The Most Arrogant Science Book Ever Written

Source: The Most Arrogant Science Book Ever Written, MQTate, 22:37, uploaded 2026-06-15.

MQTate’s video is an animated reading of Cosma Shalizi’s 2002 review of Stephen Wolfram’s A New Kind of Science. The review grants Wolfram real mathematical ability and one substantial result, then argues that the book mixes familiar ideas, unsupported speculation, and a style of authorship that turns shared scientific work into the product of a solitary genius. MQTate adds a few editorial comments, including one about Wolfram’s use of Mathematica for formulae.

Cellular automata and Wolfram’s early work

The review begins with Wolfram’s reputation as a child prodigy who earned a PhD in theoretical physics at a young age. In the early and mid-1980s he joined the renewed interest in cellular automata, mathematical systems that model space as a regular grid of discrete cells. Time advances in ticks. Each cell changes state according to a fixed rule that examines its neighbours and its own previous state.

John von Neumann introduced cellular automata in the 1950s while investigating whether a machine could reproduce itself. The answer was yes. The systems later found uses in models of fluid mechanics, pattern formation, and self-organising systems. John Conway’s Game of Life gave the subject a popular centre: a very small set of rules could produce structures that were difficult to predict. Cheaper desktop computers made these patterns easier to see, and Ed Fredkin’s work encouraged speculation that the universe itself might operate as a cellular automaton.

Wolfram’s first paper on the subject, from 1983, focused on elementary cellular automata. Each cell has two possible states, and its neighbourhood contains the cell immediately to its left and right. Eight possible neighbourhoods produce 256 possible rules. Wolfram introduced the numbering scheme still used for these rules by reading the output bits as a binary number and converting it to base ten.

He later proposed four classes for the long-term behaviour of cellular automata. Class 1 settles into a fixed state. Class 2 repeats a pattern. Class 3 becomes pseudo-random and chaotic. Class 4 produces structures that remain ordered and complicated at once. The review says the classification never became precise enough to explain much, and that even its author could not turn it into a useful working theory.

Wolfram then helped develop Mathematica, a system for symbolic mathematics and graphics. After disputes with co-authors, which the review says were later settled, he withdrew from ordinary scientific life into the Mathematica business and a larger theory about the universe. The theory treats reality as a simple discrete program of some kind. The book’s method follows from that belief: search through simple programs and see whether they reproduce striking features of the world.

The review also describes a 1986 patent application in which Wolfram claimed the use of cellular automata as discrete approximations to partial differential equations. Shalizi says the idea was already common in the field and had appeared in two papers from a 1983 conference that Wolfram helped edit. This is a claim made in the review, and the video does not supply the patent or conference papers for inspection.

A method and a claim about reality

The method in A New Kind of Science asks scientists to replace complicated continuous models, often expressed through calculus or probability, with simple discrete programs. These programs need to reproduce a phenomenon’s visible or qualitative features. Wolfram also makes the larger claim that the universe itself may be generated by a simple program, famously describing it as something that could fit into four lines of Mathematica.

The book offers cellular-automaton patterns resembling coral or trees and examples of pseudo-random number generation. Shalizi divides the result into familiar truths, new claims, and claims that remain unsupported. Simple rules producing complex behaviour is a real observation. It also belongs to a much older scientific and mathematical tradition, from the search for simple laws in physics to the work of Alan Turing, Andrey Kolmogorov, and Emil Post.

The review makes the point through a personal story. Shalizi once found a way to solve systems of linear equations and later learned that it was the established technique called reduction to Jordan normal form. His discovery was real as a private event. It did not make the method new to mathematics. He places Wolfram’s discovery of complexity from simple rules in the same category.

The book also presents Mathematica’s transformation rules as unusually close to the way the human mind works. Shalizi identifies this as a restatement of the production-rules approach to cognition developed by Herbert Simon and Alan Newell in the 1950s. That work also helped lead to Lisp, from which Mathematica descends. In the fields the reviewer knows, Wolfram’s predecessors had already developed similar ideas, then tested their consequences, found limits, and sometimes abandoned them. The problem lies in the book’s treatment of those results as isolated revelations.

Wolfram’s use of the word complexity creates a second problem. The review says he avoids existing measures and declines to give a quantitative measure of his own. He calls a thing complex when it looks visually interesting or passes standard randomness tests. Visual interest describes the observer’s perceptual system as much as the object. Passing a randomness test says that the output has avoided a low algorithmic complexity, in the sense associated with Per Martin-Löf. It does not provide the broad theory of complexity that the book needs.

What a toy model can show

The gap between an illuminating model and an explanation becomes sharper in physics. A cellular automaton might approximate classical physics if its cells were small enough and had enough states. The universe, however, is described to a much better approximation by quantum and relativistic physics. Discrete versions of special relativity can be built, and the video names Mark Smith’s 1994 dissertation as an example. General relativity and gravity remain unresolved in this framework. The review also cites Scott Aaronson’s result that Wolfram’s scheme must conflict with special relativity, quantum mechanics, or both.

Biology supplies a parallel case. A cellular automaton can produce spots that resemble a leopard’s coat. Alan Turing’s work on morphogenesis in the 1950s gives a serious basis for modelling biological patterns, and a tuned model can produce shapes resembling animal coats or butterfly wings. The resemblance does not identify the mechanism that creates the pattern in an organism. As biologists uncover the actual mechanisms of morphogenesis, they become more complicated and less elegant while still proving reliable. A model that produces leopard spots can leave the question of why polar bears lack them untouched. Evolution and adaptation disappear when visual resemblance stands in for explanation.

