gjm

Karma: 26,977

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 in about the last four years. I live near Cambridge (UK) and work for a small technology company in Cambridge. 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 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 23 Jan 2022 2:47 UTC
9 points
in reply to: Paul Crowley’s comment on: A one-question Turing test for GPT-3
A jar of mayonnaise would work tolerably: put it on top of a corner of whichever side of the book is tending to swing over and close.
(I agree that I would expect most humans to do better than almost all the AI responses shown here.)

gjm 18 Jan 2022 17:48 UTC
2 points
in reply to: tailcalled’s comment on: Entropy isn’t sufficient to measure password strength
The function is cdf. The way it’s used in the expected-utility calculation is that it’s applied to 1/p where p is the probability of a given password. My original use of the term “probability” for the reciprocal of the thing fed to the cdf function was needlessly confusing, which is why I dropped it in the rewrite.
since in my original comment, P is not the least probable password the attacker has the resources to try.
In your original comment, P is the probability of a particular password. (I say this just to confirm that I do, and did, understand that.)
But if we are going to explain what the cdf function actually is, we need to say something of the form “cdf(R) is the fraction—or, in the case of improper not-exactly-probability-distributions, something more like the total number—of attackers for whom …”. And I think the correct way to fill in that ”...” is something like “when they crack passwords, we expect that the least probable password they’re likely to crack has probability 1/R”. (Right?)
In other words, I’m trying to be more explicit about what “adversary capabilities” actually cashes out to, and I think that’s what it is.
Your more-explicit formalization of the calculation agrees with my understanding; to whatever extent you feel that what I’m describing is different from what you’re describing, I am pretty confident the cause is not that we have different understandings of the mathematics at that point. I think it’s you misunderstanding me / me communicating badly, not me misunderstanding you / you communicating badly.
(It is a lamentable misfeature of our language that—so far as I can tell—there is no good way to say “what’s going on here is that what A is trying to say is not what B is interpreting it as” that doesn’t tend to assign blame to one or other party. You have to call it misunderstanding (implicitly blaming B) or miscommunicating (implicitly blaming A). But it takes two to tango and communication failures often involve suboptimality at both ends, and even in cases where it doesn’t assigning/taking blame is often an irrelevant distraction.)

gjm 18 Jan 2022 12:16 UTC
17 points
in reply to: Vigilantibody’s comment on: (briefly) Radvac and SMTM, two things we should be doing
Thanks for the detail. I think that means that the answers to my questions are “no, not at all, for the more recent versions of RaDVaC, and in fact for earlier versions what we have is evidence that it usually doesn’t produce any immune response”, and “no, not at all, for any version of RaDVaC”.
For the avoidance of doubt, I’m not saying that this means you’re bad people, or that it means your thing doesn’t work, or that it means no one should give you money. I’m just trying to assess how likely we should think it is that what you’re doing will turn out to be useful.
I think, in particular, that when Eliezer (in the OP) says
They’ve pretty much proved themselves. They should be nurtured and scaled up to where they can start to replace US and Earth defunct state capacity to do the R&D that leads up to being able to rapidly design new vaccines that rapidly scale in production and deployment.
that first sentence is 100% false unless “proved themselves” means something like “proved that they are smart people” or “proved that they are acting in good faith” rather than “proved that they have something that works”, which means that the second is waaaay premature.
Which, again, doesn’t mean that the RaDVaC project shouldn’t be nurtured. Maybe it should. All science and technology starts out unproven, after all.
Eliezer, if you happen to be reading this: Do you, in the light of the discussion above, still consider that “they’ve pretty much proved themselves”, and are you still confident that the project needs only nurturing and scaling-up before it is ready to start replacing the planet’s existing vaccine R&D efforts? If so, what is it that you think I’m missing?

