Alan Kay: Is Computer Science an Oxymoron?
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From Abelson in the first SICP lecture: http://groups.csail.mit.edu/mac/classes/6.001/abelson-sussma...
Science is the attempt to find counterexamples to disprove your ideas on how a given system behaves. It involves conducting experiments to give input data for constructing a model, and then trying to find corner cases that break the model and allow you to refine or otherwise rework your model until it accounts for all your data.
Computer science has none of this. Computer science is the art of coming up with definitions that are of use to solving certain classes of problems, with formalisms to back them up. That is math.
Science is effectively an attempt to reverse engineer the universe. Imagine that you were given a clock by a client. A very ornate clock that he doesn't want you to take apart. Then he tells you he wants you to make schematics for the clock so precise he could put together a precise functional duplicate. But you're not allowed to take it apart.
I would say that does not that count as mathematics, although mathematics would certainly have a use as a tool to prove that the behavior is correct in all observed respects. But you could probably find a new minute difference in the way the hand moves, and that would blast all your carefully crafted mathematics to bits.
I'm not slagging on mathematics, and I'm not trying to glorify science and say that one is a more powerful superset of the other.
They're both very useful and very tightly intertwined disciplines, but they're also very different. In a way, you could say that math is the study of solving problems, and science is the study of finding physically meaningful problems.
I found that tidbit interesting. The thing is, when you invent new things, you need some type of metaphor for what already exists, or people will have a hard time adopting it or using it.