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 illustrate, it's easy to fall into parsing examples into the wrong set of features, which is how you'll remember them.
While I could solve all the problems in the article, I doubt I could solve any but the simplest if I was shown 1 image per day over 12 days and not allowed to write anything down.
Perhaps the lesson is that when you're trying to deduce a rule (say, for what conditions your software crashes in) you can increase your rule-discovering power greatly by making notes and being able to look at several examples side-by-side.
It is equally "obvious" that the heavens are governed by different laws of physics than the earth, because things on earth fall down if unsupported and naturally come to rest and things in the heavens don't. And of course all of these things are equally wrong.
One can and should apply the same lesson to social and political statements. For example, people get hung up on arguing about things like whether or not "God exists" as if they were arguing about a question of objective fact when actually what they are arguing about is the meaning of the words "God" and "exists."
I wrote a longer take on all this about six years ago:
http://blog.rongarret.info/2015/02/31-flavors-of-ontology.ht...
Once you get to the point where you have any hypothesis whatsoever, no matter how weak, a systematic approach (saving examples as test cases) helps to avoid confirmation bias and makes testing further hypothesis less costly.
Another hard one is when there is a simple, probabilistic rule. You usually end up with an over-complicated rule to cover all your data instead of the true rule. (Of course that gets down to what is at the basis of the probability: are you satisfied with a probability?)
In computing we try to write deterministic tests that either pass or fail, which means you can run them once after a change and know what the state is. Even if you just suspect flakiness you may have to run the test hundreds of times to be confident that the probability of failure is sufficiently low.
This is true for me too. Even 1 image every minute over 12 minutes would be quite difficult for me. I'm not sure I could solve any of these problems without being able to look at the figures side-by-side, back-and-forth, again and again, until I get an "aha!" moment.
On a related note, I have found that revisiting old information multiple times over sometimes longish time spans and unconsciously comparing it with newer, fresher information often helps me gain insight and greater depth of knowledge.
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 logic puzzles, where the system is constrained and you have to work within it, but these find-the-rule problems really aren't my thing so far. Maybe I'd need to develop a higher frustration tolerance for them, heh.
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; many of the games we played then are unplayable by modern standards. You had to draw maps and take notes, yourself, rather than the computer remembering things for you.
But text adventures back then sometimes weren’t meant to be played alone. The game might be single-player but it was a group activity for college students where you’d share ideas. The modern equivalent might be games where you’re expected to search the web to find recipes and strategies for things.
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.
That's not to say there isn't value in learning this way of thinking, it's gotten society a long way.
(And it illustrates the point quite well, as that is indeed probably the simplest and most general rule you can find.)
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 where I can prioritize hypotheses in a more tractable way.
Part of what I feel makes me a good puzzle solver is imagining that I'm a puzzle maker. What was going through the author's mind when they conceived the puzzle? If I can start to pull at that thread then the complexity of the puzzle will start to unravel.
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.
> 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 wondering too about AI-authored instances. Or, say, problems authored by aliens, with a different evolutionary history, and different in-built biases for cognition. Would they necessarily be solvable by humans, or our Bongard problems solvable by them? Some aspects (number maybe?) are probably universal. But even a good-faith puzzle maker has to take some assumption of shared basis for perception.
This probably connects up to the author's final point that "what objects even are" is not absolute.
There’s also the factor that some Bongard problems, independent of their difficulty factor, are just more satisfying than others. Spoiler for the fourth one, with pairs of circles: its solution is that the entries on the left have $property while the ones on the right...don’t. This makes the right side virtually useless except to check the rule that you derived from the left side.
Maybe it’s just that I don’t have research experience, and am thus unsteeled against problems that seem impenetrable, or maybe I just don’t have the mindset to be good at these, but I agree the really difficult ones can be frustrating.
It's basically the same kind of problem that one faces in the more frustrating debugging sessions where you're looking at tons of data and try to find a pattern or clue of what causes the bug under what circumstances.
