Dr. Wolfram is best known as the maker of Mathematica computer software. In his past he was known as a physics genius, earning a PhD from Cal Tech at age 20. More recently he is known for publishing a big fat book exploring cellular automata. And for being an arrogant SOB who claims that automata are going to replace conventional equation-based science. I caught a recent conversation with him in San Francisco at an event sponsored by the California Academy of Science.
Cellular automata are simple computer programs that describe how each "cell" will change or grow in the next time instant. Typically the rules will say that the change a cell will undergo in the next instant depends on the nature of neighboring cells in this instant.
The classic cellular automata software is the Game of Life. In the Game of Life colored squares cover a computer screen and the color of a square at a given iteration is some simple algorithm based on the color of the neighboring squares in the previous iteration. From simple rules can come amazing, unpredictable patterns. From rules that are too simple comes a screen full of one color, or a checker board pattern or something boring. From rules too complex comes the same. From rules just complex enough, comes magic.
Classic cellular automata in nature are ants, where each type of ant, worker, queen, etc, lives by a few simple rules. From a few ant types, and random placement of food in their environment, wonderful patterns emerge of ant behavior such as lines of ants marching to where the food is, changes in the relative populations of ant types, and so on. Ant colonies seem intelligent but individual ants are as dumb as ... an ant.
Not one for ants and nature, Steven Wolfram has locked himself in a computer room for the last ten years and has been playing with Mathematica. He has been making simple cellular automata and he has been observing what comes out. He published a book of his results and claims that he has revolutionized science and implies that he has done it single handedly, despite the fact that many people have studied cellular automata for years.
I haven't read his book yet, so it isn't clear to me if he is actually saying anything new, or if he is just turning up the volume and pointing a spotlight on himself. But he claims that modeling the world, the universe, the human brain, free-will, snowflakes, turbulent fluid flow, patterns on mollusk shells, flowers, on and on, can be better done with cellular automata than with traditional equations.
Three hundred years of science shows that in many cases simple behavioral traits measured on the smallest scale can be integrated over a larger area leading to equations that predict large scale behavior. This is calculus and the basis of all science and engineering. Wolfram believes that the next three hundred years will show that ascribing small computer programs to the small scale elements will yield even more predictive power of large scale patterns.
There is a certain intuitive appeal for me in his vision. If I were a molecule or a cell in an animal, or a chunk of ice on a snowflake, I am very likely to be affected by the molecule, cell or ice chunk next to me. When I think about how a few cells divide and grow into a fetus, I think an explanation of simple rules where cells affect their neighbors is more likely to form a reasonable model for study than a number of partial differential equations with carefully tuned boundary values. But I'm just guessing.
And guessing seems to be what the new science is about. Deducing the set of simple rules that might explain some observed behavior is impossible according to Wolfram. Therefore, the biggest critique of the great new science he has "invented" is that it has no process. With traditional approaches one can analyze a set of data and fit a curve to it. It is still a bit of an art and one may have to try curves of different forms, but there is a process that even Microsoft Excel can follow to take a rough fitting curve and tweak, adjust, primp and preen until a better fitting curve is found.
Ask Wolfram how one can "fit a cellular automata" to a scanned pattern of a snowflake and he will rant on about how it is impossible. Tweaking the automata rules can give a result with huge differences. Wolfram has managed to do it in a few cases, but this is a man who has locked himself in a closet for ten years with massively parallel computers. Perhaps his own brain has grown very adept at guessing what types of rules might lead to what types of patterns. But the art one man has taught himself in a closet is not the foundation for a new scientific method.
And playing the role of the father of a new scientific method is exactly what Steven Wolfram is all about. He is studying what others who have heralded in a new age in scientific breakthroughs have done. He wants to avoid their mistakes. He wants his new science to grow and flourish. And mostly he wants his name carved into the side of a scientific temple at MIT or Cal Tech so he can be honored after his game of life is over.
His role in the next ten years, spent outside the closet, is not only to foster this new science, but also to continue to build tools which will make exploration of this science easier. Mathematica has been a very successful tool, not just for automata research but also for traditional mathematics problem solving. Wolfram expects to make it even better.
My guess, is that his next tool will be expert at pattern recognition. Pattern recognition is very difficult. Speech recognition has taken a long time to come of age, and it still seems to be acting like a teenager. Visual pattern recognition is still just a toddler, and the science of recognizing patterns of human behavior, body language and tone of voice has yet to be conceived. If Wolfram's genius can be applied to some of these problems, they may reach maturity faster.
But I think Wolfram will do pattern recognition for one reason only - because he doesn't believe that a process for deducing simple rules to explain observed data can be done. Therefore, I predict he is going to pre-generate the first billion iterations of a million different rule sets and store them in a database. When you buy the next version of Mathematica, you'll be able to feed a data set to a server at Wolfram.com and it will offer back a short list of rule sets to explore. Click here to run rule set 567,134 for two million iterations. Click here to buy another rule set that will be even better.
Pattern recognition is not easy and the database he would have to match against is going to be huge. Matching in a timely manner is going to require some incredible traditional mathematics. Maybe the old ways will live on a bit longer.