On Thursday, June 14, 2012 1:21:07 PM UTC-4, John K Clark wrote:

Physical entropy is a measure of the number of micro-states something can 
> be in without changing its macro-state. A bucket of water can be in many 
> many micro-states and yet the end result of them all would still look and 
> act like a plain old bucket of water. 

That is a definition from statistical thermodynamics, but 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.

I am talking about classical thermodynamics, where if I lose power and the 
food in the refrigerator goes bad, it goes bad regardless of who observes 
it or what level of description they access.

So if you wanted to know the micro-state of that particular bucket over 
> there, 
if you wanted to know the position and momentum of every water molecule in 
> the bucket it would take a great deal information to distinguish that 
> particular micro-state from the huge number of states that the bucket could 
> be in and still look the same, far more information than DNA has in your 
> body. 

If the bucket was filled with DNA instead, you couldn't tell the difference 
at the macro level either. 

> The bucket has a lot of entropy and a lot of information, although it is 
> information that most humans would consider spectacularly unimportant. 

Entropy and information here are figures of speech though. There is no 
actual physical property you are talking about, only perception for a 
specific purpose of measurement.

> If the bucket of water froze the molecules would line up in a regular 
> lattice so the ice bucket would contain less entropy and less information 
> than the water bucket because fewer micro-states could produce the same 
> macro-state; with ice you would be less surprised about where a molecule is 
> and mathematical entropy is a measure of surprise.     

Ok, this is cool. I readily admit that I'm not at all qualified in this 
area and that I would defer to your knowledge on this, and in this case I 
was ready to concede your point, because indeed, the way you are looking at 
it, freezing water to ice would both decrease physical entropy of the 
water* as well as decreasing the informational energy of the ice since it 
would, as you say, be easier to compress the positions of every water 
molecule if they were lined up - but wait!

Here's the thing. Using the atomic description level is arbitrary. Shannon 
information is about data compression, and the quality and quantity of data 
is entirely dependent upon the quality and quantity of measurements you 
perform. Information entropy does not pertain to any property of the water 
itself, it pertains only to a given description sampled from the water. So 
here is a multisense example for you.

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 and boom, the warm water has very little Shannon entropy and I wind 
up with a small file output. The ice, with all of its nooks and crannies 
gradually shifting and reflecting as it melts, slides, and floats in the 
water = heavy mpeg file.

What this does for me is help clarify how information is not tied 
concretely to physics, but rather to sense perception. Objects contain no 
information and only a first person subject can be meaningfully informed. 
Information and physics do relate to each other, but indirectly, and always 
mediated by sense.

*although at the cost of increasing the entropy of the freezer - that needs 
to work hard to transfer the entropy from the water to the radiator.

> That's why if you use a lossless compression program the output tends to 
> look like white noise. White noise has maximum entropy and maximum 
> information density; you could change it in a enormous number of ways and 
> it would still look like white noise.

It doesn't matter if it looks like white noise to us. Its aesthetic 
appearance has no bearing at all on the amount of information that has been 
encoded in it. It could be the architectural drawings of the Sistine Chapel 
or TV fuzz containing no recoverable data at all, it depends entirely on 
what senses, forms, processes, and motives are employed in the encoding and 



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