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Is it that image models are particularly bad at eyes, or that humans are particularly good at noticing when eyes looks wrong versus other things?

I feel like it has to be the first one; e.g. the noses look fine. Are we really so much worse at recognizing human noses versus weird uncanny-valley noses that the AI could be getting them just as wrong as the eyes, and we wouldn’t be able to tell? Seems like a stretch...

But then why would AIs be worse at learning eyes versus noses?

so did you know you can ask the AI for catboy Gandalf and it will just

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Ghost of DALL-E 2

Mysterious girl died in tragic ML training accident, and now her spirit haunts the network weights of DALL-E 2.

source

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Yeah, that’s really the crux of the matter. If we want to actually use a logic to prove theorems, we need to have some criterion for what constitutes a valid proof. In the case of 1st-order logic, this question can be reduced to a computable decision procedure, so there’s no ambiguity about whether an alleged formal proof really is a proof. But the standard semantics for 2nd-order logic don’t permit a computably axiomatized proof theory. So what do we do, in practice? We take some computable axioms and inference rules that we agree capture some fragment of the intended meaning of 2nd-order logic, and deduce theorems from that. But then one can analyze the resulting logic as a 2-sorted 1st-order logic (one sort for 1st-order variables and one for 2nd-order variables), and apply metatheoretic results for 1st-order logic, such as that any consistent theory has a model. That’s essentially what Henkin did back in the 50′s, IIUC.

These models can’t all have standard 2nd-order semantics, where the set variables range over the full power set of the domain of the 1st-order variables. So one can say that the 2nd-order theories which don’t have standard models are invalid. E.g. in the case of models of arithmetic, the full power set of the domain should include the subset containing only standard numbers, and if that is a proper subset of the domain, the model must be nonstandard. So if two Henkin models of 2nd-order arithmetic satisfy contradictory sentences, at least one of them must not have the full power set of its 1st-order domain as its 2nd-order domain.

But we don’t have any fully general standard of evidence by which to establish intersubjective agreement about a claim that some 2nd-order theory does or doesn’t admit standard models, which leaves me skeptical of the premise that our intuitive idea of truth for 2nd-order logic is pointing at a real, objective thing. I’ve been speaking as if it is, this whole time, because that’s the easy, intuitive way to think about math, but, on a philosophical level, I think it is more prudent to regard that assumption as a useful fiction that has so far proved compatible with all available empirical evidence, rather than as self-evident truth.

“Unprovable” isn’t magic

(There’s no hard math in this post, I swear!)

You may have heard from math nerds that the Axiom of Choice or the Parallel Postulate is “unprovable” or “unknowable” or something like that. There’s a common misconception that this means something really magical, like, mathematicians have somehow proven that some fact is simply unknowable, like the Heisenberg Uncertainty Principle but for math. But that’s not what “unprovable” actually means.

I think part of what’s to blame is the way mathematicians talk about it - about the proof that it’s unprovable being some mindblowing thing. And it is! Just not for the reasons you think.

First, what does “unprovable” actually mean? Let’s illustrate with a much simpler example:

x – x = 0 is provably true.

x – x = 2 is provably false.

x + x = 2 is unprovable.

This should make it pretty obvious what’s going on here. “Unprovable” doesn’t mean that there’s a huge magically-unsolvable mystery. It means “it depends on what x is.” It means “you decide”.

So, then, why do mathematicians make such a big deal out of it? It’s because the thing that turned out to be unprovable was a thing we expected to be provable.

The Parallel Postulate is a good example here. Euclid (and many others) thought that it was provable that parallel lines would never cross each other, even though they never managed to actually prove it. So of course, thousands of years after Euclid invented geometry, everyone was surprised when it turned out that the answer is “you can’t prove it”, that the answer is “it depends” – parallel lines never touch on flat surfaces, but on curved surfaces like the surface of the earth, of course they’ll cross each other (north-south lines are “parallel” to each other, but they cross at the poles). [1]

(“But Serine, are you telling me that the smartest mathematicians over thousands of years did not realize curved surfaces exist?” Yes, a lot of math is incredibly obvious in hindsight. That’s a lot of the fun: coming up with proofs that make everyone say, “Why didn’t I think of that?”)

[1] Technically, “parallel” means “don’t cross each other”, so north-south lines aren’t actually parallel. A more precise statement of the parallel postulate would be that if two lines have the same intersection angles with a third line (what I was calling “parallel”), they would never intersect.

