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Comment by ludwik | Hacker News Reader

> there are far more ways for a system to be disordered than ordered

I'm a complete layman when it comes to physics, so forgive me if this is naive — but aren't "ordered" and "disordered" concepts tied to human perception or cognition? It always seemed to me that we call something "ordered" when we can find a pattern in it, and "disordered" when we can't. Different people or cultures might be able to recognize patterns in different states. So while I agree that "there are more ways for a system to be disordered than ordered," I would have thought that's a property of how humans perceive the world, not necessarily a fundamental truth about the universe

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You only hear these terms in layman explanations. Physics has precise definitions for these things. When we say "ordered", we mean that a particular macrostate has only few possible microstates.

Check this Wikipedia article for a quick overview: https://en.wikipedia.org/wiki/Microstate_(statistical_mechan...

Details can be found in any textbook on statistical mechanics.

Exactly. The coin flipping example is a very nice way to put it. It works since the coins are interchangeable, you just count the number of heads or tails.

If the coins were of different color and you took that into account, then it wouldn't work.

It's not intuitive to me what gravity has to do with entropy though, as it's classically just a force and completely reversible (unlike entropy)? Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed.

> Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed.

How does that work with things like black holes? If you saw an apple spiral out of a black hole, wouldn't you suspect that you were watching a reversed video? Even if you take account the gravitational waves?

If you saw a comet coming from the sun, or a meteorite coming from the moon, etc. you would also find that suspicious.

Comets are in elliptical orbits around the sun so literally half the time they're traveling away from the sun.

Sometimes they don’t make it:

https://en.wikipedia.org/wiki/Sungrazing_comet

https://www.space.com/8478-comet-collision-sun-captured-3.ht...

Yea and those happen when other forces than gravity come into play. When matter starts colliding.

Every object has been subject to forces other gravity at some point.

And the point is that sometimes comets do indeed fall into the Sun. If you object to people calling that a comet that’s fine - we can use whatever name you want.

The point is that the gravity interactions are time reversible. Not so with friction etc.

Sure, nothing in the laws of physics prevents a celestial body from distancing itself from the Sun or from the Moon. But it would like suspicious! Wouldn't you suspect that you were watching a reversed video?

You don't understand my point. If we watch purely gravity interactions, the video can be reversed and you wouldn't be able to detect it.

If a meteor crashes into the moon, there's other effects than gravity that makes the video not reversible. Ie it's not only gravity.

That's the point.

In other words, if a comet approached the moon at high speed, missed and slingshotted in another direction, it would be traveling away from the moon, but the video would be time reversible and you couldn't be able to detect it. Gravity only interaction.

I think you don’t understand my point.

Someone wrote “If you saw an apple spiral out of a black hole, wouldn't you suspect that you were watching a reversed video?”

I replied “If you saw a comet coming from the sun, or a meteorite coming from the moon, etc. you would also find that suspicious.”

I don’t know what part do you object to (if any).

> If a meteor crashes into the moon, there's other effects than gravity that makes the video not reversible.

If a meteor (or an apple) is still in a crashing trajectory when you stop recording there are no effects other than gravity. The video is reversible - it just looks weird when you play it in reverse (because the meteor seems to be coming from the Moon and the apple seems to be coming from the black hole if you try to imagine where they were before).

Well yes for example if there was a cannon firing an apple from the moon, then it would travel the same trajectory, just in reverse.

But we know there are no apple firing cannons on the moon.

Ie if an object was coming from the moon and its past trajectory intersected with the moon's surface, you could say "this is reverse video".

That was exactly my point, that an apple coming from a black hole may seem problematic but so does an apple coming from the Sun. I don't see an essential difference regarding the "reversibility" of the physical process (but I could be wrong).

Maybe this thought experiment makes it clear. There's a cannon firing straight up from the lunar pole. One cannot observe the explosion charge. The ball goes straight up, and then falls down and goes back to the barrel. The cannon is filmed from afar firing and you can see the whole ball travel.

Then you are shown two films, the normal and a reversed one. Would you be able to tell which one is which, and if so, how?

> Maybe this thought experiment makes it clear.

Everything was already clear, I think.