When I'm looking at some pattern that I'm trying to find a rule for in real-life, I don't think I'm running into the same frustration and in fact greatly enjoy trying to figure out rules for how things work (or so I believe, at least).
I think a crucial difference is that I know that the problems I encounter in real-life are only "as complex as necessary", and the data I'm looking at is a direct result of some process that serves a specific goal; presumably one I think "makes sense", as I wouldn't look for a rule otherwise. In contrast, puzzles are made to be complicated on purpose, and I suspect that annoys me subconsciously to the point where my brain complains about engaging with it. But it's only these kinds of "figure out the rules" puzzles, so there has to be another important difference compared to logic puzzles. Possibly the difference is: for the logic puzzle, the "meta-rules" for the problem are made explicit and I know the solution-space exactly. For the Bongard problems here I found myself thinking for example: "wait, is it always just two groups distinguished by single rule, or can there be dependencies on the positions of the symbols within the groups as well? What kind of solution am I even looking for?", and that also apparently frustrates me.
Sorry for the wall of text, but I've actually been trying to figure out why these kinds of problems get on my nerves for quite a long time, lol.
I use to solve chess problems at lichess, a similar concept. Maybe.
Is it really an infinite haystack? It's context. And simplest solutions first, gradually think of more complicated ones. First try to find a pattern visually, then use simple concepts, then more complex concepts.
I see people making such claims about human cognition all the time, and I have no idea how it follows. (note the author is paraphrasing "people" here)
The Church-Turing Thesis says nothing about human cognition.
It is perfectly plausible that a human can do things a computer can't. (Scott Aaronson has a paper "Why Philosophers Should Care About Computational Complexity" which sheds some light on why that might be, but it's far from the only possible reason.)
The burden of proof is on people who claim that human cognition can be simulated by computer, not the other way around. To me, it seems far more likely that it can't.
Human cognition can obviously be simulated by "the laws of physics", since brains are material, but it seems very likely that computers are less powerful than that.
That's my refutation of the (silly IMO) "simulation argument". I'd argue it's simply not possible to simulate another universe. You can simulate something like SimCity or whatever, but not a real universe. The people who make that argument always seem to leave out the possibility that it's physically impossible.
In fact I would actually take the simulation argument ("we are almost certainly living in a simulation") as proof by contradiction that simulation is impossible.
I'm not one of these people, but your rebuttal wouldn't convince me if I were. Maybe we are the SimCity of a much more complex universe.
As far as I can tell, the idea was basically made popular by movies [1], and there is no science behind it. All the science I know of points the other way -- simulating anything is incredibly hard and slow. It requires approximations and shortcuts to make it work for specific cases, and it doesn't work in the general case.
(Maybe some alternative model like quantum computation will be different, but we're MUCH much further there. I think "adding two small numbers" is still an issue for state of the art quantum computers.)
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Here's a nice example from a few days ago, trying to represent even a tiny part of the human brain in a computer:
https://news.ycombinator.com/item?id=27362883
[1] I think this is more literally true than you might expect; IIRC the published papers in philosophy liberally reference The Matrix, maybe because it attracts readers.
C-T makes a claim about computable functions on natural numbers. It seems strange to argue that humans can perform such computations on a fundamental level better than a computer, thus we might assume the same is true of more complex computations. So while I suppose you could take the position that the burden of proof is to show every individual method of computation is equivalent, since there are infinitely many methods this seems a bit unfair.
https://en.wikipedia.org/wiki/Penrose%E2%80%93Lucas_argument
Note that I am not suggesting that I concur with it.
It involves the realization that different brain regions must communicate, but also contain their own representation of reality.
Partial thought precursors echo back and forth between these regions, with each region amplifying or dampening parts of the idea that it recognizes as valid.
When multiple brain regions begin to agree on its validity to a high level, the aha moment occurs.
