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komponisto20

Do you think you use the term physical cognition in the way it's used in the literature?

"The literature" that is relevant here consists of Michael Vassar's 2013 Edge essay.

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ChristianKl00

It's relevant in the way that it doesn't use the term "physical cognition"?

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[-]Vaniver250

LW2.0 Update: Closed beta is underway, with several major bugs found and fixed. We're gradually expanding the invite list over the course of the beta, since in the early days we expect people to mostly be running into the same problems.

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[-]Wei Dai160

What's the expected utility of various activities/lessons for children (e.g., piano lessons, ballet class, sports, etc.)? My parents didn't have the time or money to deliberately cultivate these kinds of interests in me when I was a child, and I think at least partly as a result, I learned to program when I was around 10 years old (I had nothing to do but watch my dad program), and later had plenty of time to do things like learn about economics and cryptography, think about the nature of money, and solve puzzles about probabilities and decision theory. Looking for advice now, I can only find articles about whether to let your child quit a lesson/activity, but nothing about what kinds of lessons/activities are worth encouraging or starting in the first place. I'm curious what conclusions other LessWrong parents have come to, if anyone else has thought about this problem.

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[-]cousin_it140

You're probably a special case. These days I interact with kids a lot. When they have nothing to do, the default activity is watching YouTube. If you take away all devices, the default activity is playing with toys. If you take away toys as well, the default activity is running around, being loud, breaking stuff, and being annoying. Some kids are naturally interested in something and will do it when left alone, but they are the minority.

That said, piano lessons are indeed horrible and useless for most kids who aren't naturally into it. I've known many people who envy me for being able to make music as an adult, even though they studied music as kids and I didn't! They say they were forced by parents, it turned them off music and they wish they could come back. A good friend of mine is a proficient drummer who took piano lessons as a kid, and to this day he avoids the piano like fire.

I think the best activities to choose are those that help you in many ways. For example, judo can make you fit and unafraid of people. Some kind of math or programming goes a long way to make you employable, though we haven't figured out the best way to teach it. Verbally focused activities also seem surprisingly useful, though they feel like games. And of course if the kid is really into something, they should be able to study it even if it's impractical, otherwise you'll forever be the horrible parent who took away their dream.

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2Wei Dai
Thanks, your comment is helpful. That's interesting. May I ask in what capacity? What if you restrict YouTube, then give them enough free time to get bored of their toys and "generally being annoying"? What are verbally focused activities? Like competitive debating? Maybe it would be a good idea to generate a list of such subjects so we can try to avoid letting the kid get interested in them in the first place. :)
[-]cousin_it110

That's interesting. May I ask in what capacity?

Father of four, teach a programming class to some kids in my area, attend many social gatherings full of kids.

What if you restrict YouTube, then give them enough free time to get bored of their toys and "generally being annoying"?

YMMV, but I haven't seen much progress happening as a result of boredom. As a child I was in this situation and spent most of my time pointlessly reading fiction. Got serious about math and programming only due to having amazing teachers in high school (actual math and CS researchers).

On the other hand, if you're asking about your kids, maybe they'll turn out like you and get interested in stuff naturally :-)

What are verbally focused activities? Like competitive debating?

At preschool level it's games like broken telephone or I Spy. At school level I'm not sure, but I feel that my verbal abilities are low because I never did anything like debating in my teens.

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4Wei Dai
Interesting, how do you motivate the kids to want to learn? Reading fiction hardly seems pointless, compared to other pursuits a parent might push a child into. It develops vocabulary and reading comprehension (helpful when you later want to read non-fiction), general knowledge and social abilities, and can lead to other interests. I got interested in crypto and the Singularity from reading Vernor Vinge, and philosophy in part from reading Greg Egan. It seems like boredom as a strategy requires a lot of time and patience, even when it succeeds. I wasn't that serious about programming (despite learning the basics as a kid) until I got into crypto and decided that writing an open source crypto library would be a good way to help push towards a positive Singularity, and that only happened in college after I read Vinge's A Fire Upon the Deep. Your verbal abilities don't seem low to me (at least in writing). Maybe low compared to Eliezer, but then he is just off the charts. I'm worried that competitive debating trains for the wrong things (e.g., using arguments as soldiers). ChristianKl's suggestion of drama lessons doesn't seem like it would increase verbal abilities more than say reading, but I'd be interested if anyone has evidence to offer about that. I'll probably have to do some research to see what other activities are good for increasing verbal skills.
6cousin_it
That's one of those questions like "how do you play the violin" :-) There's no trick, you do it the hard way. I give lots of tiny exercises that are solvable but mildly challenging (typing, arithmetic, 2D coordinates, loops, etc). I make some simple game that fits in a screen of code, make the kids type it in from paper, then they naturally come up with tweaks and new features and add them with my help, so everyone ends up with a personalized game to show off. And so on. (Why typing code from paper? Because kids start out unable to type. They need to practice it each lesson.) The hardest part is getting the difficulty right, otherwise the kids run out of focus in 15 minutes and the rest of the lesson is wasted, or they solve everything too fast and get bored as well. I still get it wrong more than half the time, but when it works it feels great.
2Kaj_Sotala
Reading, writing, speaking and listening are all somewhat distinct skills; my guess would be that if you wanted to optimize verbal abilities, you'd want to encourage all four. Drama lessons sound like they would help with the speaking and listening skills in a way that reading doesn't. Also I'm under the impression that if you have four interrelated skills A-D, even if you were only interested in optimizing A, spending some time on each of B-D also lets you learn A better. I don't have a formal cite for that, but at least this article discusses it.
0ChristianKl
Drama lessons train the ability to act in a specific scripted way in a social situation.
4ChristianKl
Drama lessons seem to be a classic verbally focused hobby.
0Dagon
I look forward to ongoing reports related to these decisions, and how the agency of the child interacts with your deliberations.
0Dagon
This will depend a whole lot on the child and their peers. For a fairly young child, there's a lot of future value in knowing a few activities well enough to know if they want to pursue it more formally as a pre-adult. For a child old enough to have (slightly) informed opinions, your best bet is likely to let them pick the topic and you provide the balanced discipline to decide whether to stick with it or switch during the tough periods. I expect the variance in expected value between different activities is much smaller than the variance of good fit for the kid's context.
0Viliam
Piano and ballet seem like upper-class costly signalling. "I am so rich I can spend tons of time doing unproductive activities." If you are upper-class and if you want to signal it costly, it could be the right move, otherwise it is almost certainly the wrong move; such is the nature of costly signals. Sports seem useful per se. Unless you mean golf or pony riding, of course.
[-]komponisto100

Piano and ballet seem like upper-class costly signalling. "I am so rich I can spend tons of time doing unproductive activities."

Well, no need to speculate about a future Malthusian dystopia, since it appears to be already here, psychologically!

Allow me to refer you to this comment of mine, and the ensuing discussion, on Sarah Constantin's blog. Artistic pursuits may be "upper-class", but they are not unproductive. They serve to keep the upper classes practiced in physical cognition, counteracting a tendency to shift entirely into social modes of cognition (gossip and status-signaling games) as one ascends the social ladder. This is very important for the quality of decisions they make as leaders of society. (See here for more on the distinction between physical and social cognition -- which, incidentally, I myself would identify with the famous "near" and "far" modes respectively, though not everybody goes along with that.)

The fact that there has been such a decline in interest and participation in high culture among the upper classes is very worrying, and something I would not particularly hesitate to link to the intellectual decadence t... (read more)

