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| − | '''Infinity''' means beyond enumeration.<ref>This improved definition comports best with the use of the term in mathematics, in everyday life, and across cultures and languages.</ref> Appreciation of infinity -- particularly infinite time -- is remarkably useful mentally, emotionally, and personally. "Paradise" is infinite happiness; "[[Hell]]" is infinite distress; in electronics, an "open circuit" has infinite resistance.<ref>Anxiety or fear about infinity is a psychiatric condition known as "apeirophobia", which exists because infinity is real.</ref> '''''Recognition of infinite time can overcome almost any anxiety'''''. Financial-related stress can be reduced by recognizing money as being infinite. A human being has infinite potential. | + | '''Infinity''' means beyond enumeration.<ref>This improved definition comports best with the use of the term in mathematics, in everyday life, and across cultures and languages.</ref> Appreciation of infinity -- particularly infinite time -- is remarkably useful mentally and emotionally. "Paradise" is infinite [[happiness]] and [[joy]] eternally; "[[Hell]]" is infinite distress; in electronics, an "open circuit" has infinite resistance.<ref>Anxiety or fear about infinity is a psychiatric condition known as "apeirophobia", which exists because infinity is real.</ref> '''''Recognition of infinite time can overcome almost any anxiety'''''. Financial-related stress can be reduced by recognizing that money is infinite. A human being has infinite potential. |
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| − | The existence of infinity tends to prove the existence of [[God]]. Nature and the universe reflect mathematical truths, and denying the existence of God implicitly denies the existence of infinity, contrary to logic, evidence, and the enormous usefulness of the concept. | + | The existence of infinity tends to prove the existence of [[God]]. The universe reflects mathematical truths, and denying the existence of God implicitly denies the existence of infinity, contrary to logic, evidence, and infinity's enormous usefulness. |
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| − | The food supply is essentially infinite in cultures where obesity is a problem; wealth is essentially infinite for those who cannot spend it all in their lifetime; and time is infinite for those who waste it. "More" in those situations is meaningless; less is nothing to have anxiety about. Some scoff at primitive cultures that use infinity rather than large numbers, but that is a productive way to view quantities larger than meaningful. Also, infinity reinforces the primacy of the future (which is infinite) over the past (merely finite). Given that "time is money," "infinite time" ([[eternal life]]) is "infinite money" and the concept helps deal with financial anxiety. | + | The food supply is essentially infinite in cultures where obesity is a problem; wealth is essentially infinite for those who cannot spend it all in their lifetime; and time is infinite for those who waste it. "More" in those situations is meaningless; less is nothing to have anxiety about. Some scoff at primitive cultures that use infinity rather than large numbers, but that is a productive way to view quantities larger than meaningful. Also, infinity reinforces the primacy of the future (which is infinite) over the past (merely finite). Given that "time is money," "infinite time" ([[eternal life]]) is "infinite money" which helps reduce financial anxiety. |
| | [[File:Abbey Church Saint Louis.jpg|right|200px|thumb|church's infinite accessibility and outreach]] | | [[File:Abbey Church Saint Louis.jpg|right|200px|thumb|church's infinite accessibility and outreach]] |
| | Understanding infinity has advanced many fields, including: | | Understanding infinity has advanced many fields, including: |
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| | *[[architecture]], as in the [[Abbey Church]] in [[St. Louis]] that embraces infinite accessibility and outreach; | | *[[architecture]], as in the [[Abbey Church]] in [[St. Louis]] that embraces infinite accessibility and outreach; |
| | *[[mathematics]] through [[calculus]], [[set theory]] and [[singularity|singularities]]; | | *[[mathematics]] through [[calculus]], [[set theory]] and [[singularity|singularities]]; |
| − | *[[abortion]] through the realization that the unborn child has infinite potential; | + | *[[abortion]], in false denial that the unborn child has infinite potential; |
