Sunday, April 09, 2006

Thought Paradigms

I've heard it said (somewhere, ages ago) that intelligence isn't a case of learning things, but rather one of merely knowing a diverse enough range of things, and finding the similarities between them. I like this, but haven't thought much about it.

Now, though, it strikes me that to get from one (learning things) to the other (linking things) is possibly a "fundamental" jump in how we approach a subject.

In the first instance, the "things" we learn are isolated, and context-dependent - they have their own causes, their own effects, and their own "space". Thus, learning a bunch of things as a "concept" is learning just a collection of things. They link up, but only amongst themselves, within the context we learnt them in.

To find the similarities, though, requires a further step. It involves looking not at the things themselves so much as the bonds that tie them together. In other words, it is a jump from "absolute" (a collection of contextual "things") to "relative" (a collection of links). In network theory, this could possibly be mapped as the difference between nodes/vertices and edges/links.

Once you start looking at, and remembering, the relative pattern involved in concepts, pattern matching becomes a much easier task. For instance, if concept 1 is represented as two nodes and a joiner "A + B" and concept 2 a different set, dealing with different things related in a different way - "C x D" - we can learn them in two ways.

Firstly, we can place the priority on the nodes, the "things", such that we note them down as "A and B (with an addition)" and "C and D (with a multiplication)". (The concepts aren't mathematical, I'm just using mathematical notation to indicate homogoneity vs heterogeneity.)

Secondly, we can prioritise the relationship, so we note "An addition (of A and B)" and "A multiplication (of C and D)". Things are still heterogenous, but the important bit is that we can only (or we tend to) compare the parts outside of the brackets. If a concept related to similar things, we would have "A + B" and "A x B", and the former way of learning might have "an advantage".

But if we change the concepts to be "A x B" and "C x D" then all of a sudden the priorities we place on the construction of those concepts makes a big difference to what we can infer from them.

i.e. "A multiplication (of A and B)" vs "A multiplication (of C and D)". Here, now, the unbracketed part is now homogenous, forming a link between the two concepts that deal with different "absolute things", but share something in terms of relationship. This, then, may be the finding of similarity some people espouse intelligence to hold.

The mathematical notation is a little confusing. A good example would be the ability to learn languages - if you grow up with more than one language, then it's probably easier to learn another language later on in life than if you only grew up with one. Why? Because you're not concentrating on the words (the "things"), but what's linking those words - thought. Learning a new language then involves recognising and mirroring the new language's relations in terms of thought and concepts rather than mapping one word to another.

Maybe there's some research out there on this. Whichever, it certainly needs more investigation...

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