trentmkelly/LessWrong-43k huggingface dataset:
The (not so) paradoxical asymmetry between position and momentum
by Erik Jenner — 2021-03-28T13:31:08.785Z

(Cross-posted from my blog with light edits)

Related to: Which Basis is More Fundamental?

Epistemic status: Not an expert on physics, please point out any mistakes.

In physics, there appears to be a deep duality between position and momentum,
in the sense that one can switch between position-based and momentum-based views of the same system.
In classical mechanics, exchanging position and momentum via x↦p and p↦−x is a canonical transformation, meaning that it leaves the dynamics unchanged.
In quantum mechanics, the roles of position and momentum can be similarly switched
by the Fourier transform.

So mathematically speaking, it would appear that there is nothing special about either
position or momentum, both yield similar and equally good descriptions. And yet, human
cognition treats position and momentum very differently, they don't feel like dual descriptions
of reality. To us, there is a big difference between a car that is close to us and moving with a
high relative velocity (distant in momentum space) and one that is far away and more or less
stationary with respect to us.

But human cognition runs on brains, which run on physics, which seems to treat
position and momentum equivalently. So how can this be? How does the
cognitive asymmetry arise from what seems to be symmetry on the fundamental physical
level?

The motivation for this post is mostly to point out the question. Below, I'll give my best guesses for the answer, though I'm not sure that those are correct.

False assumptions?

It could be that minds don't actually "run on physics", or that they exploit unknown physics where the symmetry between position and momentum breaks in new ways. But I think most readers here will find that unlikely, at least as long as we can find a simpler explanation, so I'm not going to discuss it further.

It's also possible that the symmetry just vanishes completely in a relativistic setting (this is where actually knowing QFT would come in handy). But even then, I would also expect an explanation on a classical level because I have the intuition that you could have minds in a classical universe that perceive position and momentum differently.

Hamiltonian part I: Locality

This explanation is specific to quantum mechanics. So if it turns out to be the
reason for the asymmetry between position and momentum, this would mean
that this feature of our cognition is inherently quantu...
Inframeasures and Domain Theory
by Diffractor — 2021-03-28T09:19:00.366Z

Math prerequisites for this post: A Whole Lot of topology, some poset/lattice knowledge, have read "Basic Inframeasure Theory", just enough category theory to be familiar with functors, and other minor bits and pieces.

Domain theory is the branch of math that's like "so, what sort of topological space is a Haskell type, anyways? How do we provide a semantics for computation?"

And Inframeasure theory is about a generalization of measures which seems to hold promise for addressing several alignment issues.

Accordingly, it would be nifty if inframeasures were the sort of thing that could be worked with in Haskell. I don't know Haskell. But I do know a decent chunk of domain theory, so I can at least check how well inframeasures interface with that branch of math, as a proxy for actual computer implementation.

The major implications from this post are:

1: Yes, inframeasures do interface with domain theory quite nicely, and land in the part of it that might be feasible to implement on a computer (the ω-BC domains)

2: You can have inframeasure-like uncertainty over any Haskell type. This took some substantial generalization work, because Haskell types, as topological spaces, are very very different from the sorts of topological spaces we were working with before. Perfect for representing uncertainty about computations!

3: "take the space of inframeasures over this other type" is a well-behaved type constructor, so whatever crazy self-referential type signature you want to whip up with it (and the other usual type constructors), it'll work perfectly well. Oh, it's also a monad.

This post was cranked out in minimal time without editing, feel free to get in contact with me if there's something that needs clarification (there are probably things which need clarification).

Notation Conventions:

This section is best to refer back to if you're like "I know that symbol was defined somewhere, but it's hard to find where". This mostly just covers the stuff introduced at one point in this post and repeatedly reused. If a symbol gets introduced for a paragraph and doesn't get reused, it won't show up here.

For ordering, I reserve ≥ and ≤ for comparing numbers in R (or [0,1] or [−∞,∞] or (−∞,∞]).