| | *[[quantum mechanics]] through infinite [[uncertainty]]; | | *[[quantum mechanics]] through infinite [[uncertainty]]; |
| | *[[economics]] through the infinite opportunity discovered by the [[Coase theorem]]; | | *[[economics]] through the infinite opportunity discovered by the [[Coase theorem]]; |
| | + | *grammar through the term "infinitive", which is a description of an action without limitation in subject, time, or tense; |
| | *[[physics]] through the [[Big Bang]] (infinite [[energy]] density) and the speculative [[black holes]] (infinite mass density); | | *[[physics]] through the [[Big Bang]] (infinite [[energy]] density) and the speculative [[black holes]] (infinite mass density); |
| | *[[politics]] through dictatorships (infinite authority) and [[separation of powers]] to avoid concentration of infinite power; | | *[[politics]] through dictatorships (infinite authority) and [[separation of powers]] to avoid concentration of infinite power; |
| | *[[religion]] through the concepts like [[eternity]] (infinite time), [[Heaven]]/[[Hell]] (infinite joy/suffering), [[faith]] (infinite good from the force of will), [[Parable of the Vineyard Workers]] and the [[Prodigal Son]] (infinite wealth), [[Widow's Mite]] (infinite [[charity]]), the infinity of [[God]],<ref>https://www.newadvent.org/cathen/08004a.htm</ref> and the number of [[angel]]s (infinite);<ref>[[Epistle_to_the_Hebrews_(Translated)#12:22|Hebrew 12:22]] ("infinite").</ref> | | *[[religion]] through the concepts like [[eternity]] (infinite time), [[Heaven]]/[[Hell]] (infinite joy/suffering), [[faith]] (infinite good from the force of will), [[Parable of the Vineyard Workers]] and the [[Prodigal Son]] (infinite wealth), [[Widow's Mite]] (infinite [[charity]]), the infinity of [[God]],<ref>https://www.newadvent.org/cathen/08004a.htm</ref> and the number of [[angel]]s (infinite);<ref>[[Epistle_to_the_Hebrews_(Translated)#12:22|Hebrew 12:22]] ("infinite").</ref> |
| | *[[statistics]] through the [[central limit theorem]], which states that the distribution of the average for a series of nearly any type of distribution approaches the [[normal distribution]]; | | *[[statistics]] through the [[central limit theorem]], which states that the distribution of the average for a series of nearly any type of distribution approaches the [[normal distribution]]; |
| − | *[[literature]], as in ''An Occurrence at Owl Creek Bridge'' (1890) and many great works inspired by it, which dramatically use a nearly infinite expansion of an infinitesimal time; writings by [[Nathaniel Hawthorne]] ("Nothing for the present hour is worthy of man's infinite capacity save to imbibe the warm smile of heaven and sympathize with the reviving earth." - ''Buds and Bird Voices''); and plays by [[Shakespeare]], who used infinity copiously (see below); | + | *[[literature]], as in ''An Occurrence at Owl Creek Bridge'' (1890) and many great works inspired by it, which dramatically use a nearly infinite expansion of an infinitesimal time; writings by [[Nathaniel Hawthorne]] ("Nothing for the present hour is worthy of man's infinite capacity save to imbibe the warm smile of heaven and sympathize with the reviving earth." - ''Buds and Bird Voices''); plays by [[Shakespeare]], who used infinity copiously (see below); and 13 times in ''[[Moby-Dick]]''; |
| | *[[biology]], as observed by [[Louis Pasteur]]: “The role of the infinitely small in nature is infinitely great”;<ref>https://www.goodreads.com/author/quotes/692216.Louis_Pasteur</ref> | | *[[biology]], as observed by [[Louis Pasteur]]: “The role of the infinitely small in nature is infinitely great”;<ref>https://www.goodreads.com/author/quotes/692216.Louis_Pasteur</ref> |
| | *[[sociology]]: traditional [[marriage]] is infinitely more stable than other types of relationships; | | *[[sociology]]: traditional [[marriage]] is infinitely more stable than other types of relationships; |
| | *[[rock music]]: paradise (in love songs, such as "Two Tickets to Paradise") represents infinite happiness; | | *[[rock music]]: paradise (in love songs, such as "Two Tickets to Paradise") represents infinite happiness; |
| | *paintings: [[Salvador Dali]]'s work (including his infinite time in ''[[The Persistence of Memory]]''), and other [[Surrealism]] such as ''Mama, Papa Is Wounded!'' (1927);<ref>https://www.history.com/topics/art-history/surrealism-history</ref> | | *paintings: [[Salvador Dali]]'s work (including his infinite time in ''[[The Persistence of Memory]]''), and other [[Surrealism]] such as ''Mama, Papa Is Wounded!'' (1927);<ref>https://www.history.com/topics/art-history/surrealism-history</ref> |
