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Comment by reptation | Hacker News Reader

There are physical phenomena that do not readily become math. "Positive and minus attract" for instance does not have an obvious mathematical basis as the inverse square law.

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I'm not sure what you mean by that. Charges q1 and q2 will experience forces (all else being equal) proportional to q1*q2. This captures the way attraction/repulsion scales with amount of charge, and gives you the sign rule for "free."

Here is a fairly in-depth page about it: http://farside.ph.utexas.edu/teaching/em/lectures/node28.htm...

Those pages have some interesting observations - for example, it begins with an action-at-a-distance model, but then it goes on to say that this is inconsistent with Newton's third law in a universe in which information cannot propagate instantaneously. This is presumably implicit in the math, but does making the point in natural language go beyond that?

More generally and abstractly, does the math have anything to say about causes, and if not, is that a limitation or a profound insight?

Propagation delays are missing from Columb's law, which is what you get from Maxwell's equations when you assert that everything is static (meaning, in a practical sense, that you think everything is slow-moving enough.) This can be written in either math or English - and don't think that it's never "aesthetic" to write math in English. People do it sometimes.

>More generally and abstractly, does the math have anything to say about causes, and if not, is that a limitation or a profound insight?

The most reductive way of looking at it is that physical laws are the file-compressed versions of lots and lots of lab spreadsheets. The odd part about this picture? The compression ratio is mind-boggilingly high; and even more amazingly it can often (essentially always) predict the contents of lab spreadsheets that have not already been filled. Information theory probably has something to say about how this works out but I don't know what it would be.

It has no obvious basis because the two aren't related. The phenomenon you describe might as easily have been some other power. Several exercises in my undergrad and graduate E&M courses explored what might classical E&M look like under different models, in fact.

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