SPUG: Stick Riddle
Creede Lambard
creede at penguinsinthenight.com
Fri Jan 3 00:41:09 CST 2003
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.
On a similar subject, Isaac Asimov recounted a story from (I believe)
his undergraduate years when he was sitting in on a class with a friend.
The professor was trying to make a point about breaking a piece of chalk
in half. The proto-Good Doctor said it couldn't be done, whereupon the
instructor broke the piece of chalk.
"That's not it," Asimov said (I'm paraphrasing, because this is all from
memory). "You now have two whole pieces of chalk." The class laughed.
"And even if you do have a standard measure for a piece of chalk, how do
you know whether you've really broken it in half? What if the pieces are
.51 and .49 of a piece of chalk? What about the dust?"
For this observation he was kicked out of the class. :)
The moral of this story is . . . um, always properly define your
problem. I think. Or maybe it's don't try to one-up the instructor when
you're in a strange class.
--
* .~. `( -------------------------------------------------------------
` / V \ . Creede Lambard : You're never too old to enjoy
/( )\ creede at penguinsinthenight.com : a happy childhood
^^-^^ -------------------------------------------------------------
Perl Programmer and Linux Sysadmin, reasonable rates. Inquire within.
GPG key at http://www.penguinsinthenight.com/creede_public_key.asc
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