TO the uninitiated, it looks remarkably like just a very heavy book. It is packed with words, numbers and picturesÐ lots and lots of pictures. But this is more than just a book: it is a phenomenon, a paradigm shift, a…well, just take a look at what it says on the front: A New Kind of Science.
There are two other words on the front, and they are at least as impressive as the title: Stephen Wolfram. For had such a colossal self-published tome carried the name of almost anyone else, it would have been instantly derided as a creation of pure fantasy.
As it is, A New Kind of Science is attracting the interest of some of the world’s most renowned scientists. They are all anxious to know what this British-born physicist, software millionaire and wunderkind has been doing with his mind over the past decade or two.
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It is a mind whose power has become the stuff of scientific folklore. Wolfram published his first paper while still a schoolboy, quit Oxford after deciding its physics course was too trivial for him, signed up at Caltech instead and bagged a PhD at the age of 20. A year later he was the youngest-ever recipient of a MacArthur “genius award”. Then he went off to develop the world’s most successful computer algebra software, and became a millionaire.
But this has not been enough for Wolfram. Since the early 1980s, there have been rumours that he has been working on something big. Now we know what it is. For at the heart of this vast book is a simple but stunning claim: scientists have been thinking about the Universe in the wrong way.
For hundreds of years, one technique has dominated the understanding of natural phenomena, from the decay of sub-atomic particles to the expansion of the Universe. That technique is mathematics. It’s a way for scientists who want to understand what they observe to translate it into symbols they can manipulate. It has proved an astonishingly powerful method, but it has its drawbacks.
The biggest of these is its inability to deal with complexity. Add just a little extra realism into, say, a model of fluid flow, and the mathematics becomes horrendous. Computers can crank through the equations and spit out numerical answers, but any hope of real understanding vanishes in a thicket of symbolism. Could it be that we’re using the wrong tools?
Yes, says Wolfram: we should be using cellular automata instead. First studied almost 50 years ago, cellular automata are simple rules for generating patterns. Imagine a row of white squares, or “cells”, with a single black square in the middle. Cellular automata are rules that dictate what colour each square should take in the next row down based on its colour and those of the cells to either side (see “The seeds of complexity”). Applied repeatedly, these rules can produce patterns of striking beauty or apparent randomness.
Wolfram claims that the ability of cellular automata to convert simplicity into complexity makes them the key to understanding phenomena that have defied conventional analysis: the shapes of snowflakes, the arrow of time, quantum gravity and turbulence in fluids, to name but a few. And this is what his book is all about: how the key to our understanding of the Universe lies in the myriad cellular automata patterns illustrated throughout the pages of A New Kind of Science.
It seems that plenty of people consider Wolfram’s claims at least worth a look. His book sold tens of thousands of copies within days of its publication in May, and went straight to the top of Amazon.com‘s bestseller list. But what will be the ultimate outcome? Will the scientific community embrace cellular automata?
Not on this showing, says theoretical physicist Michael Berry of Bristol University. He put aside his qualms about the grand title of Wolfram’s book because of the reputation of its author, and read it from cover to cover. “I like big ideas and I’ve got a lot of time for those who pursue them,” he says. But after systematically working through the whole of A New Kind of Science, Berry came away underwhelmed. “I don’t think it’s going to take over in the way he hopes,” he says. “He’s in the grip of this vision, and he needs specific cases of how it works.”
The difficulty seems to be that while the overall idea might seem impressive, there is little for scientists to grab onto. Wolfram has seen what he thinks is a surprising degree of complexity arising from simple rules, and believes this might tell us about some set of simple causes behind our complex world. But he doesn’t provide much more to go on than that.
Take the problem of turbulence in fluids, for example, which Einstein himself regarded as one of the biggest unsolved challenges in classical physics. Wolfram suggests that scientists have never been able to provide any convincing underlying explanation of turbulence. One recent idea is that it’s a kind of chaotic phenomenon, in which just a small change in starting conditions produces radically different outcomes. Yet according to Wolfram, this suggestion hasn’t led to any realistic descriptions of fluid turbulence.
