Stephen Wolfram blames himself for not changing the face of physics sooner.
“I do fault myself for not having done this 20 years ago,” the physicist turned software entrepreneur says. “To be fair, I also fault some people in the physics community for trying to prevent it happening 20 years ago. They were successful.” Back in 2002, after years of labor, Wolfram self-published A New Kind of Science, a 1,200-page magnum opus detailing the general idea that nature runs on ultrasimple computational rules. The book was an instant best seller and received glowing reviews: the New York Times called it “a first-class intellectual thrill.” But Wolfram’s arguments found few converts among scientists. Their work carried on, and he went back to running his software company Wolfram Research. And that is where things remained—until last month, when, accompanied by breathless press coverage (and a 448-page preprint paper), Wolfram announced a possible “path to the fundamental theory of physics” based on his unconventional ideas. Once again, physicists are unconvinced—in no small part, they say, because existing theories do a better job than his model.
At its heart, Wolfram’s new approach is a computational picture of the cosmos—one where the fundamental rules that the universe obeys resemble lines of computer code. This code acts on a graph, a network of points with connections between them, that grows and changes as the digital logic of the code clicks forward, one step at a time. According to Wolfram, this graph is the fundamental stuff of the universe. From the humble beginning of a small graph and a short set of rules, fabulously complex structures can rapidly appear. “Even when the underlying rules for a system are extremely simple, the behavior of the system as a whole can be essentially arbitrarily rich and complex,” he wrote in a blog post summarizing the idea. “And this got me thinking: Could the universe work this way?” Wolfram and his collaborator Jonathan Gorard, a physics Ph.D. candidate at the University of Cambridge and a consultant at Wolfram Research, found that this kind of model could reproduce some of the aspects of quantum theory and Einstein’s general theory of relativity, the two fundamental pillars of modern physics.
But Wolfram’s model’s ability to incorporate currently accepted physics is not necessarily that impressive. “It’s this sort of infinitely flexible philosophy where, regardless of what anyone said was true about physics, they could then assert, ‘Oh, yeah, you could graft something like that onto our model,’” says Scott Aaronson, a quantum computer scientist at the University of Texas at Austin.
When asked about such criticisms, Gorard agrees—to a point. “We’re just kind of fitting things,” he says. “But we're only doing that so we can actually go and do a systematized search” for specific rules that fit those of our universe.
Wolfram and Gorard have not yet found any computational rules meeting those requirements, however. And without those rules, they cannot make any definite, concrete new predictions that could be experimentally tested. Indeed, according to critics, Wolfram’s model has yet to even reproduce the most basic quantitative predictions of conventional physics. “The experimental predictions of [quantum physics and general relativity] have been confirmed to many decimal places—in some cases, to a precision of one part in [10 billion],” says Daniel Harlow, a physicist at the Massachusetts Institute of Technology. “So far I see no indication that this could be done using the simple kinds of [computational rules] advocated by Wolfram. The successes he claims are, at best, qualitative.” Further, even that qualitative success is limited: There are crucial features of modern physics missing from the model. And the parts of physics that it can qualitatively reproduce are mostly there because Wolfram and his colleagues put them in to begin with. This arrangement is akin to announcing, “‘If we suppose that a rabbit was coming out of the hat, then remarkably, this rabbit would be coming out of the hat,’” Aaronson says. “And then [going] on and on about how remarkable it is.”
Unsurprisingly, Wolfram disagrees. He claims that his model has replicated most of fundamental physics already. “From an extremely simple model, we’re able to reproduce special relativity, general relativity and the core results of quantum mechanics,” he says, “which, of course, are what have led to so many precise quantitative predictions of physics over the past century.”
Even Wolfram’s critics acknowledge he is right about at least one thing: it is genuinely interesting that simple computational rules can lead to such complex phenomena. But, they hasten to add, that is hardly an original discovery. The idea “goes back long before Wolfram,” Harlow says. He cites the work of computing pioneers Alan Turing in the 1930s and John von Neumann in the 1950s, as well as that of mathematician John Conway in the early 1970s. (Conway, a professor at Princeton University, died of COVID-19 last month.) To the contrary, Wolfram insists that he was the first to discover that virtually boundless complexity could arise from simple rules in the 1980s. “John von Neumann, he absolutely didn’t see this,” Wolfram says. “John Conway, same thing.”
