Dean's Den

My 2003 defense of Stephen Wolfram

In the February 6, 2003 issue of E-Skeptic, the electronic version of SKEPTIC Magazine, David Naiditch criticized Stephen Wolfram's "A New Kind of Science":

A New Kind of Science?

David Naiditch

On February 1, physicist and computer scientist, Dr. Stephen Wolfram, spoke to a full house at Caltech's Beckman Auditorium about his grandiose proposal for a new and improved kind of science. After Wolfram spoke for about an hour, he answered questions from a panel of distinguished scientists, and then responded to questions from the audience.

Stephen Wolfram was a child prodigy. He received his doctoral degree in theoretical physics from Caltech when he was only 20, and was the youngest scientist to receive a MacArthur award for his work in physics and computer science. Wolfram made a fortune developing Mathematica--a powerful software program that has become a standard for technical computing. Then, staring in the early 1980s, he began working on cellular automata.

To understand cellular automata, imagine a grid of squares where each square can either be black or white. From an initial state of a few black squares, a simple rule is applied over and over again. This rule determines whether or not a square changes its color, and is based on the color of the square's nearest neighbors. For instance, a square might change from white to black only if its nearest left neighbor is black and its right neighbor is white. From such simple rules, intricate patterns can be generated, some of which are highly symmetric like snowflakes, others that appear random, and others that are self-similar fractals. Wolfram discovered that even the simplest programs yield patterns of astonishing complexity.

In May 2002, Wolfram published his book, A New Kind of Science, which for the first time revealed to the world the results of his research on cellar automata and related fields. Wolfram's book was an immediate success and caused a great deal of controversy. According to his publicist, the initial print run of 50,000 copies sold out the first day, with over 200,000 copies sold at the time of this writing. The book has been reviewed in most major media venues (New York Times Book Review, New York Review of Books, Science, Nature, etc.) and Wolfram has been featured in such national publications as Time and Newsweek.

Wolfram proposed a new way of doing science. For hundreds of years, scientists have successfully used mathematical equations that show how various entities are connected. For instance, Newton's equation, F=ma, shows us how force (F) is related to mass (m) and acceleration (a). The problem with this approach is that equations fail to describe complex phenomena we see all around us, such as the turbulence of boiling water or the changing weather. To describe such complex phenomena, Wolfram proposes that scientists employ the types of rules used in cellular automata and related areas of computing.

In Wolfram's theory the universe is a giant computer. This computer produces complexity through the repeated execution of simple rules. Instead of using equations to describe the results of nature's computer programs, Wolfram tells us to examine the programs themselves.

At the Caltech event Wolfram's ideas were challenged by a stellar panel of scientists: Steven Koonin, Chris Adami, John Preskill, and David Stevenson. Steven Koonin, the moderator, is a full professor of physics at Caltech and received the Caltech Associated Students Teaching Award, the Humboldt Senior Scientist Award, and the E.O. Lawrence Award in Physics from the Department of Energy. Chris Adami is faculty associate and director of the Digital Life Laboratory at Caltech, principle scientist in the Quantum Technologies Group at the Jet Propulsion Laboratory, and author of the textbook Introduction to Artificial Life. John Preskill is the John D. MacArthur Professor of Theoretical Physics at Caltech and the director of the Institute for Quantum Information. David Stevenson has been a physics professor at Caltech since 1980 and is the recipient of a Fellowship of the Royal Society of London and the Feynman teaching prize.

Although it is clear that Wolfram is no crank, not someone skeptics would label a pseudoscientist, skeptics will notice that, despite his flawless credentials, staggering intelligence, and depth of knowledge, Wolfram possesses many attributes of a pseudoscientist: (1) he makes grandiose claims, (2) works in isolation, (3) did not go through the normal peer-review process, (4) published his own book, (5) does not adequately acknowledge his predecessors, and (6) rejects a well-established theory of at least one famous scientist.

First, throughout his lecture Wolfram made the grandiose claim that his work amounts to a "paradigm shift" of how we do science. Furthermore, Wolfram claims his work will shed light on a broad range of fundamental issues that have stymied scientists for ages, including the randomness found in nature, biological complexity, the nature of space-time, the possibility of a "theory of everything," and the scope and limitations of mathematics. Wolfram even claims his insights can be used to tackle the ancient paradoxes of free will and determinism, and the nature of intelligence.

