A few weeks back, I was playing with fractal representations of
binary operations. For the math-phobic, Don't panic yet.

General binary operations are pretty simple. Suppose you have a
collection of things. A binary operation on those things is just a
way of taking two of those things, putting them together (in order),
and getting another one of those things.

For example, subtraction is a binary operation on numbers. If you
take two numbers (in order) and subtract them, you end up with a
number.

For a non-number example, suppose there is a club with four
members: Larry, Moe, Curly, and Shemp. Suppose that the
last two people to arrive at the monthly meeting must each pay $5 to
some member of the club where the recipient is totally laid out in the
by-laws based on who the second-to-last and last arrival were. For
example, the by-laws might say that if Larry arrives second-to-last
and Moe arrives last, they must each pay $5 to Shemp. The by-laws may
say that if Shemp arrives second-to-last and Curly arrives last, they
each must pay $5 to Curly. (Curly drafted the by-laws and then
railroaded them past the other members.)
If the by-laws cover all possible cases and only ever pay a
single member of the club, then the by-laws define a binary operation on
the members of the club.

**( Okay, now the math-phobic can panic...Collapse )**
**( And, the lisp-phobic, too...Collapse )**