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2ChristianKl
There are ballet competitions and I think parents do care about how their children's perform in them. The kind of parent that forces their child to play piano every day also cares about performance. The kind of hacking that Wei Dai did that lead him to write the b-money paper also isn't about winning. It's exploring ideas and having fun with them. Having a kid spent time with computer programming means that he's much more likely to engage in innovation than having the kid spent time with piano or ballet. Both piano and ballet are heavily codified and don't encourage innovation. Most discussions on LessWrong are also not about direct winning but about free exploration. The fact that people spend their free time chatting on LessWrong instead of working for the Man, suggests they already understand that working for the Man isn't everything.
2komponisto
You seem to have misunderstood my comment as some kind of salvo in a STEM vs. arts rivalry, with the result that your comment reads like a counter-attack in such a battle. This is probably due to cliché-rounding. In point of fact, a perceived opposition between STEM and arts is a manifestation of the very thing I was complaining about. Thus, to have written the kind of comment that you appear to be responding to would have been the very last of my intentions. I would direct your attention to the sentence immediately following the excerpt you quoted: This, in other words, acknowledges a kind of competitive aspect of art, one more complex than that in (most) sports. Something similar is the case in STEM. In no sense did I imply that STEM is more "about winning" than art. You seem to be addressing me as if I had said or implied such a thing, which suggests that you simply mis-parsed my comment in that respect.
0ChristianKl
If I go in a hackerspace I don't see performance that can be modeled as an ordered list but rather as a highly complex graph. A ballet competition, on the other hand, does produce an ordered list. Maybe it would help if we taboo art. What do you mean with the term when ballet and playing the piano are art but the kind of hacking you find at a hackerspace isn't?
2komponisto
I was not, in fact, using the term in such a way, but you failed to notice this! This is cliché-rounding.
0ChristianKl
The first line of your post is a quote about teaching ballet and piano to children as opposed to the kind of hacking background that Wai Dai has. Why use the term "art" when you don't mean ballet and piano, without making it explicit that you don't mean it?
2komponisto
I do mean ballet and piano, and also the kind of "the kind of hacking background that Wei Dai has". I did not expect this to be completely outside of your hypothesis space, in the way it appears to be. This is worth reflecting on.
2Viliam
Ok, allow me to say it using my own words: Roughly, human pursuits can be divided into "social games" such as gossip or conspiracies, which are usually zero-sum, or even negative-sum as they often compete in sacrificing to Moloch everything that does not provide immediate social value, and "games with nature" such as work, science, but also sports and that part of art which requires skill e.g. playing the piano (as opposed to "modern art" which is merely about who makes a media hype around you, so it requires allies instead of technical skills). The word "game" is used here as in "game theory", i.e. it may or may not refer to playful activities. And there is a risk that when people climb the social ladder, they lose touch with "games with nature", because they delegate it to people lower than them on the social ladder. With the horrifying consequence that people who rule the world may actually understand it the least. I mean, they certainly understand the social aspects of the world, that's what they specialize at, so they are good at e.g. organizing a revolution; but they have no idea how to grow grain or cook bread, so the revolution is typically followed by bread shortage and lot of suffering. Having upper-class people spend some time doing "games with nature" may keep them more sane, and as a result keep the whole society more sane. But, frankly, the "games with nature" are typically motivated, directly or indirectly, by survival (you grow grain and cook bread to avoid starvation, you learn science inter alie to achieve job safety which is to avoid starvation), and this motivation does not apply to the upper class. Having them do sports or (skill-based) art may be the only chance to get them in contact with non-social aspects of reality. Of these two, sports are more about body, and are quite repetitive, while art is more about mind and creativity. Is this approximately right? I still think that if someone is doing math or programming, they already have the
3komponisto
Probably close enough for present purposes. Of course, but these pursuits themselves are often described as artistic in character, especially by their most elite practitioners. They probably are copying what their neighbors do, but it is a good fortune if their neighbors happen to do that. Of course, the effect is dependent on how good the piano instruction is, which is dependent on the level of musical culture of the surrounding society.
1Lumifer
How do you expect humans to network, figure out who their friends and enemies are, establish trust, etc? "Games with nature" are all fine, but they imply a solitary individual who is an island. Humans are social animals, they build complex social structures and making these structures work necessitates "social games" which are definitely not all zero-sum. Not to mention that if you want some of your genes to survive into the next generation, you'd better learn to play the appropriate social games :-) I think you're getting a bit carried away. Specialization is mostly good. It's perfectly possible to run a state without having any idea how to bake bread. So are social games. For most of human history in most cultures, if a society threw you out and shunned you, your chances of survival plummeted. I think that "want [the] child to play the piano" and doing art yourself are very different things. I'm much more inclined to buy the argument that sending the child to a music school is all about social signaling for the parents (the child is just being the means) than the argument that someone who does art herself is doing art for social reasons.
0Viliam
The idea is not to ignore "social games" completely, but rather that some people - specifically, upper-class people - are in a risk of going too far, and seeing the world consisting of "social games" only. Mostly because they are liberated from forces that make lower classes play the "games with nature", such as having to bake your bread or having to keep a job. Yes, division of labor is a good thing. Problem is, with any division, you need some kind of coordination: whether a person, or an impersonal market. But when you successfully do the revolution, you may kill the competent people and make the market illegal. Then, there may be many people who know how to grow grain and bake bread, but some activities necessary for this process may be made illegal and punished by death. The result is shortage of bread. The king does not have to know how to make bread, but should not be so insane that he prevents anyone in his kingdom from making bread. And believing e.g. that "objective reality does not exist and everything is socially constructed" seems like a royal road to insanity; but at the same time it is easy to imagine how a person who only ever plays "social games" might find that credible.
2dogiv
It seems like the ideal leisure activities, then, should combine the social games with games against nature. Sports do this to some extent, but the "game against nature" part is mostly physical rather than intellectual. Maybe we could improve on that. I'm envisioning some sort of combination of programming and lacrosse, where the field reconfigures itself according to the players' instructions with a 10-second delay... But more realistically, certain sports are more strategic and intellectual than others. I've seen both tennis and fencing mentioned as sports that involve quick strategic thinking and predicting your opponent, although they lack the team element that lets you build coordination skills. Maybe some kind of group fencing would be good... or doubles tennis?
2komponisto
Exactly! Hence arts (and sports).
2Lumifer
War. Strategic, intellectual, contains the team element, and is highly motivating :-P
2ChristianKl
I don't think knowing how to grow grain and bake bread helps you avoiding to turn a free market economy into a planned economy that mismanages resources. Mao prohibited farm ownership and no amount of understanding the actual skill of baking or growing crops would have convinced him that private ownership is a good idea. Lysenko's success is also not simply about lack of farming knowledge but about having an intellectual climate that's not well-fitted from separating true theories from those that aren't.
2komponisto
What makes you so sure of this? More to the point, what makes you sure that a society that tied status more closely to such skills wouldn't have promoted someone better than Mao to the top? The point here is to get into the reasons why intellectual climates have the properties they do, with respect to the ability to develop and identify true theories. To be sure, societies could have multiple failure modes, and I am open to the possibility that the USSR and Maoist China may have been bad for reasons entirely unconnected to the relationship between status and physical cognition. However, the populist character of both makes me doubt this, as populism seems anticorrelated with both good aesthetics and good science.
1Lumifer
There have been enough revolutions and (temporarily successful) peasant revolts to demonstrate how that usually turns out. Lenin famously said that "Any cook should be able to run the country" and I don't think it worked well.
2komponisto
As I said above, Thus, by "a society that tied status more closely to such skills", I do not mean the typical conditions leading to, and resulting from, a peasant revolt.
0gjm
If only someone had thought to send Lenin to cookery school.
0Lumifer
It's more complicated :-D Like in French, most Russian nouns have masculine or feminine gender and IIRC in the original Russian the cook was specifically a female cook. And Lenin, sigh, was a cishet white male.
0gjm
If https://en.wikiquote.org/wiki/Vladimir_Lenin is to be believed then it's more complicated still because what Lenin actually said was exactly the opposite.
0Lumifer
A meme necessarily looks better than the actual source :-/
0ChristianKl
Mao was the son of a farmer. Mao actually worked on his father farm instead of learning the piano and was bullied for his farmer background in high school. I don't think good aesthetics tell you about how to grow crops or bake bread.
1Lumifer
Sure, but that's true of most every human activity under the sun (including "games with nature"). Knowing NOT to do this is in no way dependent on knowing how to grow wheat or bake bread. I agree, but here the difference between beliefs and aliefs becomes important. Besides, physical reality has a habit of rudely intruding into social constructs and if you still insist on ignoring it, well, you might be in line for a Darwin Award.
0Good_Burning_Plastic
LOL
0bogus
I would describe this more generally as real-world achievement, which is a lot clearer than a label like "physical cognition". Eric S. Raymond has a nice post which details how the beneficial effects of having a shared standard of achievement can play out socially, at least in the strictly technical realm. Oh, and by the way, good scholarship can definitely count as legitimate "achievement" in many circumstances. This most likely explains how even the most stereotypical "humanities academia" can sometimes manage to be both intellectually engaging and socially healthy. Yes, there are lots of worrying dynamics in the "X Studies" part of academia, but sometimes good work still happens there.
3komponisto
There you go again, compulsively trying to round concepts off to something else! "Real-world achievement" is considerably less clear as a way of pointing to what I am trying to point to than "physical cognition". It evokes all kinds of distracting side-issues about what constitutes the "real world". (Is pure mathematics "real-world achievement"? et cetera, et cetera). I can't tell what the point of your second paragraph is. Is it just an attempt to provide reassurance (to whom?) about the value of humanities academia, in the face of what you took to be a "boo humanities academia!" from me (in my comment on Otium)? Or are you seeking to dispute my contention that physical cognition is underpracticed and undervalued there (in which case it would tend to look like your proposal to substitute "real-world achievement" for "physical cognition" was an attempt to muddy the waters in preparation for an equivocation)? All this notwithstanding, I'm grateful for the pointer to the Eric Raymond essay, as it is relevant to what I was talking about with respect to Maslow and so forth. (In particular, it serves as anecdotal information about, and confirmation of, the distinction between Levels 4 and 5.)
3Wei Dai
Creating a distinct new concept in one's mind is an expensive operation (with both short term and long term costs), so I think it's only to be expected that people will try to match a supposedly new concept to an existing one and see if they can get away with just reusing the existing concept. I suggest that if you don't want people to do that, you should define your new concept as clearly as possible, give lots of both positive and negative examples, explain how it differs from any nearby concepts that people might try to "round off" to, and why it makes sense to organize one's thinking in terms of the new concept. (It would also help to give it a googleable name so people can find all that information. Right now, Google defines physical cognition as "Physical cognition, or 'folk physics', is a common sense understanding of the physical world around us and how different objects interact with each other." which is obviously not what you're talking about.) I think I've avoided rounding off your physical cognition to an existing concept, but I still don't understand how the concept is defined exactly or why it's a useful way of organizing one's thinking as it relates to the question of what kinds of children's activities are most valuable. Clearly there are distinct skills within what you call physical cognition, and all those skills are not equally valuable, nor does practicing one physical cognition skill improve all physical cognition skills equally (e.g., if you practice math skills you improve math skills more than piano skills, and vice versa). Given that, why does it make sense to group a bunch of different skills together into "physical cognition" and then say that practicing piano is valuable because it exercises physical cognition? Wouldn't it make more sense to talk about exactly what skills are improved by practicing piano, and how valuable the increase of those specific skills are?
3komponisto
Right, but I was reacting to a prior history with that particular commenter, who has been especially prone to doing this (very often where, in my view, it isn't appropriate). But also: I regard concept-creation as being a large part of what we're in the business of doing, here. (At least, it's a large part of what I'm here for.) That's what theorization is, and I think we're here to theorize (maybe among other things). So it's a cost that I think one has signed up to bear in a context of this sort. For the most part, it's great if one has the motivation to write up a thorough exposition of a new concept, starting from very elementary premises (although there's also the negative aspect of potentially reinforcing a norm of this level of effort being generally expected every time one wants to introduce a new concept). However, one doesn't always have that motivation (or time, etc.), so it should be allowed sometimes to just point and say "look over here; if you think about this for a while, you may traverse the same inferential path I have, which leads to this conclusion." Indeed, that's basically exactly what I want out of this forum: a place where people can state inferentially-distant conclusions you might not hear elsewhere (without necessarily needing to justify them from first principles -- such requirements might, after all, be part of why they're not heard elsewhere!). This, of course, requires a community where a certain amount of epistemic trust has been built up, but I think that happened already (c. 2009-11). For epistemic norms designed to avoid false positives, there are skeptics' forums, and scientific journals. And your grandmother (to paraphrase Feynman). Here, we could use more of the opposite approach (avoiding false negatives). Who else specializes in that (high-quality speculation)? It's basically an empty niche. Perhaps I can "strike a chord" with you in particular by talking about value uncertainty in this context. Even to the extent it's cl
2Wei Dai
I don't think that's a reasonable expectation or norm. The expected return from a reader doing something like that is way too low, even in a community like this one. Most new ideas are wrong, and if your idea is wrong then people trying to traverse the same inferential path will get nowhere, and not even know if its their own fault or not. If you write it down then people can figure out where you went wrong and point it out. Even if your idea is right and your reader can be sure of that, why shouldn't you write an good explanation once, which will then save time for potentially hundreds or thousands of readers? By trying to save that time for yourself, you cause other people to waste their time, and then you end up having to answer their confusions and perhaps not even save time for yourself. You could make an exception to this if you just had a new idea and you want to find out if anyone else already had a similar idea or can see an obvious flaw in it, before deciding to invest more time into explaining it fully, but that doesn't seem to be what you're doing here. I have some uncertainty here, but not that much. I took one semester of piano and one semester of electronic music in high school, and it was intuitively clear that the return from that time spent wasn't nearly as valuable as say reading science fiction or economics textbooks. There's obviously a lot of individual differences here, so if my kid naturally has an interest or talent in music or art and wants to study it, I'm not going to stop her. But if your position is that we should more vigorously encourage an interest in artistic pursuits, I'm going to need more evidence and/or better arguments. This is totally unclear to me. I guess even if it's true, it would be hard for me to figure out on my own since I probably haven't studied music enough to be familiar with the kind of "physicality" that you're talking about. Nor do I understand what forms of thought you're suggesting is related to such physic
3komponisto
I disagree with these statements. (Even in the case of "most new ideas are wrong", I would ADBOC.) You're basically just stating the view that "false positives are a bigger problem than false negatives", which I already disagreed with explicitly (as applied to this context) in my previous comment. Because what constitutes a "good explanation" is strongly reader-dependent, and I don't have good enough models of most readers to know in advance what will satisfy them. It's worth it to try being very foundational sometimes, but not all the time. It's also worth it for readers to sometimes practice the skill of traversing inferential paths more nimbly. I wouldn't presume to take such a detailed position on how you should relate to your child. (Though I can think of someone you might want to talk to, about not only this but the whole subject of "what to do" with children who are, or who are at "risk" of being, "gifted" -- the best way to get into contact with that person would probably be through Jonah Sinick.) My concern here is only to explain (insofar as is possible within the number of words I'm willing to expend) something about what the value of traditional artistic pursuits is, and, in particular, the ways in which it's similar to the value of less traditional artistic pursuits like programming. I think you (like many, no doubt, in the LW audience) have bad priors about this due to insufficient exposure in early life (perhaps for socioeconomic reasons -- as you said above, "My parents didn't have the time or money to deliberately cultivate these kinds of interests in me when I was a child). I myself also had relatively little deliberate exposure (for the same reasons), but, exceptionally, was drawn in the relevant direction by an unusually strong intrinsic attraction (such that, had I come from an upper-class background, I would very likely have been involved at a much higher level much earlier). As a result, I think I am in the position of perceiving something
0MaryCh
There is a kind of pleasure, when one performs a complex movement "just so", that attracts some people to e.g. martial arts without the goal of learning to defend themselves. (It was so with me, but, well, socioeconomic reasons.) There's a kind of a message that some people get out of poetry, besides the 'prosaic sense' of it, which sometimes gets related in another piece of poetry or even a very different way. I used to wonder, what exactly is its impact on different people's understanding of the whole, & might not 'understanding' be an umbrella word for some orthogonal things... Some of which get called 'spiritual' for lack of a better term:)
