Eigil Rischel

I maintain a reading list on Goodreads. I have a personal website with some blog posts, mostly technical stuff about math research. I am also on github

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Demystifying the Second Law of Thermodynamics

I hadn't, thanks!

I took the argument about the large-scale "stability" of matter from Jaynes (although I had to think a bit before I felt I understood it, so it's also possible that I misunderstood it).

I think I basically agree with Eliezer here?

The Second Law of Thermodynamics is actually probabilistic in nature - if you ask about the probability of hot water spontaneously entering the "cold water and electricity" state, the probability does exist, it's just very small. This doesn't mean Liouville's Theorem is violated with small probability; a theorem's a theorem, after all. It means that if you're in a great big phase space volume at the start, but you don't know where, you may assess a tiny little probability of ending up in some particular phase space volume. So far as you know, with infinitesimal probability, this particular glass of hot water may be the kind that spontaneously transforms itself to electrical current and ice cubes. (Neglecting, as usual, quantum effects.)

So the Second Law really is inherently Bayesian. When it comes to any real thermodynamic system, it's a strictly lawful statement of your beliefs about the system, but only a probabilistic statement about the system itself.

The reason we can be sure that this probability is "infinitesimal" is that macrobehavior is deterministic. We can easily imagine toy systems where entropy shrinks with non-neglible probability (but, of course, still grows /in expectation/). Indeed, if the phase volume of the system is bounded, it will return arbitrarily close to its initial position given enough time, undoing the growth in entropy - the fact that these timescales are much longer than any we care about is an empirical property of the system, not a general consequence of the laws of physics.

To put it another way: if you put an ice cube in a glass of hot water, thermally insulated, it will melt - but after a very long time, the ice cube will coalesce out of the water again. It's a general theorem that this must be less likely than the opposite - ice cubes melt more frequently than water "demelts" into hot water and ice, because ice cubes in hot water occupies less phase volume. But the ratio between these two can't be established by this sort of general argument. To establish that water "demelting" is so rare that it may as well be impossible, you have to either look at the specific properties of the water system (high number of particles the difference in phase volume is huge), or make the sort of general argument I tried to sketch in the post.

Demystifying the Second Law of Thermodynamics

This may be poorly explained. The point here is that

  • is supposed to be always well-defined. So each state has a definite next state (since X is finite, this means it will eventually cycle around).
  • Since is well-defined and bijective, each is for exactly one .
  • We're summing over every , so each also appears on the list of s (by the previous point), and each also appears on the list of s (since it's in )

E.g. suppose and when , and . Then is . But - these are the same number.

Biextensional Equivalence

But then shouldn't there be a natural biextensional equivalence ? Suppose , and denote . Then the map is clear enough, it's simply the quotient map. But there's not a unique map - any section of the quotient map will do, and it doesn't seem we can make this choice naturally.

I think maybe the subcategory of just "agent-extensional" frames is reflective, and then the subcategory of "environment-extensional" frames is coreflective. And there's a canonical (i.e natural) zig-zag

Biextensional Equivalence

Does the biextensional collapse satisfy a universal property? There doesn't seem to be an obvious map either or (in each case one of the arrows is going the wrong way), but maybe there's some other way to make it universal?

Efficient Market Frontier

What do you think about "cognitive biases as an edge"?

One story we can tell about the markets and coronavirus is this: It was not hard to come to the conclusion, by mid-to-late February, that a global COVID-19 pandemic was extremely likely, and that it was highly probable it would cause a massive catastrophe in the US. A few people managed to take this evidence seriously enough to trade on it, and made a killing, but the vast majority of the market simply didn't predict this fairly predictable course of events. Why not? Because it didn't feel like the sort of thing that could happen. It was too outlandish, too weird.

If we take this story seriously, it makes sense to look for other things like this - cases where the probability of something is being underestimated - because it seems too weird, because it's too unpleasant to think about, or for some other reason.

For example, metaculus currently estimates something like a 15% chance that Trump loses the election and refuses to concede. I we take that probability seriously, and assume something like that is likely to lead to riots, civil unrest, uncertainty, etc, would it make sense to try and trade on that? On the assumption that this is not priced in, because the possibility of this sort of crisis is not something that the market knows how to take seriously?

Tips/tricks/notes on optimizing investments
  • What are some reputable activist short-sellers?
  • Where do you go to identify Robinhood bubbles? (Maybe other than "lurk r/wallstreetbets and inverse whatever they're hyping").

I guess this question is really a general question about where you go for information about the market, in a general sense. Is it just reading a lot of "market news" type sites?

How much is known about the "inference rules" of logical induction?

Thank you very much!

I guess an argument of this type rules out a lot of reasonable-seeming inference rules - if a computable process can infer "too much" about universal statements from finite bits of evidence, you do this sort of Gödel argument and derive a contradiction. This makes a lot of sense, now that I think about it.

What are the best tools you have seen to keep track of knowledge around testable statements?

There is also predictionbook, which seems to be a similar sort of thing.

Of course, there's also metaculus, but that's more of a collaborative prediction aggregator, not so much a personal tool for tracking your own predictions.

We run the Center for Applied Rationality, AMA

If anyone came across this comment in the future - the CFAR Participant Handbook is now online, which is more or less the answer to this question.

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