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Well, you can give a set-theoretic proof that the second-order Peano axioms have a unique model up to unique isomorphism, and claim on that basis that all arithmetic sentences have a determinate truth value, regardless of whether they are provable/refutable. And, as you note, the standard model of the natural numbers is distinguished as the minimal one, that is, the one containing only elements that you can get to by iterating the successor operation finitely many times, whereas all other models of arithmetic must necessarily contain both all of the standard numbers, and then some additional, infinitely large elements coming after all of the standard ones.

I don’t find this entirely satisfactory, though. The same sort of infinitary reasoning that allows one to define the notion of a minimal model of arithmetic, and prove that it is the unique model of 2nd-order PA, can be axiomatized in a first-order theory T (such as ZFC, or higher-order logic with Henkin semantics), and can then be used to construct models M of T such that the object living inside M that is distinguished as the “standard” model of arithmetic according to T, is, in fact, nonstandard, just not in a such way that one can discriminate between it and the “true” standard model properly contained within it, by a formal definition in the language of T, as interpreted though M.

In particular, if P is some arithmetic formula undecided by T, then there will be models M₁ of T in which P holds in M₁’s internal ℕ, and models M₂ of T in which ¬P holds in M₂’s internal ℕ. Notionally, at most one of M₁ and M₂ can have the “real” standard internal model of arithmetic, but by what criterion are we to define this class of models of T with standard ℕ? Implicitly, we have been  appealing all along to a notion of infinitary set-theoretic truth that is even more elusive than arithmetic truth.

So we are left with a dilemma: Are we to regard the set of standard natural numbers as some ineffable thing which we are sure exists, even though it eludes all attempts to isolate it from nonstandard models via formal definition? As if “The ℕ that can be spoken of is not the true ℕ”? Or are we to regard even such a basic mathematical distinction as “finite” versus “infinite” as inescapably underdetermined and vague? The former view is certainly more compatible with how higher mathematics is actually practiced most of the time, but I’m not satisfied with it philosophically, so I’ve been trying to learn more about constructive foundations. Constructivism does make a lot of things harder, though, and for all that trouble it doesn’t offer an obviously superior philosophical picture, as far as I can tell. In particular, there still seems to be a pretty steep trade-off between the consistency-strength of constructive theories and the ontological commitments they seem to demand.

In conclusion, maybe “unprovable” is magic after all…

“Unprovable” isn’t magic

(There’s no hard math in this post, I swear!)

You may have heard from math nerds that the Axiom of Choice or the Parallel Postulate is “unprovable” or “unknowable” or something like that. There’s a common misconception that this means something really magical, like, mathematicians have somehow proven that some fact is simply unknowable, like the Heisenberg Uncertainty Principle but for math. But that’s not what “unprovable” actually means.

I think part of what’s to blame is the way mathematicians talk about it - about the proof that it’s unprovable being some mindblowing thing. And it is! Just not for the reasons you think.

First, what does “unprovable” actually mean? Let’s illustrate with a much simpler example:

x – x = 0 is provably true.

x – x = 2 is provably false.

x + x = 2 is unprovable.

This should make it pretty obvious what’s going on here. “Unprovable” doesn’t mean that there’s a huge magically-unsolvable mystery. It means “it depends on what x is.” It means “you decide”.

So, then, why do mathematicians make such a big deal out of it? It’s because the thing that turned out to be unprovable was a thing we expected to be provable.

The Parallel Postulate is a good example here. Euclid (and many others) thought that it was provable that parallel lines would never cross each other, even though they never managed to actually prove it. So of course, thousands of years after Euclid invented geometry, everyone was surprised when it turned out that the answer is “you can’t prove it”, that the answer is “it depends” – parallel lines never touch on flat surfaces, but on curved surfaces like the surface of the earth, of course they’ll cross each other (north-south lines are “parallel” to each other, but they cross at the poles). [1]

(“But Serine, are you telling me that the smartest mathematicians over thousands of years did not realize curved surfaces exist?” Yes, a lot of math is incredibly obvious in hindsight. That’s a lot of the fun: coming up with proofs that make everyone say, “Why didn’t I think of that?”)

[1] Technically, “parallel” means “don’t cross each other”, so north-south lines aren’t actually parallel. A more precise statement of the parallel postulate would be that if two lines have the same intersection angles with a third line (what I was calling “parallel”), they would never intersect.

