There's a powerful meme in the branch of science closest to the heart of philosophy that envisions the universe as a great Computation happening on a massive Computer¹ whose parts are the atoms (or subatomic particles, or quarks, or what have you) and whose principles of execution are not the laws of physics as we know them but the laws of physics as they are. Further, there are people who believe we can safely ascribe a significant probability to the postulate that we humans are actually programs or side-effects of programs running on this Computer. These are often people who strongly disbelieve in the existence of God and other invisible dragons, but for some reason they have more trouble disbelieving in an invisible Computer running a simulation that happens to be this world.

Cellular Automata in Science

Stephen Wolfram has enshrined this broken fragment of misplaced deism in his "principle of computational equivalence": "...all processes, whether they are produced by human effort or occur spontaneously in nature, can be viewed as computations" (NKS, 715). The rationale behind this principle is devious; Wolfram devotes the previous seven hundred pages of A New Kind of Science subtly broaching the following argument:

1. EITHER
   1. The laws of nature are continuous laws, specifically in the form of partial differential equations.
   2. Such laws can be approximated by cellular automata.
   OR
   1. The laws of nature are discrete laws, specifically in the form of cellular automata.
2. Science is all about the study of the laws of nature.
3. Therefore, all science can be reduced, in principle if not in fact, to the study of cellular automata.

Typically, science benefits from reductionism. In the beginning, Newton reduced the workings of Celestial and Terrestrial Mechanics (which were, since Aristotle, necessarily separate disciplines) into three or four axioms together with the efficacy of mathematical analysis. Post-newtonian engineers only need to buy one $200, 900-page textbook titled, "Mechanics", instead of two $200, 900-page textbooks. Excellent! Then the alchemists discovered through generations of blind stumbling and self-poisoning that their chemistry happened to also reduce, in many ideal circumstances, to physics. The rest of the sciences follow suit, with some exceptions made for the social sciences by pointing frantically at statistics.

However, too much reduction can be a problem². A topologist might consider a coffee cup and a donut to be equivalent, in some sense, but no sane person would put coffee in a donut with the intent to drink it. We still have a need for chemists because our physics isn't sufficient to solve anything more complicated than the fine structure of a hydrogen atom. Once you get up to the level of a human being, really nobody knows exactly what's going on, and the science drifts slowly into an art — the art of medicine, the art of psychology, the art of nutrition, and the art of physical training.

I'm aware now that I am arguing that there is some 'irreducible complexity' inherent in the different branches of science that prevents them all from collapsing into the study of cellular automata, as Wolfram would have us believe. The Intelligent Design and Creationist community, in their infinite stupidity, have already co-opted this form of argument for their continued assault on science, and so I find myself in the undesirable position of criticising their argument that certain organs have so much irreducible complexity that prevents them from simply evolving, while at the same time arguing that chemistry, biology, et. al. have their own irreducible complexity that prevents them from simply being the study of cellular automata.

The difference between these two arguments is that in the case of your run-of-the-mill Creationist, most of the things they point to as examples of irreducible complexity can be explained. How did the eye become so complex? Well, it started out as a light-sensitive cell, which then developed into a light-sensitive organ, and so on. In the case of the massive reduction of the sciences, I can point to specific theorems. Why can't we in principle compute the fine structure of all the elements, and turn chemistry into physics? Because after hydrogen, you run into the three body problem, which asserts that any system with more than three components under the influence of a force like gravity or electricity becomes unpredictable rather quickly.

Having said these things, there are actually some valid uses for cellular automata in physics. Wolfram developed some of these himself. They're particularly good for what I want to do in life: approximating partial differential equations.

Having written then about the principle of computational equivalence, the bedrock of Wolfram's point of view, I would like to point out just how frightening his and his company's treatment of computation and science is. Remember, according to Wolfram, everything — hurricanes, plant growth, cognitive patterns, mollusk shells, and so on — can all be viewed as kinds of computation. They're all programs running in the great Computer on its infinite, discrete, cellular automata grid, and those patterns of dots are more than available for Wolfram to stamp his patent and make a profit.

