gjm

Karma: 31,226

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 Jul 23, 2025, 4:41 PM
6 points
2
in reply to: aphyer’s comment on: A brief perspective from an IMO coordinator
The answers, at least for OpenAI and Google, have been posted.
OpenAI: https://github.com/aw31/openai-imo-2025-proofs/
Google: https://storage.googleapis.com/deepmind-media/gemini/IMO_2025.pdf
The OpenAI solutions are written in a weird style (I have seen some people say “RLHFed to death” and some people say “looks like internal chain-of-thought language” and some people say “it’s learned to be brief to get maximum use out of its context window”) but still basically natural mathematical language.
The Google solutions—I don’t know whether this is exactly what the model spat out or whether it’s been through any prettifying postprocessing, but would guess the former—are neatly formatted and written in nice polished English with LaTeX-formatted mathematics.
The ones I’ve looked at (which is not all of them) seem to be genuinely complete solutions, aside from the weird language of the OpenAI ones.
So far as I know, the prompts have not been posted.
(Some other people used ordinary Gemini 2.5 Pro to solve some of the problems—I forget whether they managed all of them other than #6 or not—with a bit more human assistance; I don’t think they posted their exact prompts but they did mention things like saying “Let’s proceed by induction” after the statement of Q1 and “Let’s do this with analytic geometry” after the statement of Q2. For the solutions above, I think OpenAI and Google both claim not to have given any sort of hints,)

gjm Jul 22, 2025, 4:52 PM
3 points
6
in reply to: Said Achmiz’s comment on: Just Make a New Rule!
Noted. For what it’s worth, I haven’t as yet seen much reason to believe that the LW moderators think they are empowered “to make judgement calls controlling the minute details of everyone’s behaviour”.
If you delete the word “the”, or better yet make things more explicit along the lines of “to make judgement calls about small details of what behaviour is acceptable when posting/commenting on Less Wrong”, then I dare say the moderators consider themselves empowered to do that. But that’s very much not the sort of thing that I understand when I read “make judgement calls controlling the minute details of everyone’s behaviour”, especially not at the end of an article full of examples about regulation of neurotoxic chemicals and road safety.
So perhaps this is yet another case where Zack says something that can with substantial stretching be interpreted as something true, but that (at least as it seems to me; others’ intuitions may differ) is an extremely unnatural way to say what he claims was all he was saying, and that strongly suggests something much worse but that is not actually true. I am beginning to find it rather tiring.

gjm Jul 22, 2025, 1:05 AM
13 points
11
in reply to: Said Achmiz’s comment on: Just Make a New Rule!
(I’m not sure whether that’s a serious answer or snark, but I’ll treat it as the former since I don’t think I have anything much to say to the latter.)
If that’s what Zack means, then it seems odd that the OP puts so much emphasis on how rules can be an effective way to keep people safer from literal death, brain damage, and the like.
The rules are just there to stop ourselves from trying to kill each other when your freedom and dignity is getting in the way of my freedom and dignity, so that we can focus on creating Value instead of wasting effort trying to kill each other. [...] Traffic laws make it clear to everyone when it’s safe to enter the road. If everyone just entered the road whenever they felt like it, that would be dangerous [...] Lead paint is an environmental hazard, so it was banned in 1978. Because of the ban, paint manufacturers stopped making lead paint. [...] So paint manufacturers still ended up using mercury in some paints until 1991 when that was banned, too. But once it was banned, they stopped.
Zack did mention one example of a rule that was about something less life-and-death-y, namely income tax—but that was an example of where nice clear rules aren’t so effective.
So I think either Zack wasn’t primarily taking aim at the LW moderators or his choices of examples are systematically ill-fitted to what they’re meant to be illustrating.

