THE word “invention” has the unusual quality of meaning two opposing things. That puts it in the company of a fascinating set of words including “dust” (to sprinkle something, and to wipe it off) and “oversight” (to watch over something, and to fail to do so). Most often today, “invent” means “to make up”, but it also preserves the older sense of “to discover”. Readers of the Church Times might recall the name of the feast on 14 September, the Invention of the Holy Cross.
These yoked meanings of “invent” lie at the heart of Zellini’s book (a translation of La matematica degli dèi e gli algoritmi degli uomini). On the one hand, we have “the mathematics of the gods”: abstract and eternal realities that lie before, beneath, and behind mundane reality. They would be there to be discovered. On the other hand, we have “the algorithms of men”, which offers a very different vision of mathematics. On this view, it would be that which can be elaborated, potentially from some arbitrarily chosen starting point, in a finite number of moves designed by human minds.
In 1940, Godfrey H. Hardy claimed that the majority of mathematicians took the former (“Platonic”) view, supposing their work to involve discovery rather than fabrication. The other view made strides in the 20th century, if perhaps more among philosophers of mathematics than among those for whom maths is a task to get on with. Zellini takes a more deflationary perspective. The numbers to which reality most properly belongs are those that could be calculated.
The “discover v. make up” tension in maths has promise as the subject for a book, even for a reasonably general audience, but it is not realised. Although published by a popular press, much of Zellini’s book is likely to be impenetrable for most readers. I found it hard going, and I have quite a lot of maths under my belt.
Zellini puts a good many promising leads our way, such as the part played by mathematics in Vedic religion, or that Proclus (the catnip Neoplatonist for many Christian theologians today) wrote a commentary on the first book of Euclid’s Elements. Beyond such fragments, however, the book is defeated by its lack of a sense of an overarching project unfolding, as a coherent journey for the reader. Nowhere is that lack of coherence more visible than at the conclusion, or, rather, in the absence of a conclusion. The book simply stops dead.
The past few years have been good ones for books on algorithms, approached from a human perspective. The reader might wish to look there instead, not least at Brian Christian’s and Tom Griffiths’s marvellous survey of a dozen or so central areas, conveyed with infectious enthusiasm and illustrated throughout in relation to everyday tasks (Algorithms to Live By: The computer science of human decisions, HarperCollins, 2017).
Serious attention is also being given to the ethical implications of the enormous power now invested in computerised algorithms. Catherine Besteman and Hugh Gusterson gathered some mainly cautionary essays (Life by Algorithms: How roboprocesses are remaking our world, University of Chicago Press, 2019), while Michael Kearns and Aaron Roth were considerably more optimistic (The Ethical Algorithm: The science of socially aware algorithm design, OUP, 2019). All these books seem to me to succeed as books. Zellini’s, unfortunately, does not.
The Revd Dr Andrew Davison is the Starbridge Senior Lecturer in Theology and Natural Science at the University of Cambridge, and Fellow in Theology and Dean of Chapel at Corpus Christi College.
The Mathematics of the Gods and the Algorithms of Men: A cultural history
Simon Carnell and Erica Segre, translators
Allen Lane £18.99
Church Times Bookshop £17.10