gjm 18 Jan 2022 1:04 UTC
2 points
in reply to: tailcalled’s comment on: Entropy isn’t sufficient to measure password strength
It’s a separate independent parameter for me too. My intention (though of course I may have screwed up) is that I’m describing the same thing as you are :-).
So, suppose you have a particular probability distribution for the number of guesses an attacker has. I am describing that by saying what its pdf is as a function of 1/#guesses (the thing I’m calling p). I call this f(p). You’re describing it by saying what its cdf is as a function of #guesses (the thing you’re calling 1/P). You call this cdf(1/P). These two formulations are equivalent[1].
[1] Well, maybe there are some weird technical issues if the cdf is sufficiently horribly non-differentiable—a Cantor staircase or something of the sort.
Why start with f(p) rather than cdf(1/P)? No particular reason, I guess :-). It would probably have been cleaner just to define q=1/p (as I did) and then work with either the pdf or the cdf as a function of q.
So, let me try again—I am not saying anything different, or at least not intending to, just cleaning up my notation and language and so forth—and see whether you find the result (1) comprehensible and (2) compatible with what you said before. (Again, to be clear, I am claiming only to explicate what you already said, which I found excellent but a bit terse.)
A little more detail seems worth providing. Let’s say that an attacker has “resources R” if they are willing and able to crack passwords with probabilities at least 1/R. (Is this a realistic model? I think it is provided R is fairly large, which in practice it usually will be, provided attackers know the probability distribution we are using. If I am an attacker and know e.g. that passwords of type A are used 10x more often than passwords of type B, then I will use 10x more of my resources on type-A passwords. This falls down if I have enough resources that I literally can’t do that without repeating passwords, but for actually-realistic password distributions and attackers who are likely attacking multiple victims at once this is not a problem.)
So, we can describe the distribution of attackers in terms of the pdf f(R). In some sense, as described above, values of R are reciprocals of password-probabilities; the corresponding pdf over probabilities is f(1/p)/p^2 where p=1/R. If we start with the cdf F(R) instead, the pdf is f’(R), the pdf over probabilities is F’(1/p)/p^2, and of course the cdf for probabilities is just 1-F(1/p).
In each case, tailcalled’s prescription is to take E[cdf(1/p)], the expected fraction of attackers who fail to crack our password, as our figure of merit. The expectation is taken over our passwords with the probability distribution we are using (the probability distribution over passwords, not over attackers) so it equals the sum of p.F(1/p) where F is the cdf for attacker-resources.
These things I’ve called “pdfs” and “cdfs” may not actually integrate/tend to 1; we may leave them unnormalized, or indeed they may be improper (so that the integral of the pdf / limiting value of the cdf is infinite). What we are doing with these is just maximizing/minimizing some expectation involving them; rescaling the values of the pdf/cdf doesn’t change the result (so we needn’t care about normalization) and in many cases the expectation will converge even if the pdf/cdf is improper.
Let’s look more explicitly at the examples tailcalled mentioned. A uniform distribution for R, which of course is very improper indeed, corresponds to F(R)=R or f(R)=1. The corresponding pdf for p=1/R is 1/p^2. A uniform distribution for log R, still improper, corresponds to F(R) = log R or f(R) = 1/R. The corresponding pdf for p=1/R is 1/p. This is exactly the case in which expected utility = entropy.
(As tailcalled implied but didn’t quite say explicitly, the fact that these are improper is what enables the pathology described by OP: as R gets large the cdf → infinity, so a modest probability of picking extremely-low-probability passwords can give an arbitrarily large positive contribution to the expectation we’re trying to maximize, even if most of the time we do very badly.)
We looked at pdf(p) = 1/p^2 and pdf(p) = 1/p; let’s go one step further and take pdf(p)=1, corresponding to a uniform distribution over 1/R; cdf(R) = 1-1/R, and pdf(R) = 1/R^2. Our figure of merit is E[cdf(1/p)] = E[1-p] = 1-E[p], so the expected negative utility we get is (aside from irrelevant constant offsets and scalings) E[p] = sum(p^2).
(At this point, continuing from “How does this figure of demerit do …” in the original version of what I wrote seems fine, except that the final paragraph of what I already wrote is effectively incorporated above.)

