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Re: PCBs, environmentalism, etc./rubber worm



.... Who says physicists are narrowly focussed?!

Nobody I know. I was beginning to wonder though after reading the seeming
interminable discussion on the Mac/Intel preference thread.

BTW, I was wondering if Leigh issued the rubber worm problem to the list as
a test of possible innumeracy among phys-lers? It seems that anyone who
would jump to a spreadsheet on a Power Mac for this problem has not thought
about it very deeply. A little calculus, the definition of Euler's constant,
and the Euler-Mclaurin summation formula allow this problem to be solved for
both the discrete and continuous cases to essentially any (reasonable)
precision desired with just a hand calculator that has exponential and log
functions on it. This is not a supercomputing task.

This problem has a cosmological overtone/analogy to it. Does anyone recall
the "Old Stars" thread from last July? On that thread was discussed the
problem as to how light from distant galaxies can be just now reaching us if
the universe is some 15 X 10^9 years old and the light left those galaxies
when the universe was only about ~1 - 2 X 10^9 years old and they were an
order of magnitude closer to our (proto)galaxy when their light left them
than now when their light is arriving here. The worm is like the light
signal that has left a distant young galaxy. The tractor which stretches the
rope is the Hubble expansion of the Universe, the rope is spacetime itself,
and any markers or knots on the rope are other distant galaxies which are
essentially at rest in comoving coordinates. This problem shows how it can
take much longer for the light from those galaxies to reach us than one would
naively expect by just comparing the initial distance to be covered with the
speed of light.

David Bowman
dbowman@gtc.georgetown.ky.us