gjm Jul 21, 2025, 7:57 PM
2 points
0
in reply to: Said Achmiz’s comment on: Do “adult developmental stages” theories have any pre-theoretic motivation?
My interpretation of what Kaj wrote was indeed that he disagrees about exactly what pre-theoretic facts would suggest looking for an “adult developmental stages” theory, on the grounds that he thinks there could be such a theory (and indeed a basically-Kegan-shaped one) in which the strong age/stage correlation isn’t present.
The fact that the particular pattern of stage-transitions Kaj describes is basically-Kegan-shaped isn’t relevant to the validity of the objection, except in so far as it indicates that the pattern in question isn’t somehow the wrong sort of pattern to be part of an “adult developmental stages” theory.
For what it’s worth, my notion of what the pre-theoretic facts ought to look like isn’t exactly the same as yours. I’d want to see something like: 1. a specific set of psychological characteristics that 2. each exhibit a consistent pattern of progression through an individual’s life, 3. in such a way that we can put matching labels on all the progressions and see that people generally have most or all in consistently-labelled states, 4. (slightly optionally; if this fails then “developmental” is a misleading term) such that later-reached bundles of states are generally better in some sense than earlier-reached ones, and 5. (slightly optionally; if this fails then “stages” is a misleading term) a smallish discrete set of labels sufficing in the sense that most people most of the time have most of those characteristics in states corresponding to a single one of those labels. In particular, I don’t think I care whether the characteristics in question all pertain to a single “domain” in any sense, and I don’t think anything’s gained by introducing the possibility of correlations with other characteristics besides age, when later in your list you’re specifically going to demand correlation with age. And what I want to see is progression within each individual’s life, not a population-level correlation with age.

gjm Jul 21, 2025, 5:52 PM
17 points
12
on: Just Make a New Rule!
Who are these “people who think rules are unworkable and want to empower an Authority to make judgement calls controlling the minute details of everyone’s behaviour”?
I don’t think I’ve knowingly ever encountered such a person, and I’m trying to work out whether I just move in different circles from Zack, or whether I’m failing to see something real, or whether Zack is seeing something that isn’t real.
(The first hypothesis seems the most likely, but whichever is correct a few concrete examples seem like our best bet for making one of us less wrong.)
(Those aren’t literally all the hypotheses; e.g., it could be that Zack and I are seeing compatible things but Zack’s describing them in a way I’m understanding differently. E.g., perhaps Zack’s talking about people whose position I’d express as “sometimes the rules need to allow for an element of human judgement”—cf. Nick Tarleton’s comment elsewhere in the thread—and arguing for a position I’d express as “a society’s laws need to be 100% explicitly nailed down with no room for manoeuvre”. Again, concrete examples will help clarify.)

gjm Jul 21, 2025, 5:23 PM
2 points
0
in reply to: Said Achmiz’s comment on: Do “adult developmental stages” theories have any pre-theoretic motivation?
(I agree that we mostly don’t disagree here.)
Once again I think your objection is to something other than what I take Kaj to have been saying. That is: you’re saying that Kegan’s theory specifically isn’t sufficiently clearly defined to make it meaningful to talk about what “stages” it might or might not involve, etc. That might be true. But Kaj isn’t (here, in this thread) arguing about that. He’s saying (I paraphrase): “I think that if all the rest of it turns out to make sense, the relationship between age and stage according to Kegan’s theory has such-and-such a shape, in which case the correlation wouldn’t be very strong; therefore it would be a mistake to insist on strong age/stage correlations before taking such a theory seriously”. And so far as I can see, this is a reasonable kind of argument to make, even if it might turn out that actually “Kegan’s theory” fails to be clearly definable, or something of the sort. (In that case, making the argument would turn out to have been wasted effort, but that’s OK.)
(As I said above, I think that in fact Kegan-as-described-by-Kaj does predict a strong correlation between age and stage. But that’s an entirely separate matter.)
I agree that describing things that fit such a pattern as “stages of development” isn’t and shouldn’t be the default. I don’t know what evidence (anecdotal or scientific) Kegan and others have, or think they have, to support using such a term for the psychological changes Kegan professes to have observed. But (for what it’s worth) my impression is that they aren’t just saying that anything that changes over time should be called “stages of development”. I think they think (rightly or wrongly) that the “stages” are fairly well demarcated, that it’s not common for someone to be “in stage 3 as regards X and Y but in stage 4 as regards P and Q”, that it’s usual to spend much more time unambiguously in a particular stage than in any sort of transitional state, etc. Whether any of that’s true, I don’t know. Whether in fact Kegan “stages” can be defined clearly enough for the question to have a definite answer, I don’t know. But (so far as I can make out) the Keganites are purporting to describe something different from rock-climbing in such a way that (if they’re right) talking about “stages of development” and seeing them as needing some kind of explanatory theory makes more sense for what they’re talking about than it would for rock-climbing.

