Theoretical question about spatial IQ tests

For Raven matrices type problems where you have a 3x3 grid of “patterns”. I’m wondering how many classes of patterns could exist?

I mean clearly there could be infinite patterns but not all of them would correspond to “interesting” patterns. Maybe theres some empirical laws that limit or impose some constraints on problem classes.

Are there only finite number of problem classes/typologies and could one learn most of them like we learn vocabulary? Has anyone ever created a book on mathematical taxonomy of RPM type problems? I expect it’s probably related to halting problem on some level but maybe there could still be general classes / rules that would aid in IQ tests.

Example: I know of “XOR” type problems when I see them on RPM tests and can recognize variations of this easily that’s one class of problem. There’s some I don’t have vocabulary to describe though would love to put a name to it.

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It is a very interesting approach. If a tester takes a skillful approach to IQ tests (Raven matrices type) like a mental sport or quiz, he may be able to maximize the score. In fact, the top IQ rankers I know were familiar with patterns that could find answers quickly.

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Interesting. I’d like to train like an athlete for some of these tests even if it only improves my own working memory and keeps my mind active.

Not everyone has potential to be an Olympic/world class athlete but I think we don’t know what our true potential actually is in any sport until we train for awhile.

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Probably the number of classes is as large as the number of items in all tests, as well as the number of factors in a factor analysis or cluster analysis. However, it is possible that the first (and largest) factor is sufficient to explain something like 70% of the variability, the first two factors can explain 91%, the first 5 factors can explain more than 99%, etc. So while the total number of classes is as large as we want, a small number of classes, perhaps 5 to 10 classes, is sufficient to describe the cognitive processes prevalent in more than 99% of the items in all tests of this genre.

The correct numbers should not be the ones I mentioned (would need to adjust the value of this parameter), but the structure of the problem probably has this property that there is not a finite number of classes, but a small number of main classes describes the vast majority of cases.

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This is a really good point. I’m actually familiar with clustering algorithms but I’ve never seen this applied before to RPM type problems. I wrote a program to take a sequence of natural numbers as input and output a ‘pattern’. I tried to get an ‘explanation’ of the pattern but it didn’t work well and then predicted next number in sequence. I figured out there are definitely ways to detect and even explicitly define ‘interesting’ sequences but they didn’t help in any high range IQ tests.

I can’t explain now but I think these are fundamental patterns of thought in a way and we could derive ‘laws of thoughts’ from these patterns if we could empirically analyze them.

TL;DR There’s something really deep and fundamental about IQ tests especially spatial and numerical.

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