0gjm
For me, I don't see how "physical cognition" is better, because just what "physical" means here is as unclear to me as what "real-world" means in bogus's comment, and in rather similar ways. Is doing pure mathematics "physical cognition"? What about physics? With no more context than your earlier comment where (so far as I know) you first used the term, I'd have taken "physical cognition" to mean something like "applying one's brain directly to the real world in ways involving planning and subtlety and the like", with playing a musical instrument being an example. But I now have the impression that you intend it more broadly than that, perhaps including e.g. musical composition (even if done in one's head). But exactly what you mean remains unclear to me, as does why (if I'm understanding you right) you consider "physical cognition" a more fruitful category of things to lump together than "real-world achievement". (Note for the avoidance of doubt: I am not claiming that "physical cognition" is not a more fruitful category, nor that bogus's thinking in this area is better than yours, nor anything of that kind. I am just saying that it seems unreasonable to complain of someone "rounding off concepts" when you have made no apparent effort to clarify what you do mean, and that your specific objection to "real-world achievement" seems to apply equally to "physical cognition".)
2komponisto
In my original comment, I linked to the essay that was the source of the concepts of "physical" and "social cognition" as I used them in that comment. Without the context of that essay, there is no reason to expect my remarks in this discussion to be intelligible.
3gjm
OK. Then I have a confession and three complaints. The confession is that when I wrote what I did above, I hadn't noticed that you offered that link as further explanation of the term "physical cognition". The complaints are (1) that having now followed the link, I think it leaves the meaning of "physical cognition" still less than perfectly clear; and, in so far as it does explain what the term means, (2a) it actually seems not so far from "real-world achievement" and (2b) I think it probably doesn't include music and art. (Whereas in your usage it seems like it must.) I'll elaborate a bit. Here is what that essay says about physical and social cognition. (The only actual instance of those terms is at the end of the second quoted paragraph, but I think the preceding stuff is necessary to make sense of that.) So. We start with Maslow's hierarchy. Vassar (the author of the essay) puts a division between the two "lowest" levels, which he calls "physical" (meaning that they are concerned with our physical needs and wants) and the next two, which he calls "social" (meaning that they are concerned with our interactions with others). The topmost level ("self-actualization") I think Vassar classifies as "social", which I think mostly indicates that his terminology isn't great. And he says that attempts to address needs and wants higher up in the Maslow hierarchy tend to involve vague fuzzy socailly-mediated things, which may "be fairly easily hacked" and "constitute a poor foundation for universal cognition" by comparison with activity directed at the lower levels, which tend to involve precise specific details and "constitute a good substrate for digital, and thus potentially abstract, cognition". And, finally, he says that the lower-level ones seem to be endorsed over the higher-level by the likes of Newton and Feynman. All fair enough (though I'm not at all convinced). But now you want to say that artistic endeavour belongs in the category of "physical cognition"? R
0komponisto
Like others, you seem to be interpreting my comments as if they were stating conclusions intended to be only one or two inferential steps away (from your current epistemic state). This is not at all necessarily the case! In particular, when I state a proposition X, I expect readers not only to ask themselves whether they already think X is true (i.e. conditioned on all their knowledge before my statement), but also to ask themselves why I might believe X. To engage, in other words, in at least a cursory search for inferential chains leading to X -- resulting in either the discovery of an inferential chain that they themselves agree with (in which case communication has been approximately successful), or a hypothesis about what my error is (which can then be discussed, and confirmed or disconfirmed). This mental motion seems to be missing from your (and, even more severely, others') reactions to my comments. It's as if I were expected to be modeling your epistemic state, without any corresponding expectation that you be modeling mine. Yet, insofar as I've stated a specific belief, you have some specific information about mine, whereas I have only background information about yours. This will of course change once you reply -- I will get more specific information about yours -- but the dialogue will be more efficient if your reply attempts to integrate and respond to the information you have about my epistemic state, rather than merely providing information about yours (as is the case when your reply takes the form "you have made one or more assumptions that I don't share", as here, for example). Now, to get back to the object level: You have overlooked a distinction that, while not explicitly stated in the essay itself, is nevertheless crucial to understanding the point Vassar is making: the distinction between people's needs, themselves, and the programs that they use to satisfy them. The pathology that Vassar is complaining about is the fact that as one ascends
0bogus
It seems hard to envision a society wherein belonging and esteem could be satisfied via physical cognition, at least until we can make building an AIBO pet dog robot in one's garage a common enough pasttime. So, the only realistic possibility for a meaningful change is in how self-actualization is pursued. But is it actually true that "social" paths to self-actualization are less collectively desirable than "physical" paths to the same? Well, for a start, there are certainly "fine things in life" that are best understood in social terms; for a handy example that fits squarely in the realm of art, consider so-called "literary" fiction. Now I obviously cannot claim that writing literary fiction could ever be considered an "achievement" of the purest sort (in my preferred sense), since its value is not something that can be generally assessed in any widely-agreed upon way. And yet, it is certainly the case that, to the extent that works of literary fiction are widely considered to be valuable accomplishments, this is due to what they imply about the social universe, as opposed to the physical one! The belief that I am implicitly denying here seems to be, as quoted directly from the parent comment: "To effectively create value requires skill in analytical/"near-mode" thinking" (emphasis added). And that's certainly true in many cases (it's also true, as you rightly point out, that many of the "finer things in life" are far from entirely social!) but not in general. This matters here, because it seems to lead you to incorrect conclusions about what exactly makes "self-actualization" value-creating and collectively desirable. It's not the absence of "social cognition" in its entirety but rather, of a few undesirable aspects of social interaction that are rather more pervasive at the level of "esteem" and "belonging". Vassar's essay is even quite clear that these aspects exist, and are important to his point!
0komponisto
Not hard to envision at all; only hard, perhaps, to implement. It shouldn't take all that much imagination to summon the thought of a society in which people were better rewarded with status (and all its trappings) for things like solving mathematical problems, or composing complexly-structured music, as opposed to all the various generalized forms of pure politics that determine the lion's share of status in the world we know, than they actually are in the world we know. In fact, we can look around and find historical examples of societies where that was the case. In my Otium comment I pointed to one: Imperial Germany (pre-WWI). That was a place where a figure like Max Reger could achieve high status in general culture -- without even needing to be a Nietzschean superman to do so. All he had to do was follow the rules of society, which happened to permit someone with those kinds of compositional aspirations to become a celebrity. My radical belief is that the fact that this is the same culture that also produced leading figures in every other field of creative intellection (and a place where shops in university towns sold pictures of professors in postcard form), and indeed is credited by Tyler Cowen with "deliver[ing] the goods in terms of innovation", is not a coincidence. This is an extreme example -- in fact the best I know of, at least at the level of entire nations -- but the phenomenon is a matter of degree. Yes. Narrative fiction is the least physically-oriented of the arts. Its existence is most of the reason for the qualifier "at least certain forms [of art]" in my comment on Sarah's blog. Note that it is also the only art-form that is widely appreciated at anything like a sophisticated level by the "rationalist community" as a whole. This is a problem. (Basically, it reflects an implicit belief that only STEM is about physical cognition; since all art is assumed to be almost wholly social, LWers opt for the "least pretentious" variant, i.e. the most
0ChristianKl
It would be helpful if you try to define what you mean with "art" or "physical cognition" if you see people thinking you mean something different than you do.
0bogus
Nope. More formally, I'm saying that the relation between the "physical" nature of cognition and the social benefits you talk about is essentially screened off by the more immediate fact that such physical activities are far more likely to feature a widely-agreed standard of achievement. Thus, the fact that humanities scholarship is in some sense "non-physical" (which it obviously is, since it is properly about human cultures, as opposed to physical phenomena such as the mechanics of playing an instrument) is practically irrelevant to whether or not we should consider it to be "intellectually stimulating", at least inasmuch as the merit of such scholarship is sometimes widely agreed upon. To some extent, these issues seem to be unavoidable. One reason why pure math academia is in such a "bad" shape socially is that it is only directly valued by a tiny minority. Within the subculture that values it, though, achievement is reasonably clear and thus it can at least escape the negative connotations of "social cognition". A similar situation seems to apply in newly-composed "serious" music, even though the subculture that values that might be even smaller, and the standard of "what makes this new piece worthwhile enough that I should be paying attention to it" somewhat less than clear.
0[anonymous]
Upper class folks don't spend all their time in consumption and gossip, with art as their only lifeline to the real world. They do business and politics as well.
0Wei Dai
I'm having trouble understanding this. Why do artistic pursuits constitute practice in physical cognition as opposed to social cognition? It seems obvious to me that artistic pursuits are (among other things) a type of status signaling, so I'm confused why you're contrasting the two. Please explain? (Aside from not being sure how valid the Maslow hierarchy is) I agree with this. But I don't see art/music/dance classes as a particularly good way to prepare most kids to fulfill their level 4 and 5 needs, mostly because there is too much competition from other parents pushing their kids into artistic pursuits. The amount of talent, time, and effort needed to achieve recognition or a feeling of accomplishment seem too high, compared to other possible pursuits.
3Kaj_Sotala
Basically, Maslow's hierarchy of needs is a myth, and everyone would be better off forgetting about it entirely.
2komponisto
Not necessarily; it depends on what one's default or alternative theory would be. Let's be Bayesian, after all. As I interpret it, "Maslow's hierarchy of needs" is little more than the claim that people's goals depend on their internal sense of security and status (in addition to whatever else they might depend on). When I speak about it, I'm usually talking about something like a spectrum of exogenous vs. endogenous motivation: at one end you have someone being chased by a wild animal (thus maximally influenced by the environment), and at the other, the Nietzschean "superhuman" who lives only according to their own values, rather than channeling or being a tool of anyone or anything else (thus minimally influenced by the environment in some sense, although obviously everything is ultimately a product of some external force).
5Kaj_Sotala
Self-determination theory is the standard alternative theory I usually point to (which also incorporates the spectrum of exogenous vs. endogenous motivation, but which I don't think the hierarchy of needs as usually conceived does).
2komponisto
Thanks for the link; that'll be useful to refer to. Of course, I on the contrary do think the hierarchy of needs is suggestive of this, as evidenced by the fact that I specifically interpreted it that way!
0Lumifer
It's certainly not a myth because it's a theory (or a hypothesis) which actually exists. Its weak forms are rather obvious, famished poets notwithstanding. Psychology is not physics and should not pretend to be physics, it deals in weak generalizations and fuzzy conclusions. Maslow's hierarchy should not be thought of as an iron law which applies everywhere to everyone -- it's merely a framework for thinking about needs.
2Kaj_Sotala
Sure, but we're talking about a theory that isn't even accepted as a psychological theory: psychologists themselves have examined it, decided there was no reason to believe in it, and moved on.
0Lumifer
Has it been falsified? That is, empirically shown to be not true with regard to large populations (as opposed to individual counter-examples)?
4Kaj_Sotala
That's what the quote I posted said; the individual counter-examples are one thing, but the main thing is the complete lack of evidence for it.
0Lumifer
Fair point, the quote did say that. Interesting.
2komponisto
Artistic pursuits involve a synthesis of physical and social cognition. (This is essential to their nature and is what makes them special among human activities.) There is certainly a social aspect, but it's crucial that that isn't all there is. That there is also a physical aspect is also pretty obvious, if you consider what is involved in playing an instrument, for example -- but importantly, it goes beyond that, to encompass the ways one thinks about something like music (in terms of motion, as well as ideas like connectedness, and so on). Generally speaking, whenever we think of something as being "technical", we're talking about the involvement of physical cognition. Art is social, yes, but it is also highly technical. Many people, unfortunately, underappreciate the physical, or technical, side of artistic thought. This is what I was warning against in my comments on Otium. This is actually not really true, but it's understandable that you might perceive it that way. Even so, the time and effort are part of the point: anything fulfilling this role has to involve extensive amounts of interaction with the objects or processes in question.
0Lumifer
For certain arts -- e.g. music -- this is true (in the sense in which I understand "physical cognition" -- the body is intimately involved). But a counter-example would be something like digital art where your tools are on Photoshop palettes. The physical skill involved is moving a mouse and I don't think this qualifies. And yet, digital art is highly "technical".
2komponisto
That is not what I meant -- as the excerpt you quoted was intended to communicate. Musical composition is one of the archetypal instances of a physical-cognition-loaded activity (in the sense that I mean), and yet there your physical tools are a pencil/pen and paper (or, sometimes, indeed, a mouse).
0Lumifer
So what do you mean, then? I don't understand what "physical cognition" in this context points to. What is the word "physical" doing in there? It failed.
2komponisto
See here. (This was linked in the original comment...)
0Lumifer
Sorry, still don't understand it. gjm has a fairly detailed list of complaints and I concur with them.
0ChristianKl
Do you think you use the term physical cognition in the way it's used in the literature? Or do you think you use it in a different way?
2komponisto
"The literature" that is relevant here consists of Michael Vassar's 2013 Edge essay.
0ChristianKl
It's relevant in the way that it doesn't use the term "physical cognition"?
2komponisto
From the fourth paragraph:
0bogus
For some reason, it's not overly surprising to me that both Isaac Newton and Richard Feynman would directly endorse physical cognition - what with them being natural philosophers/physicists. It's less clear however that such "physical cognition" is directly relevant to e.g. music composition, except inasmuch as both physics and music composition are linked to self-actualization - as opposed to 'mere' love, belonging and self-esteem, which (if pursued in excess, due to a lack of "self-actualizing" pursuits) might "lead[] to increased unethical behavior" or "produce anti-social narcissism" according to the essay you link to.
2arundelo
You can use ballet dancing or piano playing for status signaling but first you need to learn to dance ballet or play the piano.
8username2
Wow that seems overly dismissive of the arts. My daughter loves ballet ever since she saw a friends ballet birthday party. She is a very physical / body oriented learning type who fidgets at school. Ballet is a great outlet, builds coordination and gives her self confidence. I know I can say similar things of piano lessons. I quite shocked that you can reduce that to "upper-class costly signaling."
2Wei Dai
Sure, costly signaling has to be a big part of any analysis, but isn't sports also a costly and unproductive way of signaling one's physical and genetic fitness? Sports can also be a fun way of exercising, but some kids find ballet fun and it can also be good exercise. People have claimed various (non-signaling) benefits of learning to play an instrument as well, and that can also be an enjoyable activity for some. Apparently some parents make their kids take lessons to increase the chances of getting into private school, and eventually an elite college, so another big part of the analysis might be the costs/benefits of private vs public school and elite vs non-elite colleges. (I personally went to public school and a state university.) Another big part is, if you leave a kid a lot of free time, how likely is it they'll eventually find something valuable to do with it? Or alternatively, what are some more valuable activities we should try to guide a child into instead of the standard ones?
2NoSignalNoNoise
Disclaimer: US-centric perspective Elite colleges generally students who are "genuinely" (insert adjectives here), not yet another honor roll student with a boring essay about how their voluntourism trip to Africa changed their life. In a competitive field like that, you want to stand out, and you stand out a lot more by doing something that both clearly signals being good at things and is different from the signals that other students are sending. Therefore, doing whatever other students of your socio-economic status do is a bad strategy. Much better to do something impressive and different.
1Dagon
It's not like your kid can opt out of signalling. There's lots of aspects of the value of these activities, and demonstration of talent, conscientiousness, and the right kind of conforming excellence can be a large part of what you and the kid gets out of it. Bonus if they also get some excercise, practice and encouragement of good habits along the way.
4Wei Dai
Sure, but are the standard activities actually optimal even for this purpose? For example I learned to program as a kid, then in college wrote one of the first open source cryptography libraries, after which I had my pick of job offers. I probably put less total hours into this than someone who practiced piano for an hour a day from age 5, and got more out of it. But I'm not sure if that was luck, or if I can expect my own kid to duplicate this. Also, now that learning to program has become a standard activity that parents push kids into (just look at how many tablet games there are that purport to teach kids how to program), it probably doesn't have as much signaling or practical value due to competition, and I'm wondering what is the modern equivalent of learning to program as a kid in the 80s.
3ChristianKl
Superforcasting might be an area that will be very useful in the future.
2Viliam
Cryptocurrency investment. Imagine how your kid's peers will be impressed to hear "when I was at elementary school, I put my pocket money in various altcoins, and... long story short, I am a billionaire now". :D But maybe learning to program is the modern equivalent of learning to program. Just because there are many tablet games teaching kids how to build "a loop in a loop" programs from predefined blocks, doesn't mean that kids will bother to play the games, and will move to further stages of programming.
0Gurkenglas
Markets are anti-inductive; why do you think there's future money lying on the street in buying some of many altcoins?
[-]ChristianKl50

