[seydar]

> The presence of the negative signs in (1) may seem surprising at first, but this is due to the fact that (1) is describing the effect of a passive change of units rather than an active change of the object {x}.

This is where the limits of my brain were reached. Is there a translation of this into category theory terms? Is this where category theory could help formalize units in physics?

However, his paragraph after that is pretty interesting, which I read as sort of treating units as variables since you couldn't combine them, and he only has length, mass, and time for these examples. But then there's an exponent piece? Okay now I'm lost again.

[monktastic1]

Maybe this is obvious and not what you are asking, but he's just saying that if you increase your unit of measurement by a factor of X, then the number of such units that comprise your object decreases by the same factor.

(Also, this quote is from the Terry Tao blog post that dang links below, not the OP, right?)

[dawnofdusk]

>Is there a translation of this into category theory terms?

It's essentially the same as the relation between covariance and contravariance in category theory.

[mjburgess]

where on earth is this quote from?