https://www.conservapedia.com/api.php?action=feedcontributions&user=Recorder&feedformat=atomConservapedia - User contributions [en]2020-10-22T19:04:03ZUser contributionsMediaWiki 1.24.2https://www.conservapedia.com/index.php?title=Profiling&diff=637216Profiling2009-03-10T03:10:50Z<p>Recorder: fill in</p>
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<div>'''Profiling''' is a technique used in [[law enforcement]] to help narrow the field of potential [[criminal]] suspects. Investigators compile a list of characteristics (a "profile") likely to be descriptive of a crime's perpetrator, and then alter the focus of an investigation accordingly. A simple example of profiling would be [[airport]] security personnel looking for nervous individuals wearing bulky clothes and subjecting them to more thorough searches, since people who carry dangerous devices are more likely to fit that description. However, profiling can be extended to include complex information about behaviors, tendencies, and psychological characteristics in addition to physical identifiers.<br />
<br />
== Mental Profiling ==<br />
Experts in [[psychology]] and [[psychiatry]] are occasionally called upon to generate mental profiles of criminals. Such profiles are usually reserved for high-profile cases, repeat offenders, or particularly heinous offenses, as in cases involving [[serial killer]]s.<br />
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== Racial Profiling ==<br />
{{main|Racial profiling}}<br />
<br />
The use of [[race]] as a profiling characteristic is controversial due to critics, mostly [[liberal]]s, objecting due to concerns over [[discrimination]] and reinforcement of negative racial [[stereotype]]s. <br />
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== Liberal Profiling ==<br />
Profiling may be used to identify liberals by their characteristics. For instance, someone who actively engages in [[deceit]], [[evolutionist style|questionable science]], [[:Image:Hitler_and_Darwin.jpg|absurdities]], [[liberal hysteria|hysteria]], [[liberal tricks|dubious methodology]], [[logic]], and embraces the values of [[Hollywood values|Hollywood]] and [[Professor values|academia]] is overwhelmingly likely to be liberal.<br />
<br />
[[Category:Crime]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Racial_profiling_controversy&diff=637171Racial profiling controversy2009-03-10T02:30:01Z<p>Recorder: link</p>
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<div>'''Racial profiling''' is the use of race in [[profiling]] a suspected criminal. Wherever police have served a mixed-race population, the race of suspects has always been used, because race (or [[skin color]]) is one of the most prominent characteristic of a person, along with sex and age.<br />
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The use of race in profiling came under fire when protest groups began to complain that police were making sweeps or traffic stops based mainly on race, and thus discriminating against innocent people. Such practices as stopping all blacks for questioning - when no particular crime was being investigated - came into question.<br />
<br />
In reaction, many police forces and even the FBI began to be leery of being accused of stereotyping. The most prominent case in the tragic run-up to [[9-11]], when the FBI had cause to suspect a flight student. The FBI agent handling the case was told by their supervisor not to seek a warrant, even though the Arabic-looking man only wanted to learn how to steer a Boeing 747 but not do takeoffs or landings.<br />
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==Links==<br />
*[http://www.city-journal.org/html/11_2_the_myth.html The Myth of Racial Profiling]<br />
[[Category:Criminology]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Profiling&diff=637167Profiling2009-03-10T02:28:25Z<p>Recorder: start</p>
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<div>'''Profiling''' is a technique used in [[law enforcement]] to help narrow the field of potential [[criminal]] suspects. <br />
<br />
<br />
[[Category:Crime]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Batting_average&diff=630208Batting average2009-02-24T03:45:01Z<p>Recorder: New page: '''Batting average''' (abbreviated '''BA''') is a baseball statistic that tracks how often a batter gets a hit. Its formula is <math>BA = \frac{H}{AB}</math> where *''H'' is Hi...</p>
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<div>'''Batting average''' (abbreviated '''BA''') is a [[baseball]] [[statistic]] that tracks how often a batter gets a hit. Its formula is<br />
<br />
<math>BA = \frac{H}{AB}</math><br />
<br />
where<br />
<br />
*''H'' is Hits<br />
*''AB'' is At bats<br />
<br />
Although batting average is a traditionally popular statistic, modern [[sabermetrics|sabermetricians]] prefer other metrics, such as [[on-base percentage]].<br />
<br />
==See also==<br />
*[[On-base percentage]]<br />
*[[Slugging percentage]]<br />
*[[OPS]]<br />
<br />
<br />
{{baseball}}<br />
[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Manager_(baseball)&diff=630206Manager (baseball)2009-02-24T03:39:32Z<p>Recorder: New page: In baseball, the '''manager''' (occasionally specified as the '''field manager''') is responsible for all in-game strategy and decision making. The job is equivalent to head coach in ...</p>
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<div>In [[baseball]], the '''manager''' (occasionally specified as the '''field manager''') is responsible for all in-game strategy and decision making. The job is equivalent to head coach in other [[sports]]. <br />
<br />
In-game decisions include when to make pitching changes, whether the batter should swing away or bunt, and whether a runner should attempt to steal a base. Depending on the level of experience of his pitcher or catcher, the manager may even choose to call pitches during the game, although those duties are often delegated to the pitcher and catcher, or even the pitching coach.<br />
<br />
==See also==<br />
*[[General manager (baseball)]]<br />
<br />
[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=General_manager_(baseball)&diff=630204General manager (baseball)2009-02-24T03:32:23Z<p>Recorder: typo</p>
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<div>In [[Major League Baseball]], the '''general manager''' ('''GM''') for a team is the executive in charge of player personnel. He is ultimately responsible for scouting, drafting, negotiating with, and signing players.<br />
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The term "general manager" is used to distinguish the GM from the team's [[manager (baseball)|manager]], who is responsible for on-the-field decisions.<br />
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[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=General_manager_(baseball)&diff=630202General manager (baseball)2009-02-24T03:32:00Z<p>Recorder: New page: In Major League Baseball, the '''general manager''' ('''GM''')for a team is the executive in charge of player personnel. He is ultimately responsible for scouting, drafting, negotiati...</p>
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<div>In [[Major League Baseball]], the '''general manager''' ('''GM''')for a team is the executive in charge of player personnel. He is ultimately responsible for scouting, drafting, negotiating with, and signing players.<br />
<br />
The term "general manager" is used to distinguish the GM from the team's [[manager (baseball)|manager]], who is responsible for on-the-field decisions.<br />
<br />
<br />
[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Sabermetrics&diff=630200Sabermetrics2009-02-24T03:24:16Z<p>Recorder: specify baseball GM</p>
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<div>'''Sabermetrics''' is the name given to the systematic, objective analysis of [[baseball]] based primarily on [[statistics|statistical]] [[evidence]]. In a sense, it is the [[scientific method]] applied to baseball players, teams, and strategy. In general, sabermetric analysis and player evaluation does not rely on traditional measures of player ability, such as [[batting average]] or [[earned run average]], but places more emphasis on statistics such as [[OPS]], and [[WHIP]].<br />
<br />
==Origin of the term==<br />
The name "sabermetrics" is derived from the acronym SABR (pronounced like "sabre"), which stands for the Society for American Baseball Research. It was coined by [[Bill James]] in the 1970s.<br />
<br />
==Notable sabermetricians==<br />
Perhaps the best-known sabermetrician is [[Bill James]], who coined the term and has made numerous contributions to the field. He currently serves as a consultant to the [[Boston Red Sox]]. Other figures within Major League Baseball known as sabermetricians or widely thought to embrace sabermetric thinking are Theo Epstein, the [[general manager (baseball)|general manager]] for the Red Sox, [[Los Angeles Dodgers]] GM Paul DePodesta, and [[Oakland Athletics]] GM Billy Beane.<br />
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[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Sabermetrics&diff=630199Sabermetrics2009-02-24T03:23:32Z<p>Recorder: New page: '''Sabermetrics''' is the name given to the systematic, objective analysis of baseball based primarily on statistical evidence. In a sense, it is the [[scientific m...</p>
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<div>'''Sabermetrics''' is the name given to the systematic, objective analysis of [[baseball]] based primarily on [[statistics|statistical]] [[evidence]]. In a sense, it is the [[scientific method]] applied to baseball players, teams, and strategy. In general, sabermetric analysis and player evaluation does not rely on traditional measures of player ability, such as [[batting average]] or [[earned run average]], but places more emphasis on statistics such as [[OPS]], and [[WHIP]].<br />
<br />
==Origin of the term==<br />
The name "sabermetrics" is derived from the acronym SABR (pronounced like "sabre"), which stands for the Society for American Baseball Research. It was coined by [[Bill James]] in the 1970s.<br />
<br />
==Notable sabermetricians==<br />
Perhaps the best-known sabermetrician is [[Bill James]], who coined the term and has made numerous contributions to the field. He currently serves as a consultant to the [[Boston Red Sox]]. Other figures within Major League Baseball known as sabermetricians or widely thought to embrace sabermetric thinking are Theo Epstein, the [[general manager]] for the Red Sox, [[Los Angeles Dodgers]] GM Paul DePodesta, and [[Oakland Athletics]] GM Billy Beane.<br />
<br />
[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=On_base_plus_slugging&diff=630197On base plus slugging2009-02-24T03:10:33Z<p>Recorder: Redirecting to On-base plus slugging</p>
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<div>#REDIRECT [[On-base plus slugging]]</div>Recorderhttps://www.conservapedia.com/index.php?title=OPS&diff=630196OPS2009-02-24T03:10:04Z<p>Recorder: Redirecting to On-base plus slugging</p>
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<div>#REDIRECT [[On-base plus slugging]]</div>Recorderhttps://www.conservapedia.com/index.php?title=On-base_plus_slugging&diff=630195On-base plus slugging2009-02-24T03:09:32Z<p>Recorder: New page: '''On-base plus slugging''' ('''OPS''') is an baseball statistic used as an indicator of a player's overall offensive output. It is computed by summing on-base percentage and...</p>
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<div>'''On-base plus slugging''' ('''OPS''') is an [[baseball]] [[statistic]] used as an indicator of a player's overall offensive output. It is computed by summing [[on-base percentage]] and [[slugging percentage]]. OPS is popular among [[sabermetrics|sabermetricians]] because it is highly correlated with runs scored.<br />
<br />
==See also==<br />
*[[On-base percentage]]<br />
*[[Slugging percentage]]<br />
*[[Sabermetrics]]<br />
<br />
<br />
{{baseball}}<br />
[[Category:Baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:World_History_Lecture_Four&diff=628069Talk:World History Lecture Four2009-02-20T17:07:48Z<p>Recorder: /* Intellectual Achievements */ veritas</p>
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<div>Julius Caesar was not an emperor as stated in the Other Reasons for the Fall of the Roman Empire section. The highest title he assumed was dictator (for life).<br />
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==Intellectual Achievements==<br />
''"The Romans are not known for their intellectual achievements."'' I beg to differ. By definition, the first 4 centuries of the development of Christian thought and the organisation of the Church were by Romans. The whole intellectual base for both secular and canon law that was to underpin society during the middle ages and last into modern times was Roman. From Roman poets and philosophers, historians, theologians, lawyers, we walk upon the shoulders of Roman intellectual creativity. [[User:AlanE|AlanE]] 16:41, 19 February 2009 (EST)<br />
<br />
: For nearly 1000 years of domination, I hope you can come up with something more specific than that. In a fraction of the time the Greeks achieved infinitely more intellectually.--[[User:Aschlafly|Andy Schlafly]] 17:09, 19 February 2009 (EST)<br />
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::Yes, they did, I agree. The ''Athenian half-century'' is unique and wonderful and completely unchallenged as a period of intellectual achievement. Beside the Greeks, everyone is left behind for so much packed into so little time. But we can't say that the Romans had no intellectual achievements. The work of St Augustine, of Gregory the Great, of Justinian, to name just three, have had as big an impact on European thought as Plato or Aristotle who did not gain much traction until the Renaissance. There are as many copies of Cicero, Ovid, Tacitus, Boethius, Marcus Aurelius, Pliny, Horace, Catullus, on shelves (mine anyway) as there are of the Greeks. The whole intellectual weight of the Medieval western church rested on a Roman intellectual base, in its organisation, its ecclesiastical laws, its language and, of course, the centre of its authority.<br />
:::I am in no way meaning to denigrate the Greeks, just to argue that there is a recognised intellectual component in the Roman Empire that is alive today - especially noticeable in the development of the Christian Church and the Law. [[User:AlanE|AlanE]] 18:00, 19 February 2009 (EST)<br />
<br />
:::: I don't think the Romans even had the concept of "truth".--[[User:Aschlafly|Andy Schlafly]] 23:07, 19 February 2009 (EST)<br />
:::::Then what is ''veritas''? As in ''veritas vos liberabit''. [[User:AlanE|AlanE]] 00:19, 20 February 2009 (EST)<br />
::::::I find ''in vino veritas'' to be a more of a "true" statement ;) An interesting article on ''veritas'' is [http://www.formalontology.it/veritas.htm here].--[[User_talk:Recorder|Recorder]] 12:07, 20 February 2009 (EST)</div>Recorderhttps://www.conservapedia.com/index.php?title=SLG&diff=625971SLG2009-02-17T03:34:15Z<p>Recorder: Redirecting to Slugging percentage</p>
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<div>#REDIRECT [[Slugging percentage]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Slugging_average&diff=625970Slugging average2009-02-17T03:33:58Z<p>Recorder: Redirecting to Slugging percentage</p>
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<div>#REDIRECT [[Slugging percentage]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Slugging_percentage&diff=625968Slugging percentage2009-02-17T03:30:08Z<p>Recorder: New page: '''Slugging percentage''', abbreviated '''SLG''', is a baseball statistic used to quantify a hitter's ability to get extra-base hits; i.e., a measure of his power. It is defined a...</p>
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<div>'''Slugging percentage''', abbreviated '''SLG''', is a [[baseball]] [[statistic]] used to quantify a hitter's ability to get extra-base hits; i.e., a measure of his power. It is defined as total bases divided by at bats, and its formula is<br />
<br />
<math>SLG = \frac{(\mathrm{1B}) + (2 \times \mathrm{2B}) + (3 \times \mathrm{3B}) + (4 \times \mathrm{HR})}{AB}</math> <br />
<br />
where<br />
*1B is the number is singles<br />
*2B is the number of doubles<br />
*3B is the number of triples<br />
*HR is the number of [[Home Run]]s<br />
<br />
[[Sabermetrics|Sabermetricians]] realized that SLG can be combined with [[On-base percentage]] to generate [[On-base plus slugging]], a very good indicator of offensive player performance.<br />
<br />
[[Category:Baseball]]<br />
{{baseball}}</div>Recorderhttps://www.conservapedia.com/index.php?title=Right_hand_rule&diff=625967Right hand rule2009-02-17T03:23:08Z<p>Recorder: /* Direction of the magnetic force on a particle */ clarify</p>
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<div>In [[physics]], the '''right hand rule''' is a technique used to find the resultant direction of a [[cross product]]. Its name comes from the fact that, by convention, [[Cartesian coordinates]] are defined as "right handed", and the rule therefore requires that the right hand be used to get the correct result.<br />
<br />
==Examples==<br />
====Direction of the magnetic force on a particle====<br />
To find the direction of the magnetic force on a positively charged particle in a [[magnetic field]], hold your right hand in a "thumbs up" position. Now, keeping your thumb extended, point your index finger in the direction of the particle's [[velocity]]. Your hand should now look as if you are forming a "gun." Next, keeping your index finger pointing in the same direction, extend your middle finger so that it foms a 90 degree angle with your index finger. Rotate your hand about the axis formed by your index finger so that your middle finger points in the direction of the magnetic field. Your thumb now points in the direction of the magnetic force.<br />
<br />
Note that if the particle were negatively charged, you can still use the right hand rule, but the force is in the ''opposite'' direction (180 degrees away) from the force on the positive particle.<br />
<br />
====Direction of the magnetic field generated by a current-carrying wire====<br />
To determine the orientation of the magnetic field caused by a current-carrying wire, point your right thumb in the direction of the current, as if the current is running "through" your thumb. Keeping your thumb in that orientation, curl your fingers around the wire. The magnetic field follows the circular path of your fingers.<br />
<br />