"I am my own reality check"³

After getting out of the science business, Wolfram went on to create Mathematica, a computer algebra system. Mathematica has gained a tremendous amount of support among academics. There are many reasons for this: Wolfram Research tends to hand out cheap bulk licenses, Mathematica has a mode in which it mimics handwritten mathematical notation, several textbooks have been written whose examples are in Mathematica's language, and so on. Full disclaimer: I used Mathematica in college, under my college's discount license. I used to think it was the best thing since sliced bread, mostly because it could differentiate faster than I could. But I won't use it any more: Mathematica is written on the back of what is essentially intellectual servitude by programmer-mathematicians who have literally no right to their work.

This atmosphere of refusing to give credit where credit is due infuses everything Wolfram touches. The massive tome, A New Kind of Science, provides little to no reference to any contemporary mathematician; the end notes are worthless. The real mathematician who discovered that Wolfram's coveted Rule 110 could do universal computation? Matthew Cook was given one line of mention in the acknowledgements. After rightfully splitting from Wolfram Research, Cook and the academic institutions that published his results were hounded by lawsuits⁴.

Wolfram's history with Mathematica and the associated bits of his company's legacy in the cellular automata area has left a very sour taste in my mouth. The first rule of our business is that a result is just a conjecture until its been proven, and it's not enough to say "I've got a proof of X, but I'm not going to tell you." Nobody believed Fermat had proved something just because he said so.

Because of this fundamental principle in the sociology of mathematics, I can't accept any proof that substantially and irreplaceably relies on a proof from Wolfram's Mathematica, or a citation from one of Wolfram Research's self-edited journals, or a paper with Wolfram's name on it — in all three cases I don't have sufficient confidence that the real substance of the work is there for people to review. I can't review the code of Mathematica because it's locked away inside the executable, and the code is locked away behind a gauntlet of NDA's. I can't review what's really going on behind one of Wolfram's papers because for all I know the real work was done by some uncredited lackey at Wolfram Research, and he or she is no doubt unavailable for questions.

Contrast this with the way real mathematics works on the internet: Timothy Gowers, a mathematician at Cambridge, opened up his blog⁵ to anyone and everyone who could help contribute toward a proof in combinatorics. From the outset he specifically mentioned that credit for the proof would be shared by everyone, no matter how small their contribution, perhaps by publishing under a collective pseudonym, the way Nicholas Bourbaki did, with a link to a full list of collaborators. Such a theory of mathematical collaboration is inconceivable to Wolfram and his lot; it's The Cathedral and The Bazaar all over again.

So now I hear Wolfram and his crew of uncredited, disassociated, intellectual minions have put together a search engine. In classic Wolfram style, they've chosen to ignore what millions of people have put on the Web and instead rely on various public and private data sources. They slapped a natural language processing front-end onto Mathematica's syntax and pretended that it was an innovation. Nevermind that there's no artificial intelligence inside the thing at all; it's merely a better written, better funded example of the 16-year-old's chat bot:

if (response == "What's up?") { print "Your mom."; }
if (response == "Hello.") { print "Hello."; }

and so on.

This is really the best that the Information Age can come up with? Minsky knew back in the 60's that you couldn't expect to get to AI by hard-coding responses into the computer.

Resistance

These territory wars in science would seem far removed from the quotidian struggles of the working man and woman, were it not for the fact that today's everydayness was born out of the science and the struggle of the past. There'd be no Google if the algorithms for linear algebra were repressed behind some indefinite monopoly held by a patent troll. Our science is part of our culture, and even if only a small fragment of the population believes in it, works with it, and even likes it, it can't be held back in the monolithic Cathedral. Wolfram's operating under a business model that was outmoded before he started hiring people to develop Mathematica for him; no doubt it will collapse like a hollow idol after he is gone.

This writeup has been illustrated with comics from xkcd:

1. #505: A bunch of rocks
2. #435: Purity
3. "A Study in Complexity". Robert Lee Hotz, Technology Review (October 1997) 23-29.
4. "Matthew Cook", Wikipedia.
5. "Polymath1 and open collaborative mathematics", Timothy Gowers.