SPUG: Stick Riddle
Michael R. Wolf
MichaelRunningWolf at att.net
Fri Jan 3 12:37:24 CST 2003
Jonathan Gardner <jgardn at alumni.washington.edu> writes:
> On Thursday 02 January 2003 10:41 pm, Creede Lambard wrote:
> > On Thu, 2003-01-02 at 22:23, Jeremy Calvert wrote:
> > > > > > ... if A + B = C ...
> > > > >
> > > > > ... the probability of this happening is 0 ...
> > > >
> > > > Not so. If the first break results in two sticks of
> > > > equal length ...
> > >
> > > Is so so:). The probability of your counter-example
> > > happening is also 0. Otherwise, what is the
> > > probability that the first break results in two sticks
> > > of equal length?
> >
> > I still respectfully state that it's not so. The probability of the
> > first break being exactly in the middle of the stick is vanishingly
> > small, but so is the probability that the break appears anywhere else in
> > the stick. Does that mean the stick can never be broken, since the
> > probability of it breaking at any particular point is the same as the
> > probability of it breaking at the exact center? (This probably has
> > something to do with dividing by zero.)
> >
> > Not to mention the many, many circumstances in which the first break
> > appears at location $x along the stick, and the second break causes the
> > longer of the two sticks to split such that the longest piece left over
> > has length of .5 .
> >
> > This is obviously a problem for some sort of calculus, but I'm afraid my
> > calculus years are, ahem, many years behind me.
> >
>
> The chances of the stick breaking exactly in some predefined way is
> infinitessimally small -- hence zero.
infintessimally small is not zero
infintessimally small is infintessimally small
You're playing with Zeno's Paradox, except that you seem to be working
with a mortise (and possibly a tenon?) instead of a tortoise and
Achilles (but not a tendon!), and are therefore barking up the tree
that bore the fruits known as integral calculus.
Google for "zeno paradox" or take a quick look at this cute
description
http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp
--
Michael R. Wolf
All mammals learn by playing!
MichaelRunningWolf at att.net
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