For orderings on posets which are not the set of numbers, I use ⊑. ⊓ is infinima, ⊔ is suprema. ⨆↑&...
Infra-Domain proofs 1
by Diffractor — 2021-03-28T09:16:42.546Z

A quick note here is that whenever a proposition or theorem or something is cited with a complicated-looking number, like, not Proposition 3, but "Proposition 3.4.2.7", it's being cited from this book.

Proposition 2: If X is a metrizable space, then the pointwise limit of a sequence of lower-bounded lower-semicontinuous functions fn:X→(−∞,∞] with fn+1≥fn is lower-bounded and lower-semicontinuous.

Proof: Lower-boundedness of f∗(the pointwise limit of the fn) is trivial because f∗≥f1, and f1 is lower-bounded. For lower-semicontinuity, let xi limit to x, and n be some arbitrary natural number. We have

liminfi→∞f∗(xi)≥liminfi→∞fn(xi)≥fn(x)

Because f∗≥fn and fn is lower-semicontinuous. And, since this works regardless of n, we have

liminfi→∞f∗(xi)≥limn→∞fn(x)=f∗(x)

Since f∗ is the pointwise limit of the fn, showing that f∗ is lower-semicontinuous.

Proposition 3: If X is a metrizable space, then given any lower-bounded lower-semicontinuous function f∗:X→(−∞,∞], there exists a sequence of bounded continuous functions fn:X→R s.t. fn+1≥fn and the fn limit pointwise to f∗.

First, fix X with an arbitrary metric, and stipulate that f∗ is lower-bounded and lower-semicontinuous. We'll be defining some helper functions for this proof. Our first one is the gn family, defined as follows for n>0:

gn(x):=inf{f∗(x′)|d(x,x′)<1n}

Ie, we take a point, and map it to the worst-case value according to f∗ produced in an open ball of size 1n around said point. Obviously, regardless of n, gn≤f∗.

Now we must show that gn, regardless of n, is upper-semicontinuous, for later use. Let ϵ be arbitrary, and x be some arbitrary point in X, and xm be some sequence limiting to x. Our task is to show limsupm→∞gn(xm)≤gn(x), that's upper-semicontinuity.

First, we observe that there must exist an x′ s.t. d(x,x′)<1n, and f∗(x′)≤gn(x)+ϵ. Why? Well, gn(x) is "what's the worst-case value of f∗ in the 1n-sized open ball", and said worst-case value may not be exactly attained, but we should be able to find points in said open ball which get arbitrarily close to the i...
Infra-Domain Proofs 2
by Diffractor — 2021-03-28T09:15:15.284Z

Lemma 7: For f,f′,f′′,f′′′∈[X→(−∞,∞] s.t. f′′≪f and f′′′≪f′, and p∈(0,1), and X is compact, LHC, and second-countable, then pf′′+(1−p)f′′′≪pf+(1−p)f′. The same result holds for [X→[0,1]].

This is the only spot where we need that X is LHC and not merely locally compact.

Here's how it's going to work. We're going to use the details of the proof of Theorem 2 to craft two special functions g and g′ of a certain form, which exceed f′′ and f′′′. Then, of course, pf′′+(1−p)f′′′⊑pg+(1−p)g′ as a result. We'll then show that pg+(1−p)g′ can be written as the supremum of finitely many functions in [X→[−∞,∞]] (or [X→[0,1]]) which all approximate pf+(1−p)f′, so pf+(1−p)f′≫pg+(1−p)g′⊒pf′′+(1−p)f′′′, establishing that pf+(1−p)f′≫pf′′+(1−p)f′′′.

From our process of constructing a basis for the function space back in Theorem 2, we have a fairly explicit method of crafting a directed set of approximating functions for f and f′. The only approximator functions you need to build any f are step functions of the form (U↘q) with q being a finite rational number, and U being selected from the base of X, and q<infx∈K(U)f(x) where K is our compact hull operator. Any function of this form approximates f, and taking arbitrary suprema of them, f itself is produced.

Since functions of this form (and suprema of finite collections of them) make a directed set with a supremum of f or above (f′ or above, respectively), we can isolate a g from the directed set of basis approximators for f, s.t. g⊒f′′, because f′′≪f. And similarly, we can isolate a g′ which approximates f′ s.t. g′⊒f′′′, because f′′′≪f′.

