gjm

Karma: 31,979

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 Aug 2026 8:37 UTC
15 points
8
on: The Closure of the Internet (Research Linkpost)
Maybe I’m being dim, but at present I don’t see anywhere in the LW post a link to the original piece, which I think is https://arctotherium.substack.com/p/the-closure-of-the-internet.
I am unfortunately time-constrained right now and haven’t read that original piece; I hope it doesn’t, as the extracts quoted here rather suggest, conflate “leftists were wrong about some specific things” with “leftists were globally wrong in the same sort of way as creationists”. Every[1] group is wrong about some specific things and it may well be that leftists were systematically wrong about some specific things that perhaps the article specifies. It might in fact be true that leftists are wrong about all the key things that distinguish them from rightists and that that’s why they’re wrong about those specific things. But not necessarily, and the former would not be strong evidence for the latter, and (politics being what it is) I am worried that part of the point of the article might be to encourage to believe the latter by giving evidence of the former. But, again, time-constrained, haven’t read it properly, so hopefully my cynicism is unwarranted in this case.
[1] Yesyesyes, all universal generalizations are false.

gjm 29 Jul 2026 0:23 UTC
6 points
8
in reply to: RHollerith’s comment on: anaguma’s Shortform
It feels to me as if we just had the following discussion:
- Selfmaker662: There’s no difference between A, B, and C.
- other people: <downvotes Selfmaker662>
- Selfmaker662: Huh, why did that happen?
- gjm: Well, part of it might be that you said there’s no difference between A, B, and C, but here’s what looks like an important way in which A is different from B and C.
- RHollerith: Yeah, but the only important thing is that A, B, and C are all really bad.
You may well be right that all the AI lab CEOs are evil and stupid and their labs should be shut down. But so what? The question was “what might people not have liked about Selfmaker662′s comment?”, and part of my answer was “the claim that there’s no difference between one AI lab CEO and another”, and I think some people might have thought that was wrong even if in fact all AI lab CEOs are evil and stupid. And I also think that AI lab CEOs are not all equally evil and stupid. And also that the world is not made a better place by insisting that every discussion that mentions AI lab CEOs must be punctuated by reminders that they are all evil and stupid.
(And, for what it’s worth: no, I absolutely do not think that we should be “putting our hope in” any AI lab CEO. I’m not sure that’s even a meaningful thing to say; what exactly would I be doing if I “put my hope in”, say, Dario Amodei? and how would it be different from what I would be doing if I “put my hope in” Ilya Sutskever instead?)

gjm 28 Jul 2026 13:12 UTC
5 points
−1
in reply to: Selfmaker662’s comment on: anaguma’s Shortform
I haven’t voted on that comment one way or another, but:
- Ilya Sutskever and Demis Hassabis seem to be in quite a different category from Sam Altman or Elon Musk. (I’m not sure about Dario Amodei.) That is: before they were AI company CEOs they were extremely successful AI researchers.
  - This is relevant because when you claim “they’ll release an underwhelming product that is neither superintelligent nor safe” this is prima facie a claim about SSI’s competence as well as its ethics, and if you’re basing it on the idea that the guy in charge doesn’t know any more than (say) Sam Altman does about how to make AIs smarter or safer then you’re probably making a mistake.
- It’s not clear that building a superintelligence as such is an evil thing to try to do.
  - If you seriously think you can do it safely, it seems like the benefits might far outweigh the costs.
  - If you think you might be able to do it safely and are much more likely to do that than other people who are currently frantically trying to build a superintelligence, the overall benefits might still outweigh the costs even if they wouldn’t be if you were the only people working on it.
- It’s not clear that releasing an underwhelming product would in fact help SSI be seen as relevant.
  - At the moment I assume the typical view is something like “Ilya Sutskever is very good at what he does, he seems to think he has useful ideas, and he shows some signs of caring about safety. The most likely outcome is that SSI never produces anything useful but they might and it so it could be a very big deal”. If SSI releases an underwhelming product, then that immediately shifts to “it’s probably not a very big deal” and then SSI’s relevance comes almost entirely from their projected ability to iterate on their underwhelming first product. Would that be an improvement? Not obviously.