[[category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Cross_product&diff=625964Cross product2009-02-17T03:20:43Z<p>Recorder: wikify</p>
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<div>The '''cross product''' (or vector product) of two [[vector|vectors]] in 3-space is itself a vector in 3-space, and is written <math>a\times b</math>. The magnitude of the resulting vector is<br />
<br />
<math><br />
|a\times b|=|a| |b| \sin\theta<br />
</math><br />
<br />
where <math>\theta</math> is the angle between the two vectors. The direction of the cross product is normal to both of the vectors '''a''' and '''b'''. Since there are two such directions the chosen one is defined by the [[right hand rule]]: with your right hand, point your fingers along the direction of the first vector and curl them towards the second vector. The direction your thumb points gives the direction of the cross product. The cross product is a convenient way to find the volume of a [[parallelepiped]]. One may simply take the cross product of two legs and then find the dot product of that vector with the remaining leg (assuming that the legs are vectors). <br />
===See also===<br />
[[Dot product]]<br />
[[Category:Linear algebra]]</div>Recorderhttps://www.conservapedia.com/index.php?title=On-base_percentage&diff=625961On-base percentage2009-02-17T03:19:27Z<p>Recorder: add improvement over BA</p>
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<div>'''On-base percentage''' (abbreviated '''OBP''') is a [[baseball]] [[statistic]] designed to track the rate at which a hitter reaches base as a result of his own actions (as opposed to, for example, defensive lapses). Another way to interpret OBP is the percentage of a player's plate appearances that he does not make an out.<br />
<br />
The formula for on-base percentage is <br />
<br />
<math>OBP = \frac{H+BB+HBP}{AB+BB+HBP+SF}</math><br />
<br />
where<br />
<br />
*''H'' is Hits<br />
*''BB'' is Walks<br />
*''HBP'' is times hit by a pitch<br />
*''AB'' is At bats<br />
*''SF'' is Sacrifice Flies<br />
<br />
Because there is a high correlation between OBP and runs scored, the use of on-base percentage in player evaluation has gained favor among baseball enthusiasts and front offices in recent years. It has proven to be a more reliable indicator of a player's offensive performance than [[batting average]].<br />
<br />
==See Also==<br />
*[[Slugging percentage]]<br />
*[[On-base plus slugging]]<br />
*[[Sabermetrics]] <br />
<br />
[[Category:Baseball]]<br />
{{baseball}}</div>Recorderhttps://www.conservapedia.com/index.php?title=OBP&diff=625959OBP2009-02-17T03:17:58Z<p>Recorder: Redirecting to On-base percentage</p>
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<div>#REDIRECT [[On-base percentage]]</div>Recorderhttps://www.conservapedia.com/index.php?title=On-base_percentage&diff=625958On-base percentage2009-02-17T03:17:35Z<p>Recorder: New page: '''On-base percentage''' (abbreviated '''OBP''') is a baseball statistic designed to track the rate at which a hitter reaches base as a result of his own actions (as opposed to, fo...</p>
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<div>'''On-base percentage''' (abbreviated '''OBP''') is a [[baseball]] [[statistic]] designed to track the rate at which a hitter reaches base as a result of his own actions (as opposed to, for example, defensive lapses). Another way to interpret OBP is the percentage of a player's plate appearances that he does not make an out.<br />
<br />
The formula for on-base percentage is <br />
<br />
<math>OBP = \frac{H+BB+HBP}{AB+BB+HBP+SF}</math><br />
<br />
where<br />
<br />
*''H'' is Hits<br />
*''BB'' is Walks<br />
*''HBP'' is times hit by a pitch<br />
*''AB'' is At bats<br />
*''SF'' is Sacrifice Flies<br />
<br />
Because there is a high correlation between OBP and runs scored, the use of on-base percentage in player evaluation has gained favor among baseball enthusiasts and front offices in recent years. <br />
<br />
==See Also==<br />
*[[Slugging percentage]]<br />
*[[On-base plus slugging]]<br />
*[[Sabermetrics]] <br />
<br />
[[Category:Baseball]]<br />
{{baseball}}</div>Recorderhttps://www.conservapedia.com/index.php?title=User:Recorder&diff=625948User:Recorder2009-02-17T03:09:05Z<p>Recorder: </p>
<hr />
<div>I plan on creating and/or working on some articles related to [[baseball]].<br />
<br />
==To do list (baseball)==<br />
I think some (all?) of this stuff was lost in the recent disk problems<br />
===Stats-related===<br />
*[[On-base percentage]]<br />
*[[Slugging percentage]]<br />
*[[OPS]]<br />
*[[Batting average]]<br />
*[[Sabermetrics]]<br />
<br />
===Positions===<br />
*[[Manager (baseball)]]<br />
*[[General manager (baseball)]]<br />
<br />
===People===<br />
*[[Billy Beane]]<br />
<br />
===Other===<br />
*[[Baseball terms]], or some sort of glossary<br />
*[[:Template:baseball]]</div>Recorderhttps://www.conservapedia.com/index.php?title=User:Recorder&diff=623442User:Recorder2009-02-13T21:32:33Z<p>Recorder: fresh paint</p>
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<div>I plan on creating and/or working on some articles related to [[baseball]].</div>Recorderhttps://www.conservapedia.com/index.php?title=Momentum_(physics)&diff=608443Momentum (physics)2009-01-12T05:11:12Z<p>Recorder: fill out; try to make clearer the distinction with inertia</p>
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<div>'''Momentum''' is the "quantity of motion" an object possesses. In classical [[physics]], the linear form of momentum is defined as the product of [[mass]] and [[velocity]]:<br />
<br />
:<math> \mathbf{p} = m\mathbf{v} </math><br />
<br />
Hence, the faster an object goes, or the more mass it posesses, the more momentum it has. Momentum is a [[vector]] quantity, and therefore has both a magnitude and direction. It is important to physicists because it is a [[conservation law|conserved]] quantity, making it useful for solving problems.<br />
<br />
In common usage, the words "momentum" and "[[inertia]]" are sometimes used interchangeably. Inertia is the tendency for a body to resist changes in its motion until and unless a force acts on it.<br />
<br />
The motion of an object will continue until something makes it change its motion. A railroad car, once it gets going, will continue its motion for a long time, until the tiny forces of friction cause it to slow down and stop. This can take miles. Even putting on the brakes can take up to mile, because there is so much momentum.<br />
<br />
A [[force]] in the same direction as the body is moving will increase its speed. A force in the opposite direction will slow it down.<br />
<br />
A force coming from the side will cause a deviation from straight-line motion.<br />
<br />
An interesting case of a sideways force is a weight on the end of a string (like the Biblical slingshot used by [[David]] against [[Goliath]]). When you twirl the weight around above your head, the string is pulling the weight toward you - but it never gets any closer! This kind of force is called a [[centripetal force|centripetal]], or center seeking, force.<br />
<br />
==Angular momentum==<br />
A rotating or orbiting body possesses angular momentum. Like linear momentum, angular momentum is a vector quantity and is conserved. An object's angular momentum changes only when a [[torque]] is applied to it.<br />
<br />
The magnitude of the angular momentum of a particle orbiting some origin (such as the [[earth]] orbiting the [[sun]]) is given by <br />
<br />
:<math>L=mvr</math><br />
<br />
where<br />
<br />
*'''L''' is angular momentum<br />
*'''m''' is the mass of the particle<br />
*'''v''' is the linear velocity of the particle<br />
*'''r''' is the distance from the particle to the origin<br />
<br />
The direction of the angular momentum vector points perpendicularly to the plane formed by the object's orbit, in accordance with the [[right hand rule]]. <br />
<br />
In addition to orbital angular momentum, the earth has rotational angular momentum due to its spin. The equations for calculating rotational angular momentum depend on the object's [[moment of inertia]], and therefore the shape and density of the object. <br />
<br />
=== Generalized momentum ===<br />
The definition of momentum can be generalized in [[Lagrangian Dynamics|Lagrangian]] and [[Hamiltonian Dynamics|Hamiltonian]] dynamics, to <br />
<br />
<math><br />
p=\frac{\partial L}{\partial \dot x}<br />
</math><br />
<br />
where L is the [[Lagrangian]] and <math>\dot x</math> is the velocity. In some cases the generalized momentum is the same as the momentum defined above. For example, for a free particle the Lagrangian equals the [[kinetic energy]] and so<br />
<br />
<math><br />
p=\frac{\partial (m\dot x^2/2)}{\partial \dot x}=m\dot x<br />
</math><br />
<br />
as above.<br />
<br />
[[Category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=User:Recorder/algTemplate&diff=561012User:Recorder/algTemplate2008-11-18T00:02:41Z<p>Recorder: </p>
<hr />
<div>{| class="infobox" style="text-align:center;"<br />
<table class="infobox" style="float: right; text-align: center; font-size: 80%; clear:right; background:beige; border: 2px solid blue; margin-left:1em" cellspacing="0" cellpadding="2"><br />
|-<br />
|[[Image:Math.jpg|50px]]<br />
|-<br />
| colspan="2" |<big>'''[[Abstract algebra]]'''</big> <br />
|-<br />
| style="font-size:11px" |<br />
'''Concepts'''<br /><br />
[[Vector space]]<br /><br />
[[Group (mathematics)|Group]]<br /><br />
[[Ring (mathematics)|Ring]]<br /><br />
[[Field (mathematics)|Field]]<br /><br />
|}<noinclude><br />
{{User:Recorder/algTemplateDoc}}<br />
</noinclude></div>Recorderhttps://www.conservapedia.com/index.php?title=User:Recorder/algTemplateDoc&diff=561011User:Recorder/algTemplateDoc2008-11-18T00:01:27Z<p>Recorder: New page: {{TemplateDoc|pages=Articles relating to abstract algebra|purpose=To provide quick links to some important abstract algebra-related topics}} {{parms|}}</p>
<hr />
<div>{{TemplateDoc|pages=Articles relating to abstract algebra|purpose=To provide quick links to some important abstract algebra-related topics}}<br />
{{parms|}}</div>Recorderhttps://www.conservapedia.com/index.php?title=User:Recorder/algTemplate&diff=561010User:Recorder/algTemplate2008-11-18T00:00:36Z<p>Recorder: New page: {| class="infobox" style="text-align:center;" <table class="infobox" style="float: right; text-align: center; font-size: 80%; clear:right; background:beige; border: 2px solid blue; margin-...</p>
<hr />
<div>{| class="infobox" style="text-align:center;"<br />
<table class="infobox" style="float: right; text-align: center; font-size: 80%; clear:right; background:beige; border: 2px solid blue; margin-left:1em" cellspacing="0" cellpadding="2"><br />
|-<br />
|[[Image:Math.jpg|50px]]<br />
|-<br />
| colspan="2" |<big>'''[[Abstract algebra]]'''</big> <br />
|-<br />
| style="font-size:11px" |<br />
'''Concepts'''<br /><br />
[[Vector space]]<br /><br />
[[Group (mathematics)|Group]]<br /><br />
[[Ring (mathematics)|Ring]]<br /><br />
[[Field (mathematics)|Field]]<br /><br />
|}<noinclude><br />
{{AbstractAlgebra/doc}}<br />
</noinclude></div>Recorderhttps://www.conservapedia.com/index.php?title=Right_hand_rule&diff=523298Right hand rule2008-09-24T15:08:05Z<p>Recorder: New page: In physics, the '''right hand rule''' is a technique used to find the resultant direction of a cross product. Its name comes from the fact that, by convention, cartesian coordinat...</p>
<hr />
<div>In [[physics]], the '''right hand rule''' is a technique used to find the resultant direction of a [[cross product]]. Its name comes from the fact that, by convention, cartesian coordinate systems are defined as "right handed", and the rule therefore requires that the right hand be used to get the correct result.<br />
<br />
==Examples==<br />
====Direction of the magnetic force on a particle====<br />
To find the direction of the magnetic force on a positively charged particle in a magnetic field, hold your right hand in a "thumbs up" position. Now, keeping your thumb extended, point your index finger in the direction of the particle's [[velocity]]. Your hand should now look as if you are forming a "gun." Next, keeping your index finger pointing in the same direction, extend your middle finger and rotate your hand so that your middle finger points in the direction of the magnetic field. Your thumb now points in the direction of the magnetic force.<br />
<br />
Note that if the particle were negatively charged, you can still use the right hand rule, but the force is in the ''opposite'' direction (180 degrees away) from the force on the positive particle.<br />
<br />
====Direction of the magnetic field generated by a current-carrying wire====<br />
To determine the orientation of the magnetic field caused by a current-carrying wire, point your right thumb in the direction of the current, as if the current is running "through" your thumb. Keeping your thumb in that orientation, curl your fingers around the wire. The magnetic field follows the circular path of your fingers.<br />
<br />
[[category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Magnetic_field&diff=523156Magnetic field2008-09-24T03:38:44Z<p>Recorder: cleaned up big-time, at least in the intro</p>
<hr />
<div>A '''magnetic field''' is a [[vector]] field responsible for generating forces on electrically charged objects and magnets. Magnetic fields are generated by magnetic [[dipole]]s, moving [[electric charge]]s, or changing [[electric field]]s. <br />
<br />
Magnetic fields are linked to electric fields; [[light]], for instance, is a propagating electric and magnetic [[wave]]. Relativistically, a magnetic force in one [[inertial frame]] corresponds to an electric force in another.<br />
<br />
When trying to determine the magnetic forces and fields, the [[right hand rule]] often proves useful.<br />
<br />
==Earth's Magnetic Field==<br />
The magnetic field of [[Earth]] is directional nearly north-to-south, although slightly askance, meaning that "magnetic north" is not the same as "true north," and a person who is orienteering must take into account this change of declination, although it is truly only marginally relevant, unless you are close to either pole.<ref>Boy Scout Handbook.</ref> This field has been decaying at a rapid rate of about about 5% per century, which casts doubt on the theory that the [[Earth]] is billions of years old.<ref>K.L. McDonald and R.H. Gunst, 'An analysis of the earth’s magnetic field from 1835 to 1965,’ ESSA Technical Report, IER 46-IES 1, U.S. Govt. Printing Office, Washington, 1967.</ref> This decay suggests that, at some point, the poles will invert.<br />
<br />
[[Image:magnetic_field.gif|right|thumb|The View of "Answers in Genesis"]]<br />
Scientists have speculated about the history of Earth's magnetic field. One group that makes use of the [[Bible]] as a resource for science suggests that the history of the Earth's magnetic field is as depicted to the right.<ref>http://www.answersingenesis.org/creation/v20/i2/magnetic.asp</ref><br />
<br />
== References ==<br />
<references/><br />
[[category:physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Ampere%27s_law&diff=523144Ampere's law2008-09-24T03:14:28Z<p>Recorder: </p>
<hr />
<div>'''Ampere's Law''', named for [[Andre-Marie Ampere]], relates electric [[current]] to [[magnetic field]]s, and is one of [[Maxwell's Equations]]. It is often used in the calculation of the [[magnetic field]] at a point due to one or many [[current]]-carrying wires. It is the magnetic analogue to [[Gauss's Law]], and can be stated in integral form as<br />
<br />
: <math>\oint_C \vec{B} \cdot \mathrm{d}\vec{s} <br />
= \mu_0 I_{\mathrm{enc}}</math><br />
<br />
where <math>\vec{B}</math> is magnetic field, ''C'' is a closed curve, <math>I_{\mathrm{enc}}</math> is current enclosed by ''C'', and <math>\mu_0</math> is the permeability of free space.<br />
<br />
<br />
<br />
In differential form, Ampere's Law is written<br />
<br />
:<math> \vec{\nabla}\times\vec{B}=\mu_0\vec{J}</math><br />
<br />
where <math>\vec{J}</math> is current density.<br />
<br />
[[category:Physics]]<br />
[[category:Electricity]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Quantum_mechanics&diff=509306Quantum mechanics2008-09-02T14:39:08Z<p>Recorder: Please explain what you think is inappropriate about the intro in talk. The M-M experiment does not have much direct bearing on QM.</p>
<hr />
<div>'''Quantum mechanics''' is the branch of [[physics]] that describes the behavior of systems on very small length and energy scales, such as those found in [[atom]]ic and subatomic interactions. It is essential for understanding certain concepts that [[classical physics]] cannot explain, such as the discrete nature of small-scale interactions, [[wave-particle duality]], the [[uncertainty principle]], and [[quantum entanglement]]. Quantum mechanics forms the basis for our understanding of many phenomena, including [[chemical reaction]]s and [[radioactive decay]], as well as all [[computer]]s and electronic devices today.<br />
<br />
==History==<br />
While the roots of quantum mechanics can be traced to experiments performed in the 19th century, the theory began to emerge when [[Max Planck]] proposed a "[[quantum hypothesis]]" to explain the energy spectrum of [[black body]] radiation in 1900. In 1905, [[Albert Einstein]] suggested that light is composed of discrete packets (''[[quanta]]'') in order to explain the [[photoelectric effect]]. A decade later, [[Niels Bohr]] proposed a model of the atom in which [[angular momentum]] is quantized. Eventually, the mathematical formalism that became known as quantum mechanics was developed in the 1920s and 1930s by [[John von Neumann]], [[Hermann Weyl]], and others, after [[Erwin Schrodinger]]'s discovery of wave mechanics and [[Werner Heisenberg]]'s discovery of matrix mechanics.<br />
<br />
==The uncertainty principle==<br />
As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's [[velocity]] is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].<br />
<br />
==Applications==<br />
An important aspect of Quantum Mechanics is the predictions it makes about the [[radioactive decay]] of [[isotopes]]. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second to quintillions of years.<br />
<br />
==See also==<br />
===Concepts in quantum mechanics===<br />
*[[Schrodinger equation]]<br />
*[[Heisenberg uncertainty principle]]<br />
*[[Momentum (operator)]]<br />
===Important contributors to quantum mechanics===<br />
*[[Erwin Schrodinger]]<br />
*[[Werner Heisenberg]]<br />
*[[Niels Bohr]]<br />
*[[Albert Einstein]]<br />
*[[Max Planck]]<br />
<br />
==External Links==<br />
For an excellent discussion of quantum mechanics, see:<br />
