gjm

Karma: 25,164

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 26 Jan 2021 11:52 UTC
9 points
on: Wordtune review
Not very surprisingly, I felt that every single one of the Wordtune versions was strictly worse than your original that it took as input.
(That doesn’t necessarily mean it’s useless. It might improve worse-written text. Some of its rewrites might be usable as the basis for something better. Sometimes you might want badly-written text of a kind it’s good at creating; e.g., it looks like asking it to be “formal” produces some of the same pathologies humans sometimes produce when trying to write formally, so if you needed examples of that kind of bad writing you could maybe get some with Wordtune. Not that there’s any shortage of examples elsewhere.)

gjm 24 Jan 2021 17:14 UTC
2 points
in reply to: Gurkenglas’s comment on: Lessons I’ve Learned from Self-Teaching
I haven’t thought it through, but I suspect the theorems you want to prove about integrals are probably easier to prove with the definition TurnTrout gave than with that one.

gjm 23 Jan 2021 14:48 UTC
2 points
on: Sunzi’s《Methods of War》- The Army’s Form
Nitpick: Are you missing a “not” in “Noticing the sun and moon does indicate a keen eye”?

gjm 18 Jan 2021 21:35 UTC
3 points
in reply to: Stuart Anderson’s comment on: How do you measure conformity?
“They laughed at Galileo. They laughed at Einstein. But they also laughed at Bozo the Clown.”
It’s true that being shunned or attacked is a sign that you’ve likely done something nonconforming and transgressive. But some things are nonconforming and transgressive just because they’re stupid or obnoxious.
I think what this means is that trying to measure how non-conformist you are, and hoping that “the more non-conformist the better”, is a mistake. Being unlike other people isn’t a good goal, in itself, because most ways of being unlike other people are not improvements. What you need to identify is ways of doing better, specifically, and measuring whether they laugh at you / shun you / stone you won’t do that, because they’ll do that for being worse as well as for being better.

gjm 18 Jan 2021 3:36 UTC
12 points
on: D&D.Sci II Evaluation and Ruleset
I don’t think the trap was horrible and unfair. Rule One of data science is: always look at your freakin’ data rather than blindly feeding it into the sausage-making machine and hoping you’ll be able to eat what comes out.

gjm 14 Jan 2021 19:45 UTC
10 points
on: Discussion on the choice of concepts
“Since you’re troubled by the other possibly unwanted associations of the word stupid, how about we just agree to say that toasters aren’t highly intelligent? It doesn’t really matter whether you say that that’s because toasters aren’t the sort of thing one can call intelligent, or that it’s because you could call them intelligent if they were but they aren’t; either way we can agree that toasters are not highly intelligent agents, and that’s what matters.”
“Oh, yeah, that works.”
“Great. Let’s move on.”
(Of course, in many arguments about how one should define things there isn’t a sufficiently convenient circumlocution, either because there isn’t a good one at all or because it’s super-important to have a handy short term or because the question is exactly about how one particular term should be used.)

gjm 13 Jan 2021 13:03 UTC
2 points
in reply to: ejacob’s comment on: D&D.Sci II: The Sorceror’s Personal Shopper
Meta: there’s one word in that comment that’s kinda spoilery and you should maybe spoilerize it.

gjm 12 Jan 2021 17:02 UTC
7 points
on: D&D.Sci II: The Sorceror’s Personal Shopper
Proposed buy (no explanations but may still be spoilery; there is a lot I still don’t understand so I suspect one can do better):
WH o Ju, Pl o Pl, Ha o Ca, Pe o Ho. I expect a little under 130 mana, for a cost of 144gp.
Explanations (definitely spoilery):
Yellow-glowing things get 18-21 mana; I haven’t found patterns beyond that. Green-glowing things get 2-40 mana, always an even number; I haven’t found patterns beyond that. Red-glowing things get 2^a 3^b 5^c mana; other than the fact that somehow we never get >96 even though we separately get 64, 27, 5, I haven’t found patterns beyond that. Blue-glowing things get highly variable mana, also favouring small prime factors though 7 occurs; for these (and only these) the thaumometer gives plainly useful information, yielding the true mana gain +-1 except that items you wear yield a number too high by 22. So the two cheaper yellow items are pretty good value, as are the highest-thaumperature blue ones even though one of them is overrated. We should get at least 18+18 for the yellow ones and at least 34+54 for the blue ones.
But
I suspect there may be more going on than I yet understand with the red and green items, for which at present I don’t think I know anything useful. And maybe the finer details of the yellow and blue ones are predictable too.

