Rule 30 and Richard Feynman: Stephen Wolfram on Intuition Versus Computational Experiment

Asked about interacting with Richard Feynman at Caltech, Wolfram says they worked together quite a bit. Both were consultants at Thinking Machines Corporation, which he calls an ultimately ill-fated company. Wolfram used to say the company would not work with its strategy, while Feynman would reply that they knew nothing about running companies. Feynman considered Wolfram's interest in companies a distraction, though Wolfram sees them as a way to build a more effective machine for making things happen.

Feynman also gave advice on the technical side of Wolfram's first company, which dealt with mathematical computation. He had his own elaborate ways of doing integrals and of getting intuition about math, and his idea was to make a computer follow those intuitive methods. Wolfram says the methods that were eventually built are quite different, an industrial machine that converts integrals into special functions, and the hard part is turning results into something a human can understand. He admits with embarrassment that Feynman once gave him a pile of particle-physics calculational methods from the 1950s, which he never returned.

Wolfram says the thing Feynman was best at was calculating, but he thought it was easy because he was so good at it. He would do a complicated calculation in quantum field theory and tell nobody about it. He would then present a simple intuition for how everything works, since in his view that was the impressive part.

The result, Wolfram says, was that people followed Feynman's intuition without knowing why it worked, because the real reason was the calculation he had already done. He adds that it is a lot easier to have good intuition when you know the answer. Wolfram and Feynman also worked on quantum computers around 1980-81, before most people had heard of them, and often argued, because Feynman computed by hand and Wolfram by computer. Wolfram notes that some issues they found around the measurement process remain today, and that history in science and technology tends to repeat.

Wolfram tells a story from Thinking Machines. He had been studying the cellular automaton rule 30, which from very simple initial conditions produces complicated behavior. Using the company's parallel Connection Machine, he generated a giant printout of rule 30 on a large-format printer, and he and others crawled over it on the floor measuring features of the pattern.

Feynman took him aside and asked how he had known rule 30 would produce such complicated behavior. Wolfram said he did not know: he had enumerated all the possible rules and seen what happened. Feynman said he felt a lot better, because he had suspected Wolfram had an intuition he lacked. Wolfram told him there was no intuition, just experimental science. Fridman calls this a beautiful dichotomy, since you cannot have a compressed intuition about an irreducible system, and Wolfram thinks Feynman was on the edge of grasping that point about computation.

Wolfram says discovering rule 30 was harder than it sounds. When he first saw it, he nearly dismissed it because an intuition told him such behavior shouldn't be there, and he planned to ignore that case. Fridman asks how a physicist-trained mind became open enough to watch rules reveal complexity.

Wolfram's answer is that he did reductionistic physics first, where the universe is given and you work out what is inside it. Then he began building computer languages, which is similar in that you drill down to primitives, but different in that you choose the primitives and build up. In effect he was building an artificial universe, which gave him a different attitude: explore what can be done in such universes rather than only being constrained by the real one.

Fridman likens the computer to a brain or a telescope, and Wolfram calls it a tool that lets you see things. He says that building computational languages demands creating another level of abstraction and being open to different structures. He is aware, having seen it several times, of how easy it is to miss the obvious, and says that awareness is factored into his attempts not to, though it may not always succeed.