http://www.chemistry.ohio-state.edu/betha/qm/<br />
<br />
*[http://www.relativitycalculator.com/compton_effect.shtml The Compton Effect]<br />
<br />
[[Category:Quantum Mechanics]]<br />
[[Category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Uncertainty_principle&diff=508750Uncertainty principle2008-09-01T20:34:46Z<p>Recorder: Redirecting to Heisenberg Uncertainty Principle</p>
<hr />
<div>#REDIRECT [[Heisenberg Uncertainty Principle]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Group_(mathematics)&diff=508044Group (mathematics)2008-08-31T18:49:31Z<p>Recorder: /* Examples */ fix link</p>
<hr />
<div>A '''group''' is a mathematical structure consisting of a set of elements combined with a binary operator which satisfies four conditions:<br />
<br />
#'''Closure''': applying the binary operator to any two elements of the group produces a result which itself belongs to the group<br />
#'''Associativity''': <math>(AB)C = A(BC)</math> where <math>A</math>, <math>B</math> and <math>C</math> are any element of the group<br />
#'''Existence of Identity''': there must exist an identity element <math>I</math> such that <math>IA = AI = A</math>; that is, applying the binary operator to some element <math>A</math> and the identity element <math>I</math> leaves <math>A</math> unchanged<br />
#'''Existence of Inverse''': for each element <math>A</math>, there must exist an inverse <math>A^{-1}</math> such that <math>AA^{-1} = A^{-1}A = I</math><br />
<br />
A group with [[commutative]] binary operator is known as [[Abelian group|Abelian]].<br />
<br />
==Examples==<br />
# the set of [[integers]] <math>\mathbb{Z}</math> under addition: here, zero is the identity, and the inverse of an element <math>a \in \mathbb{Z}</math> is <math>-a</math>. <br />
# the set of the positive [[rational number]]s <math>\mathbb{Q}_+</math> under multiplication: <math>1</math> is the identity, while the inverse of an element <math>\frac{m}{n} \in \mathbb{Q}_+</math> is <math>\frac{n}{m}</math>. <br />
# the Klein four group consists of the set of formal symbols <math>\{1, i, j, k \} </math> with the relations <math> i^{2} =j^{2}=k^{2}=1, \; ij=k, \; jk=i, \; ki=j. </math> All elements of the Klein four group (except the identity 1) have [[order]] 2. The Klein four group is [[isomorphism|isomorphic]] to <math>\mathbb{Z}_{2} \times \mathbb{Z}_{2}</math> under mod addition.<br />
# the set of complex numbers {1, -1, <i>i</i>,<i>-i</i>} under multiplication, where <i>i</i> is the square root of -1, the basis of the [[imaginary number]]s. This group is [[isomorphism|isomorphic]] to <math> \mathbb{Z}_{4} </math> under mod addition.<br />
<br />
Groups are the appropriate mathematical structures for any application involving [[symmetry]].<br />
<br />
[[Category:Algebra]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Group_(mathematics)&diff=508042Group (mathematics)2008-08-31T18:48:57Z<p>Recorder: /* Examples */ specify operation</p>
<hr />
<div>A '''group''' is a mathematical structure consisting of a set of elements combined with a binary operator which satisfies four conditions:<br />
<br />
#'''Closure''': applying the binary operator to any two elements of the group produces a result which itself belongs to the group<br />
#'''Associativity''': <math>(AB)C = A(BC)</math> where <math>A</math>, <math>B</math> and <math>C</math> are any element of the group<br />
#'''Existence of Identity''': there must exist an identity element <math>I</math> such that <math>IA = AI = A</math>; that is, applying the binary operator to some element <math>A</math> and the identity element <math>I</math> leaves <math>A</math> unchanged<br />
#'''Existence of Inverse''': for each element <math>A</math>, there must exist an inverse <math>A^{-1}</math> such that <math>AA^{-1} = A^{-1}A = I</math><br />
<br />
A group with [[commutative]] binary operator is known as [[Abelian group|Abelian]].<br />
<br />
==Examples==<br />
# the set of [[integers]] <math>\mathbb{Z}</math> under addition: here, zero is the identity, and the inverse of an element <math>a \in \mathbb{Z}</math> is <math>-a</math>. <br />
# the set of the positive [[rational numbers]] <math>\mathbb{Q}_+</math> under multiplication: <math>1</math> is the identity, while the inverse of an element <math>\frac{m}{n} \in \mathbb{Q}_+</math> is <math>\frac{n}{m}</math>. <br />
# the Klein four group consists of the set of formal symbols <math>\{1, i, j, k \} </math> with the relations <math> i^{2} =j^{2}=k^{2}=1, \; ij=k, \; jk=i, \; ki=j. </math> All elements of the Klein four group (except the identity 1) have [[order]] 2. The Klein four group is [[isomorphism|isomorphic]] to <math>\mathbb{Z}_{2} \times \mathbb{Z}_{2}</math> under mod addition.<br />
# the set of complex numbers {1, -1, <i>i</i>,<i>-i</i>} under multiplication, where <i>i</i> is the square root of -1, the basis of the [[imaginary number]]s. This group is [[isomorphism|isomorphic]] to <math> \mathbb{Z}_{4} </math> under mod addition.<br />
<br />
Groups are the appropriate mathematical structures for any application involving [[symmetry]].<br />
<br />
[[Category:Algebra]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Wave-particle_duality&diff=507973Wave-particle duality2008-08-31T17:05:56Z<p>Recorder: get cat right, I hope</p>
<hr />
<div>'''Wave-particle duality''' is the concept that matter and energy have both a [[wave]] nature and a [[particle]] nature. It is a fundamental result predicted by [[quantum mechanics]].<br />
<br />
Whether waves or particles are better suited for describing a system depends on the circumstances. For example, light is usually characterized as waves in most every-day applications, but [[photon]]s (light particles) must be considered in some situations, such as the [[photoelectric effect]] and most particle physics experiments.<br />
<br />
[[Category:Physics]]<br />
[[Category:Quantum Mechanics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Wave-particle_duality&diff=507972Wave-particle duality2008-08-31T17:05:16Z<p>Recorder: New page: '''Wave-particle duality''' is the concept that matter and energy have both a wave nature and a particle nature. It is a fundamental result predicted by quantum mechanics. Wh...</p>
<hr />
<div>'''Wave-particle duality''' is the concept that matter and energy have both a [[wave]] nature and a [[particle]] nature. It is a fundamental result predicted by [[quantum mechanics]].<br />
<br />
Whether waves or particles are better suited for describing a system depends on the circumstances. For example, light is usually characterized as waves in most every-day applications, but [[photon]]s (light particles) must be considered in some situations, such as the [[photoelectric effect]] and most particle physics experiments.<br />
<br />
[[Category:Physics]]<br />
[[Category:Quantum mechanics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Quantum_mechanics&diff=507966Quantum mechanics2008-08-31T16:56:38Z<p>Recorder: /* History */ another typo</p>
<hr />
<div>'''Quantum mechanics''' is the branch of [[physics]] that describes the behavior of systems on very small length and energy scales, such as those found in [[atom]]ic and subatomic interactions. It is essential for understanding certain concepts that classical physics cannot explain, such as the discrete nature of small-scale interactions, [[wave-particle duality]], the [[uncertainty principle]], and [[quantum entanglement]]. Quantum mechanics forms the basis for our understanding of many phenomena, including [[chemical reaction]]s and [[radioactive decay]], as well as all computers and electronic devices today.<br />
<br />
==History==<br />
While the roots of quantum mechanics can be traced to experiments performed in the 19th century, the theory began to emerge when [[Max Planck]] proposed a "quantum hypothesis" to explain the energy spectrum of [[black body]] radiation in 1900. In 1905, [[Albert Einstein]] suggested that light is composed of discrete packets (''quanta'') in order to explain the [[photoelectric effect]]. A decade later, [[Niels Bohr]] proposed a model of the atom in which [[angular momentum]] is quantized. Eventually, the mathematical formalism that became known as quantum mechanics was developed in the 1920s and 1930s, with [[Erwin Schrodinger]]'s discovery of wave mechanics and [[Werner Heisenberg]]'s discovery of matrix mechanics.<br />
<br />
==The uncertainty principle==<br />
As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's [[velocity]] is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].<br />
<br />
==Applications==<br />
An important aspect of Quantum Mechanics is the predictions it makes about the [[radioactive decay]] of [[isotopes]]. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second to quintillions of years.<br />
<br />
==See also==<br />
===Concepts in quantum mechanics===<br />
*[[Schrodinger equation]]<br />
*[[Heisenberg uncertainty principle]]<br />
*[[Momentum (operator)]]<br />
===Important contributors to quantum mechanics===<br />
*[[Erwin Schrodinger]]<br />
*[[Werner Heisenberg]]<br />
*[[Niels Bohr]]<br />
*[[Albert Einstein]]<br />
*[[Max Planck]]<br />
<br />
==External Links==<br />
For an excellent discussion of quantum mechanics, see:<br />
http://www.chemistry.ohio-state.edu/betha/qm/<br />
<br />
[[Category:Quantum Mechanics]]<br />
[[Category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Quantum_mechanics&diff=507963Quantum mechanics2008-08-31T16:55:35Z<p>Recorder: whoops</p>
<hr />
<div>'''Quantum mechanics''' is the branch of [[physics]] that describes the behavior of systems on very small length and energy scales, such as those found in [[atom]]ic and subatomic interactions. It is essential for understanding certain concepts that classical physics cannot explain, such as the discrete nature of small-scale interactions, [[wave-particle duality]], the [[uncertainty principle]], and [[quantum entanglement]]. Quantum mechanics forms the basis for our understanding of many phenomena, including [[chemical reaction]]s and [[radioactive decay]], as well as all computers and electronic devices today.<br />
<br />
==History==<br />
While the roots of quantum mechanics can be traced to experiments performed in the 19th century, the theory began to emerge when [[Max Planck]] proposed a "quantum hypothesis" to explain the energy spectrum of [[black body]] radiation in 1900. In 1905, [[Albert Einstein]] suggested that light is composed of discrete packets (''quanta'') in order to explain the [[photoelectric effect]]. A decade later, [[Niels Bohr]] proposed a model of the atom in which [[angular momentum is quantized]]. Eventually, the mathematical formalism that became known as quantum mechanics was developed in the 1920s and 1930s, with [[Erwin Schrodinger]]'s discovery of wave mechanics and [[Werner Heisenberg]]'s discovery of matrix mechanics.<br />
<br />
==The uncertainty principle==<br />
As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's [[velocity]] is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].<br />
<br />
==Applications==<br />
An important aspect of Quantum Mechanics is the predictions it makes about the [[radioactive decay]] of [[isotopes]]. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second to quintillions of years.<br />
<br />
==See also==<br />
===Concepts in quantum mechanics===<br />
*[[Schrodinger equation]]<br />
*[[Heisenberg uncertainty principle]]<br />
*[[Momentum (operator)]]<br />
===Important contributors to quantum mechanics===<br />
*[[Erwin Schrodinger]]<br />
*[[Werner Heisenberg]]<br />
*[[Niels Bohr]]<br />
*[[Albert Einstein]]<br />
*[[Max Planck]]<br />
<br />
==External Links==<br />
For an excellent discussion of quantum mechanics, see:<br />
http://www.chemistry.ohio-state.edu/betha/qm/<br />
<br />
[[Category:Quantum Mechanics]]<br />
[[Category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Quantum_mechanics&diff=507959Quantum mechanics2008-08-31T16:51:20Z<p>Recorder: expand</p>
<hr />
<div>'''Quantum mechanics''' is the branch of [[physics]] that describes the behavior of systems on very small length and energy scales, such as those found in [[atom]]ic and subatomic interactions. It is essential for understanding certain concepts that classical physics cannot explain, such as the discrete nature of small-scale interactions, [[wave-particle duality]], the [[uncertainty principle]], and [[quantum entanglement]]. Quantum mechanics forms the basis for our understanding of many phenomena, including [[chemical reaction]]s and [[radioactive decay]], as well as all computers and electronic devices today.<br />
<br />
==History==<br />
While the roots of quantum mechanics can be traced to experiments performed in the 19th century, the theory began to emerge when [[Max Planck]] proposed a "quantum hypothesis" to explain the energy spectrum of [[black body]] radiation in 1900. In 1905, [[Albert Einstein]] suggested that light is composed of discrete packets (''quanta'') in order to explain the [[photoelectric effect]]. A decade later, [[Neils Bohr]] proposed a model of the atom in which [[angular momentum is quantized]]. Eventually, the mathematical formalism that became known as quantum mechanics was developed in the 1920s and 1930s, with [[Erwin Schrodinger]]'s discovery of wave mechanics and [[Werner Heisenberg]]'s discovery of matrix mechanics.<br />
<br />
==The uncertainty principle==<br />
As a result of the wave nature of the electron, the position of the electron can never be precisely known. Whenever it is attempted to be measured, knowledge of the electron's [[velocity]] is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the [[Heisenberg Uncertainty Principle]].<br />
<br />
==Applications==<br />
An important aspect of Quantum Mechanics is the predictions it makes about the [[radioactive decay]] of [[isotopes]]. Radioactive decay processes, controlled by the wave equations, are random events. A radioactive atom has a certain probability of decaying per unit time. As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time. The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second to quintillions of years.<br />
<br />
==See also==<br />
===Concepts in quantum mechanics===<br />
*[[Schrodinger equation]]<br />
*[[Heisenberg uncertainty principle]]<br />
*[[Momentum (operator)]]<br />
===Important contributors to quantum mechanics===<br />
*[[Erwin Schrodinger]]<br />
*[[Werner Heisenberg]]<br />
*[[Neils Bohr]]<br />
*[[Albert Einstein]]<br />
*[[Max Planck]]<br />
<br />
==External Links==<br />
For an excellent discussion of quantum mechanics, see:<br />
http://www.chemistry.ohio-state.edu/betha/qm/<br />
<br />
[[Category:Quantum Mechanics]]<br />
[[Category:Physics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Natural_number&diff=507944Natural number2008-08-31T16:11:16Z<p>Recorder: </p>
<hr />
<div>In [[mathematics]], a '''natural number''' is a a number from the set {0,1,2,...} or {1,2,3...}, depending on the context and the reference.<ref>0 is usually included in the list of natural numbers in modern textbooks (Bourbaki 1968, Halmos 1974). + Older books sometimes exclude [[zero]], as there is a long history of people thinking that zero is unnatural or not really a number. Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." [http://mathworld.wolfram.com/NaturalNumber.html (Wolfram)] </ref> Natural numbers were used initially for counting ("there are three cows in this field"), but they took on the purpose of ordering as well ("She is the 2nd fastest person alive). These are specific instances of the more general notions of [[cardinality]] and [[ordinality]] which slowly become more complicated as one treats [[infinite]] numbers as well. The set of natural numbers is [[countable]]- via [[bijection]], this property can be used to prove the countability of the [[integer]]s and [[rational number]]s.<br />
<br />
==Axiomatization==<br />
In the late 19th century, [[Giuseppe Peano]] (August 27, 1858 – April 20, 1932) elaborated ''the'' axiomatic system for the Natural Numbers, later named [[Peano's Axioms|Peano Axioms]] in his honor.<br />
==Reference==<br />
<references/><br />
<br />
[[Category:Mathematics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Real_number&diff=500779Talk:Real number2008-08-17T21:42:23Z<p>Recorder: /* Again: Real vs. Imaginary */</p>
<hr />
<div>==Moved comment from Anjruu==<br />
The introduction is actually a blatant misrepresentation of the truth. Real numbers are no more or less "abstract" than imaginary numbers. The author, one must conclude, was trying to allude to the fact that there cannot be an imaginary number of objects, but there cannot be a negative number of objects either. Or perhaps s/he was trying to say that the imaginary numbers cannot be represented on the number line, which is irrelevant, since they can be represented on the complex plane, an equally valid, and more complete, numerical device. Finally, perhaps the author simply meant that the square root of a negative number does not exist, which is wrong. It does exist, in the guise of an imaginary number. While this may seem cyclical, simply because a number is "unusual" does not mean that it is abstract and non-existent.<br />
<br />
Illustrations of this fact, and the incorrectness of the introduction, can be seen when solving differential equations which contain a bifurcation parameter, where the method of eigenvalues must be used. There, an complex, "imaginary" solution to one of several equations often contains eigenvalues and thus a corresponding eigenfunction. Therefore, the real-life existent solution to a real-life existent problem depends on an imaginary number. This exemplifies why complex numbers are just as valid as real numbers, and are not merely an "abstract concept," as the introduction erroneously points out. Or to be more precise, ALL of mathematics is an abstract concept, but there exists an isomorphism to the "real world"; an isomorphism that holds just as strongly in the domain of complex numbers as in the subset of complex numbers, the reals.<br />
<br />
----<br />
<br />
==The "real" world==<br />
Re: this sentence from the intro:<br />
<blockquote><br />
''They are called "real" because they actually exist as quantities in the real world, i.e. as measures, weights, temperatures. In contrast, the imaginary numbers are just an abstract concept, but do not exist concretely in the real world.''<br />
</blockquote><br />
The bulk of that statement simply isn't correct, which is why I removed it earlier. Historically, it was thought that imaginary numbers didn't "really exist," but for the last 200 years or so it's been understood that they do; I believe Cauchy and Gauss were heavily involved in putting that question to bed. Furthermore, there are indeed physical applications of complex numbers. Anything with a magnitude and phase (think alternating current, any harmonic oscillator, communications signals, etc.) is conveniently represented by complex numbers, and they are absolutely essential in quantum mechanics. <br />
