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Culture, history and society

Culture, history and society

Opening the book of revelations

29 Aug 2002

A New Kind of Science
Stephen Wolfram
2002 Wolfram Media 1197pp £40.00/$44.95hb

Radical vision

Science is a uniquely public form of knowledge. What distinguishes it from other forms of knowledge is that scientific hypotheses can be checked by anyone with the will and resources to do so. In principle, race, gender and nationality form no impediment to doing science, although the reality is sometimes different. Nor need the practice of science be confined to people. Tool-using animals, aliens and suitably programmed computers might all generate and test hypotheses, reject the bad ones and put the good ones to use.

The practice of science is, however, a social activity that differs greatly from culture to culture and from era to era. Today’s scientific world, in which research is by and large funded by universities, corporate labs and government, is very different to the one inhabited by either Newton or Darwin. The vast majority of scientists now publish articles in peer-reviewed journals – although one might be tempted to say that peer review, like democracy, is the worst method to make progress, until one examines the alternatives.

The current explosion in scientific inquiry began 400 years ago when a mechanistic paradigm for scientific investigation was first adopted. The analogy between physical systems and machines received a powerful boost from the discovery of the laws of classical mechanics and the development of calculus. The mechanization of industry, starting in the 18th century, provided further encouragement to the mechanistic paradigm, which eventually led to the development of thermodynamics in the 19th century.

Indeed so strong was the mechanistic paradigm that Maxwell felt obliged to provide a model of electrodynamics in terms of gears and pulleys – a model that was so much more complicated than Maxwell’s equations themselves that it soon fell into disuse. One can argue that the exponential growth of science and technology over the last few centuries has stemmed from a simple positive-feedback loop. Machines inspire ideas; ideas inspire machines.

Over the last 50 years, science has revolved around two exceptional machines – the cell and the computer. Biology has made huge advances by elucidating the chemical mechanisms that underlie life, while the computer has transformed how we do science and has generated entirely new fields of research. The computer is, however, completely unlike the machines contemplated by Newton and Carnot: it generates lots of heat, but it performs no work. It also processes information to an extent that has vastly exceeded expectations.

John von Neumann once claimed that the US would never need more than a handful of computers, because there would be no demand for them. To paraphrase Bob Dylan, von Neumann may know what we need, but Intel knows what we want.

Enter Wolfram

Just as those in the 17th century saw the world in terms of clockwork, so we in the 21st century are ready to see the world in terms of computation. That is the view presented by Stephen Wolfram – the physicist who developed Mathematica software – in his long-awaited book A New Kind of Science. The type of computer that Wolfram urges us to consider is the “cellular automaton” – an array of information-containing cells that update themselves in parallel using the same automatic updating rule for each.

The simplest 1D cellular automaton consists of a line of squares that can each be either black or white, like a chessboard. Each time the rule is applied the computer creates a new line of squares. The line is usually displayed underneath the previous line so that the evolution of the system can be tracked. Many different rules and initial states can be considered, and the patterns that emerge as the calculations unfold can then be correlated with observed patterns in nature.

Cellular automata, which have been used for information processing since the 1950s, can be thought of as discrete analogues of partial differential equations. They are therefore particularly useful in physics, for example to simulate the behaviour of particles moving on a lattice. It turns out that cellular automata can also exhibit self-reproducing structures analogous to living systems.

A New Kind of Science argues that a wide variety of problems in complex systems – from biology and economics to gravity and turbulence – should be approached in terms of information processing in general and cellular automata in particular. This is the “new” science of the book’s title.

Wolfram has spent more than ten years writing the book, working largely in isolation from the scientific community – apart from the help of hired research assistants. Throughout this time he has balanced his writing duties with his responsibilities as chief executive of Wolfram Research, the company that he founded in 1986 to develop Mathematica. Ironically A New Kind of Science represents a very 19th-century kind of science in which the wealthy entrepreneur retires from society and uses his fortune to produce a big, self-published book.

For make no mistake, this is a very big book – with more than 1200 pages, 350 of which are “notes” in small print. Unlike the most important scientific discoveries of the 20th century, which were published as papers in journals, Wolfram is making a bid once again to report scientific advances in the form of a popular book. Whether the book has the scientific influence it aspires to – Wolfram likens it to Darwin’s Origin of Species – will have to await the judgement of the scientists who choose to work on the topics it presents.

Revelations without references

A New Kind of Science is a curious fusion of popular exposition, original scientific work, history and prophecy. The book provides an accessible introduction to cellular automata, and includes hundreds of pictures and many examples. It also presents new scientific work, notably the proof that a simple cellular automaton is computationally universal; a proof – one discovers deep on page 1115 – that was actually discovered by Wolfram’s assistant Matthew Cook in the mid-1990s.

The 350 pages of notes contain a mine of information on the history of computation, physics and mathematics. The book also offers a large number of what can best be described as “conjectures” on the role of information processing in economics, life, perception, fundamental physics and a host of other fields. These conjectures do not represent fully worked out scientific results – they are also not presented in a form that allows them to be verified by others. Instead they are prophecies concerning many problems of complex systems and fundamental physics that Wolfram predicts we will eventually be able to understand in terms of information processing.