Second, like so many pseudoscientists on the fringe, Wolfram did his work in isolation for 20 years. Although he was running a company that required he interact with employees and customers (many of whom are scientists), his work on cellular automata was kept largely to himself.

Third, Wolfram admitted that he had enough material during this time for hundreds of scientific papers, yet he did not bother to publish any of the material or present his ideas at any scientific conferences. Thus, any critical feedback that might have improved his theory before it was cemented in inky stone was eschewed, making change at this point in the development of his theory much more unlikely.

Fourth, in May 2002 Wolfram revealed his work for the first time in his massive self-published tome, A New Kind of Science, coming in at 1,268 pages. This is not because he could not get a publisher, or that no publisher would print such a large book. Readers may recall Stephen Jay Gould's magnum opus, The Structure of Evolutionary Theory, was released about the same time by Harvard University Press, topping out at 1,433 pages. Between the two, bookstores shelves were sagging under the weight of Big Science. Wolfram self-published because he wanted to maintain tight control over the production and distribution of his life's work.

Fifth, not only did Wolfram work alone, during his Caltech lecture not once did he acknowledge the work of other scientists. In addition, throughout the 850 pages of general text, and 350 pages of notes, there are no traditional references to be found in A New Kind of Science: no references to scientific papers, no citations of books related to the topic, and no bibliography. In fact, the notes section consists mostly of further commentary on his own work earlier in the book, with occasional reference to other scientists and scholars without actually providing citations to their work. In actual fact, many of Wolfram's ideas are not new. They can be found, for instance, in James Gleick's popular book, Chaos: Making a New Science, and in Robert Wright's book, Three Scientists and Their Gods, which describes the work of Edward Fredkin. Fredkin, like Wolfram, believes that the universe is a digital computer. What is new in A New Kind of Science is Wolfram's claim that cellular automata, instead of being peripheral to science, should be central to the way science is practiced.

Sixth, Wolfram raised the hackles of the scientific panel as well as the audience when he rejected a well-established theory of a famous scientist: none other than Charles Darwin and his theory of natural selection. Although Wolfram does not claim natural selection is totally without merit, he does claim it is insufficient to fully explain the complexity found in the biological world. For instance, he claims that natural selection can explain phenomena such the lengthening of bones, but not fundamental changes to an animal's morphology. Wolfram also claims that, contrary to popular belief, evolution is not very important to biologists.

Panel member Chris Adami, who researches how complexity arises from natural selection, took exception to these claims. Adami pointed out that Darwinian evolution in general, and natural selection in particular, is of fundamental importance to biologists; without it, biology does not make sense. Adami also argued that the kind of complexity biologists are most concerned with is different from the kind of complexity presented by Wolfram. Wolfram tries to explain complex patterns such as those found on seashells. According to Adami, such complexity is based on our perception and our inability to perceive the simple rules that can generate such patterns. In contrast, biologists are concerned with functional complexity that arises as organisms adapt to various environments, thereby increasing their chance of survival and reproduction. Adami finds it inconceivable that the functional complexity of, say, a living cell, is due to a simple underlying rule. John Preskill also challenged Wolfram on this point, noting that cellular automata are very fragile. Any "mutation" to cellular automata is disastrous. Biological systems, on the other hand, must be stable even when mutations and other errors are introduced.

In addition to these criticisms, other objections were raised to Wolfram's ideas. Steven Koonin pointed out that a paradigm shift cannot arise simply by asserting something is a paradigm shift. One must convince the scientific community that this description is warranted. To the contrary, according to David Stevenson, Wolfram fails to satisfy rules of what constitutes good science. Creating programs that generate images that look like things found in nature is not sufficient. One needs specific predictions. Wolfram does not offer any laboratory experiments or observations that could verify or falsify his grand claims.

Wolfram responded that the requirement of falsifiability does not apply to mathematics or computer science. He argued that his claims have the character of mathematics rather than physics, employing calculus as an analogy. Newton= showed how calculus provides a new way of doing science. Calculus itself, however, is not tested to determine whether it is true or false. Its justification is that it works. The panel rebutted that if this analogy is true, then Wolfram is just proposing a new kind of computational method, not a new kind of science.