:: I second this motion: this sentence should be erased. ''Real numbers'' are as real - or imaginary - as complex numbers. --[[User:DiEb|DiEb]] 15:41, 15 August 2008 (EDT)<br />
'''EDIT:''' I've altered the sentence in question to reflect my comment.--[[User_talk:Recorder|Recorder]] 15:30, 15 August 2008 (EDT)<br />
<br />
==Again: Real vs. Imaginary==<br />
The statement ''The term "real number" is in contrast to the imaginary numbers.'' (RSchlafly) is IMO a false dichotomy and shouldn't be put in the article. <br />
I like the sentence: ''In classical physics, measurements of real world physical objects that can vary smoothly and continuously, like speed or temperature, are treated as real numbers. '' as it doesn't presuppose the existence of real numbers, but - analogously - you can state: ''In physics, measurements of real world physical objects that can vary smoothly and continuously - and exist from an angular compound and an absolute value - like current or voltage, are treated as complex numbers.'' --[[User:DiEb|DiEb]] 16:30, 16 August 2008 (EDT)<br />
<br />
: I don't understand your point. The terms ''real number'' and ''imaginary number'' are in common use. Are you denying that? Are you saying that they are not in contrast? What do you want? [[User:RSchlafly|RSchlafly]] 18:35, 16 August 2008 (EDT)<br />
<br />
:: Of course, I don't deny the terms. And I acknowledge that the ''terms'' - which can be understood in their historical context - are contrasting. But I don't like the idea to think of the ''real numbers'' as more '''real''' than the ''imaginary numbers'' - especially not because of an etymological reasoning: To quote Kronecker: ''"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk"''--[[User:DiEb|DiEb]] 16:47, 17 August 2008 (EDT)<br />
:::Huh? Real numbers are those people concretely use. You can express any amount of dollars with real numbers. What would 3 + 2i dollars mean? Or the length of a segment or a curve: it is "real" and expressed in real numbers. Imaginary numbers are just ''imaginary'' constructions to help our calculations. They don't refer to "real" concepts people use. Thus, the historical meaning of real vs. imaginary is still valid for normal people - and homeschooled students who use Conservapedia to learn. I absolutely agree with RSchlafly. [[User:SilvioB|SilvioB]] 16:53, 17 August 2008 (EDT)<br />
::::Actually, you can express any amount of currency with rational numbers. That doesn't make the real numbers any less "real," does it? Using your logic, I could say "Pi is a real number. What does pi dollars mean? Nothing. Therefore, the real numbers don't exist." Again, imaginary numbers are ''not'' "just imaginary." They exist just as much as any other number, and have several practical applications.--[[User_talk:Recorder|Recorder]] 17:21, 17 August 2008 (EDT)<br />
::::For currency, you use a subset of the rational numbers, i.e., finite decimal fractions (even less, generally: <math>\mathbb{Z} / 100</math>. To speak of <math>\pi</math> dollars (or even $<math>\sqrt{2}</math>) is as surreal as to speak of ''3 + 2i'' dollars. ''Real numbers'' which aren't rational, are just a figment of our imagination, invented to ''help our calculations'', too--[[User:DiEb|DiEb]] 17:25, 17 August 2008 (EDT)<br />
:::::I realized that and that's why I gave a second example, that of the length of a segment. Do you people really consider real numbers and imaginary numbers equal from the point of view of normal people? Let's not forget who is the target of this project. [[User:SilvioB|SilvioB]] 17:30, 17 August 2008 (EDT)<br />
::::::Presumably the purpose of articles like this is to provide accurate information, not to confirm misconceptions caused by terminology. Plenty of people use complex numbers regularly, and just because many people don't isn't a reason to have an inaccuracy in the article.--[[User_talk:Recorder|Recorder]] 17:42, 17 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Real_number&diff=500763Talk:Real number2008-08-17T21:21:02Z<p>Recorder: /* Again: Real vs. Imaginary */</p>
<hr />
<div>==Moved comment from Anjruu==<br />
The introduction is actually a blatant misrepresentation of the truth. Real numbers are no more or less "abstract" than imaginary numbers. The author, one must conclude, was trying to allude to the fact that there cannot be an imaginary number of objects, but there cannot be a negative number of objects either. Or perhaps s/he was trying to say that the imaginary numbers cannot be represented on the number line, which is irrelevant, since they can be represented on the complex plane, an equally valid, and more complete, numerical device. Finally, perhaps the author simply meant that the square root of a negative number does not exist, which is wrong. It does exist, in the guise of an imaginary number. While this may seem cyclical, simply because a number is "unusual" does not mean that it is abstract and non-existent.<br />
<br />
Illustrations of this fact, and the incorrectness of the introduction, can be seen when solving differential equations which contain a bifurcation parameter, where the method of eigenvalues must be used. There, an complex, "imaginary" solution to one of several equations often contains eigenvalues and thus a corresponding eigenfunction. Therefore, the real-life existent solution to a real-life existent problem depends on an imaginary number. This exemplifies why complex numbers are just as valid as real numbers, and are not merely an "abstract concept," as the introduction erroneously points out. Or to be more precise, ALL of mathematics is an abstract concept, but there exists an isomorphism to the "real world"; an isomorphism that holds just as strongly in the domain of complex numbers as in the subset of complex numbers, the reals.<br />
<br />
----<br />
<br />
==The "real" world==<br />
Re: this sentence from the intro:<br />
<blockquote><br />
''They are called "real" because they actually exist as quantities in the real world, i.e. as measures, weights, temperatures. In contrast, the imaginary numbers are just an abstract concept, but do not exist concretely in the real world.''<br />
</blockquote><br />
The bulk of that statement simply isn't correct, which is why I removed it earlier. Historically, it was thought that imaginary numbers didn't "really exist," but for the last 200 years or so it's been understood that they do; I believe Cauchy and Gauss were heavily involved in putting that question to bed. Furthermore, there are indeed physical applications of complex numbers. Anything with a magnitude and phase (think alternating current, any harmonic oscillator, communications signals, etc.) is conveniently represented by complex numbers, and they are absolutely essential in quantum mechanics. <br />
:: I second this motion: this sentence should be erased. ''Real numbers'' are as real - or imaginary - as complex numbers. --[[User:DiEb|DiEb]] 15:41, 15 August 2008 (EDT)<br />
'''EDIT:''' I've altered the sentence in question to reflect my comment.--[[User_talk:Recorder|Recorder]] 15:30, 15 August 2008 (EDT)<br />
<br />
==Again: Real vs. Imaginary==<br />
The statement ''The term "real number" is in contrast to the imaginary numbers.'' (RSchlafly) is IMO a false dichotomy and shouldn't be put in the article. <br />
I like the sentence: ''In classical physics, measurements of real world physical objects that can vary smoothly and continuously, like speed or temperature, are treated as real numbers. '' as it doesn't presuppose the existence of real numbers, but - analogously - you can state: ''In physics, measurements of real world physical objects that can vary smoothly and continuously - and exist from an angular compound and an absolute value - like current or voltage, are treated as complex numbers.'' --[[User:DiEb|DiEb]] 16:30, 16 August 2008 (EDT)<br />
<br />
: I don't understand your point. The terms ''real number'' and ''imaginary number'' are in common use. Are you denying that? Are you saying that they are not in contrast? What do you want? [[User:RSchlafly|RSchlafly]] 18:35, 16 August 2008 (EDT)<br />
<br />
:: Of course, I don't deny the terms. And I acknowledge that the ''terms'' - which can be understood in their historical context - are contrasting. But I don't like the idea to think of the ''real numbers'' as more '''real''' than the ''imaginary numbers'' - especially not because of an etymological reasoning: To quote Kronecker: ''"Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk"''--[[User:DiEb|DiEb]] 16:47, 17 August 2008 (EDT)<br />
:::Huh? Real numbers are those people concretely use. You can express any amount of dollars with real numbers. What would 3 + 2i dollars mean? Or the length of a segment or a curve: it is "real" and expressed in real numbers. Imaginary numbers are just ''imaginary'' constructions to help our calculations. They don't refer to "real" concepts people use. Thus, the historical meaning of real vs. imaginary is still valid for normal people - and homeschooled students who use Conservapedia to learn. I absolutely agree with RSchlafly. [[User:SilvioB|SilvioB]] 16:53, 17 August 2008 (EDT)<br />
::::Actually, you can express any amount of currency with rational numbers. That doesn't make the real numbers any less "real," does it? Using your logic, I could say "Pi is a real number. What does pi dollars mean? Nothing. Therefore, the real numbers don't exist." Again, imaginary numbers are ''not'' "just imaginary." They exist just as much as any other number, and have several practical applications.--[[User_talk:Recorder|Recorder]] 17:21, 17 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Essay:Greatest_Mysteries_of_American_History&diff=499912Talk:Essay:Greatest Mysteries of American History2008-08-15T21:33:01Z<p>Recorder: /* Are some of these really mysteries? */</p>
<hr />
<div>== What scope are we using here? ==<br />
<br />
Would the question of what happened to Jimmy Hoffa, Judge Crater, D. B. Cooper, and other similar famous, historic disappearances fit the article? [[User:Jinxmchue|Jinxmchue]] 00:04, 12 August 2008 (EDT)<br />
<br />
: Good suggestion. I'll add these. I'm not even aware of the Judge Crater mystery, and now you have my curiosity piqued!--[[User:Aschlafly|Aschlafly]] 20:59, 12 August 2008 (EDT)<br />
<br />
::I think the better question is, "What is the definition of 'mystery' being used here?". Some of these items are not so much mysteries as they are speculations of alternate outcomes. For example, "What happened to the Lost Colony?" is a mystery, but "Could the South have possibly won the Civil War?" is speculation. If there's agreement on this, then items #9 and #10 should be removed as not being mysteries, and relocated to new essays or debate pages instead. -[[User:DinsdaleP|DinsdaleP]] 13:39, 14 August 2008 (EDT)<br />
<br />
:::Well, no, that's not what I was asking, but you do have a good point nonetheless. [[User:Jinxmchue|Jinxmchue]] 17:14, 15 August 2008 (EDT)<br />
<br />
::Another: Amelia Earhart. Those four are probably the most famous/recognizable and of the most interest to mystery lovers. [[User:Jinxmchue|Jinxmchue]] 17:18, 15 August 2008 (EDT)<br />
<br />
== Not really mysteries. ==<br />
<br />
# What caused the USS Maine to explode? <br />
The current theory is that there was an explosion on the ship.<br />
# What caused the Great Depression? <br />
An unregulated economy and the dust bowl.<br />
# Did FDR have advance knowledge of the attack on Pearl Harbor? <br />
No... Just no.<br />
# Why did the U-2 spy plane crash-land in the Soviet Union? <br />
A surface to air missile.<br />
<br />
: You're entitled to your opinion, but it's clear you haven't solved these four mysteries. The first answer simply repeats the question; your second is obviously biased and silly; your third shows a lack of understanding of the facts; and your fails to address how high U-2's fly. Keep trying, and maybe you'll learn something in the process.--[[User:Aschlafly|Aschlafly]] 20:58, 12 August 2008 (EDT)<br />
<br />
:: While the U-2 does fly at a very high altitude (25,000 meters)<ref>h</ref>, the missiles in use at that time, S-75 Dvinas, have a higher max altitude, at 33,000 meters.<ref>ttp://www.pakdef.info/pakmilitary/army/sam/sa2guideline.html</ref> With the Maine, I should clarify, the current theory is that a spark in one of the coal shutes caused an explosion.<br />
<br />
::: If a missile hit the U-2 as you claim, then how could it have landed intact with the pilot surviving? This mystery is not solved ... yet.--[[User:Aschlafly|Aschlafly]] 23:43, 12 August 2008 (EDT)<br />
<br />
:::: No one has ever said it landed intact, there was debris, but that is to be expected, and Powers bailed out after the first salvo. 01:19, 13 August 2008 (EDT)<br />
==Columbus==<br />
Not much of a mystery. He took note of the co-ordinates and used a compass. You might as well ask "How did columbus manage to find the exact port he left from".<br />
[[User:PeterSK|PeterSK]] 00:48, 13 August 2008 (EDT)<br />
<br />
Can maybe someone address this? Its not a mystery. Columbus was a gifted sailor and navigator. Its not a mystery all. Thanks!<br />
[[User:PeterSK|PeterSK]] 21:50, 13 August 2008 (EDT)<br />
<br />
: Wow, with your approach, I could teach American History in just a few minutes! George Washington was a "gifted" President, Douglas MacArthur was a "gifted" General, and Ronald Reagan was a "gifted" leader. Somehow I think there's more to the story than that. But thanks for your comment. Godspeed.--[[User:Aschlafly|Aschlafly]] 22:51, 13 August 2008 (EDT)<br />
<br />
::Ronald Reagan was a gifted leader who used the tools he had access to, to govern. Columbus was a gifted sailor and navigator who used a compass, took note of co-ordinates and used the stars. He used the same skills to get back to the exact same port he left from. No mystery! <br />
[[User:PeterSK|PeterSK]] 22:55, 13 August 2008 (EDT)<br />
<br />
::: You could "solve" any mystery with your approach: simply work backwards and declare the successful person to have been "gifted"! In fact, of course, Columbus may not have been any more gifted than the average person. He was more motivated and prayed more, but that is generally not considered to be within the meaning of being "gifted".--[[User:Aschlafly|Aschlafly]] 23:09, 13 August 2008 (EDT)<br />
<br />
Fine, he may/or may not have been gifted but like all sailors of the time he used a compass, navigated using the stars and noted the co-ordinates. Thats how he got back to where he started also. He didnt just blindly sail. Not a mystery. <br />
[[User:PeterSK|PeterSK]] 23:13, 13 August 2008 (EDT)<br />
<br />
I retract the celestial navigation. He used a system called dead reckoning see [http://www.columbusnavigation.com/dr.shtml here]. [[User:PeterSK|PeterSK]] 23:18, 13 August 2008 (EDT)<br />
<br />
Columbus was inspired by God. <br />
*[http://www.lds.org/ldsorg/v/index.jsp?vgnextoid=21bc9fbee98db010VgnVCM1000004d82620aRCRD&locale=0&sourceId=e74d55faa5cab010VgnVCM1000004d82620a____&hideNav=1 Christopher Columbus, Inspired Seaman] <br />
*[http://www.restoredcovenant.org/Document.asp?CAT=Insights&DOC=Christopher+Columbus%3A+Part+II Christopher Columbus: Man of Vision and Faith II] --[[User:DeanS|DeanS<sup>talk</sup>]] 23:25, 13 August 2008 (EDT)<br />
<br />
Inspired by God he was but he still had a compass and still kept logs of his progress and navigated using the Dead Reckoning system. I reiterate, he didnt just blindly sail. [[User:PeterSK|PeterSK]] 23:27, 13 August 2008 (EDT)<br />
<br />
: I'm sure he did use a compass, and also his eyes. But I doubt your claim that he was "gifted" and that such was the reason for his extraordinary results.--[[User:Aschlafly|Aschlafly]] 23:48, 13 August 2008 (EDT)<br />
<br />
:: I think I must be misunderstanding you, Andrew, but are you saying that he was guided by God because he was able to return to the same port he had sailed from? [[User:Konstanty|Konstanty]]07:37, 14 August 2008 (EDT)<br />
<br />
::: Do yourself a favor and learn some history first. I'm saying it is a mystery and it requires effort to try to understand it better. Godspeed.--[[User:Aschlafly|Aschlafly]] 09:30, 14 August 2008 (EDT)<br />
<br />
<br />
:::: I have studied enough world history to know that people were able to sail to distant ports, and return back to their home port using tools and methods still in use today in some parts of the world.<br />
[[User:Konstanty|Konstanty]] [[User:Konstanty|Konstanty]] 09:43, 14 August 2008 (EDT)<br />
<br />
::::: Konstanty, you're long in talk but short in citations to support your talk. Can you give an example from the 15th century of others achieving Columbus's feat, reaching the exact same spot across an ocean as he did?--[[User:Aschlafly|Aschlafly]] 10:14, 14 August 2008 (EDT)<br />
<br />
:::People sailed all over the known world using the same methods. How do you think they got to India, with a GPS system? How did the Vikings get to Greenland and back? These method; compasses, stars, visual observations were basically all we had until maybe a 100 years ago. Why can't you just admit that? It's almost like you don't even know how to use the internet to research this stuff yourself. Just look it up! [[User:MAnderson|MAnderson]] 10:38, 14 August 2008 (EDT)<br />
<br />
::::Columbus was a skilled navigator and had years of experience sailing in the Atlantic. At the time of his voyages, the principles of navigation by celestial observations were well-understood, so where is there a mystery as to how a skilled, experienced navigator could return to a location that had its coordinates documented in a prior voyage? -[[User:DinsdaleP|DinsdaleP]] 13:23, 14 August 2008 (EDT)<br />
<br />
==Pearl Harbour==<br />
<br />
From what I remember from middle school history, the US knew an attack was coming after they picked up the words "east wind, south" (or something similar) in a broadcast to the Japanese embassy. Earlier interceptions confirmed that this would be a signal that negotiations (which had merely been a stalling tactic for some time, anyway) were to end and an attack was imminent. However, most felt the attack would be against British and Dutch territories in Malaysia. By then, however, the Imperial Navy carrier fleet was already in position to launch the attack on Pearl Harbour. This is also covered in some detail in "The Rise and Fall of the Third Reich." --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 07:24, 13 August 2008 (EDT)<br />