I'm in the process of reading Bruce Bueno de Mesquita book Predictioneer's Game. It's about himself using big computer models based on game theory to predict political events.

How many people besides Bruce Bueno de Mesquita use models like this? Is there open source software to run such models?

Reply
[-]turchin30

Wireheading bomb – a putative mechanism to stop dangerous AI.

If a reward function of an AI is presented openly in its source code, any attempt to self-improve by AI will result in its own immediate wireheading, as when it reaches its own source code, it will become able to modify it in order to get maximum reward. So we could create an AI architecture in the way that as soon as it gets access to its own source code, it stops, and use it as a way of reaching passive safety and self-limited self-improving capacity.

We also could do exactly opposite, and put... (read more)

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0dogiv
I like the first idea. But can we really guarantee that after changing its source code to give itself maximum utility, it will stop all other actions? If it has access to its own source code, what ensures that its utility is "maximum" when it can change the limit arbitrarily? And if all possible actions have the same expected utility, an optimizer could output any solution--"no action" would be the trivial one but it's not the only one. An AI that has achieved all of its goals might still be dangerous, since it would presumably lose all high-level executive function (its optimization behavior) but have no incentive to turn off any sub-programs that are still running. Both proposals have the possible failure mode that the AI will discover or guess that this mechanism exists, and then it will only care about making sure it gets activated--which might mean doing bad enough things that humans are forced to open the box and shut it down.
0turchin
The idea is a not intended to be used as a primary way of the AI control but as the last form of AI turn off option. I describe it in the lengthy text, where all possible ways of AI boxing are explored, which I am currently writing under the name "Catching treacherous turn: confinement and circuit breaker system to prevent AI revolt, self-improving and escape". It also will work only if the reward function is presented not as plain text in the source code, but as a separate black box (created using cryptography or physical isolation). The stop code is, in fact, some solution of complex cryptography used in this cryptographic reward function. I agree that running subagents may be a problem. We still don't have a theory of AI halting. It probably better to use such super reward before many subagents were created. The last your objection is more serious as it shows that such mechanism could turn safe AI into dangerous "addict".
[-]Vaniver30

The first time I read this poll...

