gjm

Karma: 31,767

Hi. I’m Gareth McCaughan. I’ve been a consistent reader and occasional commenter since the Overcoming Bias days. My LW username is “gjm” (not “Gjm” despite the wiki software’s preference for that capitalization). Elsewehere I generally go by one of “g”, “gjm”, or “gjm11”. The URL listed here is for my website and blog, neither of which has been substantially updated for several years. I live near Cambridge (UK) and work for Hewlett-Packard (who acquired the company that acquired what remained of the small company I used to work for, after they were acquired by someone else). My business cards say “mathematician” but in practice my work is a mixture of simulation, data analysis, algorithm design, software development, problem-solving, and whatever random engineering no one else is doing. I am married and have a daughter born in mid-2006. The best way to contact me is by email: firstname dot lastname at pobox dot com. I am happy to be emailed out of the blue by interesting people. If you are an LW regular you are probably an interesting person in the relevant sense even if you think you aren’t.

If you’re wondering why some of my very old posts and comments are at surprisingly negative scores, it’s because for some time I was the favourite target of old-LW’s resident neoreactionary troll, sockpuppeteer and mass-downvoter.

gjm 12 Dec 2025 23:43 UTC
4 points
2
in reply to: lsusr’s comment on: Critical Meditation Theory
I hope I will return to this when I have time to read it properly and think about it properly, but for now I’ll just drop in two things at the meta-level: (1) I don’t know how comprehensible I’d have found something more in your usual concise style, but the above certainly seems nice and clear so it seems like you probably made a good choice. (2) I’m glad to hear that I’m perfectly tactful but now I’m worried about a different issue, namely that maybe I never say anything unless I have something mean^H^H^H^Hcritical to say, which I’m aware is the exact opposite of what generations of parents have been teaching their children to do :-). (I definitely do lean in that direction, and I’m somewhat prepared to defend it in that offering hopefully-informative criticism is arguably more useful than offering compliments, but it’s still probably suboptimal.)

gjm 8 Dec 2025 16:36 UTC
4 points
0
in reply to: lsusr’s comment on: Critical Meditation Theory
I’m brand new to this field of mathematics
Me too, mostly. I took an undergraduate course on dynamical systems many years ago but I’ve forgotten most of what was in it and in any case it seems like this complex-systems stuff uses the language of dynamical systems but not always in ways I can see how to connect with the mathematics I kinda-sorta know.
I get the impression that you’re using LLM-assisted research much less—if at all
I make almost no use of LLMs. (I am not at all claiming that this is a good thing, just validating your impression :-).)
jhana isn’t just about gain. It’s also about noise
If we’re thinking about the brain as a dynamical system, how is this noise being represented? Maybe as arising from inputs coming in from outside. If jhana reduces sensitivity to those (which might fit with “pronounced self-reported sensory fading”, as described in the article) then that could reduce the overall amount of noise in the system.
But I still can’t quite make sense of this. (1) I haven’t read the article closely but it doesn’t look like it attributes their observations about jhana to reduced effects of noise. (2) The article specifically claims that jhana is associated with a lower max Lyapunov exponent—that’s the basis for its claim of “reduced chaoticity”. Doesn’t that mean, in your terms, that the article is claiming that jhana puts the brain in a state where the “gain” is lower, not higher?
The original paper that led me down this rabbit hole
Thanks—I’ll take a look. At first glance it seems to be very specifically about brains; what I’d really like to find is something that explains the general principles in terms that in principle I could apply to domains other than brains, and with enough precision and explicitness that I can see how to do mathematics to it.
The DFA exponent and so-called “fE/I” are both properties, if I am understanding correctly, of arbitrary time series (and the hope is that when the time series is derived from a dynamical system it tells you something interesting about the structure of that system). That’s good, in that they are nice and general and well defined and I can understand what they are. But if we’re talking about properties of a dynamical system rather than of some set of signals captured from it, I’d like to understand what properties are in question. Handwavily I understand that we’re looking at something along the lines of “coefficient in an exponential dependence” where <0 means things decay and >0 means things explode and interesting stuff might happen at 0. (And presumably that exponential dependence arises from something like a differential equation where again we’re looking at something like the eigenvalues in the matrix you get by linearizing the d.e.) But I don’t get the impression that people talking about subcriticality and supercriticality are actually working with concrete precisely-specified mathematical systems for which they could define those terms precisely; it seems (perhaps unfairly) more as if they are defining “supercritical” to mean something like “if we go looking for instabilities or exponential divergences, we can find things that look like that” and “subcritical” to mean the reverse, and it’s all kinda phenomenological, looking at the outputs of the system rather than at the system itself.
Which may very well be the best one can do with a brain, but it’s all a bit frustrating when trying to understand exactly what’s going on.
This is the first time you’ve commented on my posts where I don’t want to crawl into a cave and die.
Ouch!
I was going to say “I hope that indicates only that you feel very bad when someone points out issues with what you’ve written, rather than that I am incredibly tactless” … but maybe it’s actually better overall for one person to be very tactless than for one person to be painfully sensitive to criticism. Anyway, to whatever extent your past pain is the result of my tactlessness, I’m sorry.