Now, it's worthwhile to look at the exact form of g and g′. Working just with g (all the same stuff works for g′), it's a finite supremum of atomic step functions, so

g(x)=supi(Ui↘qi)(x)=supi:x∈Uiqi

and, by how our atomic step functions of the directed set associated with f were built, we know that for all i, qi<infx∈K(Ui)f(x). (remember, the Ui are selected from the base, so we can take the compact hull of them).

There's a critical ...
Violating the EMH - Prediction Markets
by sapphire — 2021-03-28T04:05:09.184Z

I am quite confident of the information in my post on the Efficient Market Hypothesis. I am happy to bet on the perp-future trade I described there since it is very safe. I will even give people betting against me a big advantage (1). However today I want to share some thoughts on prediction markets and group epistemics. Unlike the safe bets in my previous post, you can very easily lose money betting on prediction markets. I am including some good live trades.

Real Money Prediction Markets

There are basically two classes of prediction market bets: 'bonds' and 'actual bets'.

Bonds:

Bonds are bets that are close to 100% to payout. Currently, you can get ~3% returns in a month betting that Joe Biden will still be president on April 30th on Polymarket. These bets have been plentiful recently because of 'Maga money' but sometimes non-Maga examples come up. Obviously, this bet is not riskless, especially given there is some counterparty risk from Polymarket going under (though polymarket is supposedly non-custodial so there might be ways to recover funds). However, it is a relatively straightforward bet with quite good returns and might be attractive to some people.

Real Bets:

I should give an example of a live bet I think is good. I would suggest betting on the Olympics on FTX (not available in the USA). https://ftx.com/trade/OLY2021. The best argument is that FTX's probability seems way out of line with other sources: The Good Judgement Project has it as a 98% probability. I find the GJP relatively credible even though I think 98% is too high. Polymarket (2) and Betfair have it at ~92% and 86% probability respectively, although the volume is thin. FTX has it at ~76% with much more volume. However, you can find more considerations in this Twitter thread. The relay has already started. Last time the Olympics was postponed right before the relay began.

Research:

The same rationalist who made ~100K betting on Biden post-election made five figures betting on the above CO2 Market. He noticed that you could access the resolution data early if you changed a url parameter. Given this, he was able to tell the market was going to resolve 'No' before anyone else and make a large amount of money. It is possible such edges will be available in the future if you are clever.

Disclaimer:

Sometimes prices are pretty fair and polymarket has significant fees. A...
Core Pathways of Aging
by johnswentworth — 2021-03-28T00:31:49.698Z

Most overviews of aging suffer from multiple problems:

They dump a bunch of findings with no high-level picture.
Many of the claims they make are outdated, purely theoretical, and sometimes even outright disproven by existing work.
They are usually written by working academics, who are shy about telling us when their peers’ work is completely wrong.
They are shy about making strong claims, since this would also implicitly mean denying some claims of the authors’ peers.

This post is a high-level brain-dump of my current best models of the core pathways of aging, as I currently understand them. I have no particular reason to avoid calling out claims I think are wrong/irrelevant, and I’m going to present high-level models without pages and pages of disclaimers and discussions about results which maybe disagree with them (but are probably just wrong/irrelevant).

Epistemic status: I would be surprised if none of it turned out to be wrong, but there are multiple lines of evidence supporting most claims. It is not highly polished, and references are included only when I have them readily on hand. My ideal version of this piece would have more detailed references, more double-checking behind the claims, and more direct presentation of the data which backs up each claim. Unfortunately, that would take enough time and effort that I’m unlikely to actually get to it soon. So… here’s what I could produce in a reasonable amount of time. Hopefully it will be wrong/unhelpful in ways orthogonal to how most overviews are wrong/unhelpful.

Foundations

First, let’s recap a couple foundational principles. I’ll go through these pretty quickly; see the linked posts for more info.

