On Thu, Jan 9, 2014 at 2:02 PM, Jesse Mazer <laserma...@gmail.com> wrote:

> And as I've said, there is also the fact that if the laws of physics
> don't conserve phase space volume, the 2nd law wouldn't hold either.

You've got it backwards, there is no fundamental law of physics concerning
the conservation of phase space that forces matter to behave in certain
ways, rather it's just a natural consequence of the FIRST law of
thermodynamics and the statistical fact that if you make a change in a
highly orders system you will probably make it more disordered because
there are far fewer ordered states than disordered states. Liouville's
equation is all about statistics, the variables in it determine the phase
space distribution and that determines the PROBABILITY a system of things
will be in a particular infinitesimal phase space volume.

>>> For example, in Life one could define macrostates in terms of the ratio
>>> of white to black cells [...]
>> >> In the Game of Life the number of black cells is always infinite, so I
>> don't see how you can do any ratios.
> Maybe that would be true for some ideal Platonic version of the Game of
> Life on an infinite board, but any real-world implementation of a cellular
> automaton involves a finite number of squares

Maybe not. The universe is certainly a real world implementation and it
might be infinite and it might be a cellular automation, that's what
Stephen Wolfram thinks.

> usually this is done with a periodic boundary condition, so squares on
> the left edge of the finite grid are defined to be neighbors of squares on
> the right edge, and squares on the top edge of the grid are defined to be
> neighbors of squares on the bottom edge.

Then the rules governing the game have been changed.

> Another alternative would be to imagine you do have an infinite grid, but
> with a starting state where there are only a finite pattern of black
> squares surrounded by an infinite number of white squares,

So the ratio of white squares to black is a finite number divided by
infinity. Perhaps that's what a Black Hole is, a place where God tried to
divide by zero.

  John K Clark

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