<br />
: Could be that the warning signs were erroneously rejected without word getting to [[FDR]], but that seems a bit cavalier in dealing with an attack, doesn't it? Many doubt U.S. intelligence was really that weak. After all, the U.S. had clearly broken the Japanese code prior to the attack.--[[User:Aschlafly|Aschlafly]] 07:35, 13 August 2008 (EDT)r<br />
<br />
::It's possible - WW2 is littered with examples of good intelligence being ignored to the detriment of either side. Although now you have me thinking. First question is why? It would be deliberate treason to allow most of the fleet to be wiped out, giving the Japanese short-term superiority (once Renown and Prince of Wales were sunk too). What could the motivation for that be, besides enter the US into the War, which probably would have happened soon anyway. Then again, were some key ships not moved from harbour a short time before the attack (sorry, my knowledge of the history of the War tends to be more focussed on the Japanese home front, obviously). If they had been in port and destroyed too, the fleet may never have recovered. Why did they leave so soon before the attack (again, I am assuming they did) --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 09:27, 13 August 2008 (EDT)<br />
<br />
::: Two obvious reasons for allowing the attack would be (1) to ensure full American support for fighting the war in Europe, as [[FDR]] wanted to rescue England and (2) not reveal that Americans had broken Japan's codes. Churchill allowed attacks for the same reason as (2).--[[User:Aschlafly|Aschlafly]] 09:36, 13 August 2008 (EDT)<br />
<br />
:::: That does make sense, but it seems to be a high price to pay for secrecy (with regards to 2). --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 09:42, 13 August 2008 (EDT)<br />
<br />
:::::It makes absolutely no sense. Are you saying that FDR allowed the Japanese to destroy most of the Pacific fleet for these reasons? If he hoped to ensure that America entered the war in Europe and he basically knew the Japanese were planning this attack, couldn't he have ordered most of the ships and planes to leave at least 12 hours prior to the attack? Wouldn't almost any attack on American soil sealed the deal? Instead you are suggesting that knowing we would be going to war in the Pacific (at least) that he purposely let this occur thus setting us back for years when he knew there would be tremendous road ahead. In any case, by that time we were basically preparing for war in Europe anyway. We were pouring tons of money and equipment into England. Ever heard of "lend lease"? This mystery is just a conservative smeer against FDR. [[User:MAnderson|MAnderson]] 13:57, 14 August 2008 (EDT)<br />
<br />
:::::: There's no doubt we had broken the Japanese codes, there's no doubt that the attack planes were spotted early on radar, and there's no doubt that [[FDR]] badly wanted something to change public opposition to war. Now, you're free to doubt that FDR allowed the attack, but you're being illogical when you say it would not have made sense. In fact, it would have made perfect sense, and could only be described as highly successful in the long run.<br />
<br />
:::::: Churchill did essentially the same thing in allowing attacks on his soil, and Churchill and FDR conferred closely in the early stages of the war. In fact, though most Americans are unaware of this, Churchill actually stayed for months at the White House during this time! So I don't know why you would say that FDR would never, ever do what we know his friend and mentor Churchill did do!--[[User:Aschlafly|Aschlafly]] 21:43, 14 August 2008 (EDT)<br />
<br />
:::::::Can you site some reputable and current sources for the Churchill thing. I find some allegation that he allowed the bombing of Coventry but that is disputed and most sites don't even mention it. [[User:MAnderson|MAnderson]] 14:31, 15 August 2008 (EDT)<br />
<br />
==President Reagan and SDI==<br />
You ask the question - Where did President Ronald Reagan get the idea and impetus for proposing the Strategic Defense Initiative? <br />
<br />
I found some interesting answers in this document:<br />
<br />
[http://donovaneditorial.com/work/ISDcasestudy1.51130007.pdf CHANGING THE RULES: PRESIDENT RONALD REAGAN’S. STRATEGIC DEFENSE INITIATIVE (SDI) DECISION]<br />
<br />
--[[User:DeanS|DeanS<sup>talk</sup>]] 10:06, 13 August 2008 (EDT)<br />
<br />
: Very, very interesting. I'm going to study that document further and ask some people who might know more. Thanks.--[[User:Aschlafly|Aschlafly]] 10:26, 13 August 2008 (EDT)<br />
<br />
==USS Maine explosion==<br />
You ask the question - What caused the USS Maine to explode?<br />
<br />
While this article doesn't solve the mystery, it does provide an interesting analysis. <br />
[http://www.spanamwar.com/Mainemo1.htm What Destroyed the USS MAINE - An opinion] --[[User:DeanS|DeanS<sup>talk</sup>]] 22:05, 13 August 2008 (EDT)<br />
<br />
==Repeal of Prohibition==<br />
You ask the question - What really caused the repeal of Prohibition?<br />
<br />
This article provides an interesting analysis. According to the article, the problems Prohibition was supposed to solve, got worse. The public became disillusioned with the Prohibition, supporters turned into dissenters and many repeal organizations were formed. The Democrats won the presidential election and the rest is history. <br><br />
[http://www2.potsdam.edu/hansondj/controversies/1131637220.html Repeal of Prohibition in the U.S.] --[[User:DeanS|DeanS<sup>talk</sup>]] 22:28, 13 August 2008 (EDT)<br />
<br />
: Very interesting. I wonder, though, how "disillusioned" the public really was, as opposed to simple politics here and the impact of the [[Great Depression]].--[[User:Aschlafly|Aschlafly]] 22:52, 13 August 2008 (EDT)<br />
<br />
==Vikings in North America==<br />
<br />
Why is this included in a list of mysteries when the landing and settlement of Vikings in Newfoundland has been established, documented and subsequently defended here on Conservapedia? The only source ever cited here on CP to challenge the Vikings' presence in North America concluded that they never reached New England, but definitively stated that they did land and settle in Newfoundland. The Newfoundland site has been excavated and researched over decades by a variety of teams, and accusations by Aschlafly that the settlement there is a hoax using planted evidence have no supporting evidence. Are we also going to question whether the NASA moon landings took place as well? -[[User:DinsdaleP|DinsdaleP]] 13:30, 14 August 2008 (EDT)<br />
<br />
== Are some of these really mysteries? ==<br />
<br />
I understand that many things on this list can legitimately be classified as mysteries, but I'm skeptical about some of them. The items "Could the Civil War have been avoided with a peaceful solution?" and <br />
"Could the South have possibly won the Civil War?" are particularly dubious, since they don't belong to the category of "what actually happened" as much as "speculation about what ''could'' have happened differently had history taken a different course." While such speculation is fun I don't know that this page is appropriate for it. Maybe creating another page for that sort of activity is a good idea--a sort of "How would history be different if..." page.--[[User_talk:Recorder|Recorder]] 15:56, 15 August 2008 (EDT)<br />
:Sorry, didn't see the earlier post making the same point...--[[User_talk:Recorder|Recorder]] 17:33, 15 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Essay:Greatest_Mysteries_of_American_History&diff=499884Talk:Essay:Greatest Mysteries of American History2008-08-15T19:56:54Z<p>Recorder: /* Are some of these really mysteries? */ new section</p>
<hr />
<div>== What scope are we using here? ==<br />
<br />
Would the question of what happened to Jimmy Hoffa, Judge Crater, D. B. Cooper, and other similar famous, historic disappearances fit the article? [[User:Jinxmchue|Jinxmchue]] 00:04, 12 August 2008 (EDT)<br />
<br />
: Good suggestion. I'll add these. I'm not even aware of the Judge Crater mystery, and now you have my curiosity piqued!--[[User:Aschlafly|Aschlafly]] 20:59, 12 August 2008 (EDT)<br />
<br />
::I think the better question is, "What is the definition of 'mystery' being used here?". Some of these items are not so much mysteries as they are speculations of alternate outcomes. For example, "What happened to the Lost Colony?" is a mystery, but "Could the South have possibly won the Civil War?" is speculation. If there's agreement on this, then items #9 and #10 should be removed as not being mysteries, and relocated to new essays or debate pages instead. -[[User:DinsdaleP|DinsdaleP]] 13:39, 14 August 2008 (EDT)<br />
<br />
== Not really mysteries. ==<br />
<br />
# What caused the USS Maine to explode? <br />
The current theory is that there was an explosion on the ship.<br />
# What caused the Great Depression? <br />
An unregulated economy and the dust bowl.<br />
# Did FDR have advance knowledge of the attack on Pearl Harbor? <br />
No... Just no.<br />
# Why did the U-2 spy plane crash-land in the Soviet Union? <br />
A surface to air missile.<br />
<br />
: You're entitled to your opinion, but it's clear you haven't solved these four mysteries. The first answer simply repeats the question; your second is obviously biased and silly; your third shows a lack of understanding of the facts; and your fails to address how high U-2's fly. Keep trying, and maybe you'll learn something in the process.--[[User:Aschlafly|Aschlafly]] 20:58, 12 August 2008 (EDT)<br />
<br />
:: While the U-2 does fly at a very high altitude (25,000 meters)<ref>h</ref>, the missiles in use at that time, S-75 Dvinas, have a higher max altitude, at 33,000 meters.<ref>ttp://www.pakdef.info/pakmilitary/army/sam/sa2guideline.html</ref> With the Maine, I should clarify, the current theory is that a spark in one of the coal shutes caused an explosion.<br />
<br />
::: If a missile hit the U-2 as you claim, then how could it have landed intact with the pilot surviving? This mystery is not solved ... yet.--[[User:Aschlafly|Aschlafly]] 23:43, 12 August 2008 (EDT)<br />
<br />
:::: No one has ever said it landed intact, there was debris, but that is to be expected, and Powers bailed out after the first salvo. 01:19, 13 August 2008 (EDT)<br />
==Columbus==<br />
Not much of a mystery. He took note of the co-ordinates and used a compass. You might as well ask "How did columbus manage to find the exact port he left from".<br />
[[User:PeterSK|PeterSK]] 00:48, 13 August 2008 (EDT)<br />
<br />
Can maybe someone address this? Its not a mystery. Columbus was a gifted sailor and navigator. Its not a mystery all. Thanks!<br />
[[User:PeterSK|PeterSK]] 21:50, 13 August 2008 (EDT)<br />
<br />
: Wow, with your approach, I could teach American History in just a few minutes! George Washington was a "gifted" President, Douglas MacArthur was a "gifted" General, and Ronald Reagan was a "gifted" leader. Somehow I think there's more to the story than that. But thanks for your comment. Godspeed.--[[User:Aschlafly|Aschlafly]] 22:51, 13 August 2008 (EDT)<br />
<br />
::Ronald Reagan was a gifted leader who used the tools he had access to, to govern. Columbus was a gifted sailor and navigator who used a compass, took note of co-ordinates and used the stars. He used the same skills to get back to the exact same port he left from. No mystery! <br />
[[User:PeterSK|PeterSK]] 22:55, 13 August 2008 (EDT)<br />
<br />
::: You could "solve" any mystery with your approach: simply work backwards and declare the successful person to have been "gifted"! In fact, of course, Columbus may not have been any more gifted than the average person. He was more motivated and prayed more, but that is generally not considered to be within the meaning of being "gifted".--[[User:Aschlafly|Aschlafly]] 23:09, 13 August 2008 (EDT)<br />
<br />
Fine, he may/or may not have been gifted but like all sailors of the time he used a compass, navigated using the stars and noted the co-ordinates. Thats how he got back to where he started also. He didnt just blindly sail. Not a mystery. <br />
[[User:PeterSK|PeterSK]] 23:13, 13 August 2008 (EDT)<br />
<br />
I retract the celestial navigation. He used a system called dead reckoning see [http://www.columbusnavigation.com/dr.shtml here]. [[User:PeterSK|PeterSK]] 23:18, 13 August 2008 (EDT)<br />
<br />
Columbus was inspired by God. <br />
*[http://www.lds.org/ldsorg/v/index.jsp?vgnextoid=21bc9fbee98db010VgnVCM1000004d82620aRCRD&locale=0&sourceId=e74d55faa5cab010VgnVCM1000004d82620a____&hideNav=1 Christopher Columbus, Inspired Seaman] <br />
*[http://www.restoredcovenant.org/Document.asp?CAT=Insights&DOC=Christopher+Columbus%3A+Part+II Christopher Columbus: Man of Vision and Faith II] --[[User:DeanS|DeanS<sup>talk</sup>]] 23:25, 13 August 2008 (EDT)<br />
<br />
Inspired by God he was but he still had a compass and still kept logs of his progress and navigated using the Dead Reckoning system. I reiterate, he didnt just blindly sail. [[User:PeterSK|PeterSK]] 23:27, 13 August 2008 (EDT)<br />
<br />
: I'm sure he did use a compass, and also his eyes. But I doubt your claim that he was "gifted" and that such was the reason for his extraordinary results.--[[User:Aschlafly|Aschlafly]] 23:48, 13 August 2008 (EDT)<br />
<br />
:: I think I must be misunderstanding you, Andrew, but are you saying that he was guided by God because he was able to return to the same port he had sailed from? [[User:Konstanty|Konstanty]]07:37, 14 August 2008 (EDT)<br />
<br />
::: Do yourself a favor and learn some history first. I'm saying it is a mystery and it requires effort to try to understand it better. Godspeed.--[[User:Aschlafly|Aschlafly]] 09:30, 14 August 2008 (EDT)<br />
<br />
<br />
:::: I have studied enough world history to know that people were able to sail to distant ports, and return back to their home port using tools and methods still in use today in some parts of the world.<br />
[[User:Konstanty|Konstanty]] [[User:Konstanty|Konstanty]] 09:43, 14 August 2008 (EDT)<br />
<br />
::::: Konstanty, you're long in talk but short in citations to support your talk. Can you give an example from the 15th century of others achieving Columbus's feat, reaching the exact same spot across an ocean as he did?--[[User:Aschlafly|Aschlafly]] 10:14, 14 August 2008 (EDT)<br />
<br />
:::People sailed all over the known world using the same methods. How do you think they got to India, with a GPS system? How did the Vikings get to Greenland and back? These method; compasses, stars, visual observations were basically all we had until maybe a 100 years ago. Why can't you just admit that? It's almost like you don't even know how to use the internet to research this stuff yourself. Just look it up! [[User:MAnderson|MAnderson]] 10:38, 14 August 2008 (EDT)<br />
<br />
::::Columbus was a skilled navigator and had years of experience sailing in the Atlantic. At the time of his voyages, the principles of navigation by celestial observations were well-understood, so where is there a mystery as to how a skilled, experienced navigator could return to a location that had its coordinates documented in a prior voyage? -[[User:DinsdaleP|DinsdaleP]] 13:23, 14 August 2008 (EDT)<br />
<br />
==Pearl Harbour==<br />
<br />
From what I remember from middle school history, the US knew an attack was coming after they picked up the words "east wind, south" (or something similar) in a broadcast to the Japanese embassy. Earlier interceptions confirmed that this would be a signal that negotiations (which had merely been a stalling tactic for some time, anyway) were to end and an attack was imminent. However, most felt the attack would be against British and Dutch territories in Malaysia. By then, however, the Imperial Navy carrier fleet was already in position to launch the attack on Pearl Harbour. This is also covered in some detail in "The Rise and Fall of the Third Reich." --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 07:24, 13 August 2008 (EDT)<br />
<br />
: Could be that the warning signs were erroneously rejected without word getting to [[FDR]], but that seems a bit cavalier in dealing with an attack, doesn't it? Many doubt U.S. intelligence was really that weak. After all, the U.S. had clearly broken the Japanese code prior to the attack.--[[User:Aschlafly|Aschlafly]] 07:35, 13 August 2008 (EDT)r<br />
<br />
::It's possible - WW2 is littered with examples of good intelligence being ignored to the detriment of either side. Although now you have me thinking. First question is why? It would be deliberate treason to allow most of the fleet to be wiped out, giving the Japanese short-term superiority (once Renown and Prince of Wales were sunk too). What could the motivation for that be, besides enter the US into the War, which probably would have happened soon anyway. Then again, were some key ships not moved from harbour a short time before the attack (sorry, my knowledge of the history of the War tends to be more focussed on the Japanese home front, obviously). If they had been in port and destroyed too, the fleet may never have recovered. Why did they leave so soon before the attack (again, I am assuming they did) --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 09:27, 13 August 2008 (EDT)<br />
<br />
::: Two obvious reasons for allowing the attack would be (1) to ensure full American support for fighting the war in Europe, as [[FDR]] wanted to rescue England and (2) not reveal that Americans had broken Japan's codes. Churchill allowed attacks for the same reason as (2).--[[User:Aschlafly|Aschlafly]] 09:36, 13 August 2008 (EDT)<br />
<br />
:::: That does make sense, but it seems to be a high price to pay for secrecy (with regards to 2). --[[User:JessicaT|KotomiT]]<sub>[[User talk:JessicaT|''Ohayo gozaimasu!'']]</sub> 09:42, 13 August 2008 (EDT)<br />
<br />
:::::It makes absolutely no sense. Are you saying that FDR allowed the Japanese to destroy most of the Pacific fleet for these reasons? If he hoped to ensure that America entered the war in Europe and he basically knew the Japanese were planning this attack, couldn't he have ordered most of the ships and planes to leave at least 12 hours prior to the attack? Wouldn't almost any attack on American soil sealed the deal? Instead you are suggesting that knowing we would be going to war in the Pacific (at least) that he purposely let this occur thus setting us back for years when he knew there would be tremendous road ahead. In any case, by that time we were basically preparing for war in Europe anyway. We were pouring tons of money and equipment into England. Ever heard of "lend lease"? This mystery is just a conservative smeer against FDR. [[User:MAnderson|MAnderson]] 13:57, 14 August 2008 (EDT)<br />