gjm 7 Dec 2025 18:35 UTC
6 points
1
in reply to: lsusr’s comment on: Critical Meditation Theory
(I don’t think anything I said assumed you were referring to thermodynamic order/disorder.)
It sounds as if some of your definitions may want adjusting.
Dynamical systems can be described on a continuum with ordered on one end and disordered on the other end. [...] A disordered system has chaotic, turbulent, or equivalent behavior. [...] Systems more disordered than the critical point can be described as supercritical. Systems less disordered than the critical point can be described as subcritical.
Doesn’t all of this explicitly say that moving in the sub->super direction means becoming more disordered, which means becoming more chaotic?
Perhaps what you actually mean to say is of the following form?
Dynamical systems can be described on a continuum whose actual definition is too complicated to give here but in some situations can be handwavily approximated to “less versus more sensitive to small changes”, which in turn can in some situations be handwavily approximated to “more ordered versus more disordered”.
A particular point along that continuum goes by the name of “criticality”, and the dynamics of a critical system are often particularly interesting; in particular, they maximize a quantity called complexity which is a measure of entropy expressed across a variety of time scales. Systems on the less-sensitive/more-ordered side of criticality are called subcritical and systems on the more-sensitive/less-ordered side are called supercritical.
(Is there actually a proper term for the thing that increases as you move from subcritical to supercritical? I keep finding that I need ugly circumlocutions for want of one.)
And then the situation described in the article (where a certain change, in this case from mindfullness to jhana, moves in the sub-to-super direction—which would normally mean more sensitivity, hence more tendency to chaos in the mathematical sense, hence typically more disorder—but somehow also involves a reduction in chaoticity) could be explained by this system not having the usual relationship between the sub-to-super parameter and chaoticity.
But I think I’m still confused, because (as I mentioned before) the article very much doesn’t present that combination as somehow an unusual one. It says that jhana is characterized by a smaller max Lyapunov exponent, hence less chaoticity … but isn’t Lyapunov exponent much the same thing as you’re calling “gain”? Wouldn’t we normally expect reducing the Lyapunov exponent to move in the direction of subcriticality? Or am I, indeed, just still confused? The article says “Jhana decreases brain chaoticity relative to mindfulness, indicating brain dynamics closer to criticality” (italics mine), which to me seems like they’re saying that in general we should expect closer-to-criticality dynamics to come along with less chaos, which is the exact opposite of what it feels like we should expect.
I’ve had a bit of a look for a nice clear explanation of the actual mathematics here, but it seems that there are (1) things about dynamical systems generally, written by mathematicians, which talk about e.g., subcritical or supercritical bifurcations and have nice clean definitions for those, and (2) things about Complex Systems, often specifically about brains, which talk about whole systems being “subcritical” or “critical” or “supercritical” but never seem to give actual explicit definitions of the things they are talking about. Probably I have just not found the right things to read.

gjm 7 Dec 2025 2:18 UTC
4 points
1
on: Critical Meditation Theory
I am rather confused.
1. The linked article does indeed claim that deep jhana (here in comparison with mindfulness meditation) produces (a) reduced chaoticity and (b) nearer-critical dynamics.
2. lsusr’s post here says that (a) the resting brain is subcritical, (b) sub/super = less/more disordered, and (c) more disordered = more chaotic.
3. If the resting brain is subcritical then moving toward criticality means moving in the supercritical direction. If also supercritical = more disordered then this should make the brain more chaotic, not less.
  1. The article doesn’t give any indication that it’s surprising for a single thing to move in the direction of criticality and also to make the brain less chaotic.
4. A bit of casual googling finds at least one other neuroscience article that says subcritical/supercritical = less/more disordered, but also some dynamical-systems things in which it’s exactly the other way around. (E.g., these lecture notes. But here the thing being described as subcritical or supercritical isn’t the dynamical system but a bifurcation occurring in its dynamics as a parameter varies.)
What am I missing or misunderstanding here?

