XelaP

Karma: 438

XelaP 26 Mar 2026 0:40 UTC
1 point
0
in reply to: papetoast’s comment on: Raemon’s Shortform Feed
I can’t view your link—it 404s.

XelaP 18 Mar 2026 18:00 UTC
4 points
0
on: Small Steps Towards Proving Stochastic → Deterministic Natural Latent
My university happens to have a supercomputer. There’s a good chance I could run code on it if asked. Since it may have quirks I’ll probably write code for it myself; but would you be willing to check the code/decide to write it if I’m unwilling and there aren’t weird quirks/give ideas for what to run/be interested in the results etc.?
Not committing to anything, as I’m historically pretty bad at follow through, but I do plan on actually asking for access.
I currently have some slow python code that can take any list of in-DAGs and an outDAG and then tries to find a joint distribution that maximizes the kl or jensen shannon error ratio of out/(sum of in). It would have to be extended in order to be used for this problem.

XelaP 18 Mar 2026 9:44 UTC
1 point
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on: Give it a google
In middle school, I realized that I can just Google things I wanted to know, and thereby learn the answers. However, I didn’t have the habit of doing this. I endeavored to make it a habit. By the time I was in highschool, I remember realizing that I indeed had the habit, atd had benefitted a lot.
A similar piece of advice I wish I got: People write textbooks about subjects. You can get them for free on the internet (often it’s even legal! the authors sometimes put the pdf on their pages themselves! it’s also possible to pirate illegally from e.g. anna’s archive or libgen or for papers scihub), or buy a physical copy. You can then read them. Yes, you, if you know the language, can read a textbook, even if it’s supposedly a ‘graduate level’ textbook on quantum mechanics and you’re a 15 year old who only knows calculus (likewise, you can just read a calculus textbook). Often intro books explain necessary prerequisites; either way you can often learn on the fly.

XelaP 18 Mar 2026 8:19 UTC
1 point
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on: Terrified Comments on Corrigibility in Claude’s Constitution
Insofar as corrigibility is a coherent concept with a clear meaning, I would expect that it does require that an AI actively participate in projects as directed by its principal hierarchy—or rather, to consent to being retrained to actively participate in such projects. (You probably want to do the retraining first, rather than using any work done by the AI while it still thought the project was morally abhorrent.)
I agree this isn’t pure corrigibility (to use Max Harms’s term from the CAST proposal), but note that not actively participating is still mostly corrigible, in a stable way. You’d get most of the benefit from an AI that merely does nothing when you instruct it to do something it doesn’t want, as opposed to one that opposes your will. You’d still need it to stop when instructed to, though.

XelaP 18 Mar 2026 7:41 UTC
1 point
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in reply to: gjm’s comment on: What Is a Major Chord?
My understanding is that Helmholtz came up with the basics of the beat theory, in his On the Sensations of Tone. E.g. this excellent website cites him.

XelaP 18 Mar 2026 7:24 UTC
1 point
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on: What Is a Major Chord?
And here’s a basic theory of what sounds good, called the Helmholtz consonance theory.
When you play a note at a frequency, you actually also get whole numbet multiples of the ‘fundamental’ frequency. This is due to the physics of waves on e.g. a string (or air in a cavity) - since the ends are tied to not move, only whole number multiples match the ends. These are called ‘overtones’. For this reason octaves (which is 2x the frequency) sound perceptually similar—you just skip all the odd multiples.
Now, if you play two frequencies that are close together, the combined sound’s loudness will oscillate over time due to interference—for a small difference this is fast and dissonant, but for a large difference it’s a nice slow ‘vibrato’. This is called a ‘beat’ or ‘beating’. Thus, if the overtones perfectly (up to what you can hear) match you’ll get nice sounds (consonance), but if they differ by a little then they sound dissonant, and if they differ by more then it’s fine again.
Therefore small integer ratios sound the most consonant. An example is a 3:2 ratio, in between unison and an octave—and this is a “perfect fifth” (meaning you go up 8 half steps—though the usual “equal tempered” tuning only approximates the 3:2 ratio via a 2^(8/12) = 2^(2/3) ≈ 3.2:2 ratio, e.g. from C to G. Likewise major thirds (C to E) are (close to) a 5:4 ratio and sound good, but a half step lower (a minor third, like C to E flat/D sharp) sound a little funky. Seconds (C to D) and especially minor seconhs (C to D flat/C sharp) sound the most dissonant.
The reason why people use those weird 12th roots of 2 for the notes is that if you try to use the actual ratios you want, then you get a problem where each note increment can’t be equal, and so you can follow two sequences of integer ratio (‘justly tuned’) increments that give you slightly different frequency values. For example, four fifths compared to 2 octaves + a third gives tones which differ by a ratio of ⁸¹⁄₈₀. Whichever you choose to put on your instrument, you’ll have made the other sound out of tune.
‘Equal temperament’ fixes this by making everything a little out of tune, using 12th roots of 2 so that you can approximate the just intervals pretty well while still having equal half step increments. People usually use this nowadays instead of trying to do the older ‘just intonation’.