<br />
:::::: There's no doubt we had broken the Japanese codes, there's no doubt that the attack planes were spotted early on radar, and there's no doubt that [[FDR]] badly wanted something to change public opposition to war. Now, you're free to doubt that FDR allowed the attack, but you're being illogical when you say it would not have made sense. In fact, it would have made perfect sense, and could only be described as highly successful in the long run.<br />
<br />
:::::: Churchill did essentially the same thing in allowing attacks on his soil, and Churchill and FDR conferred closely in the early stages of the war. In fact, though most Americans are unaware of this, Churchill actually stayed for months at the White House during this time! So I don't know why you would say that FDR would never, ever do what we know his friend and mentor Churchill did do!--[[User:Aschlafly|Aschlafly]] 21:43, 14 August 2008 (EDT)<br />
<br />
:::::::Can you site some reputable and current sources for the Churchill thing. I find some allegation that he allowed the bombing of Coventry but that is disputed and most sites don't even mention it. [[User:MAnderson|MAnderson]] 14:31, 15 August 2008 (EDT)<br />
<br />
==President Reagan and SDI==<br />
You ask the question - Where did President Ronald Reagan get the idea and impetus for proposing the Strategic Defense Initiative? <br />
<br />
I found some interesting answers in this document:<br />
<br />
[http://donovaneditorial.com/work/ISDcasestudy1.51130007.pdf CHANGING THE RULES: PRESIDENT RONALD REAGAN’S. STRATEGIC DEFENSE INITIATIVE (SDI) DECISION]<br />
<br />
--[[User:DeanS|DeanS<sup>talk</sup>]] 10:06, 13 August 2008 (EDT)<br />
<br />
: Very, very interesting. I'm going to study that document further and ask some people who might know more. Thanks.--[[User:Aschlafly|Aschlafly]] 10:26, 13 August 2008 (EDT)<br />
<br />
==USS Maine explosion==<br />
You ask the question - What caused the USS Maine to explode?<br />
<br />
While this article doesn't solve the mystery, it does provide an interesting analysis. <br />
[http://www.spanamwar.com/Mainemo1.htm What Destroyed the USS MAINE - An opinion] --[[User:DeanS|DeanS<sup>talk</sup>]] 22:05, 13 August 2008 (EDT)<br />
<br />
==Repeal of Prohibition==<br />
You ask the question - What really caused the repeal of Prohibition?<br />
<br />
This article provides an interesting analysis. According to the article, the problems Prohibition was supposed to solve, got worse. The public became disillusioned with the Prohibition, supporters turned into dissenters and many repeal organizations were formed. The Democrats won the presidential election and the rest is history. <br><br />
[http://www2.potsdam.edu/hansondj/controversies/1131637220.html Repeal of Prohibition in the U.S.] --[[User:DeanS|DeanS<sup>talk</sup>]] 22:28, 13 August 2008 (EDT)<br />
<br />
: Very interesting. I wonder, though, how "disillusioned" the public really was, as opposed to simple politics here and the impact of the [[Great Depression]].--[[User:Aschlafly|Aschlafly]] 22:52, 13 August 2008 (EDT)<br />
<br />
==Vikings in North America==<br />
<br />
Why is this included in a list of mysteries when the landing and settlement of Vikings in Newfoundland has been established, documented and subsequently defended here on Conservapedia? The only source ever cited here on CP to challenge the Vikings' presence in North America concluded that they never reached New England, but definitively stated that they did land and settle in Newfoundland. The Newfoundland site has been excavated and researched over decades by a variety of teams, and accusations by Aschlafly that the settlement there is a hoax using planted evidence have no supporting evidence. Are we also going to question whether the NASA moon landings took place as well? -[[User:DinsdaleP|DinsdaleP]] 13:30, 14 August 2008 (EDT)<br />
<br />
== Are some of these really mysteries? ==<br />
<br />
I understand that many things on this list can legitimately be classified as mysteries, but I'm skeptical about some of them. The items "Could the Civil War have been avoided with a peaceful solution?" and <br />
"Could the South have possibly won the Civil War?" are particularly dubious, since they don't belong to the category of "what actually happened" as much as "speculation about what ''could'' have happened differently had history taken a different course." While such speculation is fun I don't know that this page is appropriate for it. Maybe creating another page for that sort of activity is a good idea--a sort of "How would history be different if..." page.--[[User_talk:Recorder|Recorder]] 15:56, 15 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Real_number&diff=499879Talk:Real number2008-08-15T19:39:56Z<p>Recorder: </p>
<hr />
<div>==Moved comment from Anjruu==<br />
The introduction is actually a blatant misrepresentation of the truth. Real numbers are no more or less "abstract" than imaginary numbers. The author, one must conclude, was trying to allude to the fact that there cannot be an imaginary number of objects, but there cannot be a negative number of objects either. Or perhaps s/he was trying to say that the imaginary numbers cannot be represented on the number line, which is irrelevant, since they can be represented on the complex plane, an equally valid, and more complete, numerical device. Finally, perhaps the author simply meant that the square root of a negative number does not exist, which is wrong. It does exist, in the guise of an imaginary number. While this may seem cyclical, simply because a number is "unusual" does not mean that it is abstract and non-existent.<br />
<br />
Illustrations of this fact, and the incorrectness of the introduction, can be seen when solving differential equations which contain a bifurcation parameter, where the method of eigenvalues must be used. There, an complex, "imaginary" solution to one of several equations often contains eigenvalues and thus a corresponding eigenfunction. Therefore, the real-life existent solution to a real-life existent problem depends on an imaginary number. This exemplifies why complex numbers are just as valid as real numbers, and are not merely an "abstract concept," as the introduction erroneously points out. Or to be more precise, ALL of mathematics is an abstract concept, but there exists an isomorphism to the "real world"; an isomorphism that holds just as strongly in the domain of complex numbers as in the subset of complex numbers, the reals.<br />
<br />
----<br />
<br />
==The "real" world==<br />
Re: this sentence from the intro:<br />
<blockquote><br />
''They are called "real" because they actually exist as quantities in the real world, i.e. as measures, weights, temperatures. In contrast, the imaginary numbers are just an abstract concept, but do not exist concretely in the real world.''<br />
</blockquote><br />
The bulk of that statement simply isn't correct, which is why I removed it earlier. Historically, it was thought that imaginary numbers didn't "really exist," but for the last 200 years or so it's been understood that they do; I believe Cauchy and Gauss were heavily involved in putting that question to bed. Furthermore, there are indeed physical applications of complex numbers. Anything with a magnitude and phase (think alternating current, any harmonic oscillator, communications signals, etc.) is conveniently represented by complex numbers, and they are absolutely essential in quantum mechanics. '''EDIT:''' I've altered the sentence in question to reflect my comment.--[[User_talk:Recorder|Recorder]] 15:30, 15 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Real_number&diff=499878Real number2008-08-15T19:37:57Z<p>Recorder: fixing misconception--please see talk</p>
<hr />
<div>'''Real numbers''' are numbers that can be represented by some infinite or finite [[decimal]] representation, such as 0.707106781187...<br />
<br />
The term "real number" exists for historical reasons; it was once thought that such numbers "actually" existed (hence the word "real"), in contrast to the supposed non-existence of [[imaginary number]]s. However, advances in [[complex analysis]] in the 19th century revealed that imaginary numbers do, in fact, exist, and the terminology of "real" and "imaginary" is now understood to be just that--terminology.<br />
<br />
In classical physics, measurements of things that can vary smoothly and continuously, like [[speed]] or [[temperature]], are treated as real numbers.<br />
<br />
In a number line representation, the real numbers correspond to all the points on a geometric line. The distance between any two points on a line is a real number.<br />
<br />
In computer programming, some computer languages such as [[FORTRAN]] include a ''real'' data type that is intended to represent real numbers.<ref>In reality, the actual values the computer uses are very-high-precision fractions which can equal or approximate real numbers</ref><br />
<br />
The real numbers include within them all of these other kinds of numbers:<br />
<br />
*The "natural numbers" or positive integers, 1, 2, 3, ...<br />
*Zero and the negative integers<br />
*Fractions, like 355/113<br />
*Any decimal representation which terminates (comes to an end), like 6.023, because this is just a way of writing a fraction (in this case, 6023/1000)<br />
*Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions{{prove}}<br />
*[[Irrational numbers]], like <math>\sqrt{10} = 3.162277660168...</math>&pi; = 3.1415926525..., whose decimal representations never repeat or terminate.<br />
<br />
==Formal definition==<br />
<br />
Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[ordered]], [[Complete (mathematics)|complete]], and [[Archimedean]]. The reals can be constructed from the [[rationals]] by means of [[Dedekind cut]]s or [[Cauchy sequence]]s, i.e. it is the completion of the [[metric space]] of rational numbers.<br />
<br />
==Infinity==<br />
<br />
The real numbers ''do not'' include <math>\infty</math> or <math>-\infty</math> (infinity and minus infinity). However, there are non-standard models of real numbers which include <math>\infty</math> or include both <math>\infty</math> and <math>-\infty</math>.<br />
<br />
There is no largest real number, because you can always make a real number larger by adding 1 (or 137.035 or 6.023&middot;10<sup>23</sup>) to it, and no smallest real number, because you can always make a real number smaller by subtracting from it. <br />
<br />
Every real number is finite. One way to see this is to observe that you cannot subtract infinity from itself&mdash;the result is indeterminate&mdash;but, for any real number '''''x,''''' then '''''x - x = 0''''', exactly.<br />
<br />
It is sometimes convenient to have a set of numbers that ''does'' include infinity. For example, in computer programming, "real arithmetic" is often done by a specific system defined by standard IEEE 754-1985; this system is built in to modern processor chips. It provides for values which print out as INF and -INF and which participate in arithmetic as if they were numbers. Thus, division by zero, which was often an error that stopped calculation on older machines, can be a legal operation which simply produces a +INF or -INF result. The system of numbers implemented in IEEE 754 is known in mathematics as the "affinely extended real numbers."<br />
<br />
==Notes and references==<br />
<references/><br />
<br />
[[Category:Mathematics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Talk:Real_number&diff=499877Talk:Real number2008-08-15T19:30:07Z<p>Recorder: </p>
<hr />
<div>==Moved comment from Anjruu==<br />
The introduction is actually a blatant misrepresentation of the truth. Real numbers are no more or less "abstract" than imaginary numbers. The author, one must conclude, was trying to allude to the fact that there cannot be an imaginary number of objects, but there cannot be a negative number of objects either. Or perhaps s/he was trying to say that the imaginary numbers cannot be represented on the number line, which is irrelevant, since they can be represented on the complex plane, an equally valid, and more complete, numerical device. Finally, perhaps the author simply meant that the square root of a negative number does not exist, which is wrong. It does exist, in the guise of an imaginary number. While this may seem cyclical, simply because a number is "unusual" does not mean that it is abstract and non-existent.<br />
<br />
Illustrations of this fact, and the incorrectness of the introduction, can be seen when solving differential equations which contain a bifurcation parameter, where the method of eigenvalues must be used. There, an complex, "imaginary" solution to one of several equations often contains eigenvalues and thus a corresponding eigenfunction. Therefore, the real-life existent solution to a real-life existent problem depends on an imaginary number. This exemplifies why complex numbers are just as valid as real numbers, and are not merely an "abstract concept," as the introduction erroneously points out. Or to be more precise, ALL of mathematics is an abstract concept, but there exists an isomorphism to the "real world"; an isomorphism that holds just as strongly in the domain of complex numbers as in the subset of complex numbers, the reals.<br />
<br />
----<br />
<br />
==The "real" world==<br />
Re: this sentence from the intro:<br />
<blockquote><br />
''They are called "real" because they actually exist as quantities in the real world, i.e. as measures, weights, temperatures. In contrast, the imaginary numbers are just an abstract concept, but do not exist concretely in the real world.''<br />
</blockquote><br />
The bulk of that statement simply isn't correct, which is why I removed it earlier. Historically, it was thought that imaginary numbers didn't "really exist," but for the last 200 years or so it's been understood that they do; I believe Cauchy and Gauss were heavily involved in putting that question to bed. Furthermore, there are indeed physical applications of complex numbers. Anything with a magnitude and phase (think alternating current, any harmonic oscillator, communications signals, etc.) is conveniently represented by complex numbers, and they are absolutely essential in quantum mechanics.--[[User_talk:Recorder|Recorder]] 15:30, 15 August 2008 (EDT)</div>Recorderhttps://www.conservapedia.com/index.php?title=Real_number&diff=497288Real number2008-08-08T18:12:40Z<p>Recorder: rm common misunderstanding about "real" and "imaginary" terminology</p>
<hr />
<div>'''Real numbers''' are numbers that can be represented by some infinite or finite decimal representation, such as 0.707106781187...<br />
<br />
In classical physics, measurements of things that can vary smoothly and continuously, like [[speed]] or [[temperature]], are treated as real numbers.<br />
<br />
In a number line representation, the real numbers correspond to all the points on a geometric line. The distance between any two points on a line is a real number.<br />
<br />
In computer programming, some computer languages such as [[FORTRAN]] include a ''real'' data type that is intended to represent real numbers.<ref>In reality, the actual values the computer uses are very-high-precision fractions which can equal or approximate real numbers</ref><br />
<br />
The real numbers include within them all of these other kinds of numbers:<br />
<br />
*The "natural numbers" or positive integers, 1, 2, 3, ...<br />
*Zero and the negative integers<br />
*Fractions, like 355/113<br />
*Any decimal representation which terminates (comes to an end), like 6.023, because this is just a way of writing a fraction (in this case, 6023/1000)<br />
*Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions{{prove}}<br />
*[[Irrational numbers]], like <math>\sqrt{10} = 3.162277660168...</math>&pi; = 3.1415926525..., whose decimal representations never repeat or terminate.<br />
<br />
==Formal definition==<br />
<br />
Formally, real numbers are defined as the unique [[Field (mathematics)|field]] which is [[ordered]], [[Complete (mathematics)|complete]], and [[Archimedean]]. The reals can be constructed from the [[rationals]] by means of [[Dedekind cut]]s or [[Cauchy sequence]]s, i.e. it is the completion of the [[metric space]] of rational numbers.<br />
<br />
==Infinity==<br />
<br />
The real numbers ''do not'' include <math>\infty</math> or <math>-\infty</math> (infinity and minus infinity). However, there are non-standard models of real numbers which include <math>\infty</math> or include both <math>\infty</math> and <math>-\infty</math>.<br />
<br />
There is no largest real number, because you can always make a real number larger by adding 1 (or 137.035 or 6.023&middot;10<sup>23</sup>) to it, and no smallest real number, because you can always make a real number smaller by subtracting from it. <br />
<br />
Every real number is finite. One way to see this is to observe that you cannot subtract infinity from itself&mdash;the result is indeterminate&mdash;but, for any real number '''''x,''''' then '''''x - x = 0''''', exactly.<br />
<br />
It is sometimes convenient to have a set of numbers that ''does'' include infinity. For example, in computer programming, "real arithmetic" is often done by a specific system defined by standard IEEE 754-1985; this system is built in to modern processor chips. It provides for values which print out as INF and -INF and which participate in arithmetic as if they were numbers. Thus, division by zero, which was often an error that stopped calculation on older machines, can be a legal operation which simply produces a +INF or -INF result. The system of numbers implemented in IEEE 754 is known in mathematics as the "affinely extended real numbers."<br />
<br />
==Notes and references==<br />
<references/><br />
<br />
[[Category:Mathematics]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Chess&diff=490238Chess2008-07-15T01:21:34Z<p>Recorder: /* Relative Value of Pieces */ b/c Knights (generally) < Bishops</p>
<hr />
<div>[[Image:Staunton chess set.jpg|right|thumb|300px|A typical chess set and tournament clock.]]<br />
<br />
'''Chess''' is a turn-based [[board game]] for two players, and is one of the most popular games in the world. The goal of the game is to place the opposing king into ''checkmate'', that is, a position in which the king is under attack but cannot escape. The game used to be treated as a status symbol of education and aristocracy and in recent times has become to be known as an [[elitist]]'s game.<br />
<br />
