To my surprise, very little seemed to have been done on these kinds of questions. At first I thought it might be possible to make progress just by applying some of the sophisticated mathematical techniques that I had used in theoretical physics. But it soon became clear that for the phenomena I was studying, traditional mathematical results would be very difficult, if not impossible, to find.
So what could I do? It so happened that as an outgrowth of my work in physics I had in 1981 just finished developing a large software system that was in some respects a forerunner to parts of Mathematica. And at least at an intellectual level the most difficult part of the project had been designing the symbolic language on which the system was based. But in the development of this language I had seen rather clearly how just a few primitive operations that I had come up with could end up successfully covering a vast range of sophisticated computational tasks.
So I thought that perhaps I could do something similar in natural science: that there might be some appropriate primitives that I could find that would successfully capture a vast range of natural phenomena. My ideas were not so clearly formed at the time, but I believe I implicitly imagined that the way this would work is that such primitives could be used to build up computer programs that would simulate the various natural systems in which I was interested.
There were in many cases well-established mathematical models for the individual components of such systems. But two practical issues stood in the way of using these as a basis for simulations. First, the models were usually quite complicated, so that with realistic computer resources it was very difficult to include enough components for interesting phenomena to occur. And second, even if one did see such phenomena, it was almost impossible to tell whether in fact they were genuine consequences of the underlying models or were just the result of approximations made in implementing the models on a computer.
But what I realized was that at least for many of the phenomena I wanted to study, it was not crucial to use the most accurate possible models for individual components. For among other things there was evidence from nature that in many cases the details of the components did not matter much—so that for example the same complex patterns