From Prodigy to Prodigal Scientist
Born in London in 1959, Wolfram was a child prodigy who studied at Eton College and the University of Oxford before earning a Ph.D. in theoretical physics at the California Institute of Technology in 1979—at the age of 20. After his Ph.D., Caltech promptly hired Wolfram to work alongside his mentors, including physicist Richard Feynman. “I don’t know of any others in this field that have the wide range of understanding of Dr. Wolfram,” Feynman wrote in a letter recommending him for the first ever round of MacArthur “genius grants” in 1981. “He seems to have worked on everything and has some original or careful judgement on any topic.” Wolfram won the grant—at age 21, making him among the youngest ever to receive the award—and became a faculty member at Caltech and then a long-term member at the Institute for Advanced Study in Princeton, N.J. While at the latter, he became interested in simple computational systems and then moved to the University of Illinois in 1986 to start a research center to study the emergence of complex phenomena. In 1987 he founded Wolfram Research, and shortly after he left academia altogether. The software company’s flagship product, Mathematica, is a powerful and impressive piece of mathematics software that has sold millions of copies and is today nearly ubiquitous in physics and mathematics departments worldwide.
Then, in the 1990s, Wolfram decided to go back to scientific research—but without the support and input provided by a traditional research environment. By his own account, he sequestered himself for about a decade, putting together what would eventually become A New Kind of Science with the assistance of a small army of his employees.
Upon the release of the book, the media was ensorcelled by the romantic image of the heroic outsider returning from the wilderness to single-handedly change all of science. Wired dubbed Wolfram “the man who cracked the code to everything” on its cover. “Wolfram has earned some bragging rights,” the New York Times proclaimed. “No one has contributed more seminally to this new way of thinking about the world.” Yet then, as now, researchers largely ignored and derided his work. “There’s a tradition of scientists approaching senility to come up with grand, improbable theories,” the late physicist Freeman Dyson told Newsweek back in 2002. “Wolfram is unusual in that he’s doing this in his 40s.”
Wolfram’s story is exactly the sort that many people want to hear, because it matches the familiar beats of dramatic tales from science history that they already know: the lone genius (usually white and male), laboring in obscurity and rejected by the establishment, emerges from isolation, triumphantly grasping a piece of the Truth. But that is rarely—if ever—how scientific discovery actually unfolds. There are examples from the history of science that superficially fit this image: Think of Albert Einstein toiling away on relativity as an obscure Swiss patent clerk at the turn of the 20th century. Or, for a more recent example, consider mathematician Andrew Wiles working in his attic for years to prove Fermat’s last theorem before finally announcing his success in 1995. But portraying those discoveries as the work of a solo genius, romantic as it is, belies the real working process of science. Science is a group effort. Einstein was in close contact with researchers of his day, and Wiles’s work followed a path laid out by other mathematicians just a few years before he got started. Both of them were active, regular participants in the wider scientific community. And even so, they remain exceptions to the rule. Most major scientific breakthroughs are far more collaborative—quantum physics, for example, was developed slowly over a quarter-century by dozens of physicists around the world.
“I think the popular notion that physicists are all in search of the eureka moment in which they will discover the theory of everything is an unfortunate one,” says Katie Mack, a cosmologist at North Carolina State University. “We do want to find better, more complete theories. But the way we go about that is to test and refine our models, look for inconsistencies and incrementally work our way toward better, more complete models.”
Most scientists would readily tell you that their discipline is—and always has been—a collaborative, communal process. Nobody can revolutionize a scientific field without first getting the critical appraisal and eventual validation of their peers. Today this requirement is performed through peer review—a process Wolfram’s critics say he has circumvented with his announcement. “Certainly there’s no reason that Wolfram and his colleagues should be able to bypass formal peer review,” Mack says. “And they definitely have a much better chance of getting useful feedback from the physics community if they publish their results in a format we actually have the tools to deal with.”
Mack is not alone in her concerns. “It’s hard to expect physicists to comb through hundreds of pages of a new theory out of the blue, with no buildup in the form of papers, seminars and conference presentations,” says Sean Carroll, a physicist at Caltech. “Personally, I feel it would be more effective to write short papers addressing specific problems with this kind of approach rather than proclaiming a breakthrough without much vetting.”
So why did Wolfram announce his ideas this way? Why not go the traditional route? “I don't really believe in anonymous peer review,” he says. “I think it’s corrupt. It’s all a giant story of somewhat corrupt gaming, I would say. I think it’s sort of inevitable that happens with these very large systems. It’s a pity.”
So what are Wolfram’s goals? He says he wants the attention and feedback of the physics community. But his unconventional approach—soliciting public comments on an exceedingly long paper—almost ensures it shall remain obscure. Wolfram says he wants physicists’ respect. The ones consulted for this story said gaining it would require him to recognize and engage with the prior work of others in the scientific community.
And when provided with some of the responses from other physicists regarding his work, Wolfram is singularly unenthused. “I’m disappointed by the naivete of the questions that you’re communicating,” he grumbles. “I deserve better.”