| − | *movie titles: as in ''From Here to Eternity'' (1953), ''Avengers: Infinity War'' (2018), ''Infinity'' (1996), and the TV show ''Forever'' (2014-15); | + | *movies: ''From Here to Eternity'' (1953), ''Avengers: Infinity War'' (2018), ''Infinity'' (1996), and the TV show ''Forever'' (2014-15); famous lines from movies include "To Infinity and Beyond!" (Buzz Lightyear in the ''Toy Story'' films). |
| | *understanding other terms: infinity helps define other terms concisely, such as "open circuit" (infinite resistance); | | *understanding other terms: infinity helps define other terms concisely, such as "open circuit" (infinite resistance); |
| − | *[[Resurrection]]: personal awareness of infinite time implies, as a matter of logic, personal realization of infinite time; | + | *[[Resurrection]]: personal awareness of infinite time implies, as a matter of logic, actual realization of infinite time through resurrection; |
| | *[[Abraham Lincoln]]: "Surely God would not have created such a being as man, with an ability to grasp the infinite, to exist only for a day! No, no, man was made for immortality";<ref>https://www.brainyquote.com/quotes/abraham_lincoln_121271</ref> | | *[[Abraham Lincoln]]: "Surely God would not have created such a being as man, with an ability to grasp the infinite, to exist only for a day! No, no, man was made for immortality";<ref>https://www.brainyquote.com/quotes/abraham_lincoln_121271</ref> |
| | + | *in [[baseball]], there is infinite time; |
| | *in [[probability]], impossibility is what is infinitely unlikely; | | *in [[probability]], impossibility is what is infinitely unlikely; |
| | *as to dignity, "Infinite Dignity" is the title of a [[Vatican]] document condemning transgender procedures as published on April 8, 2024;<ref>https://press.vatican.va/content/salastampa/en/bollettino/pubblico/2024/04/08/240408c.html</ref> | | *as to dignity, "Infinite Dignity" is the title of a [[Vatican]] document condemning transgender procedures as published on April 8, 2024;<ref>https://press.vatican.va/content/salastampa/en/bollettino/pubblico/2024/04/08/240408c.html</ref> |
| | *in [[infinity in engineering|engineering]]: in a DC circuit, a capacitor has infinite resistance, while [[Earth]] has infinite capacitance; | | *in [[infinity in engineering|engineering]]: in a DC circuit, a capacitor has infinite resistance, while [[Earth]] has infinite capacitance; |
| − | *in an [[eclipse]], the refraction of light around the [[Moon]] results in the equivalent of infinite light intensity (which can damage the naked eye); and | + | *in an [[eclipse]], the refraction of light around the [[Moon]] results in the equivalent of infinite light intensity (which can damage the naked eye); |
| | + | *in [[currency]], devaluation to zero occurs if and only if there is infinite [[inflation]]; and |
| | *in carpentry and [[materials science]]: wood of infinite density is needed to build a spiral staircase with multiple twists and no supporting column, which can hold a dozen people at once - see [[Loretto spiral staircase]]. | | *in carpentry and [[materials science]]: wood of infinite density is needed to build a spiral staircase with multiple twists and no supporting column, which can hold a dozen people at once - see [[Loretto spiral staircase]]. |
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| | The existence of an infinite [[God]] implies the necessary existence of the opposite: the void described in [[Genesis]]. Negative infinity, as implied by the existence of positive infinity, is the numeric equivalent of the [[Hell]] mentioned frequently in the [[New Testament]]. The [[logic of infinity]] permeates the [[Gospels]]. | | The existence of an infinite [[God]] implies the necessary existence of the opposite: the void described in [[Genesis]]. Negative infinity, as implied by the existence of positive infinity, is the numeric equivalent of the [[Hell]] mentioned frequently in the [[New Testament]]. The [[logic of infinity]] permeates the [[Gospels]]. |
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| − | == Teachings about infinity by Jesus == | + | == Infinity and biblical theology == |
