## Wednesday, May 30, 2012

### Thinking like a physicist

@mathematicsprof on Twitter recently tweeted a link to a page asking what it's like to understand advanced mathematics. There are a number of very interesting answers there, but one interested me particularly. I can't figure out if there's a way to link to it directly, but I'll quote it here:

A two part question to determine if you "think like a mathematician," from Prof. Eugene Luks, Bucknell University, circa 1979.

Part I: You're in a room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on the floor.  How do you make hot water for tea?
Answer to Part I: Put tea kettle on stove, turn on burner, heat until water boils.

Part II: Next, you're in another room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on a table.  How do you make hot water for tea?
Non-mathematician's answer to Part II: Put tea kettle on stove, turn on burner, heat until water boils.
Mathematician's answer to Part II: Put the tea kettle on the floor.

Why?  Because a solution to any new problem is elegantly complete when it can be reduced to a previously demonstrated case.
This might be why I'm studying physics more than maths. I can see why putting the kettle on the floor solves the problem rather elegantly - I think it's a nicer solution than the "non-mathematician's answer" up there - but it's not how I would solve the problem. Isn't it obvious that the table is negligible in this situation, so that Part II is reduced to Part I?

Mathematicians aren't, I think, supposed to say things are negligible. Assuming that the table is negligible isn't rigourous. It does, however, get to the right solution without (explicitly, at least) going via the floor. It's still elegant (if you can get over the idea of neglecting the table) and it takes less effort.

Perhaps it's related to the idea that physics is not so much about working out how to describe some given bit of the universe as it is about working out which bits of the universe we can describe and doing so. This is usually expressed in terms of finding symmetries, from what I've seen and heard. Here, I think the system is invariant under the introduction of the table, which is a symmetry.

There are probably other ways of solving the problem, too. I think it's a very interesting exercise in how people think!