[pollid:1200]

Reply
6NoSignalNoNoise
I interpreted "fullscreened" to mean "maximized", though I'm not totally sure whether that was the intent.
3Oscar_Cunningham
I was about to vote "wasn't fullscreened" even though my browser was maximised, so instead I will hold off on voting for now.
3fubarobfusco
I was on an Android tablet, which I use in a laptop-like fashion (landscape mode, with keyboard) but which usually gets the mobile version of sites that try to be mobile-friendly.
0RainbowSpacedancer
I'd expect mobiles to be under-represented in these results as you can only vote if you are logged in and I'd expect more people are logged in on their desktop rather than their mobile.
[-]hg0030

Happy thought of the day: If the simulation argument is correct, and you find that you are not a p-zombie, it means some super civilization thinks you're doing something important/interesting enough to expend the resources simulating you.

"I think therefore I am a player character."

Reply
9Lumifer
This is traditionally expressed as "Jesus loves you".
0hg00
The sentiment is the same, but mine has an actual justification behind it. Care to attack the justification?
0Lumifer
I don't see any justification. All I see is another just so story.
1MrMind
How do you know you're not a p-zombie?
[-]Screwtape30

There have been a couple of community building projects put forward that got me thinking about this, and then over in the post about ways to make the community better it was suggested that some people might want to get to know other lesswrongers through D&D*. I love that idea. Tabletop RPGs are the fastest way I know of to build a connection with someone that doesn't leave scars. While the concept of an 'expert' in those games is sort of goofy, I figure I've got plenty of experience and interest in them to run something or organize a LessWrong RPG grou... (read more)

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0dogiv
Are you talking about a local game in NY or a correspondence thing?
0Screwtape
I am not in New York actually! (I took a bus in to the solstice from out of state.) My first choice would be to play over some form of VoIP like Discord, leaning on Roll20 if imagery or dicerollers were a problem. I'm on Eastern Standard Time and work a nine to five, but have a fairly flexible schedule other than that. My second choice would be a play-by-post arrangement, which are easier to schedule but take longer to build up a sense of camaraderie. I think Chesscourt is the only rationalist forum I've heard of? ("Forum" here meaning "built for indefinite replies to a single thread" which may or may not be the technical definition of that word.) That said, I could pretty easily do both: a three hour Discord session with one group, and a forum thread on a reply-a-week basis elsewhere. That said, if there are three to five rationalists hanging out in the rural parts of VT who want to hang out in meatspace, you all should let me know =D
[-]turchin20

How many teams are working on AGI in the world now? Do we have a list? (I asked already on facebook, but maybe I could get more input here.) https://www.facebook.com/groups/aisafety/permalink/849566641874118/