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GET YOU SOME SPOONS NIGGA, HOW tf is you sPOSED TO EAT SOUP

With a knife. It’s frustrating, though. Rather like counterinsurgency.

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Not fundamentally different, but more amazing, I would say. The unprovability of Euclid's 5th postulate from the other axioms of Euclidean geometry was discovered well before  Gödel's incompleteness theorems. Some researchers in the foundations of math had been hoping that such gaps in the consequences of axiomatic theories could all be filled in by adding strong enough additional axioms. Gödel showed that, even for a theory as basic as the arithmetic of whole numbers, you can't get to a complete, computable set of axioms by just adding enough new axioms to handle any statements that turn out to be undecidable from a given starting set of axioms. He constructed a sort of algorithmic crank you can just keep turning, where you feed in any computable, consistent set of axioms for arithmetic, and it will spit out a statement undecidable from those axioms.

“Unprovable” isn’t magic

(There’s no hard math in this post, I swear!)

You may have heard from math nerds that the Axiom of Choice or the Parallel Postulate is “unprovable” or “unknowable” or something like that. There’s a common misconception that this means something really magical, like, mathematicians have somehow proven that some fact is simply unknowable, like the Heisenberg Uncertainty Principle but for math. But that’s not what “unprovable” actually means.

I think part of what’s to blame is the way mathematicians talk about it - about the proof that it’s unprovable being some mindblowing thing. And it is! Just not for the reasons you think.

First, what does “unprovable” actually mean? Let’s illustrate with a much simpler example:

x – x = 0 is provably true.

x – x = 2 is provably false.

x + x = 2 is unprovable.

This should make it pretty obvious what’s going on here. “Unprovable” doesn’t mean that there’s a huge magically-unsolvable mystery. It means “it depends on what x is.” It means “you decide”.

So, then, why do mathematicians make such a big deal out of it? It’s because the thing that turned out to be unprovable was a thing we expected to be provable.

The Parallel Postulate is a good example here. Euclid (and many others) thought that it was provable that parallel lines would never cross each other, even though they never managed to actually prove it. So of course, thousands of years after Euclid invented geometry, everyone was surprised when it turned out that the answer is “you can’t prove it”, that the answer is “it depends” – parallel lines never touch on flat surfaces, but on curved surfaces like the surface of the earth, of course they’ll cross each other (north-south lines are “parallel” to each other, but they cross at the poles). [1]

(“But Serine, are you telling me that the smartest mathematicians over thousands of years did not realize curved surfaces exist?” Yes, a lot of math is incredibly obvious in hindsight. That’s a lot of the fun: coming up with proofs that make everyone say, “Why didn’t I think of that?”)

[1] Technically, “parallel” means “don’t cross each other”, so north-south lines aren’t actually parallel. A more precise statement of the parallel postulate would be that if two lines have the same intersection angles with a third line (what I was calling “parallel”), they would never intersect.

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I like the way Hacker News does it: show everything by default, but have a button to collapse the reply thread to any given comment, so I can skip past long reply threads that I’m not interested in without having to scroll until I spot a less indented comment.

Does anyone actually like comments sections that work like this?:

Are there people out there who get angry when a page displays all the comments at once? Who smash their keyboards, saying “No! I want to have to click ‘see more comments’ before I can see any comments other than the top two! I want to keep having to do this for every two or three more comments I want to see! And it shouldn’t show me any replies to comments until I press ‘see replies’ for each individual comment I want to see replies to!“

It seems weird that every website in the world would switch to a commenting style nobody likes, but I also can’t imagine anyone liking this, so it’s just a huge mystery to me.

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Apparently I'm still not done having thoughts about this, because here's one more: My impression of the state of psychiatric medicine, partly from being a patient with very treatment-resistant problems who has tried a lot of things under the guidance of a lot of very reputable professionals affiliated with prestigious institutions, and partly from reading Scott Alexander and various other people in the field, is that, for most mental illnesses, we don't really know what causes them, or what, if any, treatment will work for whom, or why, and there are a lot of patients (like me, for instance) that we just can't seem to help. We're dealing with phenomena whose complexity has, to date, outstripped our ability to build useful models, and the literature on current practices is an unholy mess of weak empirical correlations, rendered still more confusing by methodological problems and conflicts of interest.

This sucks, but the good news for Rationalism is that, if you read Slate Star Codex, you will come away with a pretty accurate picture of this reality. If, on the other hand, you get your mental health news from Mr. meta-rational redpill galaxy-brain above, you are setting yourself up for some serious disappointment. And the same goes for everyone else peddling their One Weird Trick to solve all your problems in life. In conclusion, Scott Alexander is good and Less Wrong Rationalism is good and more of it would be even more gooder, despite what any heretical splinter sects would have you believe.