Objections were also raised that Wolfram's theory lacks explanatory power. Not everything that is useful is explanatory. For example, David Stevenson explained that Feynman diagrams are very useful and can provide answers to problems of quantum mechanics much faster than answers obtained by computational methods. However, Feynman diagrams do not provide an explanation or deeper understanding of quantum phenomena. Again, it was emphasized that Wolfram seems to be offering a new kind of computational tool, not a new kind of science.

According to Wolfram, by generating patterns on the computer screen that resemble, for instance, snowflakes, he has explained how snowflakes acquire their complex symmetric structures. Panelists countered that such inferences are unwarranted. The resemblance does not, by itself, mean nature uses rules to generate snowflake patterns. Wolfram needs to demonstrate how nature physically instantiates the rules of cellular automata. Evidence is needed to show that the shape of snowflakes was produced by a physical mechanism whose behavior resembles the rules used by a computer.

John Preskill observed that few of the ideas presented in Wolfram's book are concrete enough to be usable by research scientists. Wolfram's answer that no experts in his field yet exist, does not address the problem. For example, Wolfram's most original ideas--such as the attempt to incorporate quantum theory and gravity using random network models and path independence--are too speculative to be of use to scientists.

At the end of the Caltech program the moderator, Steven Koonin, asked the panelists to predict whether in 20 years Wolfram's A New Kind of Science will be viewed as a paradigm shift. The unanimous answer was "no." One panelist said, "it is not an approach that has much promise," while another noted that Wolfram's ideas are the "Emperors New Clothes." Wolfram tried to get in the last word by stating that this reaction from the panelists is just what one would expect from a paradigm shift. But Steven Koonin rejoined that this is also just what one would expect if Wolfram's ideas did not amount to a paradigm shift. Ultimately, time will tell who is right.

I responded immediately and, in the Volume 10, No. 3 issue of the printed version of Skeptic Magazine, my letter was published in full:

David Naiditch's comments on Stephen Wolfram well-illustrate why I don't trust the Skeptics Society:

"Wolfram possesses many attributes of a pseudoscientist: (1) he makes grandiose claims, (2) works in isolation, (3) did not go through the normal peer-review process, (4) published his own book, (5) does not adequately acknowledge his predecessors, and (6) rejects a well-established theory of at least one famous scientist."

Yet these are precisely the attributes of the greatest scientists as well. Must we skeptics be comfortable only with laboratory-based, industry-sponsored science, science that is government funded or in other ways officially sanctioned even before its results are digested? (1) In a universe still largely mysterious to us, only grandiose claims are likely to address the most intractable questions. What could be more grandiose than the claim that God plays dice with the universe? (2) If you're smarter or merely less conventional than your peers, then of course you can expect to work in isolation. (3) Did Kepler, Pasteur, Newton or Einstein really care about peer-review processes? (4) Kepler published his own book and wisely waited until he was on his death bed to do it. Many important thinkers have sold only a handful of self-published books in their lifetimes. (5) Einstein's 1905 papers have no footnotes whatsoever. Nature speaks in its own clear voice and needs no amplification by fallible observers. (6) All famously misguided theories were well-established in their day. Should any self-respecting skeptic swear allegiance to a theory merely because it is currently well-established or advanced by a famous scientist?

It's precisely this narrow, smug view of intellectual history that made me disgusted with my education at the Bronx High School of Science and turn towards the more honest and open-ended "great books" approach being offered by St. John's College in Annapolis. In 40 years I've never regretted that decision.

Science has taught us so much about the universe that we forget that we don't yet understand well what science is or why it works. It's almost inevitable that, as they did in earlier centuries, our understanding and our practice of science will themselves change -- and sooner than we'll like. I have no idea whether Stephen Wolfram will be important a century from now, but I'm quite certain that the criteria of pseudoscience offered by Mr. Naiditch will have no bearing on the question.

David Naiditch replied:

Thousands of people have offered theories that they are convinced will revolutionize science and forever place them in the pantheon of great thinkers alongside such heavyweights as Einstein and Newton. But out of these thousands of aspiring revolutionaries, only a few ever succeed. A few of these self-proclaimed revolutionaries are scientists, but most are pseudoscientists.

Pseudosientists are usually easy to identify because they typically share many attributes like those I've listed. I disagree that these attributes are "precisely the attributes of the greatest scientists as well." Although a legitimate scientist may on rare occasions possess a few of these attributes, I do not know of any who possess as many as Wolfram possesses. Thus, Stephen Wolfram is the rare exception, because he is clearly not a pseudoscientist.


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