The Chaoplexity Delusion

The Mandelbrot set symbolizes chaoplexologists’ hope that, with the help of ever-more-powerful computers, they can discover simple principles underpinning diverse, complicated things, from brains to economies.

January 20, 2024. Ah, the 80s. The era of Thriller, Like a Virgin, Back to the Future and Chaos.

Popularized by James Gleick’s superb 1987 bestseller Chaos: Making a New Science, the field of chaos was repackaged in the early 1990s as “complexity.” Both fields profess the same basic faith:

There are lots of really complicated things out there, from brains and immune systems to stock markets and nation-states, that resist traditional scientific analysis. With the help of cool new math and ever-more-powerful computers, scientists will soon understand all these diverse, complicated things and show they stem from common tendencies or laws or whatever.

In my 1996 book The End of Science, I lump chaos and complexity together into a single term, chaoplexity. Chaoplexologists, I argue, have come up with some memorable memes, like fractals, the butterfly effect and self-organized criticality; but chaoplexity has not lived up to its hype, not even close. Chaoplexologists certainly haven’t discovered any new fundamental laws of nature.

But maybe my dismissal was premature. Maybe now chaoplexity will finally fulfill its promise. That’s what physicists Sabine Hossenfelder and Tim Palmer are suggesting.

Hossenfelder brings up chaoplexity—she even uses my coinage!--in her recent video “Is Science Dying?” So far, she grants, my end-of-science prediction has held up well; decades of research haven’t produced any “revelations or revolutions” as momentous as heliocentrism, evolution, quantum mechanics, relativity, the double helix, the big bang.

Moreover, Hossenfelder acknowledges, chaos and complexity have been disappointing; in fact, scientists still lack “a proper definition of complexity.” (In The End of Science, I note that scientists have proposed more than 30 definitions.)

Hossenfelder nonetheless suggests that with the help of “new math,” scientists can discover a “law of nature that explains how and under what circumstances complexity arises.” With such a law in hand, scientists might solve a wide range of hard problems, from the origin of life and consciousness to pandemics and climate change. So Hossenfelder hopes.

In “Chaos theory and the end of physics,” Tim Palmer, who has collaborated with Hossenfelder, applauds her suggestion that chaos theory might “rejuvenate science,” or at least physics. Like Hossenfelder, Palmer points out that physics has bogged down lately. Physicists have failed to find a unified theory that accounts for all the forces of nature.

Palmer contends that chaos, more specifically “fractal geometry,” can serve as a “new paradigm” for physics. A fractal paradigm can unify relativity and quantum theory and solve quantum paradoxes such as the measurement problem; it can also help illuminate dark matter and dark energy, which comprise the bulk of the universe. So Palmer claims.

Fractals are definitely cool, which is why James Gleick dwells on them in his 1987 book Chaos. Mathematician Benoit Mandelbrot coined the term fractal in the 1970s to describe mathematical objects ­­with fractional dimensionality; they are fuzzier than a line but never quite fill out a plane. Fractals also display self-similarity, the recurrence of patterns at different scales.

The archetypal fractal is the Mandelbrot set (see above), which became an emblem of chaoplexity. Benoit Mandelbrot pointed out that diverse natural phenomena--mountains, clouds, coastlines, trees, blood vessels, stock markets--exhibit self-similarity and other fractal properties.

Fractals serve as a demonstration proof that simple equations and algorithms can generate really complicated patterns. But just because the Mandelbrot set is generated by simple rules doesn’t mean that brains and tumors and stock markets are, too. Chaoplexology stalled decades ago because it ran into that hard truth.

I don’t mean to be mean, but Hossenfelder and Palmer’s efforts to resuscitate the old tropes of chaos and complexity reinforce my point that science is running out of gas. With friends like Hossenfelder and Palmer, other scientists might think, we don’t need enemies.

In The End of Science, I note that chaos and complexity are just the latest in a long line of supposedly revolutionary paradigms that could unify science and propel it forward. Just sticking to paradigms that begin with the letter c, you also have cybernetics, catastrophe theory and cellular automata.

Each of these paradigms had its moment in the spotlight, and each eventually ran its course, as researchers bumped up against its limitations. These paradigms are all tools, like integrals and matrices and complex numbers and Bayesian analysis, that work well in certain contexts and not so well in others.

When scientists discover a new tool, they have an understandable tendency to think it can solve every problem, as in the old saying about the man with a hammer. But the history of science has taught us that no tool can do everything.

Phil Anderson, one of the wisest of the chaoplexologists, made this point. Anderson, a Nobel-winning physicist, was an enthusiastic advocate of inter-disciplinary research, like borrowing physics theories to model stock markets.

But Anderson warned in his anti-reductionist 1972 manifesto “More Is Different” that different natural phenomena usually require different explanations. “Psychology is not applied biology,” he wrote, “nor is biology applied chemistry.”

Anderson thus looked askance at chaoplexologists’ dream of finding a unified theory of complex things, which solves the riddle of reality. This dream is a delusion, Anderson told me. “When one understands everything,” he said drily, “one has gone crazy.”

But what about the meta-tool of computers? Doesn’t ongoing progress in hardware and software change everything? Couldn’t advances like ChatGPT take scientists closer to their goal of a unified theory of complex things?

Maybe, but I’m guessing not. Ever-more-powerful computers provide researchers with ever-more-ways to model reality. Computers thus promote a pluralistic and even postmodern outlook, and they undermine scientists’ faith that all their efforts will culminate in a single, true representation of reality. Here is how I put it in The End of Science:

Computer simulations represent a kind of meta-reality within which we can play with and even—to a limited degree—test scientific theories, but they are not reality itself (although many aficionados have lost sight of that distinction). Moreover, by giving scientists more power to manipulate different symbols in different ways to simulate a natural phenomenon, computers may undermine scientists’ faith that their theories are not only true but True, exclusively and absolutely true.

I wrote that paragraph three decades ago. I don’t take it back.

Further Reading:

My next column profiles legendary chaos theorist Mitchell Feigenbaum.

I’ve posted lots of other columns related to this one over the past year. They include Conservation of Ignorance: A New Law of Nature; Huge Study Confirms Science Ending! (Sort Of); Is Ultimate Truth an Equation? Nah; Should Machines Replace Mathematicians?; The Delusion of Scientific Omniscience; Pluralism: Beyond the One and Only Truth; My Doubts about The End of Science.

I explore the limits of science in my free online books My Quantum Experiment and Mind-Body Problems. The latter includes a chapter on Stuart Kaufman, one of the most creative of the chaoplexologists.