String diagrams. Pretty much every technical diagram you’ve ever seen, from electronic circuits to dependency graphs to ???, is a string diagram. Why is this such a common format for high-level descriptions? If it’s fully general for high-level natural abstraction, why, and can we prove it? If not, what is?
My explanation would be: our feeble human minds can’t track too many simultaneous interacting causal dependencies. So if we want to (e.g.) explain intuitively why the freezing point of methanol is −98°C as opposed to −96°C, we know we can’t, and we don’t even try, we just say “sorry, there isn’t any intuitive explanation of that, it’s just what you get experimentally, and oh it’s also what you get in this molecular (MD) dynamics simulation, here’s the code”. We don’t bother to make a technical diagram of why it’s −98 not −96 because it would be a zillion arrows going every which way and no one would understand it, so there’s no point in drawing it in the first place.
The MD code, incidentally, is a different structure with different interacting entities (variables, arrays, etc.), and is the kind of thing we humans can intuitively understand, and (relatedly) it can be represented pretty well as a flow diagram with boxes and arrows. So physical chemistry textbooks will talk about the MD code but NOT talk about the subtle detailed aspects of interacting methanol molecules that distinguish a −98°C freezing point from −96.
Molecular dynamics was also the first counterexample I was thinking of.
So physical chemistry textbooks will talk about the MD code but NOT talk about the subtle detailed aspects of interacting methanol molecules that distinguish a −98°C freezing point from −96.
Using heuristics here get’s easier though if you require less precision. I actually think that textbook could totally be written. Maybe not for why it is −98 rather than −96, but different heuristics and knowing the boiling points of other molecules should get you quite far (Maybe why it is −98 rather than −108). I would absolutely read that textbook.
My explanation would be: our feeble human minds can’t track too many simultaneous interacting causal dependencies. So if we want to (e.g.) explain intuitively why the freezing point of methanol is −98°C as opposed to −96°C, we know we can’t, and we don’t even try, we just say “sorry, there isn’t any intuitive explanation of that, it’s just what you get experimentally, and oh it’s also what you get in this molecular (MD) dynamics simulation, here’s the code”. We don’t bother to make a technical diagram of why it’s −98 not −96 because it would be a zillion arrows going every which way and no one would understand it, so there’s no point in drawing it in the first place.
The MD code, incidentally, is a different structure with different interacting entities (variables, arrays, etc.), and is the kind of thing we humans can intuitively understand, and (relatedly) it can be represented pretty well as a flow diagram with boxes and arrows. So physical chemistry textbooks will talk about the MD code but NOT talk about the subtle detailed aspects of interacting methanol molecules that distinguish a −98°C freezing point from −96.
Molecular dynamics was also the first counterexample I was thinking of.
Using heuristics here get’s easier though if you require less precision. I actually think that textbook could totally be written. Maybe not for why it is −98 rather than −96, but different heuristics and knowing the boiling points of other molecules should get you quite far (Maybe why it is −98 rather than −108). I would absolutely read that textbook.