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| | + | In a biblical [[theological]] context, the concept of infinity used to describe God's limitless nature, meaning that God is not bound by the constraints of space, time, or any other limitations (Other than not being able to engage in evil such as lying or engaging in illogical actions such as making a square round). God being omnipotent, omnipresent, and omniscient. God's limitless nature places God beyond human comprehension. The limitless nature of God passage of Scripture in Psalm 139:1-12 is often cited by both theologians and the wider Christian community. |
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| | + | As a result of God's limitless nature, [[Christianity|Christian]] theologians commonly declare that the world was the best of all possible worlds, as it was created by [[God]]. Therefore, even what appears to many as bad is actually part of God's perfect plan. For example, adversity improves Christian character. |
| | + | [[Image:Leibniz.jpg|thumb|left|200px|[[Gottfried Leibniz]] ]] |
| | + | [[Gottfried Leibniz|Gottfried Wilhelm von Leibniz]] (1646-1716) was a German, Christian philosopher who was born into a pious [[Lutheran]] family close to the end of the Thirty Years’ War, which had laid [[Germany]] in ruins.<ref>[https://www.britannica.com/topic/best-of-all-possible-worlds Best of all possible worlds], Encyclopedia Britannica</ref> |
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| | + | Encyclopedia Britannica's article ''Best of all possible worlds'' states: |
| | + | {{Cquote|Best of all possible worlds, in the philosophy of the early modern philosopher [https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz Gottfried Wilhelm Leibniz] (1646–1716), the thesis that the existing world is the best world that God could have created. |
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| | + | Leibniz’s argument for the doctrine of the best of all possible worlds, now commonly called Leibnizian optimism, is presented in its fullest form in his work Théodicée (1710; [[Theodicy]]), which was devoted to defending the justness of God.. |
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| | + | In rough outline, the argument proceeds as follows: |
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| | + | '''1.''' God is omnipotent, omniscient, and omnibenevolent; |
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| | + | '''2.''' God created the existing world; |
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| | + | '''3.''' God could have created a different world or none at all (i.e., there are other possible worlds); |
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| | + | '''4.''' Because God is omnipotent and omniscient, he knew which possible world was the best and was able to create it, and, because he is omnibenevolent, he chose to create that world; |
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| | + | '''5.''' Therefore, the existing world, the one that God created, is the best of all possible worlds.<ref>[https://www.britannica.com/topic/best-of-all-possible-worlds Best of all possible worlds], Encyclopedia Britannica</ref>}} |
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| | + | === Teachings about infinity by Jesus === |
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| | Infinity is depicted by several miracles, including the [[Multiplication of the loaves]] and the [[Miraculous catch of fish]]. Infinity is implicit in several parables, including the [[Prodigal Son]], and the parable of the vineyard workers.<ref>Matthew 20:1-16.</ref> In addition, one's soul is of infinite value to him and thus cannot be exceeded in value by anything else, as explained by Matthew 16:26. | | Infinity is depicted by several miracles, including the [[Multiplication of the loaves]] and the [[Miraculous catch of fish]]. Infinity is implicit in several parables, including the [[Prodigal Son]], and the parable of the vineyard workers.<ref>Matthew 20:1-16.</ref> In addition, one's soul is of infinite value to him and thus cannot be exceeded in value by anything else, as explained by Matthew 16:26. |
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| | [[Eternity]] is infinite time, a concept that was also first introduced and emphasized by Jesus. The [[Old Testament]] has few references to "eternity" and "eternal", while the [[New Testament]] repeatedly teaches it. For example, Jesus taught about infinity in connection with [[Judgment Day]] when "these will go off to eternal punishment, but the righteous to eternal life."<ref>Matt 45:26 ([[NAB]]).</ref> | | [[Eternity]] is infinite time, a concept that was also first introduced and emphasized by Jesus. The [[Old Testament]] has few references to "eternity" and "eternal", while the [[New Testament]] repeatedly teaches it. For example, Jesus taught about infinity in connection with [[Judgment Day]] when "these will go off to eternal punishment, but the righteous to eternal life."<ref>Matt 45:26 ([[NAB]]).</ref> |