This model has some characteristics of waveform collapse, and discrete task specific neural networks. When multiple tasks specific networks arrive at consensus that a model matches experience, the proto-idea forms. This proto-idea can then be evaluated, and inspected. New scenarios are reflected off this new idea, to see if it continues to make sense.
Converting an idea into words makes it useful to others, and allows sharing of ideas. This process requires refinement by echoing back and forth with the proto-idea until the words match it's shape.
In order for these words to be understood effectively, they need to make sense to the brains that are receiving them. That means the words chosen need to activate multiple brain regions that the listener may use to evaluate this new idea and have the aha moment themselves.
This process is easier when the 2 brains have many shared experiences to draw on, or communication is bi-directional to allow message refinement.
Sure, but this is complicated by regions being fuzzy and overlapping (or perhaps interpenetrating).
I'm almost thinking about how this could be turned into a device for conveying information with actual echos.
IIRC, he at one point says in his book, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics" something along the lines that the mistakes most people make are in categorization. Something along the lines of "Some things look the same but they are different, and some things look different but they are the same". It's a very interesting book and I loved how Non-Aristotelian logic was used in Null-A by A.E. van Vogt, which introduced it to me.
I do agree that most of what gets labeled rational is in fact ex post facto rationalization. I do it myself all the time, haha.
But I'm kind of over-strict about it and like to reserve "rational" for processes you can do with first-order logic. Given the complexity and lack of information in real life, that happens almost never. Of course this is not a terribly rational point of view.
Furthermore, meta-rationalists don’t really believe that if you take one map and keep updating it long enough, you will necessarily asymptotically approach the territory. First, the incoming information is already interpreted by the map in use; second, the instructions for updating are themselves contained in the map. So it is quite possible that different maps, even after updating on tons of data from the territory, would still converge towards different attractors. And even if, hypothetically, given infinite computing power, they would converge towards the same place, it is still possible that they will not come sufficiently close during one human life, or that a sufficiently advanced map would fit into a human brain. Therefore, using multiple maps may be the optimal approach for a human. (Even if you choose “the current scientific knowledge” as one of your starting maps.)
> rationalists hope that if they take one map, and keep updating it long enough, this map will asymptotically approach the territory
That is, as far as can be detected, what the human brain does. It isn't just the rationalists who have a view and keep updating it, hoping it will asymptotically approach the territory. It is exceedingly difficult to have a strategy that doesn't do that and still be a semi-functional member of society.
I'm struggling to see how someone could hold 'different' maps because they become one map in your head. Rationalists are perfectly comfortable with there being multiple possible scenarios leading to an outcome.
My guess is that this observation is going to the fact that rationalists are very, very uncomfortable (to the point of falling apart, sometimes) in accepting "because I say so" as sufficient evidence to update a view, change behaviour stop arguing and be a good sport about the whole thing. Which is very much a social faux-pas when dealing with high status people and often a mistake when dealing with inarticulate people who are nevertheless correct in their view.
They also relate directly to the philosophies of materialism and emergentism.
To abuse the analogy, a glovebox of old road atlas doesn’t beat Google maps. On the other hand mixing Google maps with your personal knowledge that a bridge is out is a useful meta map.
A commonality of all the boxes on the right is being on the right.
A commonality of all the boxes on the left is being on the left.
There is no offside in golf. The rules of the game only apply if when we are playing the game.
Here, Wittgenstein might have said Bongard problems are another language game and the confusion arises from using words in a peculiar way...the game is pretending there is a problem in a Bongard problem.
There is no offside in golf...yet. But the rules are surprisingly long, and will only get longer as loopholes are found and exploited. Humans trying to codify a game, or any system, cannot do so precisely; others can and will find the gaps between the written rules and the intended meaning, and play a different game but pretend it's the same. Or I guess, every game is a language game?
Which I think is a point of meta rationality: we can't avoid including questions of the rules of the problem. It's clouds all the way down.
"ARC can be seen as a general artificial intelligence benchmark, as a program synthesis benchmark, or as a psychometric intelligence test. It is targeted at both humans and artificially intelligent systems that aim at emulating a human-like form of general fluid intelligence."