gjm 12 Jan 2021 16:06 UTC
2 points
in reply to: Ericf’s comment on: D&D.Sci II: The Sorceror’s Personal Shopper
Then you are missing out. I have only a partial understanding of the phenomena so far, but I already have a set of four items that I think should pretty reliably get at least 120 mana for a total price below 150gp.

gjm 12 Jan 2021 15:27 UTC
3 points
on: D&D.Sci II: The Sorceror’s Personal Shopper
Wakalix the Wizard. Slogan: “Wakalix Maketh It Goe!”

gjm 8 Jan 2021 15:02 UTC
3 points
on: Condition-directedness
Nitpick about that first paragraph: that sort of backward chaining is pretty common in chess, actually. Near the end of a game you’re very often envisaging aparticular state of affairs and planning how to get there. Not necessarily the exact final state, but something like “I need his king in this corner or that corner, and I need it to arrive there when my knight is here or here so that my bishop can do that and deliver checkmate”. Even in the middle of the game you may have intermediate goals like “move my pawn safely from e7 to e5″ or “drive the knight away from e4 without weakening my king position”.
It feels as if actually there’s a continuum from “do things that make the situation better in some generalized sense” to “do things that make the situation better in particular ways that seem like they’re likely to be useful” to “do things that make the situation better in particular ways I can see likely uses for” to “do things that make the situation better in particular ways that I definitely have concrete uses for” to “do things that bring about a broad class of later states that I like” to “do things that bring about a very specific range of later states that I like” to “do things that bring about a single specific outcome that I need”.

gjm 8 Jan 2021 9:58 UTC
2 points
on: [Error communicating with LW2 server]
I think it genuinely doesn’t make sense to say that $α$ reflects our prior expectation of $α$ ; the acolyte is correct. What $α$ reflects is our prior on $h$ ; that regularization term corresponds exactly to a prior that makes $h$ (multivariate) normally distributed with mean zero and covariance $1 / α$ times the identity (i.e., components independent and each component having variance $1 / α$ ).

