http://www.explainxkcd.com/wiki/index.php?title=Special:RecentChangesLinked/994:_Advent_Calendar&feed=atom&target=994%3A_Advent_Calendarexplain xkcd - Changes related to "994: Advent Calendar" [en]2014-04-24T05:02:00ZRelated changesMediaWiki 1.19.1http://www.explainxkcd.com/wiki/index.php?title=1153:_Proof&diff=65852&oldid=425791153: Proof2014-04-22T19:10:49Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there: half of the distance between A and B. Then I must walk half the remaining distance, which would bring me to three-quarters of the original distance; then I must again walk half the now-remaining distance to reach a point seven-eighths of the way from point A, and so on. Because I would have to take an infinite number of non-zero steps, I will never reach point B. By the same argument, the lawyer in the cartoon can get closer and closer to the judge's table, but never reach it.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there: half of the distance between A and B. Then I must walk half the remaining distance, which would bring me to three-quarters of the original distance; then I must again walk half the now-remaining distance to reach a point seven-eighths of the way from point A, and so on. Because I would have to take an infinite number of non-zero steps, I will never reach point B. By the same argument, the lawyer in the cartoon can get closer and closer to the judge's table, but never reach it.</div></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>There are two possible law vs math/logic puns in the comic, on the words "approach" and "proof." "{{w|Approach the bench}}" is a legal term meaning to have a private conversation with the judge; approach in calculus means an infinite process where a function value gets closer and closer to a {{w|Limit (mathematics)|limit}} value<del class="diffchange diffchange-inline">, </del>that it never actually reaches <del class="diffchange diffchange-inline">(</del>reminiscent of Zeno's paradoxes<del class="diffchange diffchange-inline">)</del>. "Proof" is also ambiguous with different significations in formal disciplines than in {{w|jurisprudence}}; see {{w|proof (truth)}}.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>There are two possible law vs math/logic puns in the comic, on the words "approach" and "proof." "{{w|Approach the bench}}" is a legal term meaning to have a private conversation with the judge; approach in calculus means an infinite process where a function value gets closer and closer to a {{w|Limit (mathematics)|limit}} value that it never actually reaches<ins class="diffchange diffchange-inline">, </ins>reminiscent of Zeno's paradoxes. "Proof" is also ambiguous with different significations in formal disciplines than in {{w|jurisprudence}}; see {{w|proof (truth)}}.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{w|Gottfried Leibniz}} is the co-inventor of {{w|calculus}} (along with Isaac Newton). If Leibniz were to testify in this imaginary trial, he might argue that calculus invalidates Zeno's paradoxes, because the moving arrow has a different velocity than a stationary one (the function describing the motion has a nonzero derivative at the point), and the {{w|infinite series}} in the dichotomy paradox has a finite sum. Both Zeno and calculus assume a continuous, infinitely divisible, ideal {{w|spacetime}}, whereas {{w|quantum mechanics}} suggests real spacetime is discrete. However, Zeno is arguably not concerned with actually calculating the correct answer. In the real world, Zeno can be trivially disproven simply by moving and reaching a desired target. It remains a question of debate whether a mathematical approach addresses the central points in Zeno's arguments.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{w|Gottfried Leibniz}} is the co-inventor of {{w|calculus}} (along with Isaac Newton). If Leibniz were to testify in this imaginary trial, he might argue that calculus invalidates Zeno's paradoxes, because the moving arrow has a different velocity than a stationary one (the function describing the motion has a nonzero derivative at the point), and the {{w|infinite series}} in the dichotomy paradox has a finite sum. Both Zeno and calculus assume a continuous, infinitely divisible, ideal {{w|spacetime}}, whereas {{w|quantum mechanics}} suggests real spacetime is discrete. However, Zeno is arguably not concerned with actually calculating the correct answer. In the real world, Zeno can be trivially disproven simply by moving and reaching a desired target. It remains a question of debate whether a mathematical approach addresses the central points in Zeno's arguments.</div></td></tr>
</table>Davidy22