Kudos to whomever came up with the cover design for this book, which bills itself as "A True Story of Religious Mysticism and Mathematical Creativity." I might never have come across this had it not been for the subtitle and a gorgeous cover painting. A robed religious figure, holding a cane, walks alongside a scowling, pensive man who looks vaguely academic. They are in a wooded setting. The scene calls to mind perhaps Russia, perhaps some other place, but the picture immediately made me pick it up.
"Naming Infinity" is non-fiction, but it touches briefly on the world of literature, as I'll come to in a moment. The book chronicles the unlikely connections between Russian mathematicians specializing in set theory, and an enigmatic group of Russian mystics called "Name Worshippers." This sounds like the stuff of a Borges' story, with a seemingly unlikely connection between two disciplines that seem miles apart in the modern world.
About the book itself - I am no mathematician, and I have the feeling that a closer investigation of set theory would find me lost and quickly losing patience. It's a testament to both the story and the storyteller that I learned just enough to keep me interested without losing the basic narrative line. The writers wisely began with the religious side of the equation, since it is easily more accessible. (At least to this reader - to some mathematicians, it's possible the practices of the Russian Orthodox Church will seem just as indecipherable as theoretical numbers are to me.)
Name worshipping itself will be familiar to readers of J.D. Salinger's collection "Franny and Zooey," which dealt with "The Jesus Prayer" - "Lord Jesus Christ, Son of God, have mercy on me, a sinner." The idea behind the prayer is to repeat the words relentlessly until the one saying the prayer attains a bodily harmony, matching heartbeat and breath with the prayer, and one finds oneself literally "praying without ceasing." There could have been a discussion in the narrative about the similarities between this practice and Eastern mantras, but that might have easily diverted a reader already struggling with two diverging disciplines. This practice was deemed heretical by the Russian Orthodox Church, and the pre-Revolutionary Russian government moved to stamp it out.
The naming concept, the authors tell us, later was taken up by those working in set theory - literally categories, or sets, of theoretical numbers. The idea that by naming something it is given form and substance is as old as recorded history. The Egyptians, for example, felt the dead lived on as long as their names were spoken. Moses famously asked for God's name when they met at the Burning Bush, leading to God's mysterious reply, which seems to indicate that a proper name for God only serves to illustrate the awesome potentials of His existence.
But the concept mathematicians wrestle with between the covers of this book is infinity, into which our numbers as well as our imaginations ultimately stretch out. How to give a name, or a value, to something that may only be a potentiality, not an actuality? The rationalist mathematicians, acting solely within the bounds of their experience, struggled with the concept. It was only in Russia, where the lines between math, science and religion were culturally blurred, that such a concept could be made understandable.
If the book has a limitation, it is that there are the bare bones of a much longer, more engrossing story here that are never fully given form and flesh. We learn the names of the players, are given some anecdotes about their lives, some indication of their faith or their lack of it, but only enough to frustrate our curiosity. And we must take it on faith, frankly, that a connection existed in their lives between the religious and the rational, and that connection led to their breakthroughs. The authors don't do nearly enough to forge that link with supporting evidence - say diary entries, letters, or anecdotes. This may be because they were dealing almost a century later with scrupulous men who held intense, private beliefs, and later were forced by the Tsarist and the Soviet governments to forsake those beliefs, or keep them silent.
Still, a host of interesting personalities take shape between the pages of this short, bewitching book. And a host of interesting ideas. Early in the story, the authors recount the medieval notion, put forward by Gregory of Rimini, that "something that was infinite could be equal to a subpart of the whole infinite." Could such an equation yield forth ...Jesus?