gjm 3 Dec 2025 14:43 UTC
2 points
0
in reply to: Screwtape’s comment on: Change My Mind: The Rationalist Community is a Gift Economy
Noted. But it seems to me that if the trajectory was excessively altruistic → obnoxious Objectivist → something reasonable, it’s pretty plausible that without reading Rand you might just have gone straight from “excessively altruistic” to “something reasonable”.
(But of course you may well have a better sense of that having been through it from the inside.)

gjm 3 Dec 2025 14:40 UTC
5 points
3
in reply to: Czynski’s comment on: Change My Mind: The Rationalist Community is a Gift Economy
Does Lewis really advocate for extreme altruism, as such? Of course he advocates for Christianity, and some versions of Christianity advocate extreme altruism, but Lewis’s sort was mostly pretty moderate.

gjm 29 Nov 2025 23:33 UTC
6 points
0
on: Change My Mind: The Rationalist Community is a Gift Economy
This has very little to do with the actual high-level topic at issue, but it’s something I’ve seen elsewhere in rationalist discourse and I recently realised that I think it’s probably nonsense.
I still think a lot of you all need to sit down with Atlas Shrugged to get nudged in a usefully more selfish direction.
I am pretty sure it scarcely ever happens that someone who is too altruistic reads Atlas Shrugged and comes away with their altruism moderated a bit, or that someone who is too selfish reads, er, the Communist Manifesto or the Sermon on the Mount or something[1], and comes away with their selfishness moderated a bit.
[1] I don’t know whether it’s Highly Significant somehow that I can’t come up with a good symmetrical example of something advocating for extreme altruism as AS advocates for extreme selfishness.
I think what actually happens is that (usually) they say to themselves “wow, that was a load of pernicious nonsense, I resent having wasted my time reading it, and will now be even more zealous in opposing that sort of thing” and if anything have their original position reinforced, or (occasionally) they feel like the scales have fallen from their eyes and become a full-blown Objectivist or Marxist or Christian or whatever.
If I thought altruism was bullshit and everyone ought to be a Randian egoist then I might be all for giving copies of Atlas Shrugged to very altruistic people. But if what I wanted was more-moderately-altruistic people, I don’t think that would be a good strategy.
I should in fairness say that I don’t have any actual evidence for what happens when extreme altruists read Atlas Shrugged. Maybe (either in general, or specifically when they are rationalist extreme altruists) they do tend to emerge with their views moderated. But I don’t think it’s the way I’d bet.

gjm 19 Nov 2025 2:15 UTC
2 points
0
in reply to: AnthonyC’s comment on: On Writing #2
I think the information actually conveyed by this “unreasonably effective writing advice” is the fact that such-and-such a section of what you wrote prompts that question and suspect that saying “this bit isn’t clear” would be almost as effective as asking “what did you mean here?” and then saying “well, write that then”.
(It’s like the old joke about the consultant whose invoice charges $1 for hitting the machine with a wrench and $9,999 for knowing where to hit it.)

gjm 8 Nov 2025 0:46 UTC
2 points
0
in reply to: MichaelDickens’s comment on: Debunking “When Prophecy Fails”
Yes, that all seems fair. I was just struck by the parallels.
(It is not entirely clear to me exactly what if anything Kelly is claiming about the state of mind, and motives, of Festinger and his colleagues. He does say near the start “that the book’s central claims are false, and that the authors knew they were false”, but I don’t see much evidence in his article that the authors knew their central claims were false. He does offer evidence that the authors interfered more than they admitted, but that isn’t really the same thing.)

gjm 7 Nov 2025 18:27 UTC
6 points
−4
on: Debunking “When Prophecy Fails”
If Kelly’s account of things is correct, then one could describe the events as follows.
Leon Festinger and his colleagues made a dramatic and surprising prediction. When they had the opportunity to test that prediction out, things didn’t in fact go the way they had predicted. In response to this, they falsified the evidence, interpreted things tendentiously, and went ahead with a vigorous campaign to spread their theory and get lots of other people to believe it; their theory prospered and remains widely believed to this day.
So it seems like Kelly’s critique is kinda self-defeating. If Dorothy Martin’s little UFO cult isn’t really an example of the mechanism Festinger popularized, in the way Kelly describes, then Festinger and his colleagues themselves are an even better example of it.
Kelly’s paper kinda acknowledges this: “If Festinger’s theory of cognitive dissonance is right, reappraisal of the value of When Prophecy Fails may be slow.” But if he appreciates just how thoroughly he’s portrayed Festinger’s own behaviour as a perfect exemplification of the very theory he’s skewering, he doesn’t show it.
(My impression, as very much not any sort of expert, is that Kelly seems to be somewhat overselling the discrepancy between Festinger’s account and reality. But I haven’t read When Prophecy Fails, I haven’t read the recently-unsealed documents Kelly is citing, and I could well be all wrong about that.)