So can he do any better? Certainly Wolfram’s approach, in which a collection of particles bounce off each other following cellular automaton-type rules, produces pictures of turbulent flow if the particles are fed into the system fast enough. Superficially, it’s a success. But he also admits that many of the details are different from what one sees in real fluids. It is just the overall mixture of regularity and randomness that is “strikingly similar”, Wolfram says. However, this is a claim that mathematicians can also make: their equations can produce computer simulations of turbulence that are strikingly similar to the real thing.
Wolfram goes on to declare that it should be possible to find simple programs that will “manage to reproduce the main features of even the most intricate and apparently random forms of fluid flow”. In other words, he hasn’t found anything concrete yet, but there must be something out there. A New Kind of Science is about suggestions and beliefs, or as he puts it, “experience and intuition”. He’s providing signposts, not concrete methodologies for explaining the scientific world.
If recent scientific history is anything to go by, that won’t be enough for everyone. Wolfram’s case has similarities with that of the American theoretical biologist Stuart Kauffman. Over the past 10 years, Kauffman has published several books seeking to trigger big changes in the thinking of his fellow biologists. His 1993 magnum opus, The Origins of Order, sought to reveal nothing less than the source of order in living things, from patterns on seashells to the growth of human cells.
According to Kauffman, the standard evolutionary processes of random drift and natural selection aren’t powerful enough to explain many examples of natural order. They need to be supplemented by something else, known as self-organisation: the ability of complex systems to impose order on themselves. How self-organisation works, its mathematical implications and why it advances biological thinking fill the 700-plus pages of The Origins of Order. When it appeared, Nobel prizewinners waxed lyrical about its implications, and even the late Stephen Jay Gould hailed it as “a landmark and a classic”.
So did Kauffman’s book spark a revolution in understanding biological order? “In a word, no,” says Peter Holland of the University of Reading. As an embryologist studying how genes turn cells into organisms, Holland spends much of his time pondering the origins of order. Even so, he has seen no need to sign up to the Kauffman revolution. Nor have many others. “Over the years, a lot of mathematical modelling has been used in biology, and it’s been pretty unsuccessful,” says Holland. “There are just too many special cases in living systems, and overarching ideas like this are not going to work well.”
Holland adds that Kauffman’s theory-laden approach ran into another problem, one that Wolfram may also face: “Many biologists aren’t mathematical, so there was a bit of a culture clash.” Holland believes that many potential readers asked themselves a simple question: is the effort of getting to grips with Kauffman’s thesis likely to pay off in terms of new insights? “It’s a cost-benefit analysis,” says Holland. “And it failed.”
Or at least it seems that way so far. When The Origins of Order came out, much less was known about the parameters that control the emergence of order in living systems such as embryos. “That’s now beginning to change”, says Holland. So perhaps Kauffman’s real mistake was to present his ideas before biologists could really make use of them.
Either way, the fate of Kauffman’s attempt to shake up biological thought offers at least one tip for those who, like Wolfram, want to spark a real revolution: don’t expect others to drop everything and tackle unfamiliar ideas. Most working scientists simply won’t find the time unless you dangle a pretty big carrot in front of them. “It’s got to be new and interesting, and there’s got to be work in it for other people,” says theoretical biologist Robert May, who is based at Oxford University.
And May knows a thing or two about getting others to sit up and take notice: he is widely credited with turning biologists on to chaos theory. In a number of papers published in the mid-1970s, May showed how simple yet biologically relevant equations were capable of astonishing behaviour, from endless cycles to apparent randomness. Just a small change in a key parameter or starting condition could trigger radically different behaviour. In a now classic review paper in Nature(vol 261, p 459), May sketched out the kinds of equations capable of such behaviour, showed where they popped up in disciplines such as ecology, suggested some mysteries they might resolve, and gave pointers to further research. And all in just nine pages: that’s 1188 pages fewer than A New Kind of Science.
May stresses that he did not discover the mathematics of chaos: “In fact, the basic idea had been rediscovered six times, first in the 1950s.” He thinks his papers were influential because they were relevant and easily applicable to the everyday work of biologists. “It showed that this wasn’t just some cute mathematics, it was really important,” he says. “Then we went round shouting it from the rooftops.”
Wolfram might do well to realise that besides the clarity and simplicity of May’s presentation, his success could also be related to the fact that he was only shouting to his fellow biologists. Marching into other disciplines and declaring that you are going to put them straight is possibly not a smart move.