Apparently MoreRight-style nRx did not actually go away?

https://twitter.com/0x49fa98/status/1276138147521400833

This thread is hilarious.  ~��Rationalists are naifs who don’t understand that some people consistently and artfully lie, and that is why they should take advice from me, a darkly-hinting-type ex-rationalist.”

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Furthermore, you should take the fact that the aforementioned bit is bullshit into account when assessing how trusting overall you should be of the arguments of post-rationalists of Zero HP Lovecraft’s ilk. Ironically, overpromising re: the benefits of exercise is a fine example of the sort of dishonest marketing strategy that he apparently thinks rationalists have insufficient defenses against.

You see similar BS about the mental-health benefits of meditation, too. As with exercise, I don’t want to discourage anyone from trying it. It might help. Just don’t expect any miracles, and don’t trust people who promise them.

Apparently MoreRight-style nRx did not actually go away?

https://twitter.com/0x49fa98/status/1276138147521400833

This thread is hilarious.  ~“Rationalists are naifs who don’t understand that some people consistently and artfully lie, and that is why they should take advice from me, a darkly-hinting-type ex-rationalist.”

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This bit is bullshit, BTW. Not that you shouldn’t exercise, of course; it’s healthy and you should do it. But I’ve been through many long periods of time where I’ve pushed myself to do as much as I could stand to of various kinds of weight-lifting and cardio, at home, at the gym, outdoors, by myself or with others; for other long periods of time I’ve barely exercised at all. I’ve always been moderately overweight, but otherwise physically healthy and strong, especially during periods when I exercise regularly. However, it has never had any discernible effect one way or the other on my generally terrible depression and anxiety. In particular, it hasn’t affected my tendency to live in my head, overthink things, avoid things, feel uncomfortable in my own skin, etc.—all those stereotypical personality traits of neurotic nerds that supposedly can be cured through athletic activity.

I suppose some people must see some sort of mental-health benefit to exercising, or it wouldn’t be such a common refrain that exercise is good for the mind as well as the body. So if you haven’t tried it, do. At least it will be good for your body, if you do it safely. But I am a living counterexample to the premise that it will noticeably ameliorate mental illness.

Apparently MoreRight-style nRx did not actually go away?

https://twitter.com/0x49fa98/status/1276138147521400833

This thread is hilarious.  ~“Rationalists are naifs who don’t understand that some people consistently and artfully lie, and that is why they should take advice from me, a darkly-hinting-type ex-rationalist.”

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Now this post has me wondering whether/how an actual honest-to-god incel cult would even work ... We have a supply of suitably alienated, desperate individuals with limited ability to get along in mainstream society, with some shared beliefs and experiences, so now we need a leader. This hypothetical leader would need to be able to harvest some value from his followers, and offer them some kind of compelling vision of the future in exchange.

I guess flattery and servitude and whatever money he can extract from them would be the motivation for the leader, but it seems like cult leaders frequently successfully target demographics with more sexually attractive people to seduce and/or more money to steal, so why target incels?

And what vision could a cult leader offer to incels to get them hooked? Promising deliverance from inceldom would be a tough sell, since incel ideology is so much about how that is a hopeless dream for them. The other obvious option would be revenge against society, so, some sort of terrorist doomsday cult, maybe? Those tend to flame out pretty quickly, and end badly for their leaders as well as their followers, so the leader would probably have to be pretty nuts himself, rather than merely being an exploitive sociopath.

It all seems rather far-fetched, but then, you look at some of the crazier examples of real cults that have actually existed, and who knows? ...

I can’t get over the thinkpieces that are like “incel spaces encourage unhappy young men to go deeper into spirals of despair and self-hatred, and that’s not healthy” and two sentences later are like “these men, of course, are pathetic and irredeemable human trash”

It’s like, at least pick one? Either you want to discourage the unhealthy despair spirals, or you want to contribute to them. You can’t have both

(To be clear, I am not denying that many men in incel spaces say and believe some truly offensive things. I just don’t see how these thinkpieces are supposed to help anyone)

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context

If you had asked me, before I read this tweet, what I thought about the various pharmaceuticals being researched for COVID-19, I would have said pretty much what the tweet says: Convalescent plasma sounds promising, antivirals (hydroxychloroquine, remdesivir, etc.) not so much. But the weird thing is that, unlike the above doctor, I have no relevant expertise, and haven’t even read any research papers on the subject. At most maybe I clicked through from a Twitter-thread summary and skimmed the abstract of a relevant paper or two, but I don’t recall having done so for this specific question.

