The answer may lie in Irish mathematician Paolo Zellini’s recent book The Mathematics of the Gods and the Algorithms of Men: A Cultural History. The philosophical debate determines to answer the question if numbers are discovered like a diamond in a cave or invented like a new phone. Whether numbers are real or fake, it doesn’t make a difference to most people, even those who use mathematics in their everyday lives. An engineer needs to know if the physics of a bridge are sturdy enough, but probably doesn’t need to know whether those physics were invented or discovered. Still, understanding that it’s not relevant to most issues means that you can appreciate a greater philosophical inquiry by approaching the problem. Figuring it out for what it is presents those new methods of reasoning. When there’s nothing practical to gain, then the real learning begins.
So where did mathematics come from? How did we start using numbers to count things? Zellini says that, historically, “2 apples” came before the number 2 did. We saw many things in front of us and used numbers to count them. Enumeration itself was meant to give reality to these things. Mathematics and numbers were powerful, and this attribution gave them their power. Philosophers who wrote about divinity believed numbers created this reality through divine powers, as Zellini explains in The Mathematics of the Gods and the Algorithms of Men.
So if math was from the Gods, were algorithms from the men? In some way. The debates throughout the 1800s and 1900s lead to the theories of computer science in solving algorithms and difficult math problems. The ways numbers behaved in different calculations were the basis for questions of how things can change or not. Einstein’s theories of relativity and developments in the creation of computers took advantage of these methods of thinking. There, the foundation of mathematics in science and technology is apparent. But Zellini takes things a step further. Math not only showed how important calculations are to society, but dictated fundemental searches for what is real.
Numbers have a reality. This isn’t the same reality as the difference between real and imaginary numbers (such as the imaginary i unit). It’s a reality of how these numbers came about. They tell us what is and isn’t. Zellini writes their “calculability,” or this mathematical practicality, determines this. These theoretical questions of what kinds of math problems can be solved or how algorithms behave speak to how a system of rules for numbers may work. Zellini is very careful not to draw too many conclusions that math is the sole method of understanding reality or that these revelations will change every field of research that uses numbers. Instead, he presents more of a guide for how the amount of money you have in your pocket or temperature forecast tomorrow are real enough for the purposes they serve, even if other numbers aren’t as real.
Zellini’s writing is still insightful and relevant, though. Numbers are different from what they enumerate. The power of hundreds of thousands of voters supporting one candidate over the other relies on calculations in an increasingly data-driven world. The models built upon machine learning and statistics depend upon all sources of information. This data comes from a small part of our experience, though. The algorithms and computers that control the analysis, prediction, and other methods create the reality that can dominate the experience they claim to represent. As we rely increasingly on forecasts and cost-benefit models of risks, we, in many ways, find ourselves turning back to the philosophical power of numbers. Back to the big questions of what a 50% win chance in an election means adds up, Zellini reveals.
It’s disappointing, then, that Zellini’s appeal to philosophy depends so much on ancient mathematics that don’t flow so well with the philosophy itself. Making strong references to Heidegger and Nietzsche and a rambling explanation from classical philosophy are fine, but the work still falls short. It stays too well within the intellectual landscape of dead white men in a way that it doesn’t represent numbers, calculation, and algorithms as well as it could. The connections between mathematics and philosophy are still weak. Zellini even makes incorrect historical claims about the cultural history of math and philosophy.
I’m sure there are better stories of the history of mathematics and philosophy such historian David Wootton’s The Invention of Science: A New History of the Scientific Revolution. Still, Zellini’s explanation of the power of numbers is difficult to ignore in today’s issues of population and economics.