Modern international chess has a powerful, sweeping [[queen]] who was not a piece provided in the original game. The long reach of bishops today was also lacking at first. Maneuvers such as castling or capturing ''en passant'' have been developed within the past few hundred years.<br />
<br />
Today, chess is one of the most popular board games in the world. International competitions, including world [[champion]]ship events, are organized by an organization called FIDE and American competition organized by the USCF (United States Chess Federation). The only American world champion was [[Bobby Fischer]], although [[Paul Morphy]] of [[Louisiana]] was likely the strongest player in the world in the 1850s, before a formal world champion was determined. The current world champion is [[India | Indian]] Viswanathan "Vishy" Anand.<br />
<br />
==Origins==<br />
Chess has its roots in [[India]], where a game called Shaturanga was played. The earliest extant description of the game is contained in the [[Bhavishya Purana]], which dates from A.D. 300 to A.D. 600. Shaturanga used [[dice]], but [[Hinduism]] bans gambling. As a result, the game of chess developed free from any dice or chance. The exact rules of Shaturanga are not known, but the game developed further in Persia into something very like its modern form. The Persian game Shatranj - which remains popular in the middle east today - is nearly identical to modern chess. By A.D. 1200 the game reached southern Europe, and in the late fifteenth century the Europeans adopted a number of changes: the queen, which had formerly been a very weak piece, became the strongest piece on the board, and allowing pawns to move two squares on the first move became standard. These changes had the effect of speeding up play, and they brought the game into the form we know today.<br />
<br />
There has been some speculation that chess has roots in [[China]]. It's clear that chess is in some way related to [[XiangQi]] (Chinese Chess) and [[Shogi]] (Japanese Chess), but scholars disagree about whether either of these variants predates Shaturanga.<br />
<br />
==The Board==<br />
The chess board is a square, divided into 64 smaller squares arranged in eight rows of eight. The squares are alternating light and dark, with a light square in the bottom right hand corner. A chess board is the same as a [[Checkers|checker board]].<br />
<br />
The horizontal rows of squares are referred to as "ranks" and the vertical rows are referred to as "files".<br />
<br />
==Pieces==<br />
[[Image:StauntonPieces.jpg|right|thumb|300px|Staunton Style chess pieces. From left to right: King, Queen, Bishop, Knight, Rook, and Pawn.]]<br />
Each player has a total of 16 pieces; 8 pawns, 2 knights, 2 bishops, 2 rooks, 1 queen, and 1 king.<br><br />
<br />
===Relative Value of Pieces===<br />
There are several different ideas about the relative value of the pieces. It is important to note that the "points" used to assign a value to each piece are hypothetical and do not constitute a score; they are merely an attempt to quantify the relative power that each piece can hypothetically exert upon the board.<br />
<br />
The method most often used is:<br />
*[[Image:chesspawn.jpg|20px]] Pawn--1 <br />
*[[Image:chessknight.jpg|20px]] Knight--3 (some say 2.5, as Knights are generally regarded as slightly inferior to Bishops in many middlegame and endgame situations)<br />
*[[Image:chessbishop.jpg|20px]] Bishop--3<br />
*[[Image:chessrook.jpg|20px]] Rook--5<br />
*[[Image:chessqueen.jpg|20px]] Queen--9 <br />
*[[Image:chessking.jpg|20px]] King--Priceless, since its loss means the loss of the game. However, as an active piece in the endgame it is usually considered to have a value of 3.<br />
<BR>(The value to the player of some pieces will actually vary during the course of the game, for instance, in an endgame, the King has an attacking power of about 3)<br />
<br />
===Style===<br />
The most popular style of pieces are known as Staunton style pieces, the tournament standard for chess pieces, although other types exist. Often, popular themed chess sets will appear with characters from [[popular culture]] or [[fiction]] taking the places of the more common Staunton style pieces. These novelty pieces are not tournament sanctioned however, and can sometimes cause confusion during game play as to which piece is which.<br />
<br />
Although chess pieces can come in a variety of materials, [[marble]] and [[glass]] tend to be very popular, but for most chess tournaments, simple [[plastic]] pieces are usually favored. Also, while many home chess sets use heavy boards made out of [[wood]] or [[stone]] or some [[polymer]] material, tournament boards are actually roll-able mats with the board printed on it.<br />
<br />
==Gameplay ==<br />
<br />
The object of the game is to checkmate the other player's '''King''' before he checkmates your king. When a pawn reaches the far side of the board, it may be promoted to any other piece (except a King).<br />
<br />
*The players alternate moving until the game has ended.<br />
*The player with the White pieces always moves first.<br />
<br />
===Initial Conditions===<br />
The pieces are put on the board in each player's side as follows:<br />
*In the first row from left to right (with the leftmost square being black): '''rook''', '''knight''', '''bishop''', '''queen''', '''king''', '''bishop''', '''knight''' and '''rook'''.<br />
*The second row is filled with '''pawns'''.<br />
<br />
===Movement===<br />
The pieces move as follows.<br />
*The '''pawn''' moves one square forward, except when moving from its opening position, when it can optionally move two. The pawn is the only piece that captures in a way different from the way it moves. It captures opposing pieces by capturing one square diagonally forward. When another piece is on the square directly in front of a pawn it cannot move unless it is making a capture. <br><br />
*The '''knight''', which is the only piece that can jump over other pieces, moves one square in one straight direction and two in the other.<br><br />
*The '''bishop''' can move as many squares as desired diagonally.<br><br />
*The '''rook''' can move as many squares as desired in a straight direction.<br><br />
*The '''queen''' is the most powerful piece in the board. It can move as many squares as desired (without jumping over another piece), either straight or diagonally.<br><br />
*The '''king''', which is the most important piece on the board, moves one square, either straight or diagonally.<br />
<br />
====Capturing====<br />
<br />
All pieces except for the pawn capture along their lines of motion. A capture is made by moving a piece to a square occupied by one of the opponent's pieces, and removing the opponent's piece from the board. If a piece can move to occupy the location of an opponent's piece, it can capture that piece. The '''pawn''', can only capture by moving diagonally forward one square. A piece is said to be undefended if it has no piece "supporting" its position - i.e., preventing an opponent from capturing it by threat of losing his attacking piece.<br />
<br />
====Special Moves====<br />
*'''Castling'''- When a player has no pieces between a rook and his king, and he has not moved either piece, he can move the king two squares in the direction of the rook, and then place the rook on the square that the king passed over. A player cannot castle if the King is currently in check, would be in check after castling, or would move through a square which is under attack.<br />
*'''en passant'''- French for "In passing." In chess, if a player pushes his pawn far down to the end of the board, and his opponent pushes a starting pawn 2 spaces ahead, to put the pawn on the same row to avoid confrontation, the player may choose to invoke the "en passant" move, which treats the enemy pawn as though it had only moved one space. The player may capture diagonally on the square '''behind''' the enemy pawn, and remove the enemy pawn. The principle is that the two space rule for a pawn's first move cannot be used to avoid confrontation between two pawns. However, the player may only invoke "en passant" on the first turn after the opponent pushes his pawn. He cannot make it after that turn.<br />
<br />
===The end of the game===<br />
A chess game may end in a number of ways.<br />
*'''Checkmate''': The winning player checkmates his opponent's King (see below).<br />
*'''Resignation''': The losing player, facing an inevitable future checkmate, ''resigns'' rather than play out an extended series of hopeless moves. A player may indicate resignation by toppling his king on its side. <br />
*'''Loss on Time''': In games with a time limit, a player may lose by failing to make a time control, causing his clock to run out.<br />
*'''Draw''': The game may end in a draw, in which case neither player wins.<br />
<br />
====Checkmate====<br />
Checkmate is achieved when the following conditions are met. <br />
* The King is ''in check''; that is, it is directly attacked by an opponent's piece.<br />
* Every square that the King can move to is also attacked by an opponent's piece. <br />
* The Piece that is attacking the King cannot be captured. <br />
* Another Piece cannot be interposed between the attacking piece and the King to block the check.<br />
When a King is checkmated, the game is over, and the player initiating the checkmate is the winner.<br />
<br />
====Draw====<br />
There are several ways that the game can end in a draw. <br />
*'''Stalemate''': A player is said to be ''stalemated'' when he cannot make a legal move, and is not in check.<br />
*'''Draw by agreement''': The players mutually agree to a draw. In competitive chess, a player may make a draw offer after he has made his move, but before he has started his opponent's clock.<br />
*'''Draw by repetition''': Either player may claim a draw if the same position has appeared on the board three times. The three occasions need not be consecutive.<br />
*'''50 move rule''': Either player may claim a draw if fifty moves have transpired without a capture or a pawn move.<br />
<br />
==Notation==<br />
Chess notation is used to record the moves of a chess game. This has several uses. Notation can be used to record games for review at a later time. There are two major methods of chess notation, Algebraic and Descriptive.<br />
<br />
====For all forms of Notation====<br />
The notation for a chess game is taken like this. At the top of the page are the players &mdash; white listed first &mdash; with their names under their colors. Numbers go down the left side of the page to indicate the move number. (see below) <BR><br />
White, Black<BR><br />
Name Name<br />
1.<BR><br />
2.<BR><br />
3.<BR><br />
4.<BR><br />
5.<BR><br />
<br />
Moves are recorded in columns, separated by commas.<br />
<br />
Space is usually allotted on the top of tournament scoresheets to record the date and location of the game, and sometimes to record the time limit and opening name.<br />
<br />
=====Pieces=====<br />
Each piece is designated by its corresponding letter as follows:<br><br />
K = King<BR><br />
Q = Queen<BR><br />
R = Rook<BR><br />
B = Bishop<BR><br />
N = Knight (notice 'K' is reserved for the King)<BR> <br />
P = Pawn<br />
<br />
(In strict chess parlance, the pawns are not considered pieces; officially, a standard chess set consists of sixteen pieces <i>and</i> sixteen pawns.)<br />
<br />
=====Moves=====<br />
- Moves to<br />
x Captures<br />
+ Check<br />
++ Checkmate<br />
0-0 Castles king-side<br />
0-0-0 Castles queen-side<br />
e.p. en passant<br />
/ to indicate which square a piece moved from (only when needed to clarify)<br />
/Q Pawn promotion. (use /Q for queen, /R for rook, etc.)<br />
! A good move<br />
!! A very good move<br />
!? An interesting move<br />
?! A dubious move<br />
? A questionable move<br />
?? A blunder<br />
<br />
===Algebraic===<br />
Algebraic is the most commonly used method of notation. [[Image:Chessboardanote1.jpg|right]]<br />
<br />
====The Board====<br />
In algebraic notation, each file is assigned a letter, and each rank is assigned a number. Each square is designated by the letter and number from it's rank and file. a1 is the square in the bottom left corner for the white player.<br />
<br />
====Movement====<br />
Moves are recorded by indicating the piece to be moved and the square it is to be moved to, sometimes using a hyphen (-). For example, if white wants to move his Kingside Knight towards the center of the board to start the game, the notation would be: <br />
White Black <br />
1. Nf3, ....<br />
<br />
or<br />
<br />
White Black <br />
1. N-f3, ....<br />
<br />
In algebraic notation, a P is not used to indicate the pawn. A pawn move is implied when no piece is indicated. So if white wants to advance his king pawn 2 squares, and black responds by advancing his king pawn 2 squares, the notation would be:<br />
White Black <br />
1. e4, e5,<br />
2. ....<br />
<br />
Occasionally, two pieces of the same type can move to the same square. To eliminate ambiguity, the unique rank or file of the moving piece is identified after the piece symbol. For example, suppose both of Black's Rooks are on the 8th rank (on the squares f8 and a8), and there are no pieces in between them. Black moves the f8 Rook to d8. In other circumstances, the move would be annotated<br />
17. .... Rd8<br />
but because either Rook could have moved to d8, the identifying file for the f8 Rook must be included, as in<br />
17. .... Rfd8<br />
<br />
====Captures====<br />
Captures by a piece or pawn are indicated by first transcribing the symbol for the piece performing the capture, followed by an 'x', followed by the square the capturing piece or pawn moved to. For example, if White uses his Queen to capture a piece on the square h7 on move 23, the correct notation is <br />
23. Qxh7, ....<br />
<br />
Because pawns are not designated with a symbol, the system is slightly different for pawn captures. The file originally occupied by the pawn is used to identify the pawn performing the capture. If a black pawn on e5 captures a white piece or pawn on d4 on move 5, the notation is<br />
5. ...., exd4<br />
<br />
===Descriptive===<br />
In the more archaic descriptive notation, squares are described according to the starting piece positions. The square originally occupied by the Rook on the Queenside is referred to as "Queen's Rook One" (QR1), while "Queen's Rook Four" is the square directly in front of the Queen's Rook on the fourth rank. Thus, a typical opening move is described as "Pawn to King Four", and is written as <br />
1. P-K4, ....<br />
<br />
Note that in descriptive notation, pawns have the designation 'P'. The notation's disadvantages become apparent over the course of a complex game, especially because the same square has different names depending on the perspective of the White and Black pieces. King's Bishop Three (KB3) for White is King's Bishop Six (KB6) for Black.<br />
<br />
Captures in descriptive notation operate similar to algebraic notation; for example, <br />
<br />
45. .... R-xQN7<br />
<br />
means that on his 45th move, Black captured a piece or pawn on his Queen's Knight Seven square (the b2 square in algebraic notation).<br />
<br />
==Tactics and strategy==<br />
Chess players often refer to shorter, forcing sequences of moves that lead to clear advantages as ''tactics'', while moves designed to create or nurture long-term advantages are called ''strategic.''<br />
<br />
For more information on specific tactics, see [[chess tactics]]. For more information on specific strategic themes, see [[chess strategies]].<br />
<br />
==Chess Variants==<br />
There are a number of games based on chess with rule variations, and these are referred to as ''chess variants''. One of the most popular of these is ''Bughouse'', a partner-based game in which a player who captures his opponent's piece can give it to a partner on another board to drop on a square of his choosing. Another is ''Kriegspiel'', a game in which a player can see his pieces but not that of his opponent. [http://www.chessvariants.com/incinf.dir/kriegspiel.html] A simpler variant is ''Antichess'', which is also called ''Suicide chess'', in which a player must make a capturing move if any legal captures exist on the board, and in which the goal is to run out of pieces first.<br />
<br />
In 1996, [[Bobby Fischer]] introduced a variant called FischerRandom Chess, which involves scrambling the positions of the pieces on the first and eighth ranks before starting play. A number of rules govern the precise manner in which the pieces can be arranged; for example, the king must be somewhere between the two rooks, so that castling to either side is still possible, and the black and white positions must mirror one another. The rules provide for 960 possible starting positions, and for this reason the game is sometimes called Chess960. Fischer hoped his variant would encourage creative thinking and avoid the memorization associated with opening play in modern chess.<br />
<br />
==Computer Chess==<br />
Deep Blue, a computer developed by IBM, was the first computer engine to beat a human world champion in 1997, when it defeated Garry Kasparov in a six game series. This series was a rematch of 1996 series which Kasparov won, although Deep Blue had been upgraded since the first series. It should be noted that during this second match, Deep Blue was also upgraded between games to avoid falling into the same type of trap more than once.<br />
<br />
Chess engines have increased in strength in recent years to the point where humans are falling behind. In 2005, Michael Adams, one of the top fifteen players in the world, played a six game match against the engine Hydra, and lost five games with only one draw. Chess writer Eric Schiller, who uses computer assistance in writing his books, admits that "computers have taken some of the fun out of (chess)." Despite this, chess remains far from being a [[solved game]].<br />
<br />
==External links==<br />
:[http://www.fide.com/ FIDE] - World Chess Federation<br />
:[http://www.uschess.org USCF] - United States Chess Federation<br />
:[http://www.iccf.com/ ICCF] - International Correspondence Chess Federation<br />
:[http://www.chess-players.org/eng/index.html ACP] - Association of Chess Professionals<br />
:[http://www.freechess.org FICS] - Free Internet Chess Server<br />
<br />
[[Category:Chess]]</div>Recorderhttps://www.conservapedia.com/index.php?title=Chess&diff=490229Chess2008-07-15T01:13:57Z<p>Recorder: /* Movement */</p>
<hr />
<div>[[Image:Staunton chess set.jpg|right|thumb|300px|A typical chess set and tournament clock.]]<br />
<br />