gjm 5 Nov 2025 23:48 UTC
5 points
2
in reply to: Shankar Sivarajan’s comment on: GradientDissenter’s Shortform
If I am reading things correctly, section 2 of the Voting Rights Act says:
(a) No voting qualification or prerequisite to voting or standard, practice, or procedure shall be imposed or applied by any State or political subdivision in a manner which results in a denial or abridgement of the right of any citizen of the United States to vote on account of race or color, or in contravention of the guarantees set forth in section 10303(f)(2) of this title, as provided in subsection (b).
(and subsection (b) clarifies this in what seem like straightforward ways).
It seems to me that if this “asymmetrically binds Republicans” then the conclusion is “so much the worse for the Republicans” not “so much the worse for the Voting Rights Act”.
As for “the unfair advantage Democrats have had nationally for decades”:
- https://www.cookpolitical.com/cook-pvi/2022-partisan-voter-index/republican-electoral-college-advantage says that the Electoral College gives Republicans a ~2% advantage in presidential elections
- https://fivethirtyeight.com/features/the-senates-rural-skew-makes-it-very-hard-for-democrats-to-win-the-supreme-court/ says that “the Senate is effectively 6 to 7 percentage points redder than the country as a whole”
- https://fivethirtyeight.com/features/advantage-gop/ says that “The Electoral College’s Republican bias in 2020 thus averaged out to 3.5 points”.
Why different years (2022, 2020, 2020)? Because each of those was the first thing I found when searching for articles from at-least-somewhat-credible outlets about structural advantages for one or another party in presidential, Senate, and House races. I make no claim that those figures are representative of, say, the last 20 years, but I don’t think it’s credible to talk about “the unfair advantage Democrats have had nationally for decades” when all three of the major national institutions people in the US get to vote for have recently substantially favoured Republicans in the sense that to get equal results Democrats would need substantially more than equal numbers of votes.

gjm 29 Sep 2025 22:01 UTC
55 points
34
in reply to: Karl Krueger’s comment on: You’re probably overestimating how well you understand Dunning-Kruger
I’ve no idea, but I think you should collaborate with someone named Duenning to find out.

gjm 25 Sep 2025 23:13 UTC
16 points
6
in reply to: Richard Korzekwa ’s comment on: Why you should eat meat—even if you hate factory farming
Wait, there’s something very strange about those two claims. 75% got more than half their calories from animals. 15% got more than half their calories from not-animals. So what did the other 10% do? (Exactly 50% from each, obviously :-).)

gjm 23 Sep 2025 15:49 UTC
21 points
7
on: Accelerando as a “Slow, Reasonably Nice Takeoff” Story
You write “you can buy it here” but there is no link.
However, you can do better: the whole thing is available for free online. https://www.antipope.org/charlie/blog-static/fiction/accelerando/accelerando-intro.html on the author’s website is a good place to start; it has links to various versions of the book and also a little bit of explanatory material.

gjm 23 Sep 2025 15:45 UTC
6 points
2
on: Ontological Cluelessness
Nitpick: This post alternates between using “ontological cluelessness” to mean a certain sort of state of ignorance (“Ontological cluenessness is a state of knowledge that humans could be in, in which they haven’t yet discovered …”), and using it to denote the belief that we are in that state of ignorance. (“Ontological cluelessness is distinct from radical skepticism, pyrrhonism, and mysticism”.) I think it would be better not to do that.

gjm 23 Sep 2025 15:35 UTC
1 point
−1
in reply to: David Youssef’s comment on: The Only Option Left
I think it’s probably true that most political violence done to rightists is done by other rightists (but I haven’t attempted to check; surely there must be some statistics out there) and that it was dead wrong for a bunch of right-leaning commentators to assume that Kirk’s killer was an extreme leftist. (I think it would have been dead wrong for them to do so even if, say, 70% of political violence done to rightists were done by leftists.) I was just pointing out that it isn’t enough just to point to statistics saying that a large majority of political-violence-as-a-whole is done by rightists.
(Gruesome example: in the ongoing Gaza horror, the IDF has killed a lot more people than Hamas, but if you find a violently-dead Israeli soldier there then “Hamas did it” is a better hypothesis than “the IDF did it”.)

