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.
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 question about the pages in their entirety? These problems tend to be underspecified, and end up being more of a guessing exercise about the authors intentions than anything else.
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'.
These sorts of tasks are teaching you how to think a specific way which our society promotes. Mechanistic, natural, causal, rational (in the first-order logic sense) with a healthy dose of Ockham's razor and simplicity as an aesthetic.
I stress though, I'm a big fan of these things and the innovations they have enabled, but you still have to understand that they are an axiomatic underpinning. It's like Euclid's parallel postulate in a way: There is non-euclidean geometry out there.
The fact that the solution of these problems is in some sense satisfying also has a lot to do with the fact that the people making these problems are Western systematic-thinkers. They think like us (because we were trained by them).
That's not to say there isn't value in learning this way of thinking, it's gotten society a long way.
Not an alternative to systematization, but different systems. Just that the analogies or groups that make sense to one group may not make sense to others.
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 contextual information and relationships in visual attention, an emphasis on situational causes in attribution, and dialecticism (Nisbett, Peng, Choi, & Norenzayan, 2001).
"""
This also comes up a lot in cognitive test design.
The anecdote I've always heard in reference to it was
"""
What is considered wise in one society may not be considered wise in another; the value and meaning of intelligence depends on cultural norms. Demonstrating the culturally-specific nature of knowledge and intelligence, Cole, Gay, Glick, and Sharp (1971) conducted an experiment in which Western participants and Kpelle participants from Liberia were given an object-sorting task. Participants were asked to sort twenty objects that were divided evenly into the linguistic cat-egories of foods, implements, food containers, and clothing. Westerners tended to sort these objects into the groups for food and implements, while Liberian partici-pants would routinely pair a potato with a knife because, they reasoned, the knife is used to cut the potato. When questioned, Liberian participants justified their pairings by stating that a wise person would group the items in this way. When the researchers asked them to show what an unwise person would do, they did the taxonomic sort that is more familiar to the Western culture.
"""
A simple example that still constrains the puzzle to human abilities (but also makes it less universal) might be this. Rather than diagrams/images, each puzzle consists of two groups of short depictions of two people interacting. The differences are in the relationships, emotional states, or modes of expression. That kind of judgement requires different perception, intuition, knowledge, and so on compared to the puzzles based on shapes. Probably a lot of people who were good with the "standard" Bongard problems would struggle with the "interpersonal" variety, and vice versa.
The flaw with that "solution" is that if you have found the rule, you should be able to say whether a new image belong on the right or the left if it is presented to you. If you say, "I can do that, but I need one more bit of information, namely whether the new image belongs on the right or the left", that's a pretty severe defect.
There's no necessity (in general) that a new image should be able to be classified under the rule. If I give you two finite groups A={1,3,9,-2} and B={7,-11,i,5} and the rule actually is tautological, Then a new number 22 doesn't belong to either group under the rule.
A few of the examples from the article actually are similar. The two circles where one circle is either clockwise or counterclockwise from the nearest indention only admits pictures with two circles, one on the surface of the other and an indentation. There are images which wouldn't fit into either.
A math professor of mine was illustrating this point with number series (of the sort on aptitude tests, eg squares,arithmetic sequences, etc), by listing an obvious sequences whose completion ended up being an obscure function which diverged at the next point.
So, the trivial solution (and the more ultra-complicated solution) is defective basically because it's not interesting under the rules of the game which assumes the answer is somehow interesting, but not impossible to guess.