In an excellent article today at Wired, Jennifer Ouellette discusses the predicament of Simon DeDeo, a research fellow in applied mathematics and complex systems at the Santa Fe Institute. Having made the switch from physics to social systems, Mr. DeDeo discovered that the complexity of the data describing human action is so vast that modern mathematics does not have the tools to deal with it. Like many scholars of complex systems, he believes that a new discipline within mathematics — probably entailing an intellectual revolution on the order of the invention of calculus — is needed before scientists can even begin to get a handle on the relationships between variables in the systems they are studying.
“In physics, you typically have one kind of data and you know the system really well,” said DeDeo. “Now we have this new multimodal data [gleaned] from biological systems and human social systems, and the data is gathered before we even have a hypothesis.” The data is there in all its messy, multi-dimensional glory, waiting to be queried, but how does one know which questions to ask when the scientific method has been turned on its head?
. . . [Ronald Coifman, a mathematician at Yale] asserts the need for an underlying global theory on a par with calculus to enable researchers to become better curators of big data. In the same way, the various techniques and tools being developed need to be integrated under the umbrella of such a broader theoretical model.
One of the intractable data sets mentioned in Ms. Ouellette’s report belongs to a Dutch study on the genomics of women suffering from breast cancer. A topographical reorganization of the data helped researchers discover some relationships, but the technique has limitations, as all such techniques do. Genomics and breast cancer is one tiny corner of one tiny subspecialty in the field of medicine, but we may have to invent new math just to begin to wrangle the data. Think about that the next time some would-be reformer tells you that he is going to consider “all the evidence” and make policy “based on the data.” He isn’t. There are some very admirable ladies and gentlemen in Congress, and in the Obama administration as well, but I wonder: Which of them seems likely to bring about something comparable to the invention of calculus? Steven Chu probably is one of the smartest men ever to serve in government in these United States, but you wouldn’t know it from the performance of the Department of Energy under his watch. And that is because the energy industry is not an equation you can solve or a theorem you can prove. The fact is that human minds are limited, and there is no person and no committee intelligent enough to do the things that government purports to do, like calculate the “right” price for a health-insurance premium or an hour’s labor. Our best minds are perplexed by basic data-management problems in medical research, but the middling minds in politics are convinced that they can intelligently manage the health-care system in toto, from medicine to markets. Is there any evidence that they can do the thing that they intend to do?
The problem of complexity in social systems has long been of interest to me, but I’ve often been a little shy writing about it, because I do not have anything like the math skills to really dig into the subject. So it’s a little bit of a relief to me, then, that the theoretical-math guys aren’t so sure they have the tools, either. (If you’re interested in the subject, Melanie Mitchell’s Complexity: A Guided Tour, is an elegant and readable introduction.) What we have here is a mathematical variation on Ludwig von Mises’s 1920 conclusion in “Economic Calculation in the Socialist Commonwealth.” Societies and markets (and weather, and consciousness) are complex beyond understanding, and it follows that they are complex beyond management by politics. We’re limited by Bonini’s Paradox: As our models become more complete and more accurate, they become as difficult to understand as the underlying reality they are meant to represent; as they become easier to understand, they become less accurate and less complete. Or in Paul Valéry’s words: “Everything simple is false. Everything complex is unusable.”
As Mitchell puts it: “The behavior of some simple, deterministic systems can be impossible, even in principle, to predict in the long term.” And human systems are not simple. We aren’t toy soldiers or chessmen, and society is not a box of Legos or an Erector set. One of the glories of science is that to acknowledge the limitations of one’s knowledge is a point of honor; politics, unfortunately, follows a different set of operating principles.