The point is—is it possible to get to a working theory without inventing negative numbers.
So with charges and my white-red charge conservation law, I never need to subtract 5 reds from 3 reds. Unlike e.g. loaning money, this sort of problem doesn’t seem to arise with charges. When we use positive and negative charge, a large part of the algebraic machinery made available to us by negative numbers sits unused (we don’t multiply charges either; that is we do in terms of Coulomb’s law, but that’s a notational convenience). That’s why I said that electric charge is a good example of why aliens could conceivably get by w/o negative numbers. If they didn’t have them for other reasons by the time they got around to investigate electricity, they might get by with the white-red formalism just fine.
If you already know negative numbers, then sure, it’s easy to imagine just relabeling them and nothing much changes. But to people in the first millennium AD, they were a very real and tangible invention. When ancient Greeks said that something like “x+4=2” is an obviously absurd equation w/o a solution, they meant it. They didn’t go “oh, I have these I-OWE-U numbers that I use to count my debts but don’t call them “negative”, anyway, the solution is I-OWE-U-2″.
The point is—is it possible to get to a working theory without inventing negative numbers.
So with charges and my white-red charge conservation law, I never need to subtract 5 reds from 3 reds. Unlike e.g. loaning money, this sort of problem doesn’t seem to arise with charges. When we use positive and negative charge, a large part of the algebraic machinery made available to us by negative numbers sits unused (we don’t multiply charges either; that is we do in terms of Coulomb’s law, but that’s a notational convenience). That’s why I said that electric charge is a good example of why aliens could conceivably get by w/o negative numbers. If they didn’t have them for other reasons by the time they got around to investigate electricity, they might get by with the white-red formalism just fine.
If you already know negative numbers, then sure, it’s easy to imagine just relabeling them and nothing much changes. But to people in the first millennium AD, they were a very real and tangible invention. When ancient Greeks said that something like “x+4=2” is an obviously absurd equation w/o a solution, they meant it. They didn’t go “oh, I have these I-OWE-U numbers that I use to count my debts but don’t call them “negative”, anyway, the solution is I-OWE-U-2″.