gjm Jul 21, 2025, 4:01 PM
7 points
6
in reply to: Said Achmiz’s comment on: Do “adult developmental stages” theories have any pre-theoretic motivation?
I don’t know whether we need one, but it’s not clear that one would be wrong.
In any case, it feels like there’s some misunderstanding between Kaj and Said here. I take Kaj’s comment two steps upthread from here not to be making any particular claim about the correctness or coherence or importance of Kegan’s theory, but only to be saying: if Kegan’s account of things were correct, then we would not necessarily see strong correlations with age. (Implicitly: Hence, it would be a mistake to demand such correlations in order to think such a theory worth investigating.)
So … would the correlation with age be weak, if things were as Kaj describes? I think not very weak. We’d have
- everyone starting at 1 …
- … and moving to 2 at age, I dunno, somewhere between say 0 and 4 …
- … and almost everyone then moving to 3 somewhere between say 12 and 25 …
- … and then a substantial fraction of the population moving to 4 between say 20 and 40 …
- … and then a small fraction moving to 5 at some point.
That looks to me like it would give a really strong correlation with age. Kaj, do you think I’m missing something here, and if so what?
(For what it’s worth, I also don’t see anything in this scenario that makes it unrealistic to describe it as “developmental stages”. Whether that description is reasonable or not depends on details that, for the moment, we’ve abstracted away—how discretely people move from one “stage” to the next, how consistently the various features of each stage go together with one another, etc. And, in view of Said’s final comment, perhaps also how much of the alleged progression is something that any reasonable person would guess on their own after a few minutes’ thought. Rock climbing doesn’t do very well by those criteria, but that doesn’t tell us much about whether Kegan’s theory does.)

gjm Jul 20, 2025, 11:23 PM
4 points
0
in reply to: mishka’s comment on: OpenAI Claims IMO Gold Medal
My recollection from the late 1980s when I was doing IMOs is that the proportions were supposed to be something like 6:3:2:1 nothing:bronze:silver:gold, so about 8% gold medals. I don’t think I ever actually verified this by talking to senior officials or checking the numbers.
(As for Terry Tao, I agree with you that he is clearly not in denial, he’s just cross at OpenAI for preferring PR over (1) good science and (2) politeness.)

gjm Jul 20, 2025, 10:59 PM
10 points
2
in reply to: Said Achmiz’s comment on: Do “adult developmental stages” theories have any pre-theoretic motivation?
It wasn’t meant to be a realistic example! But, yes, we are in violent agreement that it isn’t very likely that anything Keganesque would be true without the sort of age correlation you describe. It just seemed worth pointing out that it isn’t a requirement.

