Maybe-Mathematical Musings — Was the cultish school you mentioned Reed? If you...

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See, that’s what the app is perfect for.

Sounds perfect Wahhhh, I don’t wanna
proofsaretalk

fenff asked:

Was the cultish school you mentioned Reed? If you had more to say about it I'd be curious to hear it. I dropped out of there quite awhile back and never sought the appropriate counseling, so this might be therapeutic for me :)

nostalgebraist answered:

Sure.  Although from the sound of it you probably disliked it more than me.

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ogingat

This was a really interesting read. From what you know (if you do), do you think Reed is distinct in this way from other, similar liberal arts colleges? Say, Pomona, or Wesleyan, or Oberlin, or Bowdoin, or whatever?

nostalgebraist

I don’t really know, TBH, though I’m curious.  I’ve known a few people who went to other liberal arts colleges, but I haven’t talked to them that much about this kind of thing.  I do get the impression that Oberlin has a similar thing going on (I’ve heard Oberlin alumni talk about “Obies” in much the same way that Reedies talk about Reedies).

I guess it would seem very weird to me if this were going on everywhere – could there really be a whole category of schools each of which is convinced that they are the special one?  (At least the Ivy League knows that the rest of the Ivy League exists.)  The Reedie Exceptionalism attitude was specifically about Reed rather than to liberal arts colleges in general, and if that were happening at every liberal arts college that would be … bizarre.

(Reed does legitimately have a number of unique or nearly unique aspects: the only undergraduate-operated nuclear reactor, which licenses more female operators than all the other reactors in the country combined; role as a feeder school for Ph.D. programs that, in the sciences, rivals only elite tech schools; basically zero grade inflation, although that is a mixed blessing; etc.)

jadagul

This definitely doesn’t match my experience as an undergrad at Pomona, or really at the LAC I teach at now.  

Like, at Pomona we were pretty sure that we thought Pomona was awesome (”The happiest campus on earth!”), and we definitely thought we were better than a lot of people.  (I have a shirt that reads “We’re not elitist; we’re just better than you”).  But we also thought there were half a dozen places that were at least directly comparable to us.  We were always trying to compare ourselves to Amherst, specifically.

proofsaretalk

Haha that’s fantastic because pretty much the lowest-common-denominator Mudder culture had two thoughts about Pomona: “haha Pomona classes are bullshit easy” and also “isn’t it crazy how Pomonites are so full of themselves” O.o

jadagul

Eh, the Mudd classes I took weren’t any harder than the Pomona classes.  (Except they give closed-book math tests at Mudd, what the hell is up with that?).

But yes, the Pomona students are kinda full of themselves.  And know it’s ridiculous, which is why I have a shirt making fun of it.  (When I was there the 5c rowing club did a fundraiser every year where they did one shirt for each college.  “I’d sell my soul for a beer and an internship”, “The odds are good but the goods are odd,” that sort of thing–I don’t remember them all but most of them were funny).

proofsaretalk

I feel like you may have missed that this was part of a series of posts, in which the point was that Mudd basically but not exactly has the same problem as Reed. (The post was supposed to be an observation that there was a lot of non-critical-ness that went into our culture, particularly our relationship with other CCs, and even more particularly with Pomona.)

I took a math course at all five CCs and the hardest one (by a landslide) was at Scripps, so I got over my elitism ruhl fast. But a lot of folks didn’t. I just assumed it was a frosh thing but then I was a senior and my friends were still doing it and I was like “seriously this shit still?”

[I’m not super convinced that closed book exams are unusual, but I don’t actually know. The only course I officially took at Pomona (read: gave a shit about exam policy for) was open-book but it was also a 72 hour test so I just kind of decided it was exceptional. The CMC course was also closed book.]

[Also, I pretty much just went through the last 25 pages of your blog skipping the philosophy; I like it a lot :P]

jadagul

Aww, thanks. 