That's the question of why time only goes forwards. It seems to be that the universe started in an extremely low-entropy state. It will go towards high entropy. In a high entropy state (e.g. heat death, or a static black hole), there's no meaningful difference between going forwards or backwards in time - if you reverse all the velocities of the particles, they still just whizz around randomly (in the heat death case) or the black hole stays a black hole.

Classical gravity doesn't work like that. An apple does not spiral into a black hole in space there. It's in an elliptical orbit. (A circle is a special ellipse.)

Think minimum description length. Low entropy states require fewer terms to fully describe than high entropy states. This is an objective property of the system.

In a deterministic system you can just use the time as a way to describe a state, if you started from a known state.

You're thinking of information entropy, which is not the same concept as entropy in physics. An ice cube in a warm room can be described using a minimum description length as "ice cube in a warm room" (or a crystal structure inside a fluid space), but if you wait until the heat death of the universe, you just have "a warm room" (a smooth fluid space), which will have an even shorter mdl. Von Neuman should never have repurposed the term entropy from physics. Entropy confuses a lot of people, including me.

And somewhat surprisingly the heat death of the universe is the maximal entropy state.

Because there are an infinite number of microstates (all the particles are interchangeable) that lead to the same macrostate: nothing happening for ever!

Maxwell's demon thought experiment implies they are the same concept. Given a complete knowledge of every particle of gas you can in principle create unphysical low entropy distributions of the particles. This[1] goes into more detail.

[1] https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_...

A fun visual explanation: https://youtu.be/8Uilw9t-syQ?si=D9sR2YAm40SPFG3a

“Number of terms” is a human language construct.

No, it's a representation construct, i.e. how to describe some system in a given basis. The basis can be mathematical. Fourier coefficients for example.

Mathematics is a human language. It being a formal language doesn’t change that.

Further, it’s not objective: you’re choosing the basis which causes the complexity, but any particular structure can be made simple in some basis.

Mathematical notation is a human invention, but the structure that mathematics describes is objective. The choice of basis changes the absolute number of terms, but the relative magnitude of terms for a more or less disordered state is generally fixed outside of degenerate cases.

The structure that most words describe is objective, so you haven’t distinguished math as a language. (Nor is mathematics entirely “objective”, eg, axiom of choice.) And the number of terms in your chosen language with your chosen basis isn’t objective: that’s an intrinsic fact to your frame.

The complexity of terms is not fixed — that’s simply wrong mathematically. They’re dependent on our chosen basis. Your definition is circular, in that you’re implicitly defining “non-degenerate” as those which make your claim true.

You can’t make the whole class simplified at once, but for any state, there exists a basis in which it is simple.

This is getting tedious. The point about mathematics was simply that it carries and objectivity that natural language does not carry. But the point about natural language was always a red-herring; not sure why you introduced it.

>You can’t make the whole class simplified at once

Yes, this is literally my point. The further point is that the relative complexities of two systems will not switch orders regardless of basis, except perhaps in degenerate cases. There is no "absolute" complexity, so your other points aren't relevant.

I didn’t introduce it, you did — by positing that formal language is more objective, as you’ve again done here. My original point was that mathematics is human language.

> The further point is that the relative complexities of two systems will not switch orders regardless of basis, except perhaps in degenerate cases.

Two normal bases: Fourier and wavelet; two normal signals: a wave and an impulse.

They’ll change complexity between the two bases despite everything being normal — the wave simple and impulse complex in Fourier terms; the wave complex and impulse simple in wavelet terms.

That our choice of basis makes a difference is literally why we invented wavelets.

Yes, that is a degenerate case. We can always encode an arbitrary amount of data into the basis functions to get a maximally simple representation for some target signal. If the signal is simple (carries little information) or the basis functions are constructed from the target signal, you can get this kind of degeneracy. But degenerate cases do not invalidate the rule for the general case.

You can safely replace the terms "order" and "disorder" with "unlikely" and "likely". Simply put, entropy is a measure of how closely a system resembles its "most likely configuration". Consider the discrete entropy of a series of coin flips. Three tosses could result in the following 8 states: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. From that we can gather that there is a 1/8 chance of getting either zero or three heads and a 3/8 chance of getting one or two heads. That latter two cases are clearly more likely (and hence associated with a higher entropy). In physics of course entropy is generally the continuous kind, not simple set of binary microstates. But the principle is essentially the same.

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