gjm Jul 20, 2025, 4:04 PM
11 points
0
on: Do “adult developmental stages” theories have any pre-theoretic motivation?
A nitpick:
Some sort of developmental-stage theory could be true without there being anything that quite looks like a strong correlation with age.
(Detailed example follows; feel free to skip if this is obvious once pointed out.)
Suppose everyone has some determinable number associated with them at any given time; let’s call it their “quality”. Everyone starts at 1. No one ever goes above 6. For a given person, quality only ever increases. But, tragically, “the good die young”, and if we classify people by the highest quality they ever reach it looks like this:
- Group 1: Q1 from age 0 to age 60.
- Group 2: Q1 from age 0 to age 40, Q2 from age 40 to age 50.
- Group 3: Q1 from age 0 to age 20, Q2 from age 20 to age 30, Q3 from age 30 to age 40.
- Group 4: Q1 from age 0 to age 3, Q2 from age 3 to age 10, Q3 from age 10 to age 20, Q4 from age 20 to age 30.
- Group 5: Q1 from age 0 to age 2, Q2 from age 2 to age 4, Q3 from age 4 to age 6, Q4 from age 6 to age 10, Q5 from from age 10 to age 20.
- Group 6: Q1 from age 0 to age 1, Q2 from age 1 to age 2, Q3 from age 2 to age 3, Q4 from age 3 to age 4, Q5 from age 4 to age 5, Q6 from age 5 to age 10.
Although the good die young, the gods smile on virtue so they are more numerous: the number of people in each group is inversely proportional to the age they will attain.
So we might suppose a population with
- 6000 group-1 people, 100 each at ages 0.5 .. 59.5, all at quality 1
- 7200 group-2 people, 144 each at ages 0.5 .. 49.5, transitioning from quality 1 to quality 2 at age 40.
- 9000 group-3 people, 225 each at ages 0.5 .. 39.5, transitioning at ages 20 and 30.
- 12000 group-4 people, 400 each at ages 0.5 .. 29.5, transitioning at ages 3, 10, 20.
- 18000 group-5 people, 900 each at ages 0.5 .. 19.5, transitioning at ages 2, 4, 6, 10.
- 36000 group-6 people, 3600 each at ages 0.5 .. 9.5, transitioning at ages 1, 2, 3, 4, 5.
And this turns out to give a negative correlation between age and quality.
For the avoidance of doubt, I don’t think it’s terribly likely, conditional on some Kegan-like thing being true, that the distributions would look anything like this. Most likely, if something Kegan-like is true, age will correlate with stage. But it’s not guaranteed.

gjm Jul 19, 2025, 5:02 PM
15 points
1
in reply to: Zack_M_Davis’s comment on: Critic Contributions Are Logically Irrelevant
“Maximizing X”, in a vacuum, does indeed mean making X as large as possible while ignoring everything else. But we are not always in a vacuum. There is such a thing as “constrained optimization”; much of the time when someone refers to “maximizing X” it’s in a context like “maximizing X while satisfying constraint C”. There is such a thing as “multi-objective optimization” where you’re trying to maximize X and also trying to maximize Y and you have to trade them off somehow.
So even in the technical language of mathematics “maximizing X” need not imply ignoring everything except X.
And, of course, someone writing or commenting or moderating on an internet forum is not literally solving mathematical optimization problems, and if you talk about them “caring about maximizing X” then it would literally never occur to me to interpret that as “caring about maximizing X and literally about nothing else”.
… Having said which, I just polled a couple of other people of my acquaintance, both mathematicians and hence presumably more than averagely aware of the technical meaning of “maximizing”, and they both said that they would interpret “X doesn’t care about maximizing Y” as being consistent with X preferring Y to be bigger but also having other concerns.
I have therefore deleted the bit of this comment where I indignantly proclaim that I see no possible reason for writing the heading the way you did other than rhetorical sleight-of-hand :-), but it still seems to me that ”… if you care about other things besides correctness” would be very much less liable to mislead or misdirect readers than ”… if you don’t care about maximizing correctness”. (And I think the wording you ended up using at the end of the text of that section indicates that it’s more natural to phrase things that way.)