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0whpearson
I would say not many at all! They might be working on something they call AGI but I think we need a change in view point before we can start making progress towards the important general aspect of it. I think the closest people are the transfer learning people. They are at least trying something different. I think we need to solve the resource allocation problem first, then we can layer ML/language inside it. Nothing is truly general, general intelligences can devote resources to solving different problems at different time, and get knowledge of solving problems from other general intelligences.
0turchin
Sometimes I think that there are fewer people who explicitly works on universal AGI than people who works on AI safety.
0whpearson
I've got an article brewing on the incentives for people not to work on AGI. Company incentives: 1. They are making plenty of money with normal AI/dumb computers no need to go fancy. 2. It is hard to monetise in the way companies are used to. No need of an upgrade cycle, the system maintains and upgrades itself. No expensive training required either, it trains itself to understand the users. Sell a person an AGI never sell them software again vs SaaS. 3. For internal software companies optimise for simple software that they people can understand and get many people to maintain. There is a high activation energy required to go from simple software that people maintain to a complex system that can maintain itself. 4. Legal minefield. Who has responsibility for an AGIs actions? The company or the user? This is solved if it can be sold as intelligence augmentation and is sold in a very raw state with little knowledge and is trained/given more responsibility by the user. Programmer incentives: 1. Programmers don't want to program themselves out of a job. 2. Programmers also optimize for simple things that they can maintain/understand. I'm guessing if ever it stops being easy to make money as a software company, then the other incentives might get overridden.
0turchin
The only real reason to make AGI is if you want to take over the world (or solve other big problems). And if you want, you will not put on your web page - if you are serious. So we will almost never see credible claims on work on AGI, and especially on self-improving superintelligence. Exception: Schmidhuber
4username2
Exception: Goertzel and just about every founder of the AI field who work on AI mainly as a way of understanding thought and building things like us.
0Thomas
Almost every flying machine innovator was quite public about his goal. And there were a lot of them. Still, a dark horse won. Here, the situation is quite similar, except that a dark horse victory is not very likely. If Google is unable to improve its Deep/Alpha product line to an effective AGI machine in a less than 10 years, they are either utterly incompetent (which they aren't) or this NN paradigm isn't strong enough. Which sounds unlikely, too. Others have less than 10 years wide opportunity window. I am not too excited about the amount of CPU/RAM requirements for this NN/ML style of racing. But it might be just good enough.
0whpearson
I think NN is strong enough for ML I just think that ML is the wrong paradigm. It is at best a partial answer, it does not capture a class of things that humans do that I think is important. Mathematically ML is trying to find a function from input to output. There are things we do that do not fall into that in our language processing. A couple of examples. 1. Attentional phrases: "This is important, pay attention," this means that you should devote more mental energy to processing/learning whatever is happening around you. To learn to process this kind of phrase, you would have to be able to create a map of input to some form of attention control. This form of attention control has not been practised in ML, it is assumed that if data is being presented to the algorithm it is important data. 2. Language about language: "The word for word in French is mot", this changes not only the internal state. But also the mapping of input to internal state (and mapping of input to the mapping of input to internal state). Processing it and other phrases would allow you to process the phrase "le mot à mot en allemand est wort". It is akin to learning to compiling down a new compiler. You could maybe approximate both these tasks with a crazy hotchpotch of ML systems. But I think that that way is a blind alley. Learning both of these abilities will have some ML involved. However Language is weird and we have not scratched the surface of how it interacts with learning. I'd put some money on AGI being pretty different to current ML.
0Thomas
Me too. It's possible to go the NN/ML (a lot of acronyms and no good name) way, and I don't think it's a blind alley, but it's a long way. Not the most efficient use of the computing resources, by far. And yes, there are important problems, where the NN approach is particularly clumsy. Just give those NN guys a shot. The reality will decide.
0Thomas
I would say about 1000. 950 of them have no chance at all. But at least 20 of those which tirelessly exercising cnn or ML or some other neural network thing, have some chances to success. And about 20 other teams may be out there, which have some other, also decent ideas. I am just speculating, but this looks plausible to me.
0turchin
I have approximately the same priors: 10 large companies, which get the most probability of creating something, and 50 percent it will be Google. 100 university professors and startups. If they create something meaningful, they will be acquired by Google 1000 freaks.
2ChristianKl
10 large companies seem to be an understatement. From my head: 1. Baidu 2. Alibaba 3. Salesforce 4. Facebook 5. Amazon 6. Palantir 7. IBM 8. Google 9. Apple 10. Samsung 11. Microsoft 12. Bridgewater Associates 13. Infosys 14. The Chinese Government 15. Toyota 16. Tencent Holding 17. Oracle
2Kaj_Sotala
Are you saying that all of those are working on AGI? That would be enormously surprising to me.
2ChristianKl
Currently, there's competition about how has the best cloud between Google, IBM, Amazon, Oracle and Microsoft. It seems that those companies believe that a successful cloud platform is one that has API's that can easily used for a wide variety of use cases. I think this kind of AI research is equivalent with AGI research. Facebooks internal AI research is broad enough that they pursued Go as a toy problem similar to how Deep Mind did so. After DeepMind's success, Tencent Holding didn't take long to debut an engine that's on par with professional players even through it isn't yet on the AlphaGo level. Apple has money lying around. It's knows that Siri underperforms at the moment, so it makes total sense to invest money into long-term AI/AGI research. Strategically Apple doesn't want to be in a situation where Google's DeepMind/Google Brain initiatives continue to put it's assistant well ahead of Apple's performance. Samsung wants Bixby to be a success and not be outperformed by competing assistants. Samsung also needs AI in a variety of other fields for military tech to internet of things applications. Bridgewater Associates is working on it's AI/human hybrid to replace Ray Dalio. Using humans as subroutines might mean that the result get's dangerous much faster. Palantir wants the money of the US military for doing various analysis tasks. Given that it's a broad spectrum of tasks it pays to have quite AI general capabilities. The US military wants to buy AI. While the CIA is now in the Amazon cloud, Palantir wants to stay competitive and don't lose projects to Amazon and that requires it do to basic research. Salesforce has the money and it will need to do a lot of AI to keep up with the times. I think Baidu and Alibaba will face similar pressures as Google and Amazon. I think both need to invest into basic AI and the have the capability to do so. Given the possible consequences of AGI for geopolitical power, I think it's very likely that the Chinese Govern
4Kaj_Sotala
Okay, you have a much broader definition of what's AGI research, then. I usually interpret the term to only mean research that has making AGI as an explicit objective, especially since most researchers would (IME) disagree with "API's that can easily used for a wide variety of use cases" being equivalent to AGI research.
0turchin
Thanks for the update. Some of the names are surprising for me, but I will check.
2cousin_it
Each cube contains a rational point, so there's at most a countable number of cubes. Or am I missing something?
0Thomas
You are not missing anything. It is true, that every cube contains a rational point, but most squares (or circles) have no rational point. Hence only aleph-zero many cubes. OTOH, you can divide any cube further to the infinite number of disjunct cubes. Infinitely many times. Now, if you can organize these divisions in such a way, that those infinities build up to more than aleph-zero cubes, the ZF is down. I don't say it's possible, it just looks like slightly probable, due to the infinite divisibility of cubes. Which can be misleading, but maybe not.
0cousin_it
I'm sorry, didn't you say that the cubes must have no common volume?
0Thomas
I said so, yes. But you can replace a cube with its smaller parts. Infinitely many cubes instead of just one.
0cousin_it
I thought you wanted a set of cubes whose volumes don't intersect with each other. (Then this set can't be uncountable because each volume contains a rational point.) I don't understand what you mean by replacing cubes... Can you explain the problem once again?
0Thomas
Assumed, that the ZF is consistent, you are right, of course. The fact, that there are rational points inside every cube, and that those cubes have no common volume, only common surfaces (lines, points) perhaps - is enough to state that there are at most aleph-zero of them. But, if the ZF is not consistent, there may be a way to encode every real number between 0 and 1 with some peculiar cubic subdivision of 3D space. You can easily encode every real between 0 and 1 via dividing (even a finite volume of) 3D space into disjunct 2D circles. Perhaps, just perhaps, it is possible to replace those circles with cubes and spheres, given the infinite volume you have. Perhaps, just perhaps, the ZF is broken.
5cousin_it
People have attacked the consistency of ZF with much more powerful tools and failed. Your attack wouldn't sound promising to these people, because it already sounds unpromising to me. Each further minute of your time spent on this problem would be a failure of rationality. If you want another problem that's really fun, prove or disprove that every division of the square into triangles of equal area will have an even number of triangles :-)
0Thomas
https://en.wikipedia.org/wiki/Monsky%27s_theorem
0gjm
Strongly agree. This problem [EDITED to add: I mean Thomas's, not cousin_it's] sounds about as much worth working on as one that says: "Can you find positive integers x,y,z such that x^3+y^3=z^3? If so, ZF is broken!" No, you can't; the proof isn't all that difficult (though harder than the one for Thomas's cube-division question); the fact that the answer is no unless ZF is broken is just another way of saying "the answer can be proved to be no". I am not much interested in searching for solutions to problems that have been proved to have no solutions.
0Thomas
Well, it hasn't been proved, that this problem has no solution. If you ask me, at least since the invention of the Yablo's paradox, the ZF is mortally wounded. But that's just me and some others. Or better, some others and me. I am only probing around, if there is a way to reformulate this paradox in some different contexts.
0MrMind
Well, there's nothing revolutionary about that. If you don't like ZF, then make up your own set of rules. I can show you how to create a different set theory in every topos. ZF is not some authority that says what is true and what is not. It's simply a model that people have found very useful in the foundation of mathematics, which has then blossomed into a discipline of its own.
0cousin_it
Yablo's paradox does not lead to any problem in ZF and there's no reason to expect any version of it would. The situation you're in now is as pure a test of LW rationality as you'll ever come across. Saving people from mistakes like yours, which defend themselves by feeding on your wishes, is pretty much why LW exists. Read the crackpot offer post. All the tools you need are right here.
0Thomas
Everybody want to save other people from the mistakes they (other people) do. Sometimes, that's a mistake.
0cousin_it
Sometimes you win the lottery too, but that doesn't mean buying lottery tickets is a good idea. You must evaluate your chance, not just say there's a chance. For this problem you have both inside view (comments from people who know math) and outside view (examples of math cranks) saying your chance is very low. For what it's worth, I'm treating this conversation as a test. How much chance does rationality have against a strong desire, in a situation that's 100% in favor of rationality, and is there any way for it to avoid losing.
0Thomas
What makes you think, that the next Monday I will still remember this problem? I will come with another crackpottery, or even some problem you are going to solve, as it has happened already. And I also don't see the necessity to actually find a crack in the ZF or to immediately find a solution for a problem posted? The problem you have presented a few days ago, it was several years before its solution. I've Googled it. Most problems posted worldwide are too trivial to even bother. Some are interesting to play with. Some are just too tough. What's your problem?
0cousin_it
There's a well known puzzle called duck and fox. A duck starts at the center of a circular pond and can swim with speed 1. On the shore there's a fox who can run with speed 4. Can the duck reach the shore without getting caught by the fox? As it is, the puzzle is pretty easy. But if you generalize it to multiple foxes that can use coordinated strategies (say, with speeds 2 and 3) it becomes much harder. If anyone can find a necessary and sufficient condition on fox speeds that allow the duck to escape, even for just two foxes, that'd be really cool.
0Thomas
It's another puzzle of a toreador chased by the bull in a circular arena. Both have the same speed. Is there a way for the toreador to always stay in front of the bull? Spoiler: Yes, it is.
0cousin_it
I don't think it's equivalent. The duck can move freely inside the circle, while the fox can only stay on the circumference. Anyway, try to solve the 2 and 3 case.
0Thomas
I didn't say it's equivalent, just another puzzle. Took years before the solution came, decades ago. But I don't see much sense into digging for old solved or unsolved problems. Invent one!
2cousin_it
Here's one I invented recently. Imagine a rating system for movies where Bob the reviewer watches a movie and declares "this is in the top three movies I will see this year". Then he watches another movie and says "this is in the top two movies I will see this year". Then he watches another movie and says "this is in the top two movies I will see this year". Then he watches another movie and says "this is in the top three movies I will see this year". But with this last statement his credibility is gone, because he's claimed that four movies will be in the top three or better. Thus we will say that the "longest credible prefix" of the list [3,2,2,3] is [3,2,2]. The puzzle is to write an algorithm that accepts a list of integers and returns the length of its longest credible prefix, whose asymptotic complexity is as good as possible. (I have found an answer that's extremely fast, but no proof that it's fastest.)
0Oscar_Cunningham
I can do time O(n^2), where n is the length of the list. Perhaps the "extremely fast" algorithm you have is O(n log n)? Surely O(n) must be impossible.
0cousin_it
O(n log n) would be nice, but you can do even better :-)
0Oscar_Cunningham
Just to check we are formalizing in the same way, do you agree that O(n) is a lower bound? Because the list [1,2,...,n] has longest credible prefix of length n, but if we reduce any of the first n-1 elements by 1 then the length of the longest credible prefix is reduced. So we at least have to spend O(n) time looking at the first n-1 elements.
0cousin_it
Yes, O(n) is a lower bound.
0Thomas
He can't say that. He doesn't even know how many movies he is going to see. If he knows, that he is going to watch another N movies this year, he can only say "this is in the top N+1 movies I will see this year". If that was the best movie so far.
3cousin_it
The problem statement should be taken on face value, not argued with. But if you're interested in the motivation, I was trying to design a review system that wouldn't suffer from score inflation and payola ("every decent movie is 4 stars out of 5"). The problem you see is in fact the whole point. If you don't feel confident enough that a movie will be in your top 3, say that it will be in your top 10. Your lack of confidence is an important signal of your true beliefs about the movie and viewers deserve to know it :-)
0Thomas
I'll pass. Maybe somebody else will solve this problem of yours. Too vague for me.
0gjm
Of course it's been proved that the problem has no solution. cousin_it already sketched a proof.
0Thomas
You mean, you can't divide 3D space into cubes, such that they have no common volume, and that there would be more than aleph-zero cubes? Yes, his proof is well based on the fact that every cube has to contain a rational point not shared with other cubes. Because there are only aleph-zero such rational points in an infinite 3D space, there may be at the most aleph-zero such cubes. That's fine. But what if, God forbid it, it's also possible to code every real number with a cubic subdivision of that space? Then we've proved A (as cousin_it has done) and proved NOT A. We can't have it. Just as we can't have a true and the same time false sentences in Yablo's paradox.
0gjm
"You mean, you can't find three positive integers, cube them, and have the sum of two equal to the third? Yes, the proof is well based on the method of infinite descent. That's fine. But what if, God forbid it, it's also possible to find three positive integers with that property? Then we've proved A and proved NOT A. Just as in Yablo's paradox." Yablo's paradox gives no more reason to expect blatant contradictions in cousin_it's cardinality argument than in Fermat's infinite descent proof. What you're saying is, in effect: Because of Yablo's paradox, we can't trust that mathematical reasoning is consistent, and if something has been proved impossible then we should see that as an opportunity to find contradictions in mathematics. Well, if that's how you want to proceed, good luck to you. But I'll be betting the other way. (Just for the avoidance of doubt: 1. Yablo's paradox is not a contradiction in ZF. 2. There is nothing ZF-specific about the cardinality argument cousin_it gives, which I'm pretty sure goes through just fine in, say, NFU. 3. There is also nothing ZF-specific about Yablo's paradox.)
0Thomas
You and cousin_it want to assure me, that there is nothing to see here, therefore nobody should even bother to look. Fine, don't. How important is that problem for me? Not very. Like 100 chess games.
0gjm
As I said: if you want to look there, go ahead. I just think you're going to fail, and the reason I think you're going to fail is that there is a proof that you'll fail. You protest that this problem is not important for you, and I think I remember you saying something similar the last time you brought up your opinion that ZF, or the very notion of infinity, or whatever it was, is likely inconsistent. For something not important to you, you seem to want to discuss it a lot.
0Thomas
For the record. I don't want to look there more than quite briefly. So don't be so worried for me. If I will ever want to climb these hills, it will be on the motorbike, so to speak. Math problems are a perfect toy for my real interests. Not by itself my highest interest. Having said that, yes, I believe that the ZF is broken, yes. But it's not more important than the fact that the rules of chess are broken. In fact, this last observation, is much more shocking and worrying. One may easily expect, that those simple rules of chess are rock solid, but they aren't. And one may easily expect, that something as rich as all the mathematics coming out of the ZF can easily have issues. But the chess? As the vertical castling, wasn't bad enough! Probably it's "nothing to see here" for you also at this chess thing. I beg to differ.
