Shape

301 Design without Thought
using only a single schema
x fi tðxÞ
where x is a triangle or a regular polygon, and t is an appropriate transformation of
x. Then the number of ways I can apply the schema to a shape in the array without
remainder corresponds to the Fibonacci number of its column. I showed this for the
series of squares inscribed in squares in the second row. The rule
and others defined in the schema work like erasing rules. Shapes are filled with ambiguity.
And there are always rules to take advantage of it, so that I’m free to look at
things in new ways. Finding the right rule to apply may require time, effort, and a little
luck, but nothing prevents it from being used.
Most of what I’ve been saying about rules and calculating with shapes is anecdotal.
I’ve been presenting decompositions as case studies. This is no surprise. The way
ambiguity is used now may have little to do with the way it’s used later. Ambiguity
won’t go away. It’s there whenever I apply rules to calculate, but it’s not handled in
the same way all of the time. That’s why ambiguity is so interesting and valuable. The
trick is to use ambiguity without limiting it by trying to generalize. There’s no chance
of this, as long as rules can vary as widely as shapes can. In this way, ambiguity always
provides the chance to try things that haven’t been tried before. It’s keeping your eyes
open when you calculate.
Design without Thought
What is design? No one ever agrees, but I used to side with Franz Reuleaux—
Invention, in those cases especially where it succeeds, is Thought.