Shape

17 Answer Number Two—Three More Ways to Look at It That Tell a Story
time I apply a rule, I define a well-formed string of brackets. And I can continue from
where I’ve left off to get more strings of the same kind. Or I might want to start calculating
from h i again to get other strings. That’s all there is to it. That’s all it takes to
calculate anything that can be calculated. Find rules for palindromes. It isn’t any harder
than angle brackets. Palindromes are a special case in which only rule 1 is tried:
hh...hi...ii. Mark the centers of strings to insert matched symbols there.
Minsky didn’t stop with symbol manipulation. He had other things to say, too.
There was the bigger idea that rules might describe how we think. Minsky was passionate
about this, and when I was a student, he showed it in his very public and uproariously
impolite argument with Hubert Dreyfus—it was about what computers can and
can’t do. Dreyfus was one of my instructors in the humanities, and he didn’t see how
computers could think. The Danish philosopher Søren Kierkegaard and others showed
why. It was about ‘‘results’’—units and counting the distinct ways they combine. It
seemed that there were things you could teach and count, and things you couldn’t.
Dreyfus and Miss H—— were saying the same kind of thing, but Dreyfus was explicit
about it and had Kierkegaard to back him up. At the time, though, it didn’t matter. It
was all emotion. Dreyfus saw through what Minsky was trying to do—there was more
to thinking than symbols in the way they’re normally used—but Minsky wasn’t listening
to what Dreyfus was trying to say. It was the perfect academic argument—thinking
was out! The line was drawn—you were either on the right side or on the wrong side of
a new technology. Dreyfus never had a chance at MIT. Yet even today, no one knows
for sure whether computers can think or not. It’s the kind of question that will probably
be resolved with a set definition. But the answer may be beside the point. If computers
can’t think, it won’t be for the kind of reasons Dreyfus gives—because his
reasons are included in calculating. Kierkegaard wasn’t enough, even with the instinctive
Miss H——. This was evident as soon as I started to play around with shapes and
rules, and to get results—going from symbols to shapes changed everything. The difference
was palpable. Calculating with shapes was an example of Dreyfus’s way of thinking,
and it let me see in the way artists do. The switch from symbols to shapes was my
big idea—it really worked—but it was still a few years off.
Meanwhile, I heard Noam Chomsky talk about language. I learned that generative
grammars—these are systems of rules something like Post’s—show how words go
together to make sentences. Almost everyone uses language in a creative way—you can
say and understand things that you haven’t said or heard before. But how is this possible?
It’s certain that no one knows every sentence in advance. Generative grammars
provide the answer. With a limited number of rules to combine words, I can generate
an unlimited number of new sentences. It’s the same kind of recursive process I used
to define strings of angle brackets. But what about design? It’s creative, too. You can
always make something different, but how? Chomsky’s grammars got me thinking—
why not shape grammars for languages of designs? With a finite number of rules,
I might be able to generate an indefinite number of things. They might even hang
together in the same style. I could finally say how to put lines on a blank sheet of
paper. I could understand creativity in design.