My experience doing quantum chromodynamics (QCD) was faintly like this. I could do the math, but it was mechanical; I always felt that the theory had a better idea of the answer than I did. On the other hand, I sensed that people who could really do physics had a visceral feel for the subject. Not only could they handle the sums, but they intuited what the answer should be.

This may be part of what skill means. One has to master both the mechanics of the knowledge, and the link between the knowledge and the intuitions that allow one to find short cuts and anticipate results. Mechanical knowledge links subject matter and theory; metaphor links theory and intuition.

In the Capgras case, the visual recognition system links a person’s appearance with their identity, and the emotional affect system links that identity with the meanings that are important to the perceiver.

To sum up the three preceding examples:

Skill in general: subject matter – theory // theory – intuitionStretching the analogy even further, perhaps this is why metaphors are so important in science and engineering. A software engineer doesn’t need metaphors like Classes-as-Containers or Programs-as-Language to get work done– the unadorned mathematics would do just fine – but analogies provide an intuitive basis that underpins thinking and provides comforting context. When a programmer tries to write about software without using metaphors, they become uncomfortably aware just how ingrained they are. The two-part model in this case:

Physics ‘n’ me: experiment – QCD // QCD – intuition

Capgras syndrome: face – spouse’s name // spouse’s name – feelings for spouse

mathematics – programming // programming – intuition

## 2 comments:

I would make that:

logic - programming // programming - intuition

The reason being I don't really see mathematics as being the subject matter of programming... but rather, it is logic. Logic is a more fundamental subset of mathematics, mathematics uses logic to quantify "things", whereas programming uses logic to represent the systems we have in our head.

And that begs the question - still, what separates programing and mathematics? Isn't mathematics using logic to represent systems, as well?

I think that mathematics is more closely tied to "reality" than programming is. For example, geometry (of all kinds) tries to mimick, well, the geometry of space (that sounds like a tautology). Number theory.... that belongs more in the realm of metamathematics...

So really, this is more enlightening about how mathematics is no longer this monolithic subject we all seem to think of it as. Instead, it is turning out to be a series of gradations between "logic" and "reality/physics".

Programming is perhaps in a tangential branch emanating from logic or number theory, but has different beginning propositions than the systems of mathematics have.

Anyways, sorry for the ramble. Hope to see you sometime this month!

That's a helpful clarification: makes sense to me. Riffing on your point - I can imagine that different branches of mathematics have lead to different kinds of programming via different kinds of logic. I wonder if the different logics contradict each other?

I vaguely recall that in "Where Mathematics Comes From," Lakoff & Nunuez discussed different set theories what were in some way contradictory, but I may be mistaken...

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