'''Chess''' is a turn-based [[board game]] for two players, and is one of the most popular games in the world. The goal of the game is to place the opposing king into ''checkmate'', that is, a position in which the king is under attack but cannot escape. The game used to be treated as a status symbol of education and aristocracy and in recent times has become to be known as an [[elitist]]'s game.<br />
<br />
Modern international chess has a powerful, sweeping [[queen]] who was not a piece provided in the original game. The long reach of bishops today was also lacking at first. Maneuvers such as castling or capturing ''en passant'' have been developed within the past few hundred years.<br />
<br />
Today, chess is one of the most popular board games in the world. International competitions, including world [[champion]]ship events, are organized by an organization called FIDE and American competition organized by the USCF (United States Chess Federation). The only American world champion was [[Bobby Fischer]], although [[Paul Morphy]] of [[Louisiana]] was likely the strongest player in the world in the 1850s, before a formal world champion was determined. The current world champion is [[India | Indian]] Viswanathan "Vishy" Anand.<br />
<br />
==Origins==<br />
Chess has its roots in [[India]], where a game called Shaturanga was played. The earliest extant description of the game is contained in the [[Bhavishya Purana]], which dates from A.D. 300 to A.D. 600. Shaturanga used [[dice]], but [[Hinduism]] bans gambling. As a result, the game of chess developed free from any dice or chance. The exact rules of Shaturanga are not known, but the game developed further in Persia into something very like its modern form. The Persian game Shatranj - which remains popular in the middle east today - is nearly identical to modern chess. By A.D. 1200 the game reached southern Europe, and in the late fifteenth century the Europeans adopted a number of changes: the queen, which had formerly been a very weak piece, became the strongest piece on the board, and allowing pawns to move two squares on the first move became standard. These changes had the effect of speeding up play, and they brought the game into the form we know today.<br />
<br />
There has been some speculation that chess has roots in [[China]]. It's clear that chess is in some way related to [[XiangQi]] (Chinese Chess) and [[Shogi]] (Japanese Chess), but scholars disagree about whether either of these variants predates Shaturanga.<br />
<br />
==The Board==<br />
The chess board is a square, divided into 64 smaller squares arranged in eight rows of eight. The squares are alternating light and dark, with a light square in the bottom right hand corner. A chess board is the same as a [[Checkers|checker board]].<br />
<br />
The horizontal rows of squares are referred to as "ranks" and the vertical rows are referred to as "files".<br />
<br />
==Pieces==<br />
[[Image:StauntonPieces.jpg|right|thumb|300px|Staunton Style chess pieces. From left to right: King, Queen, Bishop, Knight, Rook, and Pawn.]]<br />
Each player has a total of 16 pieces; 8 pawns, 2 knights, 2 bishops, 2 rooks, 1 queen, and 1 king.<br><br />
<br />
===Relative Value of Pieces===<br />
There are several different ideas about the relative value of the pieces. It is important to note that the "points" used to assign a value to each piece are hypothetical and do not constitute a score; they are merely an attempt to quantify the relative power that each piece can hypothetically exert upon the board.<br />
<br />
The method most often used is:<br />
*[[Image:chesspawn.jpg|20px]] Pawn--1 <br />
*[[Image:chessknight.jpg|20px]] Knight--3 (some say 2.5) <br />
*[[Image:chessbishop.jpg|20px]] Bishop--3<br />
*[[Image:chessrook.jpg|20px]] Rook--5<br />
*[[Image:chessqueen.jpg|20px]] Queen--9 <br />
*[[Image:chessking.jpg|20px]] King--Priceless <br />
<BR>(The value to the player of some pieces will actually vary during the course of the game, for instance, in an endgame, the King has an attacking power of about 3)<br />
<br />
===Style===<br />
The most popular style of pieces are known as Staunton style pieces, the tournament standard for chess pieces, although other types exist. Often, popular themed chess sets will appear with characters from [[popular culture]] or [[fiction]] taking the places of the more common Staunton style pieces. These novelty pieces are not tournament sanctioned however, and can sometimes cause confusion during game play as to which piece is which.<br />
<br />
Although chess pieces can come in a variety of materials, [[marble]] and [[glass]] tend to be very popular, but for most chess tournaments, simple [[plastic]] pieces are usually favored. Also, while many home chess sets use heavy boards made out of [[wood]] or [[stone]] or some [[polymer]] material, tournament boards are actually roll-able mats with the board printed on it.<br />
<br />
==Gameplay ==<br />
<br />
The object of the game is to checkmate the other player's '''King''' before he checkmates your king. When a pawn reaches the far side of the board, it may be promoted to any other piece (except a King).<br />
<br />
*The players alternate moving until the game has ended.<br />
*The player with the White pieces always moves first.<br />
<br />
===Initial Conditions===<br />
The pieces are put on the board in each player's side as follows:<br />
*In the first row from left to right (with the leftmost square being black): '''rook''', '''knight''', '''bishop''', '''queen''', '''king''', '''bishop''', '''knight''' and '''rook'''.<br />
*The second row is filled with '''pawns'''.<br />
<br />
===Movement===<br />
The pieces move as follows.<br />
*The '''pawn''' moves one square forward, except when moving from its opening position, when it can optionally move two. The pawn is the only piece that captures in a way different from the way it moves. It captures opposing pieces by capturing one square diagonally forward. When another piece is on the square directly in front of a pawn it cannot move unless it is making a capture. <br><br />
*The '''knight''', which is the only piece that can jump over other pieces, moves one square in one straight direction and two in the other.<br><br />
*The '''bishop''' can move as many squares as desired diagonally.<br><br />
*The '''rook''' can move as many squares as desired in a straight direction.<br><br />
*The '''queen''' is the most powerful piece in the board. It can move as many squares as desired (without jumping over another piece), either straight or diagonally.<br><br />
*The '''king''', which is the most important piece on the board, moves one square, either straight or diagonally.<br />
<br />
====Capturing====<br />
<br />
All pieces except for the pawn capture along their lines of motion. A capture is made by moving a piece to a square occupied by one of the opponent's pieces, and removing the opponent's piece from the board. If a piece can move to occupy the location of an opponent's piece, it can capture that piece. The '''pawn''', can only capture by moving diagonally forward one square. A piece is said to be undefended if it has no piece "supporting" its position - i.e., preventing an opponent from capturing it by threat of losing his attacking piece.<br />
<br />
====Special Moves====<br />
*'''Castling'''- When a player has no pieces between a rook and his king, and he has not moved either piece, he can move the king two squares in the direction of the rook, and then place the rook on the square that the king passed over. A player cannot castle if the King is currently in check, would be in check after castling, or would move through a square which is under attack.<br />
*'''en passant'''- French for "In passing." In chess, if a player pushes his pawn far down to the end of the board, and his opponent pushes a starting pawn 2 spaces ahead, to put the pawn on the same row to avoid confrontation, the player may choose to invoke the "en passant" move, which treats the enemy pawn as though it had only moved one space. The player may capture diagonally on the square '''behind''' the enemy pawn, and remove the enemy pawn. The principle is that the two space rule for a pawn's first move cannot be used to avoid confrontation between two pawns. However, the player may only invoke "en passant" on the first turn after the opponent pushes his pawn. He cannot make it after that turn.<br />
<br />
===The end of the game===<br />
A chess game may end in a number of ways.<br />
*'''Checkmate''': The winning player checkmates his opponent's King (see below).<br />
*'''Resignation''': The losing player, facing an inevitable future checkmate, ''resigns'' rather than play out an extended series of hopeless moves. A player may indicate resignation by toppling his king on its side. <br />
*'''Loss on Time''': In games with a time limit, a player may lose by failing to make a time control, causing his clock to run out.<br />
*'''Draw''': The game may end in a draw, in which case neither player wins.<br />
<br />
====Checkmate====<br />
Checkmate is achieved when the following conditions are met. <br />
* The King is ''in check''; that is, it is directly attacked by an opponent's piece.<br />
* Every square that the King can move to is also attacked by an opponent's piece. <br />
* The Piece that is attacking the King cannot be captured. <br />
* Another Piece cannot be interposed between the attacking piece and the King to block the check.<br />
When a King is checkmated, the game is over, and the player initiating the checkmate is the winner.<br />
<br />
====Draw====<br />
There are several ways that the game can end in a draw. <br />
*'''Stalemate''': A player is said to be ''stalemated'' when he cannot make a legal move, and is not in check.<br />
*'''Draw by agreement''': The players mutually agree to a draw. In competitive chess, a player may make a draw offer after he has made his move, but before he has started his opponent's clock.<br />
*'''Draw by repetition''': Either player may claim a draw if the same position has appeared on the board three times. The three occasions need not be consecutive.<br />
*'''50 move rule''': Either player may claim a draw if fifty moves have transpired without a capture or a pawn move.<br />
<br />
==Notation==<br />
Chess notation is used to record the moves of a chess game. This has several uses. Notation can be used to record games for review at a later time. There are two major methods of chess notation, Algebraic and Descriptive.<br />
<br />
====For all forms of Notation====<br />
The notation for a chess game is taken like this. At the top of the page are the players &mdash; white listed first &mdash; with their names under their colors. Numbers go down the left side of the page to indicate the move number. (see below) <BR><br />
White, Black<BR><br />
Name Name<br />
1.<BR><br />
2.<BR><br />
3.<BR><br />
4.<BR><br />
5.<BR><br />
<br />
Moves are recorded in columns, separated by commas.<br />
<br />
Space is usually allotted on the top of tournament scoresheets to record the date and location of the game, and sometimes to record the time limit and opening name.<br />
<br />
=====Pieces=====<br />
Each piece is designated by its corresponding letter as follows:<br><br />
K = King<BR><br />
Q = Queen<BR><br />
R = Rook<BR><br />
B = Bishop<BR><br />
N = Knight (notice 'K' is reserved for the King)<BR> <br />
P = Pawn<br />
<br />
(In strict chess parlance, the pawns are not considered pieces; officially, a standard chess set consists of sixteen pieces <i>and</i> sixteen pawns.)<br />
<br />
=====Moves=====<br />
- Moves to<br />
x Captures<br />
+ Check<br />
++ Checkmate<br />
0-0 Castles king-side<br />
0-0-0 Castles queen-side<br />
e.p. en passant<br />
/ to indicate which square a piece moved from (only when needed to clarify)<br />
/Q Pawn promotion. (use /Q for queen, /R for rook, etc.)<br />
! A good move<br />
!! A very good move<br />
!? An interesting move<br />
?! A dubious move<br />
? A questionable move<br />
?? A blunder<br />
<br />
===Algebraic===<br />
Algebraic is the most commonly used method of notation. [[Image:Chessboardanote1.jpg|right]]<br />
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====The Board====<br />
In algebraic notation, each file is assigned a letter, and each rank is assigned a number. Each square is designated by the letter and number from it's rank and file. a1 is the square in the bottom left corner for the white player.<br />
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====Movement====<br />
Moves are recorded by indicating the piece to be moved and the square it is to be moved to, sometimes using a hyphen (-). For example, if white wants to move his Kingside Knight towards the center of the board to start the game, the notation would be: <br />
White Black <br />
1. Nf3, ....<br />
<br />
or<br />
<br />
White Black <br />
1. N-f3, ....<br />
<br />
In algebraic notation, a P is not used to indicate the pawn. A pawn move is implied when no piece is indicated. So if white wants to advance his king pawn 2 squares, and black responds by advancing his king pawn 2 squares, the notation would be:<br />
White Black <br />
1. e4, e5,<br />
2. ....<br />
<br />
Occasionally, two pieces of the same type can move to the same square. To eliminate ambiguity, the unique rank or file of the moving piece is identified after the piece symbol. For example, suppose both of Black's Rooks are on the 8th rank (on the squares f8 and a8), and there are no pieces in between them. Black moves the f8 Rook to d8. In other circumstances, the move would be annotated<br />
17. .... Rd8<br />
but because either Rook could have moved to d8, the identifying file for the f8 Rook must be included, as in<br />
17. .... Rfd8<br />
<br />
====Captures====<br />
Captures by a piece or pawn are indicated by first transcribing the symbol for the piece performing the capture, followed by an 'x', followed by the square the capturing piece or pawn moved to. For example, if White uses his Queen to capture a piece on the square h7 on move 23, the correct notation is <br />
23. Qxh7, ....<br />
<br />
Because pawns are not designated with a symbol, the system is slightly different for pawn captures. The file originally occupied by the pawn is used to identify the pawn performing the capture. If a black pawn on e5 captures a white piece or pawn on d4 on move 5, the notation is<br />
5. ...., exd4<br />
<br />
===Descriptive===<br />
In the more archaic descriptive notation, squares are described according to the starting piece positions. The square originally occupied by the Rook on the Queenside is referred to as "Queen's Rook One" (QR1), while "Queen's Rook Four" is the square directly in front of the Queen's Rook on the fourth rank. Thus, a typical opening move is described as "Pawn to King Four", and is written as <br />
1. P-K4, ....<br />
<br />
Note that in descriptive notation, pawns have the designation 'P'. The notation's disadvantages become apparent over the course of a complex game, especially because the same square has different names depending on the perspective of the White and Black pieces. King's Bishop Three (KB3) for White is King's Bishop Six (KB6) for Black.<br />
<br />
Captures in descriptive notation operate similar to algebraic notation; for example, <br />
<br />
45. .... R-xQN7<br />
<br />
means that on his 45th move, Black captured a piece or pawn on his Queen's Knight Seven square (the b2 square in algebraic notation).<br />
<br />
==Tactics and strategy==<br />
Chess players often refer to shorter, forcing sequences of moves that lead to clear advantages as ''tactics'', while moves designed to create or nurture long-term advantages are called ''strategic.''<br />
<br />
For more information on specific tactics, see [[chess tactics]]. For more information on specific strategic themes, see [[chess strategies]].<br />
<br />
==Chess Variants==<br />
There are a number of games based on chess with rule variations, and these are referred to as ''chess variants''. One of the most popular of these is ''Bughouse'', a partner-based game in which a player who captures his opponent's piece can give it to a partner on another board to drop on a square of his choosing. Another is ''Kriegspiel'', a game in which a player can see his pieces but not that of his opponent. [http://www.chessvariants.com/incinf.dir/kriegspiel.html] A simpler variant is ''Antichess'', which is also called ''Suicide chess'', in which a player must make a capturing move if any legal captures exist on the board, and in which the goal is to run out of pieces first.<br />
<br />
In 1996, [[Bobby Fischer]] introduced a variant called FischerRandom Chess, which involves scrambling the positions of the pieces on the first and eighth ranks before starting play. A number of rules govern the precise manner in which the pieces can be arranged; for example, the king must be somewhere between the two rooks, so that castling to either side is still possible, and the black and white positions must mirror one another. The rules provide for 960 possible starting positions, and for this reason the game is sometimes called Chess960. Fischer hoped his variant would encourage creative thinking and avoid the memorization associated with opening play in modern chess.<br />
<br />
==Computer Chess==<br />
Deep Blue, a computer developed by IBM, was the first computer engine to beat a human world champion in 1997, when it defeated Garry Kasparov in a six game series. This series was a rematch of 1996 series which Kasparov won, although Deep Blue had been upgraded since the first series. It should be noted that during this second match, Deep Blue was also upgraded between games to avoid falling into the same type of trap more than once.<br />
<br />
Chess engines have increased in strength in recent years to the point where humans are falling behind. In 2005, Michael Adams, one of the top fifteen players in the world, played a six game match against the engine Hydra, and lost five games with only one draw. Chess writer Eric Schiller, who uses computer assistance in writing his books, admits that "computers have taken some of the fun out of (chess)." Despite this, chess remains far from being a [[solved game]].<br />
<br />
==External links==<br />
:[http://www.fide.com/ FIDE] - World Chess Federation<br />
:[http://www.uschess.org USCF] - United States Chess Federation<br />
:[http://www.iccf.com/ ICCF] - International Correspondence Chess Federation<br />
:[http://www.chess-players.org/eng/index.html ACP] - Association of Chess Professionals<br />
:[http://www.freechess.org FICS] - Free Internet Chess Server<br />
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[[Category:Chess]]</div>Recorder