Editing 1153: Proof
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{{w|Zeno of Elea}} was an ancient Greek philosopher who devised several apparent paradoxes of motion called {{w|Zeno's paradoxes}}. Here are the two relevant to the comic: | {{w|Zeno of Elea}} was an ancient Greek philosopher who devised several apparent paradoxes of motion called {{w|Zeno's paradoxes}}. Here are the two relevant to the comic: | ||
− | :'''Arrow paradox:''' At any instant in time, an arrow suspended in mid-air is no different from an arrow in motion. How, then, can motion occur? | + | :'''Arrow paradox:''' At any instant in time, an arrow suspended in mid-air is no different from an arrow in motion. How, then, can motion occur? The lawyer presumably intends to use this argument to prove that his client could not have used the arrow to commit murder. |
− | :'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there | + | :'''Dichotomy paradox:''' Suppose I need to go from point A to point B. First I must walk halfway there. Then I must walk a quarter of the way there, then an eighth of the way there, and so on. Since I have to make 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. |
− | There are two | + | There are two mathematics/law puns present 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 (reminiscent of Zeno's paradoxes). "Proof" can mean a {{w|mathematical proof}} or a {{w|Evidence (law)|legal proof}}. |
− | {{w|Gottfried Leibniz}} is the co-inventor of {{w|calculus}} (along with Isaac Newton | + | {{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 a moving object has a different derivative (velocity) than a stationary one, and an {{w|infinite series}} can be completed in finite space and time. However, Zeno is arguably not concerned with actually calculating the correct answer. One can to be sure show Zeno's conclusions to be wrong by simply moving. It remains a question of debate whether a mathematical approach addresses the central points in Zeno's arguments. |
[[994: Advent Calendar]] is also about Zeno. | [[994: Advent Calendar]] is also about Zeno. | ||
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{{comic discussion}} | {{comic discussion}} | ||
[[Category:Philosophy]] | [[Category:Philosophy]] | ||
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