Abstract and construct

I've noticed a pattern that seems pretty universal when discovering and exploring systems. First, you attempt to distill the system down into its most minimal and general representation. That is, you abstract it: you can describe a shape as a mesh of triangles. You can describe triangles as lines. You can describe lines as points. You can describe points as numbers. And you can describe numbers as other stuff too. But abstraction is only half the story. After you have created this minimal and general representation, you work backwards from the abstraction to build new concrete things. That is to say, you construct.

One of the most accessible demonstrations of abstract-and-construct is cartooning. You take real people, animals and other objects, distill them down into abstract shapes, and then manipulate and distort those shapes in ways that would be impossible in the real world. You see something surprising and your eyebrows raise. Abstract: eyebrow height = maximum(surprisedness × eyebrow sensitivity, eyebrow limit). Construct: let's set the eyebrow sensitivity and limit really high. And suddenly you get surprised cartoon characters with their eyebrows flying out the top of their heads and smacking into the ceiling. (If you're interested, I recommend Understanding Comics, which I probably lifted that example from).

Perhaps a more rigorous example is the periodic table. Mendeleev was able to abstract the structure of the chemical elements into various repeating patterns, and then use that abstraction to theoretically construct new elements that were only later isolated in the real world. That's not to say that abstract-and-contruct always works out usefully. Physics, for example, has generated lots of wacky things like tachyons, perfectly reasonable constructions that have never (and probably will never) be observed in the real world.

There are some truly wonderful things you can do by distilling down to an abstraction and then constructing back out again. But a part of me also wonders: is it truly universal? The cartoon example seems to show us that there is something quite intuitive about the way abstract-and-construct works: we don't have any trouble believing that the high-eyebrowed character is just a very, very surprised person. Could this process just be an artefact of how our brains work?

If that's the case, a different kind of intelligent being might have some other way of finding truth that works as well for them as abstract-and-construct has worked for us. Maybe it would be able to view many things as being very similar to each other without needing to wrap them up in an abstract concept. Maybe if it was powerful enough it could just store all the information it learns and mine it directly for truth. Maybe the answer to the Fermi paradox is that the aliens all think we're too dumb to know how our own eyebrows work.

Of course, the most vexing part is that the only way I can think to explore that question is to abstract and construct. So let's hope that's enough.