Time and Space!

A conversation on another blog has me thinking about the difference between multiplication and addition.

Somewhere I've seen a discussion, maybe in Lawvere?, of multiplication being more "natural" than addition. The categorical product is available in more categories than the categorical coproduct, I think.

Alexandre Borovnik suggests that since time intervals are not multiplied, but are added and compared, tropical mathematics is more natural for time and concurrency than ordinary arithmetic. Tropical mathematics replaces ordinary "x and +" with "+ and max", where max gives the larger of two numbers.