In my current thrashing about within AI and computational science topics, I returned once again to consider Wolfram’s New Kind of Science material. In brief review, Steve Wolfram has spent the better part of his life fascinated with computational complexity arising from simple algorithms. Initially working from cellular automata systems, Wolfram has built up an impressive set of equivalent computational systems all exhibiting the same fundamental patterns of behavior. These patterns are classified into four types – Type 1 systems evolve into static conditions; Type 2 evolve into periodic patterns; type 3 become “chaotic”; Type 4 evolve into the most interesting behaviour that is best described as “complex” or structured randomness. After spending many years studying a vast variety of simple systems, Wolfram published an enormous treatise, “A New Kind of Science”, back in 2002 to describe his findings.
I had been following Wolfram and the general field of complexity, and in particular automata, off and on throughout my post-college years. When I heard of this new work, I couldn’t wait to receive a copy (a Christmas present from my wife, if I recall correctly). I devoured the book upon receiving it, and was thoroughly…. shocked and disappointed! Here was not a revolutionary theory explaining computational complexity. Instead, Wolfram had produced an overwhelmingly conceited presentation of example after example of complexity arising from simple systems, but with nothing to offer in the way of theory. Indeed, in his opening remarks, he describes his “new kind of science” as that which doesn’t fit the traditional dogma of science requiring hypothesis and proof, and the build up of mathematical explanatory theory. Rather, this seems to be “science by example”. Although intriguing examples are presented, he offers no hope of creating a method by which to discover which simple machines are good at representing a given phenomenon. The applied use of this “science” instantly becomes highly questionable. Wolfram seems to favor brute force searching for machine rules which are of interest.
He is wrong in describing his form of “science” as new. Rather, he should have used the term “primitive”. Wolfram’s study (and those of his followers) is reminiscent of early observational astronomy. When I read through the vast number of examples, presentations of “interesting” observations, displays of aesthetically pleasing patterns, and hear this described as “science”, I am reminded of Tyco Brahe cataloging the exact positions of points of light in the firmament. Even in modern astronomy, there is this role of the passive observer who catalogs observation after observation.
About a month ago, I was driving my family home from the movies, and I observed a fireball. My wife doubted what we had seen, but from my previous experience I was sure it was a fireball. A couple of days later, I happened upon the American Meteor Society (amsmeteors.org), and actually filled out a fireball observation report. Sure enough, within a few days I received an email indicating that three other observations corroborated my sighting. Although this was a “fun” exercise, what purpose is served by the AMS? They simply catalog observations. Meteors are just about fully understood, and certainly no set of amateur sightings is going to advance the state of our knowledge of meteors.
Returning to Wolfram’s field, what I see here is a very primitive set of observations. From both reading his enormous book, and looking through the discussion forums he has sponsored (wolframscience.com), I see very little interest in the creation of an explanatory or predictive theory for computational complexity. I see a fascination with examples, I see an overblown interest in aesthetics (which are truly meaningless, as they are purely a function of the presentation of the data generated by these systems), and just about no interest in applications of the field of knowledge to address real world problems. What I see, in essence, is an amazingly powerful failure.
Despite my grim assessment of Wolfram’s approach to the field of study he has (primarily) defined, I still believe it is a fundamental key to understanding much of the world that surrounds us.