gjm 22 Sep 2025 13:59 UTC
10 points
7
on: The Only Option Left
I think there’s something a bit off about your discussion of the right’s leap-to-conclusions about the guy who murdered Charlie Kirk. I do basically agree with you—they were absolutely not entitled to talk as if they knew he was some sort of radical leftist before any evidence was in—but I don’t think I buy that the relevant base rate is the fraction of all domestic terrorists or all extremist murderers, because your typical right-wing domestic terrorist isn’t trying to murder a right-wing propagandist like Kirk, he’s trying to blow up a mosque or an abortion clinic or murder a Democratic congressperson.
The appropriate prior for “guy who shot Charlie Kirk is a radical leftist” certainly wasn’t anything like the 99% that might have justified the immediate see-how-the-left-persecutes-us rhetoric from people on the right. But it also wasn’t the 5% or whatever you would guess just from the fraction of domestic terrorism that’s perpetrated by leftists.
(My understanding of the current state of the evidence is that the killer wasn’t in any useful sense a radical leftist, but that his motives for murdering Kirk were more left than right. On the other hand, I suspect that his more-right-than-left background helps to explain why the course of action he chose was shooting Kirk rather than anything else.)

gjm 22 Sep 2025 13:47 UTC
7 points
4
on: The Only Option Left
My political leanings are similar to yours and I agree that the Trump administration is a disaster, and that many people around here seem not to have predicted this, and that its disastrousness gives some evidence for Team Left over Team Right (which suits me fine since Team Left is my team). But I have some concerns about your presentation here, and in particular about how you set forth your claim that Team Left’s doing better at making correct predictions than Team Right.
First, looking backward, your “ledger” of implicit predictions. (1) I am not sure you get to ascribe predictions to people who didn’t actually make those predictions. (2) These look cherry-picked, in that you’ve picked specific bad things that turned out to happen and complained that people didn’t expect them, without showing predictions of those specific bad things from your side of the table. I think if you’d asked me about several of those things before Trump took office I’d have said “I wouldn’t put anything past those guys but I don’t know whether they’ll do that in particular” rather than “yes, a Trump administration will definitely do that”.
And then you say “look at those probabilities”. Those probabilities which … you just made up? If you’d picked smaller numbers, would the case against some LWers’ past complacency magically be much stronger?
Second, looking forward, your “forward predictions” are unfortunately not such as to provide much evidence for or against your position whatever happens. The odds ratio for “David is right about everything” versus “David is wrong about everything” is only .65/.35 .6/.4 .6/.4 .75/.25 .55/.45 or about 15:1, and the biggest factor there is from your prediction that the Deputy Director of the FBI will not be replaced, within a year, by someone with a better background; what do the base rates look like on that? (My guess: much the same as your prediction.)
At least one of them doesn’t seem like it’s “about” the relevant political issues. “At least 2 additional states formalize independent public-health compacts beyond current ones”: if this happens, as you predict with probability 0.6, I don’t see how that’s evidence that the Trump administration is worse than if it didn’t (it’s a matter of how people who are very much not the Trump administration behave), nor evidence that leftish political views are more accurate than rightish ones (it’s maybe evidence that the Trump administration’s treatment of healthcare is disastrous, but I doubt many people around here would dispute that anyway).

gjm 20 Sep 2025 22:39 UTC
25 points
0
in reply to: davekasten’s comment on: davekasten’s Shortform
USCIS says this does not apply to existing H1-B visas, only to new applications: https://www.uscis.gov/sites/default/files/document/memos/H1B_Proc_Memo_FINAL.pdf
(I am not a lawyer nor a spokesperson for the US government and cannot advise on how likely it is that they will somehow backtrack on this.)

gjm 8 Sep 2025 13:12 UTC
2 points
0
in reply to: jacob_cannell’s comment on: Hyperbolic model fits METR capabilities estimate worse than exponential model
I agree. (Or perhaps we should plot in log space when measuring/minimizing errors in log space, and plot in linear space when measuring/minimizing errors in linear space. The former is nearer to the Right Thing here than the latter.)
There are several things I find unsatisfactory in my own analysis here and either I will write a followup or Valentin2026 and I will write one together. (We’re still discussing.)