gjm 28 Jul 2026 1:08 UTC
15 points
5
on: RL & search is a terrifying way to build AGI (an FAQ)
To what you’ve said about humans and existing LLMs not being horribly sociopathic all the time because their motivations aren’t constructed from RL + search, I would add the following: One of the more obvious examples of how humans get put into an RL-like environment is the way CEOs of companies are constantly being evaluated on what’s approximately a pure profit-maximizing objective, and as a group they don’t exactly have a reputation for not being sociopathic.
I’m not sure whether something similar applies in other instances where people are consistently rewarded for maximizing something. Salespeople, perhaps: at least a bit of a reputation for sociopathy there. Children at school? Empirically most schoolchildren most at the time care a lot about things other than the stuff their teachers are evaluating them on, so I don’t know how good an example that is. Athletes? Not particularly thought of as sociopathic, I think.
This seems like the sort of thing some psychologist has probably done a lot of interesting research on. Which probably failed to replicate.

gjm 28 Jul 2026 0:56 UTC
10 points
0
on: Simulated Users & Sad AIs
When you say that
if you run an LLM for a long time, on a task that seems impossible to the LLM, something that looks functionally like the emotion of “desperation” activates in its circuits as they contemplate the tests failing again and again. This “desperation” is functionally connected to “reward hacking”-like behavior.
it seems to me that this is rather hard to distinguish from—perhaps in fact identical to—this:
if you run an LLM for a long time, on a task that seems impossible to the LLM, it starts trying to “think outside the box” and find increasingly nonobvious ways to attack the problem
which seems to me exactly what an intelligent entity should be doing when faced with a problem that seems insoluble by normal means.
If so, then the problem isn’t the thing you describe as “desperation”, it’s the range of things the LLM is willing to try once it starts to get desperate.

gjm 21 Jul 2026 13:27 UTC
5 points
0
on: War – What is it Good For?
Purely pedantic correction:
One of your footnotes says: if there are ~200 countries in the world then there are ~4000 pairs of countries, and usually the great majority of those pairs of countries are not at war.
If there are 200 countries then there are about 20000 pairs of countries, not 4000.
Less pedantically, I’m not sure this observation is actually evidence favouring the book’s thesis. You say that 68% of pairs of countries have negative expected utility from going to war. Or, to put it differently, nearly ¹⁄₃ of pairs of countries have positive expected utility from going to war. And yet, as you observe, the vast majority of pairs of countries are not at war.
The main thing this suggests to me is that very little of the not-war in the world is explained by negative expected utility.

gjm 18 Jul 2026 23:30 UTC
8 points
0
in reply to: Ruby’s comment on: A Mechanistic Explanation of Prompt Injection (and why you should study roles)
When I first glanced at this comment, I was really hoping that it would turn out to be by the original author, attempting a role-spoofing attack on the LW admins. Alas, unless something really devious is going on it is in fact by an LW admin. (But maybe the <notice>...</notice> thing is, even so, a deliberate nod to the subject matter of the post?)
[EDITED because I accidentally a word]

gjm 28 Jun 2026 0:11 UTC
8 points
3
in reply to: johnswentworth’s comment on: johnswentworth’s Shortform
I think this is right, but I am uncomfortable with the framing of the last paragraph.
YES, you have to choose between “maybe not truly knowing what I want” and “maybe discovering that I want something I would much much rather not want”.
But, at least on the face of it, that’s symmetrical. Turning “you can’t have both A and B” into “In order to have A, you have to give up B” seems like it presupposes that A-and-not-B is a better option than B-and-not-A. Which might be true in this case, but—for the reasons Karl Kruger’s reply describes—it might not.
I think that if I had to choose between having a deeply-repressed sexual attraction to children, so deeply repressed that I didn’t even know I had it, or having an entirely-apparent sexual attraction to children, one that I was aware of and couldn’t ignore, I would choose the former. The latter might mean another highly unwelcome choice: between constant frustration and doing things that are likely extremely harmful and certainly illegal, socially unacceptable, and contrary to my values.
Which, yes, means that I might not be able to know for certain whether or not I have some sort of deeply-repressed sexual attraction to children, or a deeply-repressed desire to murder everyone around me, or all sorts of other possible deeply-repressed nasties. And I’m OK with that. What I do know with some confidence is that I don’t have a not-so-deeply-repressed desire to murder people or rape children or whatever, and that seems enough for practical purposes.
Maybe for some people (maybe for me, in some circumstances) self-knowledge is so vital that it’s worth making whatever efforts one might have to make[1] to discover whether one has such deeply-repressed nasties, even though the case in which this tells you something new is also the case in which discovering it might have very bad consequences. But I wouldn’t expect that situation to be so common that “in order to know … you need to …” to be a good way of putting it.
[1] Assuming that there is actually a reliable way to find out. There might not be.

gjm 28 May 2026 14:41 UTC
3 points
0
in reply to: Vladimir_Nesov’s comment on: Vladimir_Nesov’s Shortform
Aha. I had missed that footnote; my apologies.