Qualitative agreement also fails when a question needs quantitative accuracy, whether for engineering or for choosing between several hypotheses that produce the same visible result. Toy models can be quantitatively accurate in special circumstances. The review treats those cases as limited conditions rather than a general licence to replace established models with simple programs. It quotes Wolfram’s summary of his method, “I am my own reality check,” as the clearest statement of the problem.

Rule 110 and the question of credit

The book does contain an impressive new result. Rule 110, one of the elementary cellular automata, can support universal computation. Alan Turing showed in 1936 that a Turing machine can compute every recursively definable function and that a universal machine can emulate any other Turing machine. Emil Post’s tag systems are equivalent to Turing machines. Wolfram describes a cyclic tag system and sketches how gliders in Rule 110 could implement one on an infinite lattice. Rule 110 became the simplest known cellular automaton with universal computational power.

The result matters to researchers who study dynamic models of computation. The review places that community at roughly a thousand scientists and mathematicians and points out that universal computation appears in many systems. Christopher Moore’s idealised pinball machine, described in a 1990 paper, is one example. Wolfram’s wider conclusion is that the equivalence of universal computers lets us learn about the whole universe by studying Rule 110. The review says that conclusion does not follow from the proof.

The authorship dispute makes the result central to the video’s account of Wolfram’s arrogance. Matthew Cook, a graduate student working for Wolfram, developed the intricate construction that implements a cyclic tag system in Rule 110. The review describes a contract that gave Wolfram control over when the result could become public and allowed him to claim it himself. Wolfram treated the result as a trade secret. After Cook and Wolfram fell out, Cook presented the proof at a 1998 conference. Wolfram sued, or threatened to sue, Cook, the conference organisers, and the proceedings’ publishers. The dispute was eventually resolved, and Cook’s paper appeared under his own name in Complex Systems.

The book’s style and its missing predecessors

Shalizi’s review turns from substance to style through the acknowledgements. Scientific acknowledgements usually credit sources, colleagues, and the people who endured the work. Wolfram thanks people for giving him the chance to develop ideas that he presents as his own. The review reads this as a deliberate refusal of ordinary scientific modesty. It also notes Wolfram’s use of the passive voice when describing other people’s work and his claim that this style helps readers understand difficult ideas.

References perform a practical job in scientific writing. They show what a result relies on, what it changes, and where its author disagrees with existing work. A New Kind of Science runs to about 1,100 pages, written over a decade, yet Wolfram deliberately leaves out the usual citations. The review allows that Darwin omitted references from The Origin of Species to get the book into print quickly. Wolfram had time to identify his predecessors. In the endnotes, where he does discuss earlier work, Shalizi finds claims that are misleading, wrong, or both.

The review borrows Martin Gardner’s description of the sincere pseudo-scientist from Fads and Fallacies in the Name of Science. Such a person regards himself as a genius, treats colleagues as fools, sees persecution around him, attacks the most established scientists and theories, and coins difficult terms. Shalizi considers the first, second, and fourth traits clear in Wolfram’s book. The third is absent or muted. The fifth appears only weakly. MQTate adds an editorial objection: Wolfram writes mathematical formulae in the endnotes as Mathematica code, even where ordinary notation would make the mathematics clearer.

The video also mentions a warning attached to the Wikipedia article about A New Kind of Science, which suggested that undisclosed payments may have influenced its creation or editing. That is an editorial aside in the video rather than part of the review’s scientific case, and it needs independent verification before it can support a claim about the book or its reception.

A serious result inside a bad book

The review’s final division is plain. The book contains common truths about simple rules and complex outcomes, a large body of speculative claims, and one mathematically important result whose central construction came from Cook. Wolfram presents the whole body of work as the insight of a solitary genius working outside a complacent scientific establishment.

Shalizi does not object to speculation, radical proposals, strong personalities, or very long books. He asks for arguments, evidence, criticism, and honest credit. His objection concerns a book that ignores criticism, claims familiar ideas before popular audiences, and turns a thousand-page defence of its author into a display of self-regard. The conclusion is a judgement about scientific conduct as much as a judgement about cellular automata. Wolfram had talent and had shown promise. The review says he spent both on a book that will set its field back by years.

Further reading / references

• Cosma Shalizi, “A New Kind of Science”, 2002.
• Stephen Wolfram, A New Kind of Science, 2002.
• Stephen Wolfram, “Random Sequence Generation by Cellular Automata,” Advances in Applied Mathematics, 7(2), 123–169, 1986.
• Christopher Moore, “Unpredictability and Undecidability in Dynamical Systems,” Physical Review Letters, 64(20), 2354, 1990.
• R. Adejoh, A. Jakoby, S. Mohanty, and C. Schindelhauer, “How Pinball Wizards Simulate a Turing Machine,” arXiv:2510.02560, 2025.
• H. A. Lim, “Cellular-Automaton Simulations of Simple Boundary-Layer Problems,” Physical Review A, 40(2), 968, 1989.
• Martin Gardner, Fads and Fallacies in the Name of Science, 1957.