Homeostasis and “Root Causes” in Aging

: the vast majority of proteins, cells, etc, in the human body turn over on a timescale from days to months. At any given time, their level (e.g. protein concentration, cell count, etc) is in equilibrium on the turnover timescale - i.e. the rate of creation approximately equals the rate of removal. For any X with turnover much faster than aging (i.e. decades), if we see the level of X increase/decrease on the timescale of a human lifetime, then that is not due to permanent “accumulation of X” or “depletion of X”; it is due to increase/decrease in the rate of creation/removal of X. For instance:

DNA damage is typically repaired on a timescale of

hours or faster

, depending on the

...
Nash Equilibria in Litigation Settlement Negotiation in the U.S.A.
by supposedlyfun — 2021-03-27T23:26:56.871Z

Epistemic status: Confident. Relevance: depends on how fast you think takeoff will be.

The overwhelming majority of legal disputes don't go to trial. They either settle (66+% of cases, according to this article; up to 95% is the common wisdom) or get dismissed (some for lack of merit, some because the case settled but the parties' public filings just show that they dismissed all their claims against each other).

So if you're a trial lawyer who wants to get optimal results for your clients, settlement negotiation is a much more important skill than trial presentation.[^1] And the keys to understanding how settlement works and why are all the typical tools of rationality.

[^1]: Provided that your opponent knows you can put on a good trial presentation if things get that far.

Settlement Structure

"Settlement" usually just means that 1) one side pays the other some money and 2) both sides give up, forever, any claims they have against the other and dismiss any pending lawsuits between them.

You might think that a better solution is for brilliant lawyers to swoop in and propose a seven-part swap involving a muskrat farm and Bitcoin futures that somehow maximizes both parties' outcome and leads their children to a dynastic marriage that will one day rule Sealand, but you'd be mostly wrong; in my experience, by the time people are suing each other, they never want to do business together again, and they are primed to be wary of uncertainty. As observed in this post, contracts are all about risk apportionment, and if you think the other side is more likely than everyone else to breach (based on the evidence that they already did breach), the risk of doing business with them again isn't worth it even if you get every risk-apportionment clause you want, because it's expensive[^2] to enforce a contract even if your eventual win is guaranteed.

[^2]: The lowest estimate I would give a client for taking their extremely simple case to full trial, including all the necessary discovery, is $50,000.

Negotiation in Practice

When creative solutions are impractical, lawyers almost always negotiate by starting at extreme numbers (usually "plaintiff's best possible day in court", so a home run, and "defendant's best day," which is typically $0 but can also be a monetary judgment in the defendant's favor) and incrementing and decrementing:

Plaintiff: Our openin

...
Making a Cheerful Bid
by DirectedEvolution — 2021-03-27T19:37:27.790Z

Asking someone for their cheerful price is asking them for the price at which they'd certainly do what you ask.

This opens the door to asking for whatever you want. Prostitution, murder, watching 'The Bachelor' on loop for all your waking hours for a year: what is your cheerful price? The answer may easily be 'I don't have one,' because my emotions can't always be indefinitely swayed by money.

This is easy, though. The harder problem is being asked your cheerful price for something you would be willing to do for money, but where the transactions costs, risks, and trust issues prevent you from negotiating it.

If you ask me my cheerful price for writing a software program, not just the work but my professional reputation is at stake. You might use your cheerful price request to justify asking me for things I'm very reluctant to do, and wouldn't do at a fair or market price.

If your service request is under-specified, you really need to ask my cheerful price to negotiate my cheerful price. How do I know you won't complain to others that my quoted price was unprofessionally high, neglecting to mention and explain that we'd agreed to a cheerful price? What if you keep inflating quality and scope demands after I commit to turn my cheerful price into a merely fair price?

You need enough of my trust in advance for me to be willing to quote you my cheerful price. I need to structure a cheerful price in a way that defends my reputation and accounts for the risk you'll say 'no,' in which case I'll have wasted my time coming up with the offer. These issues can make being asked for a cheerful price feel strangely uncomfortable.

I propose an alternative, the 'cheerful bid.' The one who wishes to pay a cheerful price comes up with a proposal of what they'll pay to cheerfully negotiate a 'cheerful price' for a product or service, with full freedom for either party to walk away from the negotiation at any time.

