gjm

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.

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Yes , I know what the middle-child phenomenon is in the more literal context. I just don't have any idea why you're using the term here. I don't see any similarities between the oldest / middle / youngest child relationships in a family and whatever relationships there might be between programmers / lawyers / alignment researchers.

(I think maybe all you actually mean is "these people are more important than we're treating them as". Might be true, but that isn't a phenomenon, it's just a one-off judgement that a particular group of people are being neglected.)

I still don't understand why the distribution of talent/success/whatever among law students is relevant. If your point is that very few of them are going to be in a position to make a difference to AI policy then surely that actually argues against your main claim that law students should be getting more attention from people who care about AI.

Having read this post, I am still not sure what "the Middle Child Phenomenon" actually is, nor why it's called that.

The name suggests something rather general. But most of the post seems like maybe the definition is something like "the fact that there isn't a vigorous effort to get law students informed about artificial intelligence".

Except that there's also all the stuff about the distribution of talent and interests among law students, and another thing I don't understand is what that actually has to do with it. If (as I'm maybe 75% confident) the main point of the post is that it would be valuable to have law students learn something about AI because public policy tends to be strongly influenced by lawyers, then it seems like this point would be equally strong regardless of how your cohort of 1000 lawyers is distributed between dropouts, nobodies, all-rounders, CV-chasers, and "golden children". (I am deeply unconvinced by this classification, by the way, but I am not a lawyer myself and maybe it's more accurate than it sounds.)

It looks as if you're taking a constructive Dedekind cut to involve a "set of real numbers" in the sense of a function for distinguishing left-things from right-things.

Is that actually how constructivists would want to define them? E.g., Bishop's "Foundations of Constructive Analysis", if I am understanding its definitions of "set" and "subset" correctly (which I might not be), says in effect that a set of rational numbers is a recipe for constructing elements of that set, along with a way of telling whether two things constructed in this way are equal. I'm pretty sure you can have one of those but not be able to determine explicitly whether a given rational number is in the set, in which case your central argument doesn't go through.

Are Cauchy sequences and Dedekind cuts equivalent if one thinks of them as Bishop does? There's an exercise in his book that claims they are. I haven't thought about this much and am very much not an expert on this stuff, and for all I know Bishop may have made a boneheaded mistake at this point. I'm also troubled by the apparent vagueness of Bishop's account of sets and subsets and whatnot.

More concretely, that exercise in Bishop's book says: a Dedekind cut is a pair of nonempty sets of rationals S,T such that we always have s<t and given rationals x<y either x is in S or y is in T. Unless I'm confused about Bishop's account of sets, all of this is consistent with e.g. S containing the negative rationals and T the positive rationals, and not being able to say that 0 is in either of them. And unless I'm confused about your "arbitration oracles", you can't build an arbitration oracle out of that setup.

(But, again: not an expert on any of this, could be horribly wrong.)

It is not true that "no pattern that suggests a value suggests any other", at least not unless you say more precisely what you are willing to count as a pattern.

Here's a template describing the pattern you've used to argue that 1+2+...=-1/12:

We define numbers  with the following two properties. First, , so that for each  we can think of  as a sequence that's looking more and more like (1,2,3,...) as  increases. Second,  where , so the sums of these sequences that look more and more like (1,2,3,...) approach -1/12.

(Maybe you mean something more specific by "pattern". You haven't actually said what you mean.)

Well, here are some  to consider. When  we'll let . When  we'll let . And when  we'll let . Here,  is some fixed number; we can choose it to be anything we like.

This array of numbers satisfies our first property: . Indeed, once  we have , and the limit of an eventually-constant sequence is the thing it's eventually constant at.

What about the second property? Well, as you'll readily see I've arranged that for each  we have . So the sequence of sums converges to .

In other words, this is a "pattern" that makes the sum equal to . For any value of  we choose.

I believe there are more stringent notions of "pattern" -- stronger requirements on how the  approach  for large  -- for which it is true that every "pattern" that yields a finite sum yields . But does this actually end up lower-tech than analytic continuation and the like? I'm not sure it does.

(One version of the relevant theory is described at https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation.)

Once again you are making a ton of confident statements and offering no actual evidence. "is a high priority", "they want", "they don't want", "what they're aiming for is", etc. So far as I can see you don't in fact know any of this, and I don't think you should state things as fact that you don't have solid evidence for.

Let us suppose that social media apps and sites are, as you imply, in the business of trying to build sophisticated models of their users' mental structures. (I am not convinced they are -- I think what they're after is much simpler -- but I could be wrong, they might be doing that in the future even if not now, and I'm happy to stipulate it for the moment.)

If so, I suggest that they're not doing that just in order to predict what the users will do while they're in the app / on the site. They want to be able to tell advertisers "_this_ user is likely to end up buying your product", or (in a more paranoid version of things) to be able to tell intelligence agencies "_this_ user is likely to engage in terrorism in the next six months".

So inducing "mediocrity" is of limited value if they can only make their users more mediocre while they are in the app / on the site. In fact, it may be actively counterproductive. If you want to observe someone while they're on TikTok and use those observations to predict what they will do when they're not on TikTok, then putting them into an atypical-for-them mental state that makes them less different from other people while on TikTok seems like the exact opposite of what you want to do.

I don't know of any good reason to think it at all likely that social media apps/sites have the ability to render people substantially more "mediocre" permanently, so as to make their actions when not in the app / on the site more predictable.

If the above is correct, then perhaps we should expect social media apps and sites to be actively trying not to induce mediocrity in their users.

Of course it might not be correct. I don't actually know what changes in users' mental states are most helpful to social media providers' attempts to model said users, in terms of maximizing profit or whatever other things they actually care about. Are you claiming that you do? Because this seems like a difficult and subtle question involving highly nontrivial questions of psychology, of what can actually be done by social media apps and sites, of the details of their goals, etc., and I see no reason for either of us to be confident that you know those things. And yet you are happy to declare with what seems like utter confidence that of course social media apps and sites will be trying to induce mediocrity in order to make users more predictable. How do you know?

"Regression to the mean" is clearly an important notion in this post, what with being in the title and all, but you never actually say what you mean by it. Clearly not the statistical phenomenon of that name, as such.

(My commenting only on this should not be taken to imply that I find the rest of the post reasonable; I think it's grossly over-alarmist and like many of Trevor's posts treats wild speculation about the capabilities and intentions of intelligence agencies etc. as if it were established fact. But I don't think it likely that arguing about that will be productive.)

What's going on is that tailcalled's factor model doesn't in fact do a good job of identifying rationalists by their sociopolitical opinions. Or something like that.

[EDITED to add:] Here's one particular variety of "something like that" that I think may be going on: an opinion may be highly characteristic of a group even if it is very uncommon within the group. For instance, suppose you're classifying folks in the US on a left/right axis. If someone agrees with "We should abolish the police and close all the prisons" then you know with great confidence which team they're on, but I'm pretty sure the great majority of leftish people in the US disagree with it. If someone agrees with "We should bring back slavery because black people aren't fit to run their own lives" then you know with great confidence which team they're on, but I'm pretty sure the great majority of rightish people in the US disagree with it.

Tailcalled's model isn't exactly doing this sort of thing to rationalists -- if someone says "stories about ghosts are zero evidence of ghosts" then they have just proved they aren't a rationalist, not done something extreme but highly characteristic of (LW-style) rationalists -- but it's arguably doing something of the sort to a broader fuzzier class of people that are maybe as near as the model can get to "rationalists". Roughly the people some would characterize as "Silicon Valley techbros".

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