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Re: Looking for a new soapbox

At 6:07 AM on 2/25/97, <> wrote:

And now for something completely different!

I call this (inappropriately) "The Rubber Worm Problem": You are provided
with an elastic rope exactly one kilometer in length. At time t=0 a worm
starts to crawl from one end of the rope to the other at a speed of one
centimeter per second. The rope itself is attached to a tractor which
is stretching the rope at a rate of one kilometer per second. The problem
as it was originally stated specifies that the rope lengthens by one
kilometer at the end of each second, and it is this discrete version of
the problem I will continue with here. At the end of one second the worm
has marched one centimeter toward the other end of the rope. At that
instant he is instantaneously transported to the 2 centimeter mark on a
rope which is now two kilometers in length. By calculation you will see
that at the end of the second second he will be three centimeters along
his way on the two kilometer rope, which will then lengthen to three
kilometers, taking the worm to the 4.5 cm point, etc.

First question: Has our worm embarked on a Sisyphusian journey; will he
ever reach the end of his rope? If not, prove that.

Good problem. I started my computer calculating the position of the worm
as a function of step number. (Thank goodness for those multi-tasking
Macs). It seems I will have to train the worm to make each step in say a
tenth the time it took to take the previous step, but I can't program the
Mac to do this! (Is that a Windows feature?) And of course the end of the
string will have to be moving well over the speed limit in short order.
What is the life span of this worm anyway?

I estimate he's within 10^4466 steps of getting there.