Entropy explained, with sheep (2016) • Hacker News Board

Re: Entropy explained, with sheep (2016)

#61

Post by 0134340 » Fri, Aug 14, 2020, 9:51 PM UTC

layer8 wrote: post #54

kergonath wrote: post #52

Earlier quoted context omitted.

We don’t have an answer to this question. I don’t want to discuss metaphysics here, but there is a very interesting discussion on that subject here: https://youtube.com/watch?v=-6rWqJhDv7M

Let me rephrase maybe: Given the state of affairs I described above, I don’t understand what is the convincing argument that entropy does indeed increase in the long run. Any argument given should also work in the reverse direction, given the symmetry of time, shouldn’t it? (And thereby create a kind of reductio ad absurdum.) If not, why not?

>symmetry of time

Time isn't symmetric.

"Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal." - https://en.wikipedia.org/wiki/T-symmetry

Re: Entropy explained, with sheep (2016)

#62

Post by imcoconut » Fri, Aug 14, 2020, 9:55 PM UTC

bobsoap wrote: post #47

I love how the notion of entropy permeates into so many other things. It's fundamental, universal, and at the heart of nearly every aspect of our existence. Take philosophy. If the ultimate state of everything culminates in chaos (according to the theory of entropy), the human existence constitues the exact opposite: controlling the chaos that surrounds us, and shaping it into something useful and, in entropy-speak,…

It's true. Have you read the book "What is Life?" By Schrodinger? He discusses the very concept you're talking about as he speculates on the physical substrate of genetic information (which was discovered to be DNA not long after the book was published).

Re: Entropy explained, with sheep (2016)

#63

Post by combatentropy » Fri, Aug 14, 2020, 9:57 PM UTC

bobsoap wrote: post #47

I love how the notion of entropy permeates into so many other things. It's fundamental, universal, and at the heart of nearly every aspect of our existence. Take philosophy. If the ultimate state of everything culminates in chaos (according to the theory of entropy), the human existence constitues the exact opposite: controlling the chaos that surrounds us, and shaping it into something useful and, in entropy-speak,…

> Survival is the battle against entropy

See my username ;) But my inspiration was from trying to make a difference within corporate culture, not raw survival.

> controlling the chaos that surrounds us, and shaping it into something useful

i.e., work

> In the long run, life will lose.

Unless there is a transcendent being beyond our universe, an explanation believed by many people for why, a long time ago, entropy was microscopic. The article admits it can't come up with a materialistic explanation and ends by calling it a "mystery".

Re: Entropy explained, with sheep (2016)

#64

Post by kergonath » Fri, Aug 14, 2020, 9:59 PM UTC

layer8 wrote: post #54

kergonath wrote: post #52

Earlier quoted context omitted.

We don’t have an answer to this question. I don’t want to discuss metaphysics here, but there is a very interesting discussion on that subject here: https://youtube.com/watch?v=-6rWqJhDv7M

Let me rephrase maybe: Given the state of affairs I described above, I don’t understand what is the convincing argument that entropy does indeed increase in the long run. Any argument given should also work in the reverse direction, given the symmetry of time, shouldn’t it? (And thereby create a kind of reductio ad absurdum.) If not, why not?

It’s fundamentally an empirical law, even if one of the best-verified ones. I don’t think there really is a convincing argument, other than “we haven’t seen a single instance of the opposite being true”.

It’s a missing piece in quantum mechanics (linked to decoherence) and quantum loop gravity (in which time is...interesting).

The issue you mention (how can the 2nd law and the fact that the laws of Physics don’t care about the direction of time be true at the same time) is a big problem.

I really recommend watching the video if you haven’t, it is fascinating and well worth the time.

Re: Entropy explained, with sheep (2016)

#65

Post by [deleted] » Fri, Aug 14, 2020, 10:14 PM UTC

layer8 wrote: post #54

kergonath wrote: post #52

Earlier quoted context omitted.

We don’t have an answer to this question. I don’t want to discuss metaphysics here, but there is a very interesting discussion on that subject here: https://youtube.com/watch?v=-6rWqJhDv7M

Let me rephrase maybe: Given the state of affairs I described above, I don’t understand what is the convincing argument that entropy does indeed increase in the long run. Any argument given should also work in the reverse direction, given the symmetry of time, shouldn’t it? (And thereby create a kind of reductio ad absurdum.) If not, why not?

[deleted]

Re: Entropy explained, with sheep (2016)

#66

Post by kgwgk » Fri, Aug 14, 2020, 10:20 PM UTC

layer8 wrote: post #42

That still doesn’t answer the question how, if the laws of physics are time-symmetric, the universe as a whole can have a time-asymmetric evolution of entropy. I.e., if something forces entropy to increase in the long run, then that should hold in both directions of time. So what is it that causes entropy to only increase in the direction of the future, but not in the direction of the past, given that the laws pf phy…

Thermodynamic entropy is not really a physical property of a system, it is a property of our description of the system subject to some macroscopic constraints.