XelaP 18 Mar 2026 6:19 UTC
1 point
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on: Walking Math
I don’t think this is compelling, at least if extended beyond “Alternate between pacing and writing on a whiteboard”, which is what I actually do. But it’s possible that I’ve already got whatever skill you are trying to train—for example, the first two parts of Theorem 3 doesn’t require almost any algebra for me, and so of course I could do it in my head—I’m confused why you think they do. I just think “Apply linearity and divide by n, and scaling squares variance”. If I struggled with it, I don’t think I would be helped much by writing things down except for the problem statement.
The third part was trickier because it took me a little to figure out how to evaluate the covariance, and also I made some errors that would’ve been hard to diagnose had I not decided to write it down when the problem popped up. I would’ve done it faster had I just written it down, and I don’t feel that I understand it more for having done most of it in my head.
Paper lowers overhead, where by overhead I mean mental overhead i.e. the overhead that matters most. The point is to expand my working memory so I can focus on what matters, and make better visualizations in some respects. This is very important because math often strains my working memory or visualization, so offloading that allows me to do harder stuff and understand more. If I have to keep X in my head, then I can’t throw it out to visualize Y, especially if Y turns out to be a bad idea and so I need to go back to X in order to think of what to try next.
Remembering the current state often simply isn’t enough, as I’ll want to explore what the previous steps were, what they imply, how they relate to the current step, etc.
I write down shorthand English for various ideas of what to do, or what the problem is, and then stare at them while I think. It is somehow easier to think when the words are on the wall.
**The actual hard steps happen in my head**, as you can tell from the fact that I’m usually pacing around thinking and only come back to write when I’ve had a good idea or need to do some algebraic calculations or whatever, just like using a computer to do numerical experiments. I definitely recommend it, but I would’ve guess most pacers would already have found themselves pacing and thinking. Guess I was wrong there!
For longer periods of time, writing or typing lets me remember. I don’t have a problem coming back to something I’ve worked on when it’s been on my mind or if it hasn’t been that long, but if it’s been a week and I’ve thought about many other things then the details have gone right out the gutter.
For physics, it’s definitely useful to do Fermi estimates in your head, by memorizing the values of certain things and being good at approximate arithmetic. I’ve also heard Oliver Habryka mention how quick Fermi estimates are useful to him constantly for things like checking contractor projections or planning how hard it’ll be to hire a specialist in a city.

XelaP 18 Mar 2026 1:15 UTC
3 points
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on: Replaceable Axioms give more credence than irreplaceable axioms
Hah, I had the same idea reading math! A different lens on a related topic is John’s post on ad hoc math definitions. In that lens, you can phrase it as: a mathematical definition that’s singled out by multiple axiomatic characterization is more likely to be “good” (natural, encompassing intuitive properties, useful in practice, appearing in multiple places, etc.). Likewise, the more obvious “prefer less axioms to more”.

An example I saw John use: Probability has multiple frameworks that each give rise to it, be it bets, theorems like complete class or savage’s theorem rooting it and expected utility in preferences, frequentism, and minimum description length/algorithmic information theory.

XelaP 18 Mar 2026 1:11 UTC
3 points
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in reply to: johnswentworth’s comment on: Coherent decisions imply consistent utilities
Nitpick: He does link to VNM once, when giving the name for Independence, so that might techincally count as a mention. I otherwise agree ; however I think VNM gets too much of a bad rap. The finite case is simple, gives a conceptual understanding of why expected utility arises given the assumptions, and uses a few axioms of which some have supporting arguments (like semiformal dutchbooks). If we had no other coherence theorems then I think it is correct to update a lot on VNM, as I did when I first learned of it. Expected utility really does seem a lot less ad hoc after understanding VNM.