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| − | == Mistranslated as "unsearchable" == | + | === Mistranslated as "unsearchable" === |
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| | Many translations of the [[Bible]] mistakenly use the term "unsearchable" when "infinite" is the intended meaning. Ancient Greek lacked a word for "infinity", and instead used "apeiron" for indefinite or unlimited.<ref>Some say that the obscure Greek term "aphorismenon" was closer to the modern term of infinity.</ref> | | Many translations of the [[Bible]] mistakenly use the term "unsearchable" when "infinite" is the intended meaning. Ancient Greek lacked a word for "infinity", and instead used "apeiron" for indefinite or unlimited.<ref>Some say that the obscure Greek term "aphorismenon" was closer to the modern term of infinity.</ref> |
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| | == Anselm and Shakespeare == | | == Anselm and Shakespeare == |
| | + | [[File:Anselm-CanterburyVit.jpg|thumbnail|right|300px|A 19th-century stained-glass window depicting [[Anselm]] as archbishop]] |
| | [[Anselm]] focused on infinity to prove the divinity of [[Christ]]. [[Chaucer]] referenced "infinity" in 1374, according to the Oxford English Dictionary. But [[Shakespeare]] used infinity more than anyone up until his time, in such classics as [[Hamlet]] ("A king of infinite space") and [[Romeo and Juliet]] (“My bounty is as boundless as the sea, My love as deep; the more I give to thee, The more I have, for both are infinite.”). This passage from Hamlet is particularly memorable in referring to the infinite:<ref>Hamlet, 2.2.314</ref> | | [[Anselm]] focused on infinity to prove the divinity of [[Christ]]. [[Chaucer]] referenced "infinity" in 1374, according to the Oxford English Dictionary. But [[Shakespeare]] used infinity more than anyone up until his time, in such classics as [[Hamlet]] ("A king of infinite space") and [[Romeo and Juliet]] (“My bounty is as boundless as the sea, My love as deep; the more I give to thee, The more I have, for both are infinite.”). This passage from Hamlet is particularly memorable in referring to the infinite:<ref>Hamlet, 2.2.314</ref> |
| | {{cquote|What a piece of work is a man! how noble in reason! how infinite in faculty! in form and moving how express and admirable! in action how like an angel! in apprehension how like a god! the beauty of the world! the paragon of animals!}} | | {{cquote|What a piece of work is a man! how noble in reason! how infinite in faculty! in form and moving how express and admirable! in action how like an angel! in apprehension how like a god! the beauty of the world! the paragon of animals!}} |
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| | In [[baseball]], a pitcher has an infinite Earned Run Average (ERA) when he allows earned runs without obtaining any "outs" by the opposing team, because the ERA is a pitcher's average earned runs allowed per nine innings pitched (i.e., 27 outs obtained). In 2019, Nationals relief pitcher Trevor Rosenthal had an infinite ERA until he finally obtained an out.<ref>https://www.freep.com/story/sports/mlb/2019/04/11/trevor-rosenthal-nationals-reliever-infinity/3433399002/</ref> | | In [[baseball]], a pitcher has an infinite Earned Run Average (ERA) when he allows earned runs without obtaining any "outs" by the opposing team, because the ERA is a pitcher's average earned runs allowed per nine innings pitched (i.e., 27 outs obtained). In 2019, Nationals relief pitcher Trevor Rosenthal had an infinite ERA until he finally obtained an out.<ref>https://www.freep.com/story/sports/mlb/2019/04/11/trevor-rosenthal-nationals-reliever-infinity/3433399002/</ref> |
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| − | Baseball has a potentially infinite duration, with no time limits. For this and other reasons, the game has been described as timeless. | + | Baseball has no clock and no time limits. For this and other reasons, this classic game has been described as timeless (which is the same as infinite time). |
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| | == Ongoing disputes about infinity == | | == Ongoing disputes about infinity == |