Multiplication

Multiplication is [TODO]

Examples

My thesis is that multiplication always identifies quantities resulting from a unit-conversion (i.e. a change in unit-perspective) of some sort.

Examples which obviously come from unit-conversion

Suppose you wish to find the number of squares in a rectangular grid. You measure that there are $n$ squares per column, and that there are $m$ columns. In total, therefore, there are $nm$ squares.

Each pack of hot dog buns contains 6 buns, so if I buy 10 packs then I will have enough buns for 6*10 = 60 hot dogs.

Examples which don't obviously come from unit-conversion

The volume of a disk of radius r = 2 meters is approximately 3.14 * 2 * 2 = 12.56 square meters. It could be argued, however, that this does come from unit-conversion: the derivation consists of finding the area $2\pi r\times dr$ of small annuli (which is done by unit conversion and approximation), then adding their areas together.

A for loop which runs $n$ times, inside of a for-loop which runs $m$ times, will take approximately $nm$ steps to run. Again, I think this does come from a unit-conversion.

A coin flip has 2 possible outcomes, and so a series of 3 coin flips has 2 * 2 * 2 = 8 possible outcomes.