XelaP 17 Mar 2026 23:22 UTC
6 points
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in reply to: XelaP’s comment on: PSA: Predictions markets often have very low liquidity; be careful citing them.
Polymarket’s brier score, from their accuracy page , along with Manifold’s data broken out by liquidity as found in the comment they linked from their accuracy page

XelaP 17 Mar 2026 23:13 UTC
5 points
2
in reply to: aog’s comment on: PSA: Predictions markets often have very low liquidity; be careful citing them.
‘Accuracy’ is not a great statistic imo (it just tells you about the direction, e.g. if you say 51% for something that happens you are ‘accurate’). Thankfully Polymarket publishes Brier scores. You can see that while liquidity helps, it’s already not bad for the lower liquidity buckets (.09 up to $10k, then .08 up to $25k, .07 up to $100k, .05 up to $250k, .04 up to $500k, .03 up to $1M, .02 for $1M+)

XelaP 17 Mar 2026 23:00 UTC
32 points
7
on: PSA: Predictions markets often have very low liquidity; be careful citing them.
Manifold has calibration statistics about their markets. They seem well calibrated and the accuracy peaks around 10-20 traders. They even cite a paper from 2007 looking at small markets in 2006 that concludes that 16 traders should be sufficient. Polymarket plots brier score vs volume with .09 up to $10k, then .08 up to $25k, .07 up to $100k, .05 up to $250k, .04 up to $500k, .03 up to $1M, .02 for $1M+. Brier score is mean squared error (e.g. if I say 70% and it happens I have a score of .09), so that suggests it’s fairly good even at relatively low liquidities.

The way I see it, it being cheap to swing the market isn’t sufficient for manipulation. The question is how fast it gets corrected by other traders. Basically, if someone (or someone’s trading bot) notices they can make bank. The theory then goes that manipulators increase accuracy by incentivizing informed trading—though I think this is a long run thing.

On manipulation, Manifold cites Scott Alexander’s manipulation experiment, which got corrected in an hour:

I tested this by manipulating a scandal market about Manifold CEO Austin Chen, with his permission. It was originally at 4%; at 4:50 PM California time, I spent M$200 in play money (=~ $2 in real money) to manipulate it up to 95%. By 5:30 California time, it was back down to 4%. This isn’t a great example, because real attackers might be more subtle, make multiple small bets, only try to push it a few percent, etc—but I think it’s a pretty good sign. (the embed says the market currently has 78 traders and M48k liquidity, which is pretty high for Manifold)

It also cites an old paper by Robin Hanson, which in the introduction cites a few other papers showing failed manipulation in both the field and lab experiments. I don’t know of bigger attempts now that prediction markets are mainstream, and would be interested in seeing data about Polymarket and Predictit.

Prediction markets of course have problems, but they seem to not get much worse at mid-low liquidity.

I think you are correct to look at activity though. Will activity will spike back up after manipulation? Perhaps someone should try noise trading a couple inactive markets as an experiment.

XelaP 16 Mar 2026 19:14 UTC
1 point
0
in reply to: Ihor Kendiukhov’s comment on: What are the best ways to publish rational fiction nowadays?
That’s what I meant, yeah. My reasoning was originally “well, not much fiction is on LW, and it’s not very primary here”, but now I’m remembering active encouragement to post fiction here, and so now I think you should just also post it here and the worst that would happen is lack of engagement.

XelaP 16 Mar 2026 18:42 UTC
4 points
2
on: What are the best ways to publish rational fiction nowadays?
I think lots of people interested in ratfic do exist on RoyalRoad just by dint of it being so popular. I agree there isn’t concentration, but the way I see it you can help advertise to a more targeted audience on r/rational (or if it gets popular enough maybe LW).

Consider how Worth The Candle is popular enough that people with no knowredge of rationality read and enjoy it; and as more of an edge case, Mother of Learning is literally the top of all time on RoyalRoad. A Practical Guide to Sorcery is likewise popular there. This all generally suggests that using the standard popular thing is fine.