0gjm
The current official rules of chess -- which I think are here -- are perfectly clear that an en passant capture is a thing the opponent does on the next move and doesn't mean that the pawn "never reached" the square it was moved to. They are also perfectly clear that castling occurs only on a player's first rank. (And, just to add one you didn't mention, that a pawn can promote only to a piece of the same colour.) At some times in the past, the rules of chess have been drafted carelessly enough to have consequences that were clearly not intended by their drafters nor expected by ordinary chess players. Perhaps they are now, though I don't know of any such consequences of the present rules. The "holes" in the laws of chess -- at least, those found so far -- have generally been extremely simple, and not many people have actively explored the exact consequences of the rules. If there were errors in, say, the axioms of ZF set theory that are as simple as the ones there have been in the rules of chess, they would surely have been caught by now. (Consider e.g. Frege's system, a hole in which was found by Russell before he'd even finished publishing it; or the original version of Quine's ML, a hole in which was found by two people independently within a couple of years of publication. ZF has been looked at a lot more than either of those, for longer.) I'm not claiming to know that ZF is consistent. I don't know that ZF is consistent. No one does. But if it is inconsistent, I would be flabbergasted if its inconsistency were found by the sort of thing you're proposing here, where you find a really easy proof that something is impossible and suggest looking for counterexamples.
0Thomas
According to the rules of chess you have linked, it is perfectly clear to you, who wins in the game I have linked. Black or white? It is not perfectly clear to me. It's kind of "ill defined".
2entirelyuseless
Black wins because White's last move is not a legal move, since it doesn't get White out of check. As gjm said, there is nothing vague about this.
1gjm
In the position you've linked, it goes like this. White plays Bg2+. He calls it checkmate but of course it isn't. Black plays d5#. This is checkmate. The fact that white can (or could, if it got him out of check) capture the pawn on d5 en passant doesn't meant it never really got to d5; the rules are perfectly clear that a White capture en passant is a thing that happens (if it does) on White's following move. The etymology of the term is neither here nor there. White cannot, in fact, now play cxd6 e.p. because that move doesn't get him out of check. And despite White's fanciful interpretation of how the game rules, an e.p. capture does not, in fact, have any sort of retroactive effect. Of course Black's pawn got to d5; it is already there.
0Thomas
This is true, as long as white has no pawn intersecting power. Which today is a defacto standard. And "en passant" isn't "en passant", but "as if en passant, but only after the taken pawn has occupied some other field than the one his slayer occupies know". This should be make clear, or things are vague, ill-defined.
1gjm
I think you are complaining that the official rules of chess merely define the rules of chess, and don't also take care to offer explicit contradictions for every confused notion someone reading them impressionistically might arrive at. There is nothing in those rules to imply or even suggest that either player has "pawn intersecting power", if by that cryptic phrase (perhaps you mean "intercepting" but the meaning is still obscure) you mean some sort of retroactive interference with a previous move. It's true that the rules also don't explicitly deny that -- in the same way as they don't explicitly deny (say) that if you push the same pawn three times in a row then you get to remove one of your opponent's pieces. They don't need to, because neither is something a reasonable person would expect on reading the rules. "En passant" is merely a technical term. It is not necessary for the rules to say explicitly "even though the term comes from the French for 'in passing', the pawn completes its move and is then removed only by the capture next move" because that is obvious from the actual rules as stated. Just as it is not necessary for them to say explicitly "even though the term 'checkmate' comes from words meaning 'king dead', checkmate is achieved as soon as the king is in check and has no way to escape; actually capturing the king is not required". Or "even though the players are called white and black, it is not necessary for the actual players to be white and black respectively". Or "even though the knight in some sense represents a man on a horse, a knight's move can pass over intervening pieces representing things that would be too high for a real horse to jump over". There is nothing ill-defined here (at least, not so far as the example you've given tells us; there might be errors or omissions I haven't noticed).
0Thomas
Yes, you are right. Otherwise we don't agree at all about this. But there is a way to decide who is right here. By reviewing some chess engine code, how this instance is handled. There, rules of the chess are explicitly written down. It would be interesting to see how this is handled and what are the rules.
0gjm
I would be happy to bet my $100 against your $10 that none of the 10 most widely used chess engines takes a different view of this situation from the one I describe. ... Well, actually I wouldn't, because the nuisance of agreeing details and testing chess engines and so on greatly outweighs the value to me of $10, but in principle I would. I don't really see that this would "decide who is right", though; if people had been writing chess engines back when the rules failed to stipulate that castling has to be horizontal or that promotions have to be to pieces of your own colour, I bet they would mostly have implemented those features in the "expected" way. If there are subtle omissions in the present-day rules, they probably aren't reflected in actual chess engine code.
0Thomas
I think, chess engines probably do it right. The question is, how their rules of engagement looks like. Especially, what is the mechanism dealing with the en passant? Is it plain like in the FIDE's rules? I don't think so. They are different. You see, pure mathematics is like a program in Python written on a sheet of paper. You actually don't know, if it would run or not. The same goes for the game rules. Humans do out-negotiate from most situation if not all, but that doesn't mean that the rules of the game (in this case chess) are without a problem.
0gjm
I'm not sure I understand your question about "their rules of engagement". But I took a look at one chess engine's source. This is Robert Hyatt's "Crafty", which at one time was one of the leading engines (others have overtaken it now). Many things are represented as 64-bit bitmaps. Here, accordingly, is its special code for e.p. captures. First, in a function called GenerateCaptures there is a line that says this: target = Occupied(enemy) | EnPassantTarget(ply); Everything from "|" inclusive to ";" exclusive would be omitted if there were no e.p. captures. Second, there is some special-cased code for generating moves when in check (since of course you then only need to consider moves that might get you out of check). Here's the relevant code: targetc = Occupied(enemy) | EnPassantTarget(ply); targetc = targetc & target; if (Pawns(enemy) & target & ((side) ? EnPassantTarget(ply) >> 8 : EnPassantTarget(ply) << 8)) targetc = targetc | EnPassantTarget(ply); Without e.p. captures this would be simplified in fairly obvious ways. Third, as well as generating moves there is some code for validating moves (I haven't looked at how it's used, but I guess it's just for verifying that an opponent's move is legal; I'm not sure why it isn't good enough to generate all legal moves and see if the given move is among them, since it's hard to see how efficiency would matter for this). Here's the relevant bit: if ((PcOnSq(To(move)) == 0) && (PcOnSq(To(move) + epdir[wtm]) == ((wtm) ? -pawn : pawn)) && (EnPassantTarget(ply) & SetMask(To(move)))) return 1; Finally, of course that thing EnPassantTarget needs to be defined. Its definition is simple: #define EnPassantTarget(ply) (EnPassant(ply) ? SetMask(EnPassant(ply)) : 0) This is basically a wrapper around this: #define EnPassant(ply) (tree->status[play].enpassant_target) and this thing needs initializing, setting when a pawn advances two squares, incorporating (since e.p. status is a sometime
0Thomas
We have 3 somewhat separated questions here. The first is this about chess. How the rules of chess are defined for chess engines, are they really just a copy of what the official FIDE rules are, and how this is going to play out for some crucial positions. I argue, that the human rules are a bit vogue and that some engines are very likely well designed, but their rules are a bit different. At least more complete. The second is about mathematics, how likely everything is consistent there. Very unlikely, if you ask me. But almost certainly very likely all is okay, if I ask you. Even if there are paradoxes, they are so very well hidden, that no surface scanning is going to find one. The ZF has been scrutinized quite deeply and all is okay. That's your view if I understand you correctly. The third is about math and software. You are saying, that a lot of mathematics is constantly used by a lot of programs and that program bugs are somewhat a problem, but that there is almost certainly no math bugs. Here we disagree again. I think there might be some unseen math bugs, too. Probably not in finite simple mathematics, but maybe even there. But quite possibly when things get really complicated. Perhaps I will not refer to another problem involving infinities here. Just to avoid some unnecessary disputes.
0Oscar_Cunningham
Why is this particular puzzle relevant to ZF? If we had provided contradictory solutions to any of your previous puzzles then that would also doom ZF, no?
0Thomas
It just MIGHT be relevant to the ZF. Writing down every real from the interval (0,1) onto the Euclidian plane using some (arbitrarily resizable) Lucida console or whatever font, (in an abstract way, of course), would be enough to have the consistency crisis in the ZF. You can do this in a finite volume amount of 3D space, using flat 2D font. But that's okay, regarding ZF, because most numbers written this way, covers no rational point when in 3D space. You don't need to actually write them down in a font, you can instead represent every real from the interval (0,1) with just some small circle or square, or with whatever shape with an area, and they also should not overlap. And with all that, the ZF is done. But you don't need to use every real from (0,1), just say aleph-middle of them. What is aleph-middle? It's some Cohen's cardinality between aleph-zero and aleph-one, you can always postulate. This MIGHT be feasible. If it is, it's enough. I don't know, if it's feasible, let alone how exactly. Then, you don't even need finite area shapes, you need shapes with at least one rational point. Then, those shapes MAY overlap. Just not in that rational point, but everywhere else. I wouldn't be too much surprised, if someone comes with such a construction. With all the necessary rigor, of course. Yes, but I don't find those likely to have two opposite simple solutions. At least not less than extremely complicated. Which is practically useless. We could never have agreed about something that complicated.
0gjm
I think all this means is that you find this proof less obvious than some other proofs. That's fair enough, but finding something difficult to grasp doesn't mean it's likely to be wrong. The way it looks to me: no, it's not feasible, it's plainly not feasible, for exactly the reason cousin_it gives; you might as well be asking for three positive integers with x^3+y^3=z^3. (Actually, even more so; I find the cardinality argument here clear at a glance, but Euler's infinite-descent argument intricate and requiring sustained concentration. But, again, the fact that I can't just look at it and immediately see why there are no solutions in no way calls into question the proof that there are no solutions.)
0entirelyuseless
Yablo's paradox cannot be formulated in ZF because it uses the idea of truth. If you reformulate it so that every sentence says that the rest of the sentences can be disproven, all of the sentences will be false, but there will be no proof in ZF of this for any of them. This simply shows that ZF is not (and cannot be) complete, not that there is anything wrong with it.
0Thomas
It is not necessary that the YP is "formulated in ZF". It's enough that ZF yields some byproduct, like countably infinite sets, which are used to make (in this case a semantic) paradox. Then something must be wrong either with ZF, either with the semantics which allows YP formulation. Possibly with both, but at least with one of them. If the list of Yablo's sentences is a finite one, then the last statement of the list is just true. And all those before the last are false and no paradox there. This doesn't mean, that something is necessary wrong with ZF, only likely. There might be a problem solely with the semantics which permits Yablo's sequence. Still possible. But the YP formulation is a very elementary one. There might be others, equally elementary. I didn't say they are, but that they might be. The "infinite geometry" looks suspicious to me.
0entirelyuseless
Once again, as others have already told you, Yablo's paradox cannot generate any sort of paradox whatsoever in ZF.
0Thomas
I told the others, that the countably infinite sets MIGHT be infected, since a finite list of Yablo sentences DOESN'T yield a paradox. While a countably infinite list of Yablo sentences - DOES yield the mentioned paradox. AFAIK, the infinities come out of ZF. Don't they?
0entirelyuseless
There are countably infinite lists in ZF. That doesn't make the general fact that in some situations you can produce a paradox with a countably infinite list, a reason to think you can do that in ZF. You might as well argue, "We can produce paradoxes in natural language. So maybe we can do it in mathematics too." And maybe you could have made that argument, before people tried it. As others have pointed out, many people have looked for contradictions in ZF for a very long time, and none have been found. There is no reason to think there are any.
1MrMind
This is the 3D version of the countable antichain condition (commonly known as c.c.c.). c.c.c. is implied by a property called separability, which is part of the definition of the real line (the unique linear complete separable order). So you can fit aleph1 "cubes" only if you operate in a modified notion of space which is not c.c.c. On the other hand, the real line contains aleph1 points only in some model of set theory. The precise quantity is 2^aleph0.
0Thomas
It's just a magnificent toy, this ZF construction. And those others set theories as well. No wonder some people here don't want it to be broken. With passion, may I add? Let us take the aleph-zero dimensional R. Countably infinite dimensional Euclidean space, in other words. Then take a point T and all those points which are finitely far away from this point T. By the standard metrics of sqrt(dx1^2+dx2^2+...). This space is separable into continuum many such subspaces. Where in every such subspace every two points are close. Close means only a finite distance. And every two spaces are far from each other. Where far means an infinite distance between any two points from two different subspaces. You probably are familiar with this also.
0MrMind
Well, whomever is going to show ZF to be contraddictory is sure to receive great glory in the mathematical community, and is going to be probably considered the next Godel. If only ZF wasn't already been shown coherent with the notion of an inaccessible cardinal. Which has shown to be coherent with the notion of a measurable cardinal. Which has shown to be coherent with the notion of a compact cardinal... and so on. ZF's coherence is a hairy, hairy subject. Well, you cannot do that: the euclidean norm is not defined for an infinite-dimensional space. I have no idea what this paragraph means. Yes, I can divide a many dimensional space into continuum continuums, that's a basic property of cardinal arithmetics. And in each subspace two points can be as closed as you what. But the rest of the paragraph I cannot parse. Besides, what is the point of all this? What is it that you're trying to show?
0Thomas
Why not? It is the square root of the sum of (dxi)^2, where i goes through all dimensions. Sometimes it is a finite value. Otherwise the distance is infinite. The points T0(0,0,0,0....) and T1(0,1/sqrt(2),1/sqrt(4),1/sqrt(8)...) are 1 apart.
0Good_Burning_Plastic
A metric is supposed to be always finite. Note the round right bracket in https://en.wikipedia.org/wiki/Metric_(mathematics)#Definition.
0arundelo
Fixed link.
0Thomas
This is probably not the intended link.
0[anonymous]
Lbh pna'g unir nyrcu-bar phorf orpnhfr rnpu phor zhfg pbagnva ng yrnfg bar cbvag jubfr nyy guerr pbbeqvangrf ner engvbany, naq gurer bayl ner nyrcu-mreb fhpu cbvagf.
0Gurkenglas
Given aleph-one cubes with no common volume in 3D space, replacing each cube with the largest sphere that fits in it will give you aleph-one spheres with no common volume in 3D space.
0Thomas
Unfortunately we don't know how to fill aleph-one cubes into 3D space in a way, that they don't overlap with 3D intersections. We can easily do so with aleph-zero cubes, but have no known way to do it with aleph-one cubes. Others are telling me, not to even try, because it's surely impossible and I will suffer some great misfortune, if I try. I am not sure, if it's really impossible.You can surely fil N dimensional hyperspace with aleph-one N-1 dimensional hypercubes. That IS possible. Now, what if we have countably infinite amount of space dimensions. How many (rational) points are there? And how many countably infinite dimensional hypercubes we can squizz there? I don't know, but it's possible to calculate and to see how the ZF would handle that.
0Gurkenglas
The first sentence of your post on protokol2020 is "There are at most aleph-zero disjunct 3D spheres in 3D space.", so I gave a way to make aleph-one spheres from aleph-one cubes, in order to disprove the possibility of aleph-one cubes. Aleph-zero-dimensional space has aleph-one rationals. Note that the union of all finite-dimensional spaces (each embedded in the next as a slice) has aleph-zero rationals. Science demands that you notice an anvil dropped on your head, and my heuristics are also saying you're turning into a math crank. Then again, if in all spacetime there's one Jesus and a million madmen believing they're Jesus, would we rather that they all believe themselves madmen?
0gjm
No one is telling Thomas that he will suffer any great misfortune if he tries, beyond the misfortune of almost certainly wasting his time. Thomas, you made a similar claim earlier and I explicitly rejected it and reiterated that if you choose to go looking for mathematical contradictions I wish you well. Why are you telling untruths about other people? I think that's rude. Continuum-many, because e.g. any sequence of 0s and 1s corresponds to an integer (hence rational) point in aleph0-dimensional space. And you can put a side-1/2 cube around each of them to get continuum-many disjoint hypercubes in that space. The cardinality of the space itself is continuum^aleph0 = continuum, so in this case you have as many disjoint hypercubes as points. (None of this is difficult, controversial, contradictory, or indicative of any sort of inconsistency.)
0Thomas
Let us stick to the essentials here. Aleph-zero dimensions give you aleph-one (=continuum) rational points. And also aleph-one hypercubes. Since those two numbers are equal, this is not a way to reproduce a paradox in such a space. Fine, no problem, just another rock with no snake under it. In other words, the ZF has survived another test, as it has survived one billion or so tests before. As long as you believe, the Yablo's paradox has nothing to do with the ZF, that it is completely isolated from the ZF, then we have no case against ZF, whatsoever. Well, I don't, you guys do believe that the semantics Yablo used, cannot be used against the ZF. I think that this is a correct and honest description of our disagreement.
[-]satt00