gjm 8 Jan 2021 9:54 UTC
2 points
on: [Error communicating with LW2 server]
You’ve dropped a factor of $α$ about half-way through your calculation. And then you’ve multiplied by $X^{- 1}$ between two lines separated by “=”; the idea is that both sides are zero so it kinda-sorta makes sense but it’s super-misleading. If you restore the factor of $α$ then your last equation ends up as $h = Y (X + α X^{- 1})^{- 1}$ .
But even this is wrong, I’m afraid. You can’t multiply by $X^{- 1}$ there at all. There is no $X^{- 1}$ ; $X$ is not (except by coincidence, and in an ML application if this coincidence happens then you don’t have anything like enough data) a square matrix and in general it has no inverse.
There are problems earlier in the derivation, too, which I think are encouraged by some of your nonstandard notation. E.g., you write $h x_{t}$ rather than $h \cdot x_{t}$ or $x_{t}^{T} h$ , and this has fooled you into writing down something wrong for what you write as $\frac{d}{d h} E$ . That’s also nonstandard notation; it’s defensible but again it makes it easy to get things wrong by mixing up left and right multiplications. Let’s do it with more standard and explicit notation, which will make it harder to make mistakes:
$0 = \frac{\partial}{\partial h_{j}} (E + C) = \frac{\partial}{\partial h_{j}} [(X h - Y)^{T} (X h - Y) + α h^{T} h] = \frac{\partial}{\partial h_{j}} [h^{T} X^{T} X h - h^{T} X^{T} Y - Y^{T} X h + Y^{T} Y + α h^{T} h]$
The $Y^{T} Y$ is constant and its derivative is zero. The terms linear in $h$ are one another’s transposes and readily yield $2 (X^{T} Y)_{j}$ . The second quadratic term is just $α \sum h_{k}^{2}$ whose $\frac{\partial}{\partial h_{j}}$ is $2 h_{j}$ . The first quadratic term is similarly $\sum (X h)_{k}^{2}$ which equals $\sum_{k} {(\sum_{l} X_{k l} h_{l})}_{l}^{2}$ whose $\frac{\partial}{\partial h_{j}}$ is $\sum_{k} 2 (\sum_{l} X_{k l} h_{l}) \frac{\partial}{\partial h_{j}} (\sum_{l} X_{k l} h_{l}) = \sum_{k} 2 (\sum_{l} X_{k l} h_{l}) X_{k j} = (2 X^{T} X h)_{j}$ .
So what ends up being zero is the $j$ th component of $2 X^{T} (X h - Y) + 2 α h$ and if you like you can write $\frac{d}{d h} (E + C) = 2 [X^{T} (X h - Y) + α h]$ . But again you need to be very clear about what you mean by that; $\frac{d}{d h} f (h)$ means “the $A$ such that to first order $f (h) = const + A h$ ” and so actually the Right Thing to use for the “derivative” is the transpose of what I wrote down above.
Finishing off the correct derivation, we have
$X^{T} (X h - Y) + α h = 0$ so $(X^{T} X + α) h = Y$ so $h = (X^{T} X + α)^{- 1} Y$ .

gjm 8 Jan 2021 9:04 UTC
4 points
on: Linear Regression is Matrix Multiplication
I’m afraid this is badly wrong.
You can’t go from $\sum_{t} (h_{j} x_{t j} - y_{t}) x_{t j} = 0$ to $\sum_{t} (h_{j} x_{t j} - y_{t}) = 0$ . Not even if you were allowed to assume that $x_{t j} = 0$ .
Concrete example: suppose we have two $t$ values, we have $x_{1 j} = 1$ and $x_{2 j} = 2$ , and $y_{1} = 2$ and $y_{2} = 3$ . Then the first equation says $1 (1 h_{1} - 2) + 2 (2 h_{2} - 3) = 0$ which simplifies to $h_{1} + 4 h_{2} = 8$ , whereas the second equation says $(h_{1} - 2) + (2 h_{2} - 3) = 0$ which simplifies to $h_{1} + 2 h_{2} = 5$ . These are not the same equation and do not have the same consequences.
If you attempt to perform linear regression using the equations you have derived, you will get the wrong answer.
Linear regression is reducible to matrix arithmetic, but the correct equations are slightly more complicated; the thing you need to invert is not the matrix $X$ (which in general is not square and has no inverse) but $X^{T} X$ .

gjm 4 Jan 2021 13:39 UTC
2 points
in reply to: jsalvatier’s comment on: Open & Welcome Thread—January 2021
The first two links are broken for me but Amazon seems to have Beksinski 1-4: https://www.amazon.com/Beksinski-1-4-complete-Zdzislaw/dp/B077W8ZCZY/ref=pd_sbs_14_1/141-5378130-9367012?_encoding=UTF8&pd_rd_i=B077W8ZCZY&pd_rd_r=856b6a41-858c-4529-b369-5be519ee9b9a&pd_rd_w=GTPiD&pd_rd_wg=JXU4w&pf_rd_p=ed1e2146-ecfe-435e-b3b5-d79fa072fd58&pf_rd_r=JC0EH8JKZAXCC9ZHXW69&psc=1&refRID=JC0EH8JKZAXCC9ZHXW69
Out of curiosity, what’s the art criticism project? The other two things seem very different in kind from this one, on the face of it.