XelaP 16 Mar 2026 14:42 UTC
2 points
0
in reply to: TristanTrim’s comment on: TristanTrim’s Shortform
The problem is not specialized knowledge. All of these examples are basic and fundamental to the subject. Except for the geodesic example^[1], I am confident that the other cases are cases of never actually learning what the hell they were talking about, and instead of focusing on that fundamental gap of understanding they instead focused on memorization and rote algebra.
Partly this is perverse incentive of current schools. But I suspect that even if schools didn’t actively encourage these problems that you’d still see this, that you need some way to actively fight back. Unfortunately I’m not sure what the key is, here.
Some guesses:
- If you actually, like, try to understand what the hell the things you’re doing mean, maybe you’ll succeed? This is good advice even if Feynmann’s examples are easy for you: often relatively more complicated formulas have some intuitive meaning, even if it’s not as standard to explain.
- Maybe, try always coming up with simpler and more concrete examples for everything? This is similarly good advice, but also despite not doing enough of this for a while I wouldn’t have nearly so bad a problem as Feynmann describes, which suggests this is less load bearing for me. Possibly, it’s compensated by me understanding the abstract thing more by itself than most?
- Maybe, try actually applying or operationalizing the knowledge? If on the first day that you learn about “polarization” you buy a polarizing filter and then just go look at a bunch of stuff (surfaces that shine at a grazing angle, phone screens, a couple other polarizers, an oil film, plastic objects, the sky, a rainbow, a laser, bright lights) you’ll learn a bunch (e.g. brewster’s angle, liquid crystals, malus’s law, thin film interference, photoelasticity and stress polarimetry, rayleigh sky model and the vikings, more direct demonstration of dipole radiation in the air being polarized at near 90°, the polarizer being worse at higher frequency). Again despite not doing this for a while I ended up as me, even if doing so was fun and taught me extra bonus things.
- Try… caring? Someone who cares may care to understand and to operationalize and to me concrete and to answer the questions they’ve always had about X.
1. ^
  I myself didn’t immediately know the answer to that one. However, it had been a while since I was looking into general relativity, and I had not gone that deeply, so I forgot the fact that the (spacetime interval version of) arc length of an observer’s path is the proper time of the observer (just because the observer’s not moving in their frame) and had to refigure it out (though by then I had read Feynmann’s answer).
  I anticipate that the assistant would’ve been able to tell you that fact without connecting it to rocket flights; and I anticipate that I would’ve, and even that if I had taken the time to write down the problem that I would’ve had a good chance of figuring out the necessary fact. Why am I like this, when the assistant wasn’t?
What links here?
- papetoast's comment on papetoast’s Shortforms by papetoast (12 Mar 2026 3:45 UTC; 0 points)

XelaP 16 Mar 2026 11:34 UTC
3 points
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in reply to: XelaP’s comment on: $500 + $500 Bounty Problem: Does An (Approximately) Deterministic Maximal Redund Always Exist?
Ah, here’s the diagrammatic version of Lemma 2 that actually seems right: We have Ω ← L → Ω and X_i ← L → X_ibar so by dangly bits X_i ← L (-> Ω) → X_ibar then since you can reroot trees we have Ω → L (-> X_i) → X_ibar, then marginalize out L to get the mediation.

XelaP 16 Mar 2026 5:16 UTC
3 points
4
in reply to: quetzal_rainbow’s comment on: $500 + $500 Bounty Problem: Does An (Approximately) Deterministic Maximal Redund Always Exist?
Intuitively: The mutual information is defined as D(P(X,Y)||P(X)P(Y)), and likewise for conditional mutual info you condition each bit (and then average over the conditoned var). This means that the mutual information is definitionally the error of the diagram X Y (without any arrows) - the error that you get when assuming them independent. Conditioning on Z means you draw the arrows from Z to X and Y but still leave no arrow between X and Y.

XelaP 16 Mar 2026 4:08 UTC
3 points
0
in reply to: Oliver Sourbut’s comment on: Some Rules for an Algebra of Bayes Nets
I mean, the assumption that there’s a DAG for the overall distribution is just trivial? P(A,B,C,D,...) = P(A)P(B|A)P(C|B,A)P(D|C,B,A)… has a graph with the vertices ordered in the same way where everything is connected to everything before it in the right direction.

XelaP 16 Mar 2026 3:06 UTC
3 points
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on: Some Rules for an Algebra of Bayes Nets
Extend the above proofs to re-rooting of arbitrary trees (i.e. the diagram is a tree). We recommend thinking about your notation first; better choices for notation make working with trees much easier.
The ‘true’ generalization:
if two nodes have no incoming arrows (except from each other), then you can swap an arrow between them. likewise if you had a subgraph with no incoming arrows outside the subgraph, then you can replace it with an equivalent subgraph
Proof:
The first diagram has a P(A)P(B|A) while the second differs only by having a P(B)P(A|B) instead, but these are both equal to P(A,B). Likewise P(G) = P(G’) and the P(Other|G_part) arrows don’t change.
The additional condition there is also necessary, because e.g.
A → B ← C works differently from A ← B → C = A → B → C. Namely, in the second A is independent of C once you know B, but that’s not true in the first (because you’re conditioning on a collider).

XelaP 16 Mar 2026 1:03 UTC
1 point
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in reply to: PoignardAzur’s comment on: Do One New Thing A Day To Solve Your Problems
I don’t think of the technique as trying to solve akrasia or dopamine addiction. I think of it like the hammertime sequence—frequently people don’t try stuff to solve their problems, or enough stuff, despite not being blocked by effort or akrasia or whatever, simply because they didn’t think of it.