Re: Entropy explained, with sheep (2016)

#67

Post by thaumasiotes » Fri, Aug 14, 2020, 10:34 PM UTC

PaulDavisThe1st wrote: post #19

This was really great. It's how I was taught entropy at college (biophysics and molecular biology) though without the sheep. "Statistical Mechanics" was the name our professor used. The only tiny change I'd like to make is to add a line or two near the end, something along the following lines: There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid.…

> There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid. Most arrangements of water molecules look like a liquid, and so that's the likely endpoint even if they start arranged as an ice cube.

Except this is, as an insight, obviously wrong. The arrangement you get is determined by temperature: cold water will spontaneously freeze, and hot ice will spontaneously melt. The model you state predicts that

- Hot ice will spontaneously melt (correct)

- Cold ice will spontaneously melt (nope)

- Cold water will not spontaneously freeze (nope)

Re: Entropy explained, with sheep (2016)

#68

Post by PaulDavisThe1st » Fri, Aug 14, 2020, 10:40 PM UTC

layer8 wrote: post #54

kergonath wrote: post #52

Earlier quoted context omitted.

We don’t have an answer to this question. I don’t want to discuss metaphysics here, but there is a very interesting discussion on that subject here: https://youtube.com/watch?v=-6rWqJhDv7M

Let me rephrase maybe: Given the state of affairs I described above, I don’t understand what is the convincing argument that entropy does indeed increase in the long run. Any argument given should also work in the reverse direction, given the symmetry of time, shouldn’t it? (And thereby create a kind of reductio ad absurdum.) If not, why not?

I think it collapses down to an even simpler, perhaps even tautological point (though I think that it really isn't).

In a system with energy present, the system is continually and randomly shifting between microstates.

We identify macrostates, and analytically can identify certain macrostates as having more or less possible microstates.

Given the constant random movement between microstates (thanks, energy!), the system's macrostate is most likely to be one represented by large numbers of microstates.

The system isn't really "increasing its entropy" - it's simply randomly exploring all accessible microstates. If we could observe the microstates directly, we'd probably never think of entropy at all. But since we observe the macrostates, we also end up noticing that over time, systems with energy tend toward macrostates representing large numbers of microstates.

If the opposite were true, you'd basically be saying "more probable things are actually less probable", which is contradictory. Increasing entropy is really just a different way of saying that "more probable things tend to happen".

Because of the relationship between microstates and macrostates, and our cognitive biases towards certain macrostates, we tend to notice things moving towards what we consider disorder. All that is really happening that things just tend toward "more probable" macrostates, because they represent larger numbers of possible microstates.

Again, if you were unaware of the macrostates, you'd see no asymmetry.

Re: Entropy explained, with sheep (2016)

#69

Post by PaulDavisThe1st » Fri, Aug 14, 2020, 10:55 PM UTC

thaumasiotes wrote: post #67

PaulDavisThe1st wrote: post #19

This was really great. It's how I was taught entropy at college (biophysics and molecular biology) though without the sheep. "Statistical Mechanics" was the name our professor used. The only tiny change I'd like to make is to add a line or two near the end, something along the following lines: There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid.…

> There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid. Most arrangements of water molecules look like a liquid, and so that's the likely endpoint even if they start arranged as an ice cube. Except this is, as an insight, obviously wrong. The arrangement you get is determined by temperature: cold water will spontaneously freeze, and hot ice will…

In keeping with the level of explanation in the article, I was omitting the role of energy in describing the exploration of possible microstates by the system.

A system with zero energy is highly constrained in its exploration of possible microstates, and thus is unlikely to undergo a change in its macrostate.

A system with a lot of energy is much less constrained, and is more likely to undergo macrostate changes.

This wasn't really covered in the article, so I didn't want to put it into my (perhaps foolish) add on sentences.

Re: Entropy explained, with sheep (2016)

#70

Post by thaumasiotes » Fri, Aug 14, 2020, 10:57 PM UTC

PaulDavisThe1st wrote: post #69

thaumasiotes wrote: post #67

Earlier quoted context omitted.

> There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid. Most arrangements of water molecules look like a liquid, and so that's the likely endpoint even if they start arranged as an ice cube. Except this is, as an insight, obviously wrong. The arrangement you get is determined by temperature: cold water will spontaneously freeze, and hot ice will…

In keeping with the level of explanation in the article, I was omitting the role of energy in describing the exploration of possible microstates by the system. A system with zero energy is highly constrained in its exploration of possible microstates, and thus is unlikely to undergo a change in its macrostate. A system with a lot of energy is much less constrained, and is more likely to undergo macrostate changes. Th…

This followup still predicts that cooling water cannot cause it to freeze. (And relatedly, it predicts that cold ice will take a long time to melt, but not that it won't melt. In fact, it won't melt.)