I've thought a bit about writing a summary/review of Christopher Achen & Larry Bartels's recent book Democracy for Realists: Why Elections Do Not Produce Responsive Government for LW, since I expect it'd interest quite a few people here. But I'm fairly sure I won't bother now; a week ago a decent summary appeared on the blog of a couple of FRI researchers.

Also relevant:

... (read more)
Reply
[-]ChristianKl00

How will internet satellites affect China? Currently SpaceX and other want to launch satellites to make satellite internet access radically cheaper.

If the Chinese buy their internet access from SpaceX instead of Chinese internet providers, the might have more trouble with blocking websites.

Are there mechanisms that will allow China to keep the ability to censor with their firewall in that scenario?

Reply
0Lumifer
Forbid the Chinese to "buy their internet access from SpaceX instead of Chinese internet providers".
0ChristianKl
In related news, it seems China just (in 2017) made the move to outlaw VPN's https://www.engadget.com/2017/01/23/china-vpn-illegal-internet-censorship-government-approval/
[-]ChristianKl00

Does the PLOS study https://mjambon.github.io/vim-vs-emacs/ argue convincingly that emacs is better than Vim?

How do we reason rationally about whether on of the editors is better?

Reply
5Lumifer
By rigorously defining "better".
[-]cousin_it00

I've been thinking about the unexpected hanging paradox again.

Until today, I always thought the right solution was given by Fitch in "A Goedelized Formulation of the Prediction Paradox". Let's define a sentence in Peano arithmetic called Surprise, which will refer to five other sentences Mon, Tue, Wed, Thu, Fri. Surprise will be defined recursively using the diagonal lemma, as a conjunction of these sentences:

1) Exactly one of Mon, Tue, Wed, Thu, Fri is true.

2) If Mon is true then "Surprise implies Mon" isn't provable.

3) If Tue is true... (read more)

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1Manfred
Do you intend "'Surprise implies Mon' is false" to mean "Not (Surprise and Mon)"? I'm just a little confused because I think in classical logic, if Surprise is false then all the implication statements are true. Therefore if at least one of Mon-Fri is true, Surprise cannot be false. Maybe I should have read the paper you reference. Personally, I think the original presentation is already sufficient. If the judge really refuses to hang the prisoner if they're not surprised, and the judge is in some sense transparent to the prisoner, so that the prisoner knows what logic they will follow, then the judge will not hang the prisoner. The paradox is in the punchline that if the judge then hangs the prisoner on wednesday, the prisoner is surprised. But this is simply because it's a counterfactual that won't happen, given the toy model of how the judge works. If the prisoner merely has a bad model of the judge and therefore makes wrong predictions, this isn't much of a paradox, though still a decent joke. I think this problem is clearer if we imagine a game where the judge outputs a probability distribution over which day the prisoner will be executed, and the prisoner is postulated to be clever enough to figure out what probability distribution the judge will output. In this scenario, it is very easy for the judge to surprise the prisoner most of the time - a uniform distribution will suffice. If the judge's goal is to minimize the expected information the prisoner has about whether they'll die, on the day of the execution, then maybe you get some slightly more complicated probability distribution. But within this game, it is impossible for the judge to output a probability distribution such that the prisoner is always surprised, never unsurprised. Every probability distribution supported on Mon-Fri has a final day, on which the prisoner is not surprised. So if the judge says they're going to output a probability distribution such that the prisoner will definitely be
0Thomas
It's a finite probability (greater than zero) for Monday, that it's a hanging day. So, the hangman will not be unexpected on Monday. It's a finite probability (greater than zero) for Tuesday, that it's a hanging day. So, the hangman will not be unexpected on Tuesday. .... It's a high probability for Friday, that it's a hanging day. So, the hangman will not be unexpected on Friday. The "unexpected day" was a judge's small lie. Much like when the judge says "you will be hanged alive until you die next week twice". He is just joking. No real paradox here.
0entirelyuseless
That is my position, although I consider it being reasonable rather than stubbornly insisting that nothing can be deep and mysterious.
0[anonymous]
I think liar type paradoxes are exactly as mysterious as this Python function: def f(): return not f() If your intuition is like a Turing complete language, you can't insist that all functions must terminate.
1Lumifer
This function just never returns. That's not what the Liar's Paradox is about.
[-]Gunslinger00

How do you move from a superficial relationship (I see you at work) to a more meaningful relationship? (friends)?

Reply
3[anonymous]
Concrete suggestions: * 1) Making plans to meet outside of work. (e.g. getting lunch, going to an outing in the city, hiking, meeting up for an outside project, etc.) * 2) Continuing casual conversation offline / digitally. (e.g. chatting on Facebook.) * 3) Opening up, talking about more personal things (e.g. mentioning you had a bad day, slight window into how you're feeling, let the other person reciprocate)
2Elo
"logistics" make plans, invite people along, exchange details.
0Gunslinger
What do you mean by "logistics"?
0Elo
You asked a "how" question. I assume you are saying, "I am looking to cause relationships to be meaningful, how do I go about doing that?". I suggest, if you organise yourself such that you meet with people outside of work it will be a step in the right direction. If you meant to ask something other than a "how" question you are going to have to be more specific otherwise:
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