Thu Apr 4 10:37:29 EDT 2019

Why is math good for modeling design?

Math is really about concepts that have good properties.

Discovering these things is always indirect.  We really don't have a
way to go from properties to concepts other than

1. stumbling into them by accident

2. recognizing known patterns and applying them

Since it is hard to make that shit up, it makes a lot of sense to
study these patterns, to get to know them, so you can recognize them
when they show themselves.

Architecture is about organization.  It really doesn't matter how
things are organized, as long as the organization principle has some
good properties.  It is those properties that implement abstraction,
information hiding.

Why are OO patterns no good?  Because they are severely limited by the
hidden context associated to the idea of objects.

Information hiding is not necessarily a bad thing, but it needs to be
done by "actually forgetting" things, i.e. a non-invertable function
(a projection), not by assuming some hidden connection.

So why is math important for design?

Mathematical concepts are "clean".
They are constructed in a hig-leverage way.