gjm 27 May 2026 21:54 UTC
2 points
0
in reply to: Vladimir_Nesov’s comment on: Vladimir_Nesov’s Shortform
This
About 40GW … might be available to an AI company by the end of 2030, enabling pretraining for about 2e29 FP8 FLOPs (using 10GW)
feels like a type error to me, which probably means I’m missing something.
A gigawatt is a measure of the rate at which you can get/use energy, but a FLOP here is a measure of the total amount of computation done. Is there an assumption about how long a pretraining run is allowed to take? Or perhaps not an assumption about that as such but an assumption that everyone always uses about the same amount of time for their pretraining runs, so that the ratio between compute-per-unit-time available and amount-of-computation-done-for-a-run is fixed?
(My guess is the latter, but not very confidently.)

gjm 26 May 2026 11:08 UTC
2 points
0
in reply to: Vaniver’s comment on: Intelligence Dissolves Privacy
Claude Sonnet 3.something could do it for me, and I am a much much less public figure than Kelsey. (On the other hand, I am also older and so there is more of my writing out there on the interwebs. Also, I only tried it once and didn’t run any sort of carefully controlled experiment on it, so maybe it just got lucky.)

gjm 12 Apr 2026 0:06 UTC
19 points
6
on: Dario probably doesn’t believe in superintelligence
I don’t understand why you express the opinion that I think you’re expressing here as
Dario probably doesn’t believe in superintelligence
rather than as
Dario probably anticipates superintelligence as having less impact than I do.
As e.g. Tenoke has said, “a country of geniuses in a datacenter” is, whatever else it may be, definitely something much smarter than a human being.
How do other people use the term? Here’s Nick Bostrom, from his book “Superintelligence”:
This chapter identifies three different forms of superintelligence, and argues that they are, in a practically relevant sense, equivalent. [...] As previously indicated, we use the term “superintelligence” to refer to intellects that greatly outperform the best current human minds across many very general cognitive domains. [...] Speed superintelligence: A system that can do all that a human intellect can do, but much faster. [...] Collective superintelligence: A system composed of a large number of smaller intellects such that the system’s overall performance across many very general domains vastly outstrips that of any current cognitive system. [...] Quality superintelligence: A system that is at least as fast as a human mind and vastly qualitatively smarter.
The Less Wrong wiki … actually just quotes Bostrom, in slightly different words from the above:
“An intellect that is much smarter than the best human brains in practically every field, including scientific creativity, general wisdom and social skills.”
The Oxford English Dictionary gives three meanings, none of them quite the one we’re after here; I mention it because I looked and don’t want to be cherry-picking my sources. Wiktionary is less academic but more up-to-date, and says “Intelligence surpassing the level of a human genius.” with a few citations that all roughly match that and don’t require that said intelligence confer godlike powers or anything of the kind.
There’s probably a definition in Yudkowsky & Soares’s recent book but I don’t have a copy. I had a look at the transcript of his TED talk from 2023, titled “Will superintelligent AI end the world?”; he doesn’t define “superintelligence”, but it’s there in the title, and the scenario he talks about is: “At some point, the companies rushing to scale AI will cough out something that’s smarter than humanity”.
All these people are using “superintelligence” to mean some variation on the theme of “something much smarter than we are”. Many of them think that such a thing would in fact have vast world-changing impact, but they’re not making it part of the definition and I don’t understand how it makes sense to say that someone “doesn’t believe in superintelligence” merely because their estimate of the likely impact of something much smarter than us is different from yours.

gjm 11 Apr 2026 23:28 UTC
2 points
0
on: Claude Mythos: The System Card
Also, whoa hang on. Yes, very obviously the results were consistent with Mythos not being a drop-in L4. But why is that the question? The question should be, are these results inconsistent with it not being a drop-in L4? And the answer seems like no.
I think there’s an extra “not” there. Those two questions are equivalent questions; I am pretty sure Zvi meant to say
The question should be, are these results inconsistent with it being a drop-in L4? And the answer seems like no.