In the late 1980s, physicist Per Bak of the Niels Bohr Institute in Denmark discovered a phenomenon he called self-organised criticality (SOC), which he claimed cast light on everything from avalanches to traffic jams to the evolution of life. According to Bak, they all involve a critical state in which a slight disturbance can cause a huge change, followed by suddenly rearrangement, or “self-organisation”, into a more stable state. In 1996, Bak published a book about his findings called How Nature Works. It was a provocative title which inevitably raised eyebrows in academic circles. But the content raised tempers as well, especially Bak’s perceived dismissive attitude towards those working in other fields.
Many palaeontologists were outraged by his sniping at the mathematical abilities of one leading researcher, and his claim that mass extinctions obey laws similar to those governing avalanches. Seeing Bak as a swaggering outsider, some decided to hit back. In 1998, Nature carried a paper by two palaeontologists, James Kirchner and Anne Weil from the University of California at Berkeley, which showed that the supposed law did not apply to mass extinctions after all.
Yet the most telling criticism has come from within Bak’s own community. Some fellow SOC enthusiasts accused him of displaying arguably the most perilous trait for would-be science revolutionaries: seeing evidence for what they propose everywhere they look.
For example, SOC phenomena such as avalanches are characterised by so-called “power laws”. In systems that follow a power law, minor upheavals are pretty frequent but major ones are fairly rare. Yet the converse is not necessarily true: a system that obeys a power law is not necessarily an instance of SOC. There may simply be another explanation.
Bak’s example suggests a few more things to bear in mind for those keen to trigger a sea change in scientific thought. First, make clear precisely why anyone should give up precious time to understand your Big New Idea. Then do what May did, and show how to wield its power via some familiar, and preferably unsolved, problems. If the idea has applications in many different fields, say so: that can boost the chances of it taking off in at least one of them. But be careful about alienating people: researchers may not take kindly to being “sorted out” by an outsider. Failing to talk with them or acknowledge previous work is not recommended either. And most important of all, be wary of believing that your theory really is the answer to Life, the Universe and Everything.
In light of all this, what are Wolfram’s chances of being remembered as the creator of a new kind of science? What will his target audience think? Berry suspects Wolfram has made a fundamental error in his attitude to other people’s work. The book carries no detailed, direct references to prior research, and Wolfram spends much of the first chapter bemoaning the lack of progress by researchers in many scientific fields.
“It won’t endear him, and it’s not right,” Berry says. He is also less than impressed with Wolfram’s ability to admit there might be flaws in his work: “He finds he can’t get the field equations for general relativity, and then says there must be something wrong with Einstein’s theory.”
Theoretical physicist John Ellis at CERN in Geneva also thinks Wolfram has failed to provide any hard, scientific reason for taking cellular automata seriously. “I saw nothing in the chapter on fundamental physics that could be falsified,” he says. “And indeed nothing that I could see using in my research.”
May comes to a similar conclusion. “I frankly doubt that it is going to cause a revolution, or even indeed achieve a sort of lesser status as a minor cult object,” he says. And that’s not because of Wolfram’s modus operandi. May doubts that Wolfram’s big new idea is either big or new. He points out that Wolfram himself demonstrated that cellular automata could produce complex patterns back in the mid-1980s.
But Wolfram is unfazed by the less than rapturous reception his work has received so far. “I’m trying to do a big thing, and it is utterly inconceivable to me that everyone would understand and agree with it all immediately,” he says. “Even though I hope my book presents my discoveries well, I would still expect it to take substantial time for people to come to terms with them.” Time, he believes, will prove his point.
He may be right: Per Bak’s claims for self-organised criticality have turned out to be more than just empty hype. Despite the rancour Bak’s book caused, researchers in many different fields are now taking his ideas on board and learning new and useful ways to classify phenomena.
Many scientific advances throughout history, from the existence of atoms to continental drift, weren’t accepted for decades, and Wolfram remains convinced that he’s onto something equally important. He sees ultimate answers embedded in the myriad patterns scattered throughout A New Kind of Science. The signs are, however, that the rest of the scientific community can still see only patterns.
- A New Kind of Science is published by Wolfram Research, priced £40