The Creativity Code: Art and Innovation in the Age of AI

by Marcus du Sautoy

Overfitting can make you miss overarching trends by inviting you to model too much detail, resulting in some bizarre predictions. Here is a graph of twelve data points for population values in the United States since the beginning of the last century. The overall trend is best described by a quadratic equation, but if we use an equation of degree 11 to match the point exactly and extend this equation into the future, it takes a dramatic lurch downward, absurdly predicting complete annihilation of the US population in the middle of October 2028. (Or perhaps the mathematics knows something we don’t!)

The Mayans, who were doing sophisticated astronomy, needed big numbers to keep track of large spans of time. They came up with a clever system that avoided the Roman problem. Called the place-value system, it is the one we use today to write numbers. In our decimal system, the position of a digit indicates what power of ten it relates to. Take the number 123. Here we have one lot of a hundred units, two lots of ten units, and three single units. There is nothing special about the choice of ten beyond the fact that we can use our fingers to count up to ten. Indeed, the Mayans’ symbols went up to twenty and the position of their digits indicated different powers of twenty. So, in Mayan mathematics, the number 123 would denote one lot of twenty to the second power, two lots of twenty, and three single units. (That’s 443 to us.)

Indeed, when the nineteenth-century mathematician David Hilbert lectured on geometry he stressed this point: “One must be able to say at all times—instead of points, lines, and planes—tables, chairs, and beer mugs.” His point was that, provided the things had the relationship expressed by the axioms, the deductions would make as much sense for chairs and beer mugs as geometric lines and planes.

In the 1970s, for example, a computer played a major role in settling the proof of the Four-Color Theorem, which had gone unsolved for over a century. This problem theorized that, if you wanted to illustrate a map—perhaps of Europe but really of any region actual or fictional—so that no two countries that shared a border were shown in the same color, you would need no more than four colors in total. Some maps could be executed in just three colors, but in no case would a fifth color be required. Already, the proof had been constructed for the claim that five colors would suffice, but before 1976 no one had yet been able to reduce this to four. That year, two mathematicians, Kenneth Appel and Wolfgang Haken, succeeded in doing so, after adding an interesting twist to their approach. They first established that, although there are infinitely many possible maps you can draw, there is a way to show that they can all be reduced to an analysis of 1,936 maps. But analyzing even this many maps by hand was going to be impossible—or, to be more accurate, impossible for a human. Appel and Haken managed to program a computer to go through the list of maps and check whether each one passed the four-color test. It took over a thousand hours for their lumbering computer of the 1970s to run through all the maps.

Spiders on speed create fast coherent webs, but the webs of caffeinated spiders are a total mess.

One of the classic texts on which many young musicians cut their teeth is The Jazz Theory Book by Mark Levine, who has played with Dizzy Gillespie and Freddie Hubbard, two of the greatest jazz improvisers of the last century. Levine introduces that book by announcing: A great jazz solo consists of: 1% magic 99% stuff that is Explainable Analyzable Categorizeable Doable This book is mostly about the 99% stuff.

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