfy (e.g. closure under finite intersections and arbitrary unions).

Derivative (calculus)

2012-02-09T04:25:33Z

Bogart12:

A '''derivative''', one of the fundamental concepts of [[calculus]], measures how quickly a [[function]] changes as its input value changes. Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point. For example, the derivative of <tt>y = x2</tt> at the point <tt>(1,1)</tt> tells how quickly the function is increasing at that point. If a function has a derivative at some point, it is said to be '''differentiable''' there. If a function has a derivative at every point where it is defined, we say it is a '''differentiable function'''. Differentiability implies [[continuous|continuity]].

One of the main applications of differential calculus is '''differentiating''' a function, or calculating its derivative. The First [[Fundamental Theorem of Calculus]] explains that one can find the original function, given its derivative, by [[integration|integrating]], or taking the integral of, the derivative.

==Definition==
The derivative of the function <tt>f(x)</tt>, denoted <tt>f'(x)</tt> or <math>\frac{df}{dx}</math>, is defined as:

:<math>f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}</math>

In other words, it is the limit of the [[slope]] of the [[secant]] line to f(x) as it becomes a [[tangent#Other_Uses|tangent line]]. If the tangent line is increasing (which it is if the original function is increasing), the derivative is positive; if the function is decreasing, the derivative is negative.

For example, <math>\frac{d}{dx} ( 2x ) =\lim_{h \to 0}\frac{2(x+h)-2(x)}{h} = \lim_{h \to 0}\frac{2x+2h-2x}{h} = \lim_{h \to 0}\frac{2h}{h} = \lim_{h \to 0}\ 2 = 2</math>
In general, <tt>f'(mx) = m</tt>; that is, the derivative of any line is equal to its slope.

===Higher order derivatives===

A higher order derivative is obtained by repeatedly differentiating a function. Thus, the second derivative of x, or <math>\frac{d^{2}y}{dx^{2}}</math>, is <math>\frac{d}{dx}\left(\frac{dy}{dx}\right)</math>

Similarly,
:<math>\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)</math>

and so forth.

A common alternative notation is <math>f''(x)</math>, <math>f'''(x)</math>, and <math>f^{(n)}(x)</math> for the second, third or n th derivative.

===Partial derivatives===
A ''partial derivative'' is obtained by differentiating a function of multiple variables with respect to one variable while holding the rest constant. For example, the partial derivative of <tt>F(x,y)</tt> with respect to x, or <math>\frac{\partial}{\partial R}</math>, represents the rate of change of F with respect to x while y is constant. Thus, F could be [[windchill]], which depends both on wind velocity and actual [[temperature]]. <math>\frac{\partial windchill}{\partial velocity}</math> represents how much windchill changes with respect to wind velocity for a given temperature.

Partial derivatives are calculated just like full derivatives, with the other variables being treated as constants.

'''Example:'''
Let <math>f(x_1,x_2) = \frac{x_1^3}{1+x_2^2}</math>. Then there are two partial derivatives of first order:
*<math>f_1(x_1,x_2) = \frac{\partial f(x_1,x_2)}{\partial x_1} = \frac{3x_1^2}{1+x_2^2}</math>
*<math>f_2(x_1,x_2) = \frac{\partial f(x_1,x_2)}{\partial x_2} = \frac{- 2 x_1^3 x_2}{(1+x_2^2)^2}</math>

Note that the two partial derivatives <math>f_1(x_1,x_2)</math> and <math>f_2(x_1,x_2)</math> in this example are again differentiable functions of <math>x_1</math> and <math>x_2</math>, so higher derivatives can be calculated:

*<math>f_{11}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_1 \partial x_1} = \frac{6 x_1}{1+x_2^2}</math>
*<math>f_{12}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_1 \partial x_2} = \frac{- 6 x_1^2 x_2}{(1+x_2^2)^2}</math>
*<math>f_{21}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_2 \partial x_1} = \frac{- 6 x_1^2 x_2}{(1+x_2^2)^2}</math>
*<math>f_{22}(x_1,x_2) = \frac{\partial^2 f(x_1,x_2)}{\partial x_2 \partial x_2} = \frac{8 x_1^3 x_2^2 -2 x_1^3 -2 x_1 x_2^2}{(1+x_2^2)^3}</math>

Note that <math>f_{12}(x_1,x_2)</math> equals <math>f_{21}(x_1,x_2)</math>, so that the order of taking the derivative doesn't matter. Though this doesn't hold generally, it's true for a great class of important functions, specifically continuous functions.

==Uses==

In mathematics, derivatives are helpful in determining the [[maxima|maximum]] and [[minima|minimum]] of a function. For example, taking the derivative of a [[quadratic]] function will yield a linear function. The points at which this function equals zero are called [[critical point]]s. Maxima and minima can occur at critical points, and can be verified to be a maximum or minimum by the ''second derivative test''. The second derivative is used to determine the [[concavity]], or curved shape of the graph. Where the concavity is positive, the graph curves upwards, and could contain a relative minimum. Where the concavity is negative, the graph curves downwards, and could contain a relative maximum. Where the concavity equals zero is said to be a point of ''inflection,'' meaning that it is a point where the concavity could be changing.

Derivatives are also useful in [[physics]], under the "rate of change" concept. For example, [[acceleration]] is the derivative of [[velocity]] with respect to time, and velocity is the derivative of [[distance]] with respect to time.

Another important application of derivatives is in the Taylor series of a function, a way of writing certain functions like <math>e^x</math> as a power series.

==Rules for finding derivatives==
*[[Power rule]]
*[[Constant-multiple rule]]
*[[sum rule]]
*[[Chain rule]]
*[[Product rule]]
*[[Quotient rule]]

[[Category:Calculus]]
[[Category:Differentiation]]