Yeah, I didn’t originally read your post as a criticism of Mudd (though it looked more like that after you blogged in this chain more).  

When I was there (a while ago), I had a lot of non-Pomona friends, which was atypical for a Pomona student, because I was on the dance team.  And most of the Mudders I knew were also dance people so less likely to stereotype that way.

But I later had a couple of friends (and a Scripps friend in particular) who felt super judged by their Mudd friends a lot.  I definitely believe your account.

As for tests–partly this is just me ragging on the idea of timed closed-book math tests as an attempt to test any serious understanding.  My first two years I mostly took classes at Pomona, and they were mostly open book and/or untimed on the one hand, or intentionally-trivial in-class tests on the other.  (My analysis professor liked to give two-week-long open-book no-collaboration takehomes).  Then I was mostly out of Pomona classes to take, so started taking classes at Mudd, and Mudd mostly had timed closed-book takehomes.  And I found it really annoying.

A special complaint goes out to book-work problems, of the form “State and prove the Lesbesgue Dominated Convergence Theorem.”  That just seems so wrong to me in terms of skills one actually needs as a mathematician.  Knowing what sort of results exist?  Important.  Knowing where to find them?  Important.  Being able to decipher and adapt their proofs?  Important.  Being able to recite all the details?  Not important.

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I really liked this Sarah Constantin article on why current AI approaches fundamentally aren’t going to lead to AGI.

Her discussion of ontological robustness reminded me of the point I was making the other day, about how GPT on a deep level can’t learn.

And for the agent to be able to conceive of [the possibility that its fundamental model might be wrong] and count it as something to avoid, for it to be able to say I don’t want my loss function to be spoofed by something that kills me, it needs to have a “goal” or a “value” that goes beyond its loss function.

AKA, not a static terminal goal. A way to distinguish the “true real-world goal” from one’s mere current specification of it, and update the specification as necessary.

AKA, cross-ontological transfer of goals.

GPT-like systems just…can’t do this. They have their training weights, and that’s what they have; nothing ever updates.

And of course there are ways to retrain them and fine-tune them, but that’s awkward, and manual, and not feeding off of any of the AI capabilities that GPT has. There’s no iterative improvement; and there’s no obvious or even really suggested path for how to get there.

Sarah says no one is even really working on this, and I believe her. I haven’t encountered anyone genuinely working on this; and it doesn’t seem terribly commercially useful, while it does seem super hard. And this is part of why I’m just not terribly worried about the AI apocalypse.

ai gpt ml

More generally, Yudkowsky has long been

  1. Correct that a powerful optimization agent that we don’t understand the inner workings of would be extremely scary, and
  2. Wrong in his belief that creating such a thing would be easy.

If you grant that a super-powerful uncontrolled optimization process is about to be launched, you should in fact worry quite a lot. But it’s not.

In particular, the successes of GPT and the Transformer should reduce the credibility of Yudkowskian arguments, not raise it. Yudkowsky was arguing from a premise that any recognizable AI would necessarily have a certain collection of capabilities. GPT either does, or probably will soon, satisfy the conditions of a “recognizable AI”, but it doesn’t have those capabilities.

And the Yudkowskian conclusion is basically, therefore it must have those capabilities somewhere.

ai ml gpt yudkowsky

bulbous-oar

We don’t know that no possible large neural network implements an optimizer. If one does, we could stumble into it via gradient descent, just as we’ve stumbled into large neural networks that have world models.

Sure, we don’t know that no possible neural network implements an optimizer. In fact, I’ll go farther: it seems like if it’s possible to write one, which it probably is, we should probably be able to encode one in a large neural network. It’s just a very flexible framework for a model.

(Of course that flexibility is also the weakness: if it could be anything it has no strong pressure to be a specific thing.)

But I can say something stronger and also dumber than that, right? If an optimizer exists, then it’s possible that if I have my computer spit out 10TB of random bits and then interpret that as the source code to a C program, it will compile to that optimizer. It’s just…unlikely.

