1153: Proof

2013-01-02T20:20:24Z

128.220.160.2: /* Explanation */ Calculus: it works, bitches.

{{comic
| number = 1153
| date = December 28, 2012
| title = Proof
| image = proof.png
| titletext = The prosecution calls Gottfried Leibniz.
}}

==Explanation==
{{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? 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. 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.

{{w|Gottfried Leibniz}} is the co-inventor of {{w|calculus}} (along with Isaac Newton). He is called in to bring a mathematical point of view. Since mathematics started to be able to handle infinite processes, it has been suggested that the Dichotomy paradox is resolved by showing that:
# a moving object is indeed different from a stationary one, in that its derivative (instantaneous velocity) is different;
# the infinite number of terms involved add up to a finite sum;
# infinitely many steps can be traversed in finite time if each interval decreases geometrically (as in this case).
However, some philosophers dispute that this mathematical approach addresses the central points in Zeno's arguments.

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}}.

[[994: Advent Calendar]] is also about Zeno.

==Transcript==
:Zeno: My client couldn't have killed anyone with this arrow, and I can ''prove'' it!
:Judge: I'd like to examine your proof, Zeno. You may approach the bench.
:Zeno: — But never reach it!

{{comic discussion}}

[[Category:Philosophy]]

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1153: Proof