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
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 useless concept, because we don’t have good explanation for much if any mental activity, nor conscious access to much of it. By these definitions, nearly everything is “intuition,” so it’s not a meaningful category."
I think the author could have spent longer trying to come up with a better definition of what someone would mean by intuition with relation to these problems instead of just setting up a poor one then immediately tearing it down. Intuition here would be contrasted against the deliberate procedural thinking of "let's list out qualities of these shapes" and would be something like seeing the solution straight away, but can also be combined with the procedural thinking too with the intuition originating possible useful avenues and then the deliberate part working through them. The contrast is that you could easily write down one set of the steps to be replicated by others (the deliberate part: "I counted the sides on all shapes") but less so the other (intuition: "I thought x", "x jumped out").
The second is that the example they use for mushiness really isn't. There is a perfectly concrete solution to that that doesn't involve any mushiness and is simply that the convex hull of one set is triangular while the others are circular. The only mushiness involved is that saying "triangles vs circles" feels like enough of answer to us to not need to specify any more. We think that we can continue with just this answer and be able to correctly identify any future instances so it seems mushy but you can probably think of examples that would confound the mushy solution but be fine under the more concrete convex hull one.
Imagine trying to write code that identifies that. However it's one of the most obvious to me.
Edit: Found a recent article mentioning both and discussing a NeurIPS paper on using Bongard problems to test AI systems [3].
[1] https://github.com/fchollet/ARC
[2] https://arxiv.org/abs/1911.01547
[3] https://spectrum.ieee.org/tech-talk/artificial-intelligence/...
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.
Oddly, this page is on that site but not linked from the table of contents, nor does it show up as a recently changed page.
triangle never in circle - circle never in triangle
compared to the given answer:
triangle bigger than circle - circle bigger than triangle
My solution is more general (worse), because it ignores size in non-containment arrangements, but also slightly more specific (better), because it constrains the single containment example in each set.
Neither of the rules say anything about overlapping cases, but there are no overlapping examples in the given sets. So there is a underlying constraint of no overlaps, but it applies to both sides, so it is not a distinguishing factor.
> In a Bongard problem, you have to figure out what the rule is. You are given twelve specific images, and the result of applying the rule to each. (The rule assigns an image to either the left or right group.) Once you have discovered the rule, applying it to new images would be trivial.
Your rules don't do that. Most of the pictures have neither "triangle in circle" nor "circle in triangle", so your rules don't apply to... Ten out of the twelve pictures.
I think you and the author might disagree on the meaning of "opposite" here. I think they mean logical negation and you are using a more colloquial interpretation.
Is this tongue in cheek or is it a very strange thing to say? That's definitely not a statement that should be made with no justification. I can guess what the author meant, but I don't really want to guess at basics of their argument.
I think a better candidate for human complete is “knowing what other humans are thinking”. AKA “theory of mind”.
It is easier to guess the state of minds of people who are similar to you. Because then your natural algorithm "what would I feel in such situation? what would make me say these words, act this way?" is more likely to match how they feel and think.
I suspect that many people overestimate their ability to "read other people's minds". First, they rarely verify their guesses. (I see another person and conclude that they are angry. I usually don't approach them and ask "hey, are you angry?". Therefore, if my guess was wrong, I am not going to learn it.) Second, if they turn out to be wrong, it's always the other person's fault. (If an autist cannot guess a neurotypical person's thoughts, it's the autist's fault. If a neurotypical person cannot guess an autist's thoughts, guess what, that's also the autist's fault.) Third, it is easier to guess thoughts of people we frequently talk to, because people usually think today the same thing they thought yesterday, and they already told us what they thought yesterday.
But whether that means artificial general intelligence is solved is another question. Most people can’t play Go very well either.
It’s difficult to say whether the solution will generalize without having it, but easy to imagine that it might.
It is about computable functions and abstract machines.