gjm 22 Mar 2026 15:46 UTC
2 points
0
in reply to: Sting’s comment on: Maybe there’s a pattern here?
On your specific example:
It’s plausible that a typical Harry Potter fan gets at least $1 worth in value from having one of the books or watching one of the movies. But in a hypothetical world where JKR never exists, I think that typical Potter fan is a fan of something else instead. They read a different book, watch a different movie. Maybe they get a bit less enjoyment from it than from the corresponding Harry Potter thing back in our world—after all, in that world they chose Harry Potter over the other thing. But maybe not; which books/movies/songs/… turn out to be big successes seems to owe a lot to luck. At any rate, I don’t think we can credit Rowling with all the value the fans get from her work.
Also, the process by which a Harry Potter fan gets value from Rowling’s work doesn’t only involve them and Rowling. The book probably got significantly improved by the editors (at least, the first few books did, before JKR got big enough to ignore their good advice). The movies needed actors and directors and film crews. Books and movies alike needed distributing and selling.
On the broader point of whether the reason for rising inequality is that we have “a smaller fraction of people producing a greater fraction of value”:
First of all, what causes inequality is a smaller fraction of people capturing a greater fraction of value, and it sure looks like that’s a thing that’s happening; e.g., CEO salaries have become much higher relative to those of their employees, and it’s far from obvious to me that much of the value is being created by the CEO rather than the employees. Second, even if it’s true that fewer people are producing a greater fraction of the value, that isn’t necessarily a matter of the few Very Greatest Value-Producers doing their thing more effectively; it could equally be that there are lots of roughly equally good value-producers, and today’s market dynamics are more ruthless about picking a few basically at random and making them the ones everyone’s heard of, who therefore get all the profits. It’s then true that those few people are the ones providing the value, but all the others could have done just as good a job if they’d been the ones to get lucky instead.
Third, inequality occurs at different scales. There’s the inequality of the super-rich versus everyone else; here you give the example of Rowling, though most of the richest people are owners of businesses rather than creators of art and entertainment. But there’s also inequality between broader groups. Rich nations versus poor ones. Rich industries versus poor ones. Bosses versus minions. My understanding is that these sorts of inequality have increased too, and it’s not obvious that it’s for the reasons you describe.
On the overarching point of whether rising inequality is actually bad:
It’s certainly possible for something to happen that increases inequality but is good overall. If the world gets much richer and the gains are very unevenly distributed, this might be a net improvement. But I don’t think you can just gesture at that situation, say “look, this is better overall”, and conclude that inequality isn’t a problem! There are two separable things there, the increase in wealth and the increase in inequality, and maybe the first is Just Good and the second is Just Bad and we merely got lucky that the first one outweighed the second. I think you need to ask questions like: is the increase in inequality an important part of why the increase in overall wealth happened? and: is there a way we could have less inequality while keeping most or all of the increase in wealth? -- and I don’t think these are easy questions to answer.
(BTW, I think it’s very clear that inequality-as-such has bad consequences, whether or not in a given case it’s bad when considered as part of the whole economic situation. It means big differences in political influence, which in turn means that the poorer people get more badly screwed than they would with less inequality. And it means, if compared with a more equal situation with the same total wealth level, less total utility because of decreasing marginal gains. And it means more envy and resentment, which means less social stability. Again, it may turn out that those are just prices that you have to pay for overall progress that helps everyone, but I think that needs more supporting arguments than just “look, the world is getting richer” or whatever. It certainly needs more than “look, I’ve identified an otherwise-benign thing that causes increasing inequality”; the problem with inequality is its consequences more than its causes.)

gjm 8 Jan 2026 13:17 UTC
2 points
0
in reply to: Dagon’s comment on: silentbob’s Shortform
So far as I can tell, the most plausible way for the universe to be deterministic is something along the lines of “many worlds” where Reality is a vast superposition of what-look-to-us-like-realities, and if the future of AI is determined what that means is more like “15% of the future has AI destroying all human value, 10% has AI ushering in a utopia for humans, 20% has it producing a mundane dystopia where all the power and wealth is in a few not-very-benevolent hands, 20% has it improving the world in mundane ways, and 35% has it fizzling out and never making much more change than it already has done” than like “it’s already determined that AI will/won’t kill us all”.
(For the avoidance of doubt, those percentages are not serious attempts at estimating the probabilities. Maybe some of them are more like 0.01% or 99.99%.)

gjm 8 Jan 2026 13:12 UTC
7 points
0
in reply to: silentbob’s comment on: silentbob’s Shortform
Is it actually true that egoism, in the sense of “some degree of egoism” or “at least mildly egoistic”, has a bad reputation?
My impression is that (1) almost everyone cares at least a bit about random other people but cares a lot more about themself, and (2) almost everyone is aware of #1 and doesn’t see it as particularly bad. If you call someone altruistic you aren’t generally claiming that they don’t give higher priority to their own interests than others’ at all, only that they care more about others relative to themselves than is usual.
I agree that it’s more broadly accepted when companies care scarcely at all about the interests of others—we largely accept corporate behaviour that would be universally regarded as sociopathic if done by an individual—and that this is a bad thing.

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
6 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?