gjm 17 Jan 2022 19:35 UTC
2 points
in reply to: tailcalled’s comment on: Entropy isn’t sufficient to measure password strength
I said “probabilities” but should really have said something like “reciprocals of numbers of trials”. The thing you called P, when you wrote things like “E[1/P]” and “E[log 1/P]”. This has the same “units” as probability; if you wanted to express it in explicitly probabilistic terms it would be something like “least probable password the attacker has the resources to try”.

gjm 17 Jan 2022 19:29 UTC
7 points
on: Working through D&D.Sci, problem 2 (solution)
You asked what Guy and I were looking for that led us to notice the prime-factors thing. In my case, the answer is just that by training I’m a pure mathematician and I can’t help noticing that sort of thing. For whatever reason it didn’t occur to me to, e.g., look at the distributions of the exponents of 2, 3, and 5 or anything like that, not that doing so would have led me to pick different items or anything.
(I was glad to see that you liked “Wakalix Maketh it Goe”.)

gjm 17 Jan 2022 17:03 UTC
2 points
in reply to: tailcalled’s comment on: Entropy isn’t sufficient to measure password strength
A little more detail seems worth providing. If you have a pdf (over probabilities) f(p), which may or may not actually integrate to 1 or to any finite value, then the corresponding pdf for our measure of attacker-capability q=1/p is f(1/q)/q^2; the relevant CDF here is the integral from 0 to q of this.
Conversely, if we start with a given cdf F(q), its pdf is F’(q), and the corresponding pdf for p is F’(1/p)/p^2.
So a uniform distribution over q (obviously improper) corresponds to F(q) = q and a pdf of 1/p^2. A uniform distribution over log q (again, obviously improper) corresponds to F(q) = log q and a pdf of 1/p.
If we continue this “one step further”, a (no longer improper) uniform prior on p means F’(1/p)/p^2 = const or F’(q)=const/q^2 or F(q) = const/q; obviously the constant should be negative. That is, this would mean trying to minimize the expected probability of the password we pick. Equivalently, trying to minimize sum(p^2) over all our possible passwords. So, in particular, for a fixed set of passwords this says to pick them all with equal probability.
How does this figure of demerit do for the example in the OP? Let’s generalize it a little, so that with probability p we pick one password and with probability 1/p we pick one of N passwords.
- The entropy here is p log 1/p + (1-p) log N/(1-p). If we call this E(p,N) then note that E(1/2,N) >= E(1, 2N), so setting p=1/2 can be “fixed” by doubling N.
- The sum-of-squared-probabilities is p^2 + (1-p)^2/N. When p=0 this is 1/N. When p>0, even in the limit of infinite N it’s 1/p. So for any N, if you increase p beyond 1/sqrt(N) you cannot hope to compensate for this by increasing N further.
The implied model of our attackers here is that the probability that an attacker can afford to guess at least N passwords goes down in proportion to 1/N. Not obviously very realistic, but not obviously worse than the improper priors considered above either :-).
tailcalled alluded to the following but didn’t make it explicit: If your prior is improper then you can make that CDF get unboundedly large, which means you can compensate for badness elsewhere that way, which means the pathology OP is about can happen; if your prior is proper then you can’t. So propriety is in some sense exactly the property we want here.
[EDITED to add two things:] 1. After some discussion with tailcalled, there’s a rewritten and hopefully clearer version of most of the above in a comment of mine further downthread. 2. I see that this one has received someone’s strong-downvote. For the avoidance of doubt, I’m not complaining; you should strong-downvote things that you think are very bad; but it would be much more useful information if I understood what the problem is, and right now I don’t. Did I make a mathematical error? Was my writing too unclear to be useful (e.g., because “probabilities” was a bad way to refer to 1/attacker_capacity, or because looking at things as a function of p = 1/attacker_capacity is needlessly confusing)? Did it feel as if I was trying to restate what tailcalled already said and take credit for it? Etc. Thanks!

gjm 17 Jan 2022 14:37 UTC
5 points
in reply to: Lachouette’s comment on: Guidelines for cold messaging people
It’s not just that they’re thoughtlessly maximizing responses at the expense of recipients’ time: recipients are liable to notice this, be annoyed by it, and therefore be less likely to respond as a result. So maybe they’re (in some sense) trying to maximize responses and not caring about recipients’ time, but in practice they aren’t even doing that; they could probably get more responses by being a bit more thoughtful and polite.

