On Thu, Jun 14, 2012  Craig Weinberg <whatsons...@gmail.com> wrote:

> if entropy is to mean anything objectively, then how it looks and acts on
> one level compared to another can't matter since the difference between
> micro-states and the macro 'end result' is a matter of subjective
> perception, not physical law.

It's true that as I've described it using nothing but English it does sound
a little subjective and vague about where exactly the transition between
micro and macro states occurs, however if you use mathematics you can
become much more rigorous and show that  for some things, like a bucket of
water, changes at smaller and smaller scales produce exponentially smaller
changes at larger and larger scales; while for other things, like a perfect
diamond, that effect is much less pronounced.  So we can say (using the
language of mathematics not English) with objectivity and precision that
the bucket of water has a lot of entropy and the diamond much less.

> > Entropy and information here are figures of speech though. There is no
> actual physical property you are talking about

If that's true then I don't understand why soot or charcoal is different
from diamonds, physically they are made of exactly the same thing, carbon
atoms. Assuming you weigh 200 pounds I don't understand why you are
different from 36 pounds of charcoal, 3 pounds of calcium, 2 pounds of
phosphorous, and tanks filled with 130 pounds of oxygen gas, 20 pounds of
hydrogen, 6 pounds of nitrogen, and about 3 ponds of a powder made of
potassium sulfur sodium and magnesium.

The physical property of something can not just be the parts it's made out
of, the physical property depends on how those parts are put together. In
other words it depends on information, I can't imagine how anyone could
hope to make sense of the world without understanding this, yes there is no
other word for it, information.

> > I have a glass of ice (low physical entropy). I make a movie of the ice
> melting so that it takes one hour to melt completely. Then I keep the
> camera rolling for another hour at the glass of water. I compress them as
> mpegs

Bad example, MPEG and JPEG files deliberately loose information that, due
to the particular nature of the human visual system, make a only a small
contribution, considering their large size, to the look of the final movie
or picture. A Martian who's eyes work differently might throw away
different information. We should use lossless compression algorithms like
GIF or ZIP in examples like this.

> and boom, the warm water has very little Shannon entropy and I wind up
> with a small file output.

Warm water has more entropy than ice not less, and the compressed water
file might be smaller than the uncompressed water file but it would still
be larger than the compressed ice file. I said "might" because as entropy
increases the less difference lossless compression makes, that's why with a
file with maximum entropy, such as a movie of white noise, a lossless
program would be useless, the "compressed" and regular file would be the
same size. But you could still use lossy compression, like MPEG, because
human eyes can not easily tell one variety of white noise from another,
it's all just a bunch of hash, although Martians might see things

  John K Clark

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