Church Of Thermodynamics

[Ziggurat]

I didn't go that far. I said that thermodynamics is a local approximation

You can say that, but it's not true.

I do not expect the entire universe to be crunched into a point, and I do not expect heat death.

And yet, you cannot tell us in any reasonable (let alone scientific) way what you think will happen. What you have said is so ambiguous as to be meaningless

Approximations can predict things after a long time, but not an infinite time.

Oh, but they can. In fact, many approximations become MORE accurate with time. For example, the discharge of a capacitor through a resistor. Simple exponential decay towards zero. That's an approximation, since a real circuit will also have self-inductance, but it's an approximation which becomes increasingly accurate over time, not less. And it will converge on the real answer in the limit of infinite time.

Any subset of the universe other than the whole universe has a kolmogorov complexity more than 0, so it exists, but together the kolmogorov complexity of 0 does not exist.

That's word salad. It means nothing. And applying kolmogorov complexity to the universe is unscientific, as I already pointed out and which you have yet to respond to.

It has never been proven that we interact with only a finite part of the universe

And it's never been proven that leprechauns don't exist either. But if general relativity is correct (and everything we've observed indicates it is), then we do only interact with a finite part of the universe.

and there is no way you can prove it, therefore it is not a scientific theory.

You are apparently deeply misinformed about what science is. Science is never provable. It is disprovable. General relativity (which constrains out interactions to a finite region of the universe) is disprovable, and therefore scientific.

Kolmogorov complexity 0 means nonexistance. What do you think it means?

That given a particular language (a prerequisite for kolmogorov complexity), no additional information is required to describe whatever it is you're considering. Which means that the language uniquely specifies it.

If you only mean nonexistence, well, you don't need kolmogorov complexity for that. But that's so self-evidently wrong that we can discard it immediately.

If the universe is a fractal (and I think it is)

What does that even mean? I don't think you actually have any concrete idea behind this statement, I think all you've got are some vague half-notions.

 

[edd]

Just a point about thermodynamics, BenRayfield: you do realize that the "laws" of thermodynamics are not necessarily fundamental, right? What are commonly referred to as the "laws" of thermodynamics are actually the result of the most probable outcome of large numbers of interacting particles within a system, also known as statistical mechanics.

That's not true of the first law is it?

 

[Dancing David]

Those are not the exact definitions I was using. I'll give an example to make the difference clear:

My theory says that the 4 forces will decay into some other patterns of forces the same way mass/energy decays as described by thermodynamics.

And this manifests in the visible world of evidence how?

Does it shows up where exactly?

Note: I am not saying that it could not, however what you stated would have a great impact on sub-particle and particle physics on a large scale.

 

[MattusMaximus]

That's not true of the first law is it?

Correct. Thanks for the catch on that. The first law is essentially an expression of the conservation of energy.

 

[Ziggurat]

Most definitions of entropy for non-physicists (like me) are a bit, er, misleading. Or simply incomprehensible.

Sadly, that's true, even though the actual definition is pretty simple.

"Disorder" is a frequently used synonym for entropy, but as I (not? mis?)understand the concept, it seems rather like too much order, similarity, to me - an equilibrium, a melange, like coffee and cream totally mixed into one indistinguishable light brown brew. Order is reliable, unchanging, frequently boring. Disorder means action, violent clashes, shaking up things in everyday language.

Indeed, our intuitive perception of order doesn't precisely match the thermodynamic definition of entropy.

I've tried to explain order and disorder, so maybe Ziggurat can explain entropy to me.

Sure. Imagine you've got a macroscopic system (a solid, a liquid, whatever), and you know the macroscopic parameters of this system (volume, total energy, the number and kinds of atoms, etc). Those macroscopic parameters don't completely specify the state of the system (basically, the position and momentum of every particle), of course, they only put constraints on the system. For a given set of macroscopic constraints (which specify a macrostate), there will be some very large number of possible configurations of all your microscopic parameters (which specify a microstate). Entropy is a measure of the number of accessible microstates (that is, the number of microstates that "fit" under your macrostate). Now, we don't use the number of microstates itself, and here's why. If we consider two systems, the total number of accessible microstates for the combined system is the product of the number of accessible microstates for each individual system. But that's inconvenient: I'd like a quantity that adds, not multiplies. So I take the logarithm of the number of microstates, because the log of a product of two numbers is the sum of the logs of each number. So entropy is the logarithm of the number of accessible microstates, nothing more and nothing less.

Now, this number has some relationship to what we consider as disorder (more states = more "disorder", roughly speaking). But even though I've defined entropy rigorously, I can't actually define disorder rigorously in a way that matches your intuitive sense. Take the coffee example: the partially mixed milk & coffee seems more disordered to you than the thoroughly mixed, apparently uniform blend. But the entropy of the former is quite definitely smaller than the latter: I can find more ways to mix coffee and milk molecules so that they look uniform than I can to make them look non-uniform. So whether or not it meets our intuitive sense of disorder, the thermodynamics is quite clear: uniformly mixed milk and coffee has a higher entropy than partially mixed milk and coffee. Which is why it's a one-way process: swirling the spoon will always mix, not unmix, coffee and milk.

 

[dlorde]

...
On a related subject - randomness - can "real randomness" as it applies to information theory even be achieved by a computer, by itself, without someone to wriggle the mouse for "extra randomness"?

Strictly speaking, no, AIUI, not without a hardware based random number generator. This is not so difficult to do - you can extract random numbers out of noise in fairly simple circuits. But computational pseudo-random number generators can be pretty good - i.e. good enough to make the output hard to distinguish from true randomness - however, devising a good test is itself difficult - which is partly why computational pseudo-random numbers are generally considered good enough for most purposes.

 

[Eligbak]

To continue my classes at the night college of thermodynamics:

Entropy is a measure of the number of accessible microstates (that is, the number of microstates that "fit" under your macrostate).

I just deleted my little opus because I got sidetracked by Wikipedia's definition of micro- and macrostates - here's a better one.