gjm 16 Jan 2022 13:49 UTC
8 points
in reply to: Vigilantibody’s comment on: (briefly) Radvac and SMTM, two things we should be doing
Is there any empirical evidence yet that RaDVaC’s alleged vaccines are in any way effective in making those who use them less likely to get COVID-19, or less likely to get it badly?
[EDITED to add:] I did take a look on the RaDVaC website, and if I’m understanding the FAQ there correctly the answer is (1) you have “positive indications” from your “preliminary assays” (I am guessing this means: very weak evidence?) that RaDVaC elicits some sort of immune response in the nose, and (2) you have no direct evidence at all that it has any effect on either whether one gets COVID-19 or how severe its effects are if you do. But maybe you can say more here than you have on your website?

gjm 14 Jan 2022 16:34 UTC
2 points
on: Open Thread—Jan 2022 [Vote Experiment!]
My immediate (kneejerk System-1-ish emotional) reaction to the experimental voting popup is along the lines of “meh, too much effort, won’t bother”.
My slightly less immediate reaction turns out to be much the same. So e.g. I think “I should give this a try”, take a look at the comment currently presented to me first, and … well, there are now 9x as many things to decide about it as before (overall opinion, 4 “axes”, and 4 possible reaction emoji), and all but the first feel as if they require substantially more mental work to arrive at a useful opinion about, and I just don’t wanna.
But!
In practice, the way I usually use the LW karma system (other than “implicit” uses like reading the comments in the order the UI presents them to me in, which is affected by karma) is something like this: I vote only when something I read strikes me as especially good or bad, in which case I consider briefly whether it’s good/bad enough to be worth voting on, and whether if so it warrants a strong up/down-vote. This process seems like it might cope fine with the more complex interface—if I’ve been particularly impressed or unimpressed by something I’ll have some sense of what about it is impressive or unimpressive to me, and having a finer-grained way to express that seems like a gain rather than a loss.
So it may be that the answers to the questions “is explicitly deciding what to do with a particular post or comment easier or harder with this experiment?” and “is voting as I actually do it easier or harder with this experiment?” are substantially different.
[EDITED to fix an inconsequential typo.]

gjm 14 Jan 2022 15:42 UTC
2 points
on: Open Thread—Jan 2022 [Vote Experiment!]
I’m not sure what it says about LW that in the current Open Thread there is only one comment that isn’t either (1) about the voting-system experiment or (2) deleted.
(And I slightly suspect that that one comment may have been inspired at least slightly by the voting-system experiment, not that there’s anything at all wrong with that.)

gjm 7 Jan 2022 0:37 UTC
3 points
in reply to: CraigMichael’s comment on: Covid 1/6/22: The Blip
I also don’t like “Law” for this, and cynically suspect that the use of “Law” for this sort of thing is at least sometimes at least partly an attempt to co-opt the prestige of actual laws while using “oh I just meant like Murphy” for plausible deniability.
It sounds as if you may be proposing “razor” as a general term for this sort of thing, which I don’t like because there’s a reason why Occam’s Razor is called a razor rather than something else: it’s a tool for trimming off low-value hypotheses. This particular proposition of Zeynep’s is in fact razor-ish, though, so I endorse calling it a razor.
But “first” is ugly, and Zeynep doesn’t use it. I suggest simply “Zeynep’s Razor”.
The “razor” formulation is better than “law” not only because it makes weaker claims to Universal Truth, but also because it correctly suggests a different kind of thing that this is: a methodological principle, of the form “consider these hypotheses before those ones”. Of course the boundary between “consider these hypotheses first” and ”… because they are more likely to be true” is a fuzzy one.

gjm 2 Jan 2022 22:29 UTC
10 points
on: Scott Alexander 2021 Predictions: Market Prices—Resolution
I think the post should mention the fact that Zvi’s forecasts were made after reading Scott’s.