gjm 23 Dec 2020 17:25 UTC
3 points
in reply to: Angela Pretorius’s comment on: Gauging the conscious experience of LessWrong
I endorse all these, and also all of roryokane’s that you haven’t taken issue with, except that to me “bright” doesn’t just mean high notes but also notes whose timbre includes a lot of energy at high frequencies. Also, “soft” is ambiguous between something like Rory’s meaning and simply “quiet”. (It maybe also suggests to me the opposite of “bright”.)

gjm 23 Dec 2020 14:05 UTC
2 points
in reply to: Razied’s comment on: Gauging the conscious experience of LessWrong
I have #1 but not #2.
My visual acuity is unusually good (or at least it used to be; 50-year-old eyes don’t work as well as 25-year-old ones). I wonder whether there’s a noise/resolution tradeoff here.
(Note: by “acuity” I mean something like “resolution after aberrations are corrected”; it’s not the same thing as whether you need glasses/contacts, it’s how well you see with whatever optical corrections you require.)

gjm 23 Dec 2020 13:56 UTC
4 points
in reply to: Kaj_Sotala’s comment on: Gauging the conscious experience of LessWrong
Perhaps people are answering with figures for vividity relative to expectations in some sense.
[EDITED to add:] A specific sense of “relative to expectations” that I think is probably the main thing that’s going on here: Vision is an extremely high-bandwidth sense, hearing decidedly less so. If there’s limited bandwidth / processing available for synthesizing imaginary/remembered sense experiences, then we should expect visual experiences to fall further short than auditory ones.
(Of course that’s an oversimplification. E.g., just how high that bandwidth would need to be may depend on what “level of processing” the imagined/remembered experiences get fed in at; we may be constructing fine details on demand and not notice; etc.)

gjm 21 Dec 2020 3:31 UTC
2 points
in reply to: MikkW’s comment on: Ideal Chess—drop chess perfected
I’m not keen on giving the king long-range moves either. It’s possible that if you don’t debuff the other pieces, nothing much like crazyhouse will fail to be terrifying in something like the way crazyhouse is.
I think you’re right that small increases in mobility can make a big difference to how hard to checkmate the king is. But the particular increase in mobility you’ve proposed doesn’t change anything at all while the king is on the back rank, and doesn’t change much while it’s on the second rank. In normal chess, and I think also in crazyhouse, the kings typically stay on the back rank for their own protection, at least until the endgame. Maaaaybe with the extra mobility the kings won’t need to stay hidden to the same extent, but I think being exposed is still going to be dangerous even for the enhanced king.
[Meta: I notice that in both of the threads where I’ve discussed things with you, all my comments have been downvoted. It looks as if the same has happened to other people who have posted comments disagreeing with things you’ve said. I find that, rationally or not, this makes me a bit reluctant to attempt to discuss anything with you. I suspect the effect on others may be the same. If you are indeed downvoting every comment you don’t agree with, you may wish to consider whether the effects of doing so are the ones you want. For the avoidance of doubt, I’m neither complaining nor objecting; a policy of downvoting things one disagrees with is perfectly permissible, although perhaps a bit rude. Also for the avoidance of doubt, I am not claiming that you are downvoting every disagreeing comment; it looks that way but of course there are other possible explanations.]