I just got a vague impression by osmosis that this was the state of play, by following a handful of random smart people on Twitter, none of whom are even M.D.s. (I saw the tweet because I follow Noahpinion, an economist.) This has pretty much been the story of my entire experience of the pandemic: Follow rationalists & assorted other smart people (mostly w/o credentials in relevant fields) on social media, develop a vague impression of what’s going on, see that impression confirmed in the mainstream media a week or two later.

It’s weird. It feels like I’m a human neuron in a hive-mind.

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source

Can someone explain to me why people are protesting the COVID shutdowns?

Like….Is it cabin fever? Do they think everything’s fine? Is it worry about the economy / their jobs / their financial situations? 

What’s going on???

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Epistemic spot-check time!

All right, this checks out w.r.t. every form of economic organization that I bother to have an opinion about, so I’m pretty sure it holds in general.

There are no “essential workers,” just essential work.

This is true under every form of economic organization.

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The very very very best part of Tumblr is screenshots of the best part of Twitter? ... Yeah, based on the past month or so of COVID-19 discourse, I’d say that checks out.

(ETA: How the fuck did we end up in a world where the best blogging platform for surfacing useful information from obscure first-hand sources is the one where you have to chop up your posts into 280-character chunks?)

(ETAx2: And how the fuck, in the year two-thousand-and-fucking-twenty, are fucking SCREENSHOTS the default means of block-quoting sources between different blog/social-media platforms? Or even just on a single platform (Twitter), if you want to quote more than one tweet? Ted Nelson must be rolling in his grave sensory-deprivation tank.)

This is capitalism's vast irrationality and inhumanity in action. Markets and The Economy™ matter more to capitalism than the concrete distribution of resources according to tangible human need.

Resources exist in abundance -- give them to people. Housing sits empty -- give it to people. The rules of the feast table should apply to our economic system -- no one gets seconds until everyone has gotten a plate.

We stand at a crossroads in these chaotic times: socialism or barbarism! The ruling class repeatedly chooses the latter. We need to organize and choose the former!

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It’s so bizarre to me to see people talking about the US presidential election without emphasizing the fact that we’re in the midst of the worst economic contraction since the GREAT DEPRESSION! (I’m also reacting to this twitter thread.) How does that not overshadow all other considerations? I mean, I’m not working on any more sophisticated a model of US electoral politics here than “recent economic contraction => bad for incumbent party,” but that is a robust historical pattern, is it not?

The persistent leftist delusion that Biden is necessarily doomed to lose is really something to behold.

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It’s not just Communists; sufficiently respectable, well-established religions also get infinitely many chances, no matter how embarrassing their history, and for essentially the same reason: They talk a good game about universal moral values that most people endorse, and thus, for some psychological reason that I don’t claim to understand, their brand gets a halo effect in the public consciousness.

The Fascist and the Confederate brands don’t get that halo effect, probably due to some combination of not pretending hard enough to be about universal morality, as opposed to ethnonationalism, not pretending hard enough to be about uplifting the underdog, and having lost the wars they started.

I date communists all the time, why not date fascists?

Communism was an incredible disaster, but to some extent it springs from noble impulses. There are lots of genuinely terrible inequities in the modern world which should be stamped out, and capitalism really does screw over lots of people. To turn to Marxism is an error, since it doesn’t work in practice, but imo an understandable one. To quote Marx’s vision of the future, “I could fish in the morning, hunt in the afternoon, rear cattle in the evening and do critical theory at night, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic.” Not a bad utopia! I could imagine being seduced by that. Not every communist joins for such high minded reasons – there are plenty of apparatchiks and sadists and self-dealers – but communism is not rotten in its initial impulse, no matter how bad its consequences turn out to be.

Fascism, on the other hand, springs from a lust for violence and blood-and-soil nationalism and worship of unadulterated power. There is no reason to become fascist that I find the least bit sympathetic. You’re joining a bad movement for bad reasons. It is simply vile. Communism and fascism are pretty comparable in terms of how catastrophic they are, but on an individual level being a fascist is far less defensible. If there is ever any justification for not dating someone because of their politics, fascism is it.