gjm Jul 18, 2025, 1:31 PM
23 points
2
on: Critic Contributions Are Logically Irrelevant
The article has a heading of the form “X, if you don’t care about maximizing correctness” followed by a (correct) discussion showing that “X, if you don’t care exclusively about maximizing correctness”.
Those two things are very different. In particular, around here almost everybody cares about maximizing correctness, but I would guess that very few people care about literally nothing else.
That discussion also makes the decision to take “ad revenue”, something readers here may reasonably be expected to have some contempt for, as its working example of something other than correctness. I think this is part of the same rhetorical move: Zack acknowledges, formally, that it can be reasonable to care about things other than correctness (he also mentions, but decides not to use, the example of “total number of interesting ideas” which I would guess almost everyone here would agree is a thing worth wanting), but then he (1) chooses to instead emphasize something that most of us will feel icky about the idea of optimizing for[1] and (2) heads the section with a title that accuses people of not caring about correctness, which is extremely very utterly different from caring about other things besides correctness.
[1] Also something that, so far as I know, cannot possibly be a concern here on Less Wrong where there is no advertising revenue to try to maximize.
(I remark that this is not the first time I have had a discussion with Zack of much the same shape, where Zack implicitly or explicitly claims that epistemic virtue means caring only about one thing even when there seem (at least to me) to be other things a would-be clear thinker might reasonably care about. I think it might be the third or fourth time.)
[EDITED to add:] I realise that that last paragraph might be misleading; this is an instance of “me having a discussion with Zack” only in the sense that this comment here is by me and it’s replying to something Zack wrote. I don’t mean to imply that what Zack wrote had anything at all to do with me; it didn’t.

gjm Jul 18, 2025, 1:22 PM
13 points
2
on: Critic Contributions Are Logically Irrelevant
I don’t think this is an important factor that makes a big difference, but the identity of the author can make a difference to the value of the comment in the following way.
Consider a correction like the one Zack received on his post about discontinuous linear functions. A reader who sees such a correction from someone they know is good at mathematics can (at least in the absence of further argument about the correction) trust that they got it right, and update their opinions accordingly. If they see such a correction from some rando they know nothing about then they can’t do that, and need to work through the mathematics themself, or wait for someone else to do it, or just put up with not knowing who’s right.
(This is a separate point from the one, already acknowledged by Zack in the OP, that our estimate of comment value may be higher if we know the commenter is expert; I am saying that the actual value of a correct comment is higher if readers know the commenter is expert.)

gjm Jul 13, 2025, 2:42 AM
4 points
0
in reply to: thiccythot’s comment on: the jackpot age
They show up properly for me now.

gjm Jul 12, 2025, 4:13 PM
8 points
0
on: the jackpot age
I think readers using Firefox (or forks thereof) with its “enhanced tracking protection” turned on will not see images here; at any rate, they are blocked for me with the note “Socialtracking” in the network tab of the devtools, which I think means that ETP blocked them.
I don’t know whether there’s some other place to host images for LW articles that won’t provoke such issues.

gjm Jul 9, 2025, 8:20 PM
13 points
1
on: Subway Particle Levels Aren’t That High
I’m curious as to whether the “pretend it’s a completely different person” schtick was just for fun or whether there was a deeper purpose to it (e.g., encouraging yourself to think about past-you as an entirely separate person to make it easier to rethink independently).

gjm Jul 9, 2025, 8:18 PM
8 points
1
in reply to: Raemon’s comment on: Raemon’s Shortform Feed
This sounds like maybe the same phenomenon as reported by Douglas Hofstadter, as quoted by Gary Marcus here: https://garymarcus.substack.com/p/are-llms-starting-to-become-a-sentient

gjm Jul 5, 2025, 11:16 PM
10 points
6
in reply to: Proof of Ineffective Input’s comment on: Kaj’s shortform feed
Could you please clarify what parts of the making of the above comment were done by a human being, and what parts by an AI?

gjm Jul 5, 2025, 11:13 PM
2 points
1
in reply to: Kabir Kumar’s comment on: Kabir Kumar’s Shortform
Sure, but plausibly that’s Scott being unusually good at admitting error, rather than Tyler being unusually bad.

gjm Jul 5, 2025, 12:14 AM
4 points
1
in reply to: Kabir Kumar’s comment on: Kabir Kumar’s Shortform
It’s still pretty interesting if it turns out that the only clear example to be found of T.C. admitting to error is in a context where everyone involved is describing errors they’ve made: he’ll admit to concrete mistakes, but apparently only when admitting mistakes makes him look good rather than bad.
(Though I kinda agree with one thing Joseph Miller says, or more precisely implies: perhaps it’s just really rare for people to say publicly that they were badly wrong about anything of substance, in which case it could be that T.C. has seldom done that but that this shouldn’t much change our opinion of him.)