Tis true -- Ben's Message Board

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Subject: Tis true

Author:
Damoclese

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Date Posted: 08/16/04 1:37pm
In reply to: Duane 's message, "Tristam Shandy Exposed!" on 08/16/04 1:30am

>
>Well, actually, the simplest way to explain away this
>apparent paradox is the following:
>
>If the total distance travelled == 1, then Zeno's
>description of motion describes the summation of
>
> 1/(2^n)
>
>from n=1 to n=(infinity), which is a "summable
>series." (whose sum is, incidentally, 1)

I certainly don't disagree with any of this, as this problem is of a class of problems that very elementary calculus disposes of quite neatly as you've done here.

>
>But your point is well made, that infinite series,
>sets, etc. make for many apparent paradoxes, and that
>in a sort-of hand-wavy, non-rigorous way, you might
>say that, "If your paradox involves infinity, you're
>probably just being clever, and it really isn't a
>paradox."

Precisely. Infinity begets paradoxes.

>
>I think your example clearly illustrates how Tristam
>Shandy falls into the same class of paradox.
>
>Duane

I'm glad at least someone did. I was beginning to think that my powers of communication had been gravely altered.

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