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A first lesson in meta-rationality

metarationality.com

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Re: A first lesson in meta-rationality

#81

Post by mckirk »

rrmm wrote: post #26
mckirk wrote: post #12

Am I the only one that gets driven kind of crazy by these kinds of problems? I'm not completely sure so far what it is, but I'm guessing it's the frustration of having to find a needle in a haystack of essentially infinite size, as depending on how complicated you want to see the problem, there's an infinitude of potential 'solutions' and you never really know which level of complexity the author had in mind. I love…

Don't worry you can always solve these problems trivially: The examples on the left side are all on the left side, while the examples on the right side are not.

Thanks for that, actually made me chuckle :)

(And it illustrates the point quite well, as that is indeed probably the simplest and most general rule you can find.)

Re: A first lesson in meta-rationality

#82

Post by teknopaul »

OisinMoran wrote: post #13

This was a good read and I really enjoyed it (I'm another person who was turned onto Bongard problems by Hofstadter), but two parts weren't particularly strong. The first one was the dismissal of intuition in a way that seemed pretty straw man like to me: "Mostly, “intuition” just means “mental activity we don’t have a good explanation for,” or maybe “mental activity we don’t have conscious access to.” It is a useles…

I thought that one was the most interesting too. The convex hull appears circular but it is not, in one case you have to join the dots between the center point of triangles, none of the points on the triangles are on a circle, or maybe all of them are if we discard the hull abstraction, in which case there are three circles.

Imagine trying to write code that identifies that. However it's one of the most obvious to me.

Re: A first lesson in meta-rationality

#83

Post by rrmm »

nerdponx wrote: post #68
Buldak wrote: post #54

Earlier quoted context omitted.

Yeah, the author says that for any of these problems "there should only be one reasonable rule." But I suspect that "reasonable" here really points to contingent facts about human psychology, i.e. some rules just strike us as more intuitive or appealing than others, but they aren't correct in any objective sense. That sort of gives the lie to the notion that what we're exercising here is "meta-rationality."

The problem with these puzzles is that, without rules for the system, you can just make up your own rules and then solve the puzzle within the context of those rules. For example, in the second puzzle, the arrangement of black-and-white shapes is the same on the left and right pages, but the right page is rotated relative to the left page. Is the question about the shapes as in an ordered collection? Or is the questi…

Yeah I think a lot of it is learning to think like how the people who thought up the problem think.

It still may not be a bad exercise (like art students at a gallery copying a master's work), but you shouldn't get too far ahead of yourself claiming it's some sort of 'exercise in pure reason'.

Re: A first lesson in meta-rationality

#84

Post by timboy03 »

yewenjie wrote: post #8

David Chapman has multiple sites for approaching the same problem. However, all the sites (or 'books') are incomplete. Every time I come across something by him I just want to read a complete book on the topic of metarationality from cover to cover.

Chapman's long-term hidden-agenda project is to teach us all by extended example that the notion of a "book" is intrinsically nebulous, and that the decision of whether and where one of his books stops and another begins (necessary for, say, counting how many books he has written) is itself dependent on the purpose you have for reading his books.

Re: A first lesson in meta-rationality

#85

Post by mckirk »

aaron-santos wrote: post #69
mckirk wrote: post #12

Am I the only one that gets driven kind of crazy by these kinds of problems? I'm not completely sure so far what it is, but I'm guessing it's the frustration of having to find a needle in a haystack of essentially infinite size, as depending on how complicated you want to see the problem, there's an infinitude of potential 'solutions' and you never really know which level of complexity the author had in mind. I love…

I can see where you're coming from. I always have to judge my working solutions using the parsimony of features and parsimony of rules to navigate the feature/solution landscape of Bongard problems. The underlying assumption is that the problem's author has followed the same rules which is an assumption of good faith on my part. This narrows down the feature-solution space considerably or at least biases it in a way…

Hmmmm yes, this assumption of good faith might actually be an important part of approaching these problems. I think I instinctively look for approaches to problems that would work even for adversarial examples. In the case of these puzzles, that of course doesn't work, because you then imagine the rule to be something completely outlandish and give up before you've even checked the easy options.

Something like "I know it's _possible_ the author has chosen a ridiculous rule, so it doesn't make sense for me to look for it, because even if I find it, I just got lucky and didn't actually solve the problem."

That might be a side-effect of perfectionism, actually.

Re: A first lesson in meta-rationality

#86

Post by aaron-santos »

b3morales wrote: post #74
aaron-santos wrote: post #69

Earlier quoted context omitted.