Here's how it might work:

Alice: Hey Bob, can I pay you $0.25/minute to negotiate your cheerful price to write some software for me?

Bob: What kind of software?

Alice: Careful, Bob, you just worked for free! I want to know if you'd accept $0.25/minute, potentially for several hours, to discuss that with you. During that negotiation we would try to find a price I am willing to pay, and you would feel delighted to accept.

Bob: Sounds weird, plus I barely know you, plus I have a lo

...
Think like an educator about code quality
by Adam Zerner — 2021-03-27T05:43:52.579Z

It's been said a thousand times: code is for humans to read, not for machines to execute. However, writing code that is easy for humans to read is much easier said than done. It's something that takes years to learn, and decades to master.

I think I might be able to offer a shortcut though: think like an educator about code quality.

Ok, "shortcut" is a strong word. It's not a shortcut. But I think that perspective counts for a lot. And Alan Kay said it counts for 80 IQ points.

Know your audience

Rails

At work we are using Rails, Node, and Vue. The main app is written in Rails, parts of the front end in Vue, and then we have lambda functions in Node. In a perfect world, Rails people write Rails, Node people write Node, and Vue people write Vue, but that's not how things work out in practice. In practice, we run into situations where the Node and Vue people end up having to read and/or write Rails code.

Rails, to put it mildly, is a quirky framework. There is a lot of magic that happens. Convention over configuration. For example, if you have:

# app/controllers/api/foo/bar/baz_controller.rb

def show
end

Rails will automatically look inside of app/views/api/foo/bar/baz for something like show.html.erb or show.jbuilder to respond with. But if you're not a Rails programmer... you wouldn't know this! All you see is an empty method that appears to be doing nothing!

And more importantly, you wouldn't be able to figure it out. The answer isn't hidden in some parent class or mixin. Instead, it's locked away in this sort of book of tribal knowledge.

I'm not sure if this example of controller actions is a good one. In practice, it's something you'd pick up pretty quickly, or someone on your team could identify and help you with right away. But there are other situations where you can do quirky things with Rails that only those with the right sort of tribal knowledge would understand.

When you are working in a team of highly experienced Rails experts, this isn't a problem. In fact, these sorts of quirky things can help Rails experts be more productive. But if you are working on a team with people new to Rails, the noobs will, without fail, end up hopelessly stuck and frustrated.

Here's where thinking like an educator comes in. Imagine that you're a professor. If you're standing in front of a small group of PhDs giving a highly specialized, focused seminar you can use fancy te...
Calibrating Adequate Food Consumption
by Gunnar_Zarncke — 2021-03-27T00:00:56.953Z

There is no such thing as healthy or unhealthy food; instead, there is only appropriate or inappropriate diet. [1]

The word 'healthy' is tabooed at my home. My kids - and maybe guests - have to use other descriptions of what they mean. At our soup party, there are frequently sweets on the table. Unhealthy? Forbidden! And there are carrot slices. Healthy? Forbidden! You may ask: Does it provide needed vitamins or nutrients? Why are these needed specifically? Does it improve digestion, e.g., via fiber? Why is that needed? Does it provide proteins for growth or carbohydrates for energy?

Really, the word 'healthy' is an oversimplification that is exploited by food ads and diet books. But it is worse. If 'healthy' would only suffer from not matching reality well, like in the Blegg/Rube example, then talking more might help. But many seem to add a halo of goodness to it that suppresses any need to add nuance.

I worry about what these distortions might lead to. With everything getting classified as healthy or unhealthy, does that leave any space for normal or adequate nutrition?

So here I want to ask: What are the types of everyday diet that are just normal? How do you eat? What part of your diet do you consider in the OK range. The goal is to collect a long list of ways people eat where you probably do not have to worry about your health. Feel free to comment on whether you think the total amount of food is too much, but that shouldn't be the main focus. Please also leave Interventions to increase Longevity and Nootropics off the table. Instead, think: What would you offer your guests, friends, or family?

Factors that Influence the Perceived Healthiness of Food (https://www.mdpi.com/2072-6643/12/6/1881/pdf )