The book is also notable for what it lacks. There are almost no references to the thousands of previously published articles or books on the subjects covered, with the exception of some of Wolfram’s own papers. The main text studiously avoids mentioning the origins of many of the ideas presented. Rather these ideas are said to have arisen from an ongoing series of scientific revelations experienced by Wolfram. The tone of these pages is elevated, almost ecstatic.

This approach is likely to appeal to the general reader who is hungry for inspiration. But those who are familiar with the field will find it alarming to see page after page of results – bearing a striking similarity to previously published work – represented as Wolfram’s personal scientific revelation. For example, Wolfram repeatedly insists that he was the first to discover that simple computational systems can give rise to arbitrarily complex behaviour. But only a legalistically narrow definition of the word “simple” can make this statement true.

More than half a century ago Alan Turing, Alonzo Church and Kurt Gödel discovered simple computational systems that can give rise to arbitrary complexity. What Wolfram has done is to provide a computationally universal cellular automaton that requires a smaller number of states than von Neumann’s computationally universal cellular automaton. (In addition Wolfram’s computationally universal cellular automaton, though simple in its dynamics, requires a complicated initial condition to perform universal computation.)

Time and again, Wolfram takes credit for results that closely resemble the work of others. Of course, if egotism excluded one from doing science, then there would be few scientists left. Wolfram is at least aware of his lack of modesty, and claims to have avoided giving credit to make the book as readable as possible. This excuse may ring hollow for the hundreds of other scientists who have contributed to the field.

Conjectures and prophecies

The 350 pages of notes do rectify some of these omissions. Here Wolfram goes into considerable detail about the history of various ideas, and takes lawyerly pains to differentiate his approach from that of others. This detailed exposition naturally puts Wolfram’s ideas into a more balanced perspective. In many ways the notes are the most interesting part of the book. But readers who refuse to plough through them – unfortunately that will include most people – will fail to grasp the true impact of A New Kind of Science.

Three key points emerge from the notes.

* A large part of the book is devoted to a popular exposition of cellular automata. This part is well written and accessible, and is illustrated by copious pictures of cellular automata in action.

* The book does contain a number of new scientific results that could be verified by others. These include the proof that simple cellular automata can be computationally universal, and the definitions for a variety of computational structures. These results are confined to a relatively narrow field of computer science, but are likely to be of interest to some computer scientists. The actual verifiable scientific results make up a relatively small part of the book, roughly equivalent to a few papers in Wolfram’s journal Complex Systems.

* Much space has been devoted to prophecies – conjectures on the way that ideas such as computational universality are likely to affect economics, biology, quantum gravity and so on. These prophecies are the most fascinating parts of the book. They are not scientific results per se, being in too preliminary a form to be directly verified, rather they are predictions of the future direction of science. Wolfram is candid about the prophetic nature of his work, and he states repeatedly that it will be years before scientists appreciate the true impact of his book. Given the uncertainty associated with foreseeing the future, many or most of these prophecies are likely to prove false. But if any of them do prove to be true, then that would be interesting indeed.

Some of Wolfram’s prophecies are more likely to be correct than others. These include the idea that computational universality is related to the generation of complexity in the universe. This idea was published by others before Wolfram, but the author is a convincing and passionate advocate for the importance of computational ability in the universe.

Wolfram’s prediction that many physical systems are non-ergodic – and so do not obey the second law of thermodynamics – seems less likely to be true. The mere existence of non-ergodic reversible cellular automata is not enough to falsify the second law. Similarly his prediction that classical computational structures may be able to reproduce quantum structures in space-time also seems somewhat unlikely given the nature of quantum correlations. (On the other hand, as I and others have suggested, quantum cellular automata might be able to reproduce these structures.) The answers to these and other questions must await the scientific development of Wolfram’s ideas.

A New Kind of Science deserves to be popular. Whether or not computers are the paradigm for all future scientific advances, learning how to perceive the world in terms of information processing is fun. The book’s grandiose vision has generated considerable controversy. Readers’ reviews posted at the on-line bookstore Amazon.com were running four to one against at the time of writing, although when I first checked the site a practitioner of the new kind of science had hacked in and replaced all the reviews with the single phrase “I don’t like it”.

But many parts of the book are rewarding. The ideas are good, the predictions are entertaining, and the accurate notes provide some inoculation against the presentation of science as a series of Wolfram’s revelations. However, the lack of references is a serious hindrance to young scientists wishing to use the book as a starting point for research on complex systems. By failing to tell us where the ideas in his book come from, Wolfram has done himself a disservice. He detracts from the truly new ideas that he presents.

Wolfram has plans for an on-line bibliography for the books – although not the papers – that he consulted in writing his book. In my view Wolfram should write a few, good old-fashioned peer-reviewed papers – with references – presenting his results in a way that put them in the context of existing work and allows others to reproduce them. Now that might really start a new kind of science.

Buy the book
A New Kind of Science: Amazon UK/Amazon US

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