gjm 2 Jan 2022 9:27 UTC
5 points
in reply to: A.Omega’s comment on: Religion’s Claim to be Non-Disprovable
[EDITED to add: The following was written in response to a comment that has now been deleted—not, I believe, by its author. The comment took exception to what Eliezer said about moral horrors in the Bible.]
The problem with biblical ethics isn’t that the Bible describes things that we now find morally terrible, it’s that it endorses things that we now find morally terrible while claiming (or being claimed) to speak authoritatively for a perfectly good god.
So no one is complaining that the Bible says Joseph was sold into slavery by his brothers. They’re complaining about things like Exodus 21:7-10 (where God, speaking through Moses, provides instructions on how best to sell your daughter as a sex slave) or 1 Chronicles 13:9-10 (where the Ark of the Covenant is being transported, and the oxen stumble, and some well-meaning chap puts out a hand to steady it—and God himself strikes him dead for it) or 1 Samuel 15:1-3 (where God, speaking through Samuel, commands an outright genocide of the Amalekites as a punishment for something their ancestors had done) or Deuteronomy 22:28-29 (where God, speaking through Moses, commands that when a man rapes a woman who is neither married nor betrothed, he pays a fine to her father and she becomes his wife). These aren’t merely reporting that moral atrocities happened; they are endorsing and even commanding moral atrocities in the name of God.
From which a reasonable person will conclude that one of three things is true. (1) These documents are not in fact providing reliable information about the god they claim to speak of and speak for. (2) The god in question has moral values so different from ours that we should very decidedly not be worshipping that god. Or (3) the god in question has moral values that have changed radically since those documents were written, in something like the same way as humans’ values have changed. Of these, #1 seems much the most likely, and there is plenty more evidence for it (e.g., the discrepancies between biblical accounts of historical events and the best information we can find about them from other sources) but any of them would mean that these documents do not give us a trustworthy account of how we ought to live.

gjm 28 Dec 2021 0:26 UTC
5 points
in reply to: Michael McCabe’s comment on: Leave a Line of Retreat
Evangelism and creationism don’t tend to go down very well here, but you know what’s likely to go down even less well? Claiming to have conclusive evidence against things near-universally believed here (e.g., evolution) and not bothering to provide us with any of it.
I don’t want to mislead you; if you do tell us some of the things you regard as demonstrating that evolution is “a fairy tale”, those things are not likely to get the sort of reception you would prefer them to get. (I say: because you’re claiming to offer conclusive evidence of something that is in fact false, and of course this conclusive evidence is likely to be much worse than you think it is. You might have other explanations.) But just turning up and saying “I know that you guys are catastrophically wrong” but not saying why? Hopeless. That’s not what you do when you actually want to help. It’s what you do when you want to gloat.
(You may not be aware of how smug what you wrote comes off as being, to those who don’t already agree with you. That’s kinda fair, because I am very confident that a lot of things here that assert or presuppose atheism come across as equally smug to you. But, again, if you are actually hoping to help anyone escape from darkness and ignorance, you might want to avoid coming across as smug. But I’m not sure you are. After all, you believe in a god who might well “choose to hinder their understanding”. Why, believing in such a god, you find yourself willing to believe anything that god is purported to have revealed to you, I don’t really know. But if that’s the sort of god you believe in, it’s not surprising if your belief that you are in the light and we are in the dark leads you to gloat rather than to try to enlighten.)
Anyway, I just thought it might be helpful to offer a few words of explanation of the torrent of downvotes you will likely receive if anyone else actually reads what you wrote. I expect you will think of other explanations which are more flattering to you and to your religion, and you may prefer to believe those, but I wouldn’t want not to have tried.

gjm 22 Dec 2021 3:33 UTC
0 points
in reply to: Unreal’s comment on: Quis cancellat ipsos cancellores?
Thanks. I am not sure I would trust the author of the post (1) not to lie outright and (2) to kinda-not-exactly-lie by taking the view that one doesn’t know oneself, but your report is certainly some evidence that they are two different people (with, apparently, somewhat similar attitudes to Aella and to Leverage).

