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 | | From: | John Baez | | Subject: | Re: too much information! | | Date: | Thu, 13 Jan 2005 06:09:36 +0000 (UTC) |
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 | In article <41E5F13D.BD5B2F20@worldnet.att.net>,
Lewis Mammel wrote:
>On John Baez's page
http://math.ucr.edu/home/baez/information.html
>the entropy of an object was stated as being,
>"how much information it takes to completely specify all the positions
>and velocities of all the particles composing it."
You may have read a preliminary version. Later I decided
this sort of statement would make people wonder if I'd
forgotten about the uncertainty principle. So, I decided
to be a wee bit clearer, and say:
A gram of water (at room temperature and pressure) holds
2.81 x 10^{24} nits
of information.
In other words, this is how much information it takes to completely
specify all the positions and velocities of all the particles composing
it, up to the limits imposed by the uncertainty principle! (If the
uncertainty principle didn't cut in, the information would be infinite -
that's one reason we need quantum mechanics.)
Even this is oversimplified, because I'm not trying to give a
course on entropy here. I'm just trying to give the reader a rough
sense of how entropy is related to information.
If I were trying to be more precise, I might have said that in
quantum theory the entropy is the amount of information it takes
to specify the microstate of a system, given the macrostate.
>To me, this indicates the STRICTLY classical viewpoint, Just as
>though one had said "all the rocks" or "all the marbles" instead
>of "all the particles".
No, we really want and *need* to take quantum theory into account
to properly treat issues like the entropy of water starting from
first principles.
But, I wasn't trying to explain this stuff in detail - just
compute the amount of information in a raindrop! So, I just
wanted to say the bare minimum about entropy, information and
quantum mechanics needed to give the reader a vague idea of
what the computation actually meant.
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| | From: | Lewis Mammel | | Subject: | Re: too much information! | | Date: | Thu, 13 Jan 2005 08:16:58 GMT |
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John Baez wrote:
>
> In article <41E5F13D.BD5B2F20@worldnet.att.net>,
> Lewis Mammel wrote:
>
> >On John Baez's page
>
> http://math.ucr.edu/home/baez/information.html
>
> >the entropy of an object was stated as being,
> >"how much information it takes to completely specify all the positions
> >and velocities of all the particles composing it."
>
> You may have read a preliminary version. Later I decided
> this sort of statement would make people wonder if I'd
> forgotten about the uncertainty principle. So, I decided
> to be a wee bit clearer, and say:
>
> A gram of water (at room temperature and pressure) holds
>
> 2.81 x 10^{24} nits
>
> of information.
>
> In other words, this is how much information it takes to completely
> specify all the positions and velocities of all the particles composing
> it, up to the limits imposed by the uncertainty principle! (If the
> uncertainty principle didn't cut in, the information would be infinite -
> that's one reason we need quantum mechanics.)
I saw this, but it leaves the classical view intact, merely placing
a limit on it, which is necessary, as you say, if one is to pursue
the quantification of the information involved.
> Even this is oversimplified, because I'm not trying to give a
> course on entropy here. I'm just trying to give the reader a rough
> sense of how entropy is related to information.
You never did this. You merely asserted a proportional relation
with no justification except that it had been "figured out".
Since this assertion is a paraphrase of the immortal S = k log W,
I guess that's something, but this is the point that requires
explanation. It seemed to me you glided over it and chose to
dwell unduly on superficial arithmetic.
> If I were trying to be more precise, I might have said that in
> quantum theory the entropy is the amount of information it takes
> to specify the microstate of a system, given the macrostate.
There you go. Quantum theory is necessary to have any grasp
of this. Classical physics is utterly incompetent to reveal
the secrets of entropy.
> >To me, this indicates the STRICTLY classical viewpoint, Just as
> >though one had said "all the rocks" or "all the marbles" instead
> >of "all the particles".
>
> No, we really want and *need* to take quantum theory into account
> to properly treat issues like the entropy of water starting from
> first principles.
Yes, we need to chuck classical physics overboard when speaking
of the microstate of water, so why did you adhere to the idea
that its state can be specified as a classical microcanonical
ensemble? You're pandering to classical revanchism!
I'm looking at Schroedinger's booklet, Statistical Thermodynamics,
from 1944 - "In principle we have always in mind a quantum-mechanical
system" - Go for it!
> But, I wasn't trying to explain this stuff in detail - just
> compute the amount of information in a raindrop! So, I just
> wanted to say the bare minimum about entropy, information and
> quantum mechanics needed to give the reader a vague idea of
> what the computation actually meant.
But you didn't compute it, in any meaningful sense. You looked
up the entropy in a table and asserted that it measured the
information required to specify etc. etc. ... which really, it
doesn't.
Well, I'm being way to critical, as I keep saying, and I can
reduce all my objections to quibbles if I work at it. But these
were my thoughts.
Lew Mammel, Jr.
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