I can see where you're coming from. I always have to judge my working solutions using the parsimony of features and parsimony of rules to navigate the feature/solution landscape of Bongard problems. The underlying assumption is that the problem's author has followed the same rules which is an assumption of good faith on my part. This narrows down the feature-solution space considerably or at least biases it in a way…

I was thinking along these lines too when the author went into machines solving the problems. One bit that jumped out was the quote from Hofstadter: > They depend on a sense of simplicity which is not just limited to earthbound human beings. Followed immediately by a problem whose solution depends on having a sense of 3-D objects in gravity! Solving Bongard problems is surely a hard thing to get an AI to do, but I am…

> Followed immediately by a problem whose solution depends on having a sense of 3-D objects in gravity!

I can think of a Bongard problem where the images on the left are rebuses which spell English words, and images on the right are rebuses which spell Russian words. That's baking a LOT of a priori knowledge into the the puzzle. Alexandre Linhares' A glimpse at the metaphysics of Bongard problems talks a bit about what assumptions can go into this problems:

> An interesting but generally ignored aspect of Bongard problems is that their difficulty for a given subject is directly associated his or hers (or the system’s) previous experience.Since the problems consist of geometric figures, one may be led to believe that cultural factors do not influence the performance of a person attempting to solve them. This is not the case.

> Solving Bongard problems is surely a hard thing to get an AI to do, but I am wondering too about AI-authored instances.

I like where you're going. I left out the search I did of "generative adversarial networks bongard" because no good results popped up. (Hint: this would make for a fantastic HN post if any researcher wants to earn fake internet points).

Finally, this[2] comment stuck with me over the years. As always, would solving or generating Bongard problems be a quantum leap in AI or would they, like so many other problems, be subsumed into the category of AI-solvable problems and we all move on to the next problem at the frontier?

[1] - http://app.ebape.fgv.br/comum/arq/Linhares2.pdf [2] - https://news.ycombinator.com/item?id=8964017

Re: A first lesson in meta-rationality

#87

Post by mckirk »

skybrian wrote: post #64
mckirk wrote: post #12

Am I the only one that gets driven kind of crazy by these kinds of problems? I'm not completely sure so far what it is, but I'm guessing it's the frustration of having to find a needle in a haystack of essentially infinite size, as depending on how complicated you want to see the problem, there's an infinitude of potential 'solutions' and you never really know which level of complexity the author had in mind. I love…

I think this has to do with tolerance for being stuck, and that varies depending on how rewarded you think you’ll be for figuring it out and getting unstuck. Real science and math involves getting stuck on problems, perhaps for weeks, months, or years. I guess we should be happy that there are people who can tolerate being stuck. My tolerance for getting stuck on a mere game has dropped dramatically since I was a kid…

Yep, we aren't exactly being conditioned towards higher frustration tolerance nowadays... I don't think I could still deal with a PC without an SSD.

I think there are different kinds of being-stuck, though. With many problems in science, there's at least things you can try to gather more data. So you're stuck, but you can come up with new experiments to get new insights into the problem. Here, you're only given the one set of examples and have to make do. I guess you could still see the process of generating hypothesis and testing them against the examples as a sort of "experiment", but it still feels a lot "stuckier" if you don't get anywhere with it.

Re: A first lesson in meta-rationality

#88

Post by ghodith »

rrmm wrote: post #57
ghodith wrote: post #53

Earlier quoted context omitted.

Could you give an example of a different type?

Broadly, for example, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2838233/ """ Analytic cognition is characterized by taxonomic and rule-based categorization of objects, a narrow focus in visual attention, dispositional bias in causal attribution, and the use of formal logic in reasoning. In contrast, holistic cognition is characterized by thematic and family-resemblance-based categorization of objects, a focus on c…

That actually explains a lot! Thank you, that's a great anecdote

Re: A first lesson in meta-rationality

#89

Post by timboy03 »

One tricky thing about Bongard problems is that for any given problem there are likely many different rules that could distinguish the six positive examples from the six negative examples.

For example, maybe a problem that is "really" about circles vs. triangles also happens to have more black pixels in the left images than in the right images.

A key skill in solving these problems is not just to find a compact and discriminating description, but to find such a description that is also one that a human Bongard problem designer would be likely to think was a cool and elegant puzzle that needs an "Aha" moment to recognize. If you find such a description, then you're very likely to be right.

I suspect that that last part (recognizing when you have found a solution that is pleasing enough to be the answer) is likely to be the biggest challenge for ML-based approaches to Bongard problems

Re: A first lesson in meta-rationality

#90

Post by ScottBurson »

tlb wrote: post #7

An interesting category of problems are like Bongard problems in that you have to deduce the rule from examples, but the examples are presented one at a time at random long intervals so you have to work from memory. Most real-world learning is like this. When working from memory, it's normal for your memory to have already parsed the previous situation into features. As some of the later examples in the blog illustra…

Here's a deduce-the-rule problem that completely stumped me until I wrote down a series of examples: https://illuminations.nctm.org/lessons/petals/petals.htm
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