gjm 21 Dec 2021 22:31 UTC
2 points
in reply to: Spiracular’s comment on: Quis cancellat ipsos cancellores?
Is it known whether the author is the same person who commented on the “Frame Control” post under the name of “blueiris” (and, after that account was banned, “blueiris2”, and then “blueiris3″) complaining about how Aella was taking unfair advantage of her feminine wiles to get her stuff well received on Less Wrong?

gjm 17 Dec 2021 21:38 UTC
2 points
in reply to: ChristianKl’s comment on: Covid 12/16: On Your Marks
Yes, the basic literal meaning of the word “late” is that something should have happened earlier. But not all actual uses of it have exactly that meaning, and I think Scott’s use of it at the start of his post is an example.
(I agree with GWS’s reading of Scott’s opening sentence, and also with his examples of the sort of thing Scott might have written if he had actually intended to tell us that he ought to have written a post about ivermectin much sooner and that he hadn’t because he was scared.)
I did not disagree that Scott thought there was an “early promising phase”. What I was asking was where Scott said, as you implied he did, that “the meta-analysis we have points in the direction of ivermectin working” was the state of evidence two months ago. I take your reply as confirming that he did not say that, as I suspected he probably hadn’t.
He does say that rationalists did no better than anyone else. That doesn’t mean that he, personally, believed that there was good evidence that ivermectin is substantially helpful against Covid-19. (Both because “rationalists didn’t do better” and “no individual rationalist did better” are entirely different propositions, and because I was questioning your account of what he said at that point, not your account of what he thought. Though I don’t think much of your account of what he thought either.) Maybe he did believe that, maybe not; I don’t know; but he does not appear to have said that he believed that, and you said that he did. I don’t think you should do that.
(Another thing I don’t think you should do: quote what I wrote with a bunch of important words removed from it, so that it looks as if I said “Scott’s position on ivermectin as described in his big blog post about it is X” when in fact what I did was to say that you were claiming that and I think you were wrong.)

gjm 17 Dec 2021 15:25 UTC
4 points
in reply to: ChristianKl’s comment on: Covid 12/16: On Your Marks
Where does he say “that he should have written earlier”?
So far as I can tell, you’re referring to the opening of his piece where he says
I know I’m two months late here. Everyone’s already made up their mind and moved on to other things.
He may be saying “you might have preferred me to write this two months earlier”. That is not at all the same as “I didn’t dare say anything earlier”, and it is not at all the same as “it would in fact have been better for me to write this two months ago”. Also, two months before Scott’s post on ivermectin is not obviously the early “looks promising so far” phrase; stories were going around crediting ivermectin for the fairly short duration of India’s huge Delta wave back in May.
The rest of what you say is just speculating about Scott’s motivations. Maybe your speculation is right, maybe not (I think probably not, but of course I could be wrong) but in any case it’s entirely separate from what you said above, which claims that Scott’s position on ivermectin as described in his big post about it is that there was an early promising phase in which he dared not say anything about it in public. So far as I can tell, that’s entirely false because (1) Scott didn’t say that he was scared to write about ivermectin in public and (2) Scott’s position on ivermectin as described in his big post about it is a bunch of propositions about ivermectin, not about Scott’s mental state months ago.
I do not profess to know why Scott didn’t write about ivermectin two months (or four months, or six months) ago. I can think of plenty of reasons that don’t involve the dishonest motivations you’re trying to pin on him.
Incidentally, when you say
that was the state of evidence according to Scott
what “according to Scott” are you referring to?

gjm 17 Dec 2021 11:47 UTC
7 points
in reply to: ChristianKl’s comment on: Covid 12/16: On Your Marks
That seems to me a staggeringly inaccurate characterization of Scott’s post about ivermectin. (He does mention an “early phase of ‘looks promising so far’”. He doesn’t, I think, say that during that phase he didn’t dare say anything publicly about the topic. And none of that is “Scott’s position on ivermectin” as opposed to “one incidental remark while Scott is describing his actual position on ivermectin”. You can find his actual position right at the end of that post under the words “The Summary”.