Large neural networks like GPT are not attempting to create optimizing agents. The training process is (outer-)optimizing for something, and the thing it’s optimizing for is very much not an (inner-)optimizer.

So this argument is something like, maybe writing an extremely powerful optimizer is so easy that we’ll do it by accident. And then not only will we create one, but it will be so powerful that it can out-optimize us, even if we’re trying to stop it, even though that’s if anything counterproductive to what we were training the model to do. That’s not impossible but it seems extremely unlikely.

(In contrast, I don’t think we “stumbled into” world models exactly; they are something we were more or less explicitly trying to get for the past couple years. This is part of Sarah’s point: people are trying to get world models, but they aren’t trying to get ontological stability or train inner optimizing loops basically at all.)

ai ml gpt
jaydaigle.net

A Fictional History of Numbers, Part 2: Measurement, Estimation, Completeness, and Reality

This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones. We start by asking for the area of a circle, get exhausted by Archimedes's method for finding the answer, and take a tour through the idea of limits to construct the complete field of real numbers. We resolve one of the oldest mathematical flame war topics on the internet, and finish by worrying the real numbers are just too weird to actually use.
Jay Daigle

A new post up on my blog!  Last time we talked about the algebraic numbers, and how just wanting to solve simple equations can create a ton of different numbers.  But they don’t get us everything.

So this time we start off with the idea of measurement, and wind up inventing the real numbers.  The real numbers are weird.  Real weird.  But they show up when we start asking questions about size or measurement.  And in part 3, we’ll see they’re exactly the right way to do calculus.

blog math number theory calculus analysis
youzicha
raginrayguns

ok this is dumb and not important BUT neural networks are not piles of linear algebra, they're piles of matrix multiplications. Linear algebra is the name of the mathematical theory we use to prove theorems about matrix multiplications.

This is the same pedantic losing battle as me objecting to the use of "biology" to mean "life", "chemistry" to mean "chemical reactions", etc

youzicha

My main complaint with this phrase is that they are not linear. Like, that's exactly what makes them more powerful than the linear regression models and factor analysis models that people were using in the 20th century, right? That's a pretty significant thing that happened...

jadagul

Well, unless you’re using floating point operations.

But yeah, it’s a pile of linear operations with mildly nonlinear buffers in between.

ml ai linear algebra
jaydaigle.net

Evaluating Students is Important, Too

Adam Mastroianni wrote a very interesting essay on his substack about how the difference between teaching and grading, and how much he dislikes the latter and all the problems with it. And I don't really disagree, but I don't agree either. So here's my response. Grading sucks, but it's important.
Jay Daigle

I have a new post up on my blog.  Trying to experiment with writing faster and shorter so I can get more regular content out—which in this case means it’s only two thousand words and only took me a week to publish.

blog I profess grading
loki-zen
transgenderer

its an interesting choice that link is mute from the players perspective but clearly conveying ifnromation, seemingly verbally, to other characters. i think the implicaiton is that link is speaking, we just dnt know what hes saying. i guess to make him more of a "blank slate". im not sure.

max1461

Mario does this also. Nintendo thing. Very interesting I actually like it a lot.

jadagul

It’s a pretty common video game thing! Especially in earlier games. Link and Mario are always mute. But like Crono is also mute. In the Golden Sun games, whichever character is the protagonist at the time is mute. (And the Pokemon protagonists are mute, but that’s Nintendo again.)

In general if you want one character to be a standin for the player, it can be helpful for them to have no literal dialogue; the menu selections the player makes are “your dialogue”. That’s why modern pokemon games give you a bunch of dialog prompts where you can choose between “yes” and “of course” or some shit—the point is not to give you a choice, it’s to give you a line.

That doesn’t work well with modern voice-acted games, so it’s died out of those. But with a purely text-based interface it’s often the most reasonable choice.

video games
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