gjm 19 Dec 2020 2:59 UTC
2 points
in reply to: MikkW’s comment on: No, Newspeak Won’t Make You Stupid
On objection 2: Your expectation of finding the same pattern whatever two languages you compare is not evidence that in fact it holds. For the avoidance of doubt, I do in fact expect a weak form of the pattern to hold near-universally: languages with, say, fewer bits needed to specify each phoneme will tend to be spoken with those phonemes occurring more rapidly. But you’re making a substantially stronger claim—that this will occur to just the extent required to hold the rate of information transfer constant, and that this will apply when there are vocabulary differences as well as when there are phonological differences—and it seems to me that when making so strong a claim you really ought to provide more evidence. (Or else present it as a conjecture rather than a factual claim.)
On objection 4: ah, so in fact I should have said not that you did the calculation only for one pair of languages, but that in fact you didn’t do the full calculation for any pair of languages!
On objection 6: I’m not sure I understand your objection to my objection :-). If “ganru” and “nuakiagu” actually express the same notions as “momentum” and “derivative” then all that means is that Sona does in fact have those words (I don’t see that the fact that they are constructed from simpler parts is significant), and then I don’t see what a comparison between Sona and English tells us about differences in vocabulary. (Of course it may only “have those words” for Sona speakers who have learned some physics and mathematics, but that’s true of English too: to people without the relevant technical knowledge, “momentum” is the name of a splinter group in a UK political party and “derivative” means “copied from other works” or “one of those weird finance things”.)
If you were only ever claiming that a language that lacks certain terms can be extended by adding new words that mean the same as those terms do … well, sure, I agree, but I thought you were saying something much stronger than that.
Much the same goes for “body-flight”. If that means (approximately?) the same thing as “momentum” then what that means is that ballet dancers have discovered some of the same ideas as physicists, and like physicists have coined a word for it. Again, the fact that it’s a word made out of smaller meaningful parts doesn’t seem relevant to me. Unless you’re suggesting, here or in the case of Sona, that just from those parts you can work out the full meaning, so that if you use a smaller language then you never need to learn about momentum because you can just slam together “body” + “flight” and get the right concept by magic. But I bet you aren’t suggesting that, because it seems to me very obviously not true.
What? My previous comment was exactly an argument to show that. [that my “obvious naive explanation” explains nothing—gjm]
Well, as I said, I don’t see anything in that comment that looks to me like an argument showing anything of the sort. Of course it’s entirely possible that you did in fact make an argument, perhaps a very strong one, with that conclusion, and I just failed to grasp it. (The way it looks to me is that you made some non sequiturs.) If you want to persuade me, then I think you will need to make your argument clearer and more explicit. (Of course you are in no way obliged to make that effort.)
You first had to learn the word ‘momentum’, and second, you had to store this sound and its meaning in the brain. [this is answering my question of what extra effort I need to expend on account of saying “momentum” rather than using a circumlocution—gjm]
OK, sure. But those are both one-off extra efforts, and (so it seems to me) this effort is amply repaid by the reduced effort every time I need to use the concept thereafter. (Compared, again, to a hypothetical situation in which I don’t have a word for “momentum”. It seems a bit as if you’re now shifting to what seems to me an entirely different claim, namely that we would do better with a different word for “momentum”, one whose origins are more transparent. That might be true but if it has anything to do with what you were originally saying, I don’t see what.)
So it looks to me as if when I learned the word “momentum” I was paying an immediate price for a larger future benefit. This absolutely is a thing human brains do all the time.
Not every instance of learning a new word will end up actually being a benefit on net. (To take another technical example, once upon a time I learned the meaning of “regular” when applied to a topological space. So far as I can recall, I have never once had a need to use that term or the concept it names, and I probably never will again.) But it seems to me that much vocabulary-learning has positive expected net benefit.
Again, it’s possible that the case of technical terminology is misleading; learning the meaning of “luxuriant” isn’t much like learning the meaning of “momentum” and its benefits are different. So, while I think it’s very obvious that “momentum” pays its way, I wouldn’t make nearly so strong a claim for “luxuriant”. But I think that, to put it mildly, it is not obvious that having more words has insufficient non-signalling value to explain the fact that lexicons grow, and I am never impressed by “I am not convinced that X is practically useful, therefore X must really be all about signalling”, which is what it seems to me your argument comes down to: there are just too many guesses and gaps in the chain from “languages with richer phonology tend to be spoken slower”, with which I do agree, to “languages with richer phonology are spoken exactly slower enough to cancel out the difference in information rate” and then to “the same applies to languages with richer vocabulary” and then to “and the same goes for thinking as for communication” and then to “and this doesn’t merely hold on average, it holds for every specific case”—which is the point at which I think you’d have a reasonable basis for claiming that there must be some “non-functional” explanation for large vocabularies, though not necessarily for identifying signalling as the specific best explanation.