Chaoplexity

The archetypal fractal is the Mandelbrot set, which became an emblem of chaoplexity. Benoit Mandelbrot pointed out that many 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 astonishing advances such as 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.