by Asim Jalis
At its core mathematics is a kind of merciless refactoring where
we take statements that are true and generalize them as far as we
can. We cut out all the specifics, or refactor them out and the
see what's left.
For example, this dog weighs more than this cat. This is a
general statement which might be true. But now if we refactor out
the specific animals, and also the concept of "weighs" we are
left with the concept of more-ness. We can even refactor this out
and be left with a concept of a relationship. We notice that
more-ness is transitive, so we can formulate a theory of
relations that is transitive.
Once we have created this machinery we could apply it to
something that is not quantifiable. For example, we could apply
it to belongs-to. Or contained-in.