The Mathematics of the Gods and the Algorithms of Men: A Cultural History by Paolo Zellini
My rating: 2 of 5 stars

An Abuse of Mysticism

In their arguments, conspiracy theorists and religious fundamentalists reveal more about themselves than about their point of view. Sometimes so do really enthusiastic academic mathematicians like Zellini.They all typically want to make the point that the rest of us are persecuting them. What makes some mathematicians so defensive about their subject? Are they victims of derision on the street? Do their academic budgets suffer because of underestimation of their intellectual worth? Or did they just feel unloved as children?

Whatever the reason for the apparent existential crisis in mathematics, the solution proposed by books like this one is ridiculous. Zellini wants us to know not just how important mathematics is but also how real it is. For him mathematics is so real that it permeates the universe. It is a force that exists quite independently our thinking about it. And he wants us to appreciate this reality as much as any evangelical preacher wants us to believe on the Lord.

Zellini’s specific grievance that there is “distorted image of mathematics as a merely linguistic game” (He doesn’t name names, but you know who you are!). He wants us to accept the fact that the language of mathematics is spoken everywhere throughout the cosmos if we only listen carefully enough: “... ancient arithmetic and geometry were beginning to assume the role not so much of describing or simulating real things as offering a foundation for the very reality of which they were a part.”

So for Zellini, mathematics is the most real thing there is: “... we are faced with a great mass of knowledge [in mathematics] designed to capture the most internal and invisible – as well as the most real – aspect of the things that exist in nature.” This should give mathematicians comfort. The things they do are essentially revelatory and spiritual in nature. They see what others can’t, the essence of reality. We must listen.

This is, of course, all nonsense. It takes a very profound inferiority complex to make such outrageous claims. Zellini‘s issue seems to stem from the body-blow to mathematical certainty in the early 20th century. Essentially, mathematicians themselves showed that even elementary arithmetic could not be proven to be consistent in its own terms. Mathematics was constructed on foundations of sand; its coherence, much less its reality, was questionable.

But, thinks Zellini, there is a way to restore confidence in mathematics. The saving concept is the algorithm. “The concept of algorithm would inherit the sense of mathematical reality”, he thinks. In other words, what is real is not numbers per se, as Pythagoras and Plato thought, but a process by which numbers reveal what is actually there. Algorithm is the carrier, as it were, of reality: “... in order to be real , the very same mathematical entities [numbers] that have been constructed through a process of calculation must be capable of being thought of in the same way as efficient algorithms.”

The book has some interesting things to say about the ancient connections between mathematics and religion. And no doubt there are intriguing mystical aspects to mathematics. But it seems that for Zellini mathematics is indeed a religion in itself, and a highly dogmatic one at that. The algorithm is its creed. His references to ancient Vedic and Greek theological texts are not merely intellectually inspirational; these texts are sacred scripture. How Zellini can construe the reality of an algorithmic relationship as more real than the numbers which are part of that relationship is beyond what I am able to follow in his discursive arguments except as quasi-religious principles emanating from these texts.

What I am able to understand is a sort of neurotic compulsion to prove that mathematics is the ur-language of the universe. This is scientism, the thinker’s attempt at world domination. I can only recommend therapy, or escape to a sympathetic totalitarian country.

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