Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity. By Loren Graham and Jean-Michel Kantor. Cambridge, MA: Belknap Press. 2009. 256 pages. Hardback. $25.95.
It is normal for one to read popular literature telling the story of the “rivalry” between science and religion. Few look to see if this is true. Positivism has convinced enough that this is how things go, that one is condemned as a cultural heretic if one denies this fact. Religion and science are rivals, and never the twain should ever meet. Just keep repeating that mantra and keep showing how those who hold to a religious faith are idiots, and you end up getting true believers in scientism.
Obviously, a thorough examination of the history of science will show this is not exactly the case. While one can find circumstances where religious leaders have hindered scientific development, one can also find examples of the reverse, where religion has helped promote the sciences, and religious ideas have inspired scientific research. Naming Infinity is a book about one such case, where a disputed, controversial form of mathematics was taken up by Russian mathematicians because their religious views allowed them to accept the philosophical ramifications of that research. The authors of the book do not want to make a strong case suggesting that mysticism and religious beliefs will necessarily help scientific research, but rather, a more modest proposal, that sometimes the two can and do help each other as they pursue common lines of thought. “In our opinion, therefore, it is simplistic to insist on either an inherently ‘conflictual’ or an inherently ‘harmonious’ relationship between science and religion. One must look at the contexts and details of individual cases, without prejudging the issue” (197-8). And that is what we get; we see the development of set theory as a means to understand infinity. The idea started in France, but it became too controversial for the French positivistic landscape of the late 19th century. It would take Russian mystical mindset to take it up again in the early 20th century, and there, it was once again, those who claim to promote “rational science” were the ones who tried to hinder (and did hinder, sometimes with violence) those mathematicians who were engaged in this new theory.
The question of infinity has plagued mathematicians (and theologians) for quite some time. “How does one define infinity? Does it really exist, or is it only an abstraction? Is there only one ‘infinity,’ or are there several, perhaps many? Can some infinities be ‘larger’ than others?” (20). In the 19th century, with the advent of set theory, somewhat established (in name) by Bernard Bolzano (a Czech priest), and further developed by Georg Cantor (a Russian Jew), a few prominent French mathematicians, Émile Borel, Henri Lebesgue and René-Lous Baire, were given a new insight in the question, and they took upon themselves to investigate the question of infinity further. However, the more they explored the question, the more troubling it became to them. They found their theories controversial, in part because of the philosophical implications of what they wrote. What they discovered seemed to contradict the rationalistic core they believed mathematics should have. Irrational, non-linear, random sets just did not appeal to the positivistic mind. Conflicted, with criticism given to their ideas by their fellow mathematicians, they eventually abandoned their research, but not before it was introduced to an outstanding Russian mathematician, Nikolai Bugaev, who did not hold their reservations to the implications of their theories. Bugaev, acting as mediator between France and Russia, was able to keep set theory active, despite the controversies surrounding it in mathematical circles around the world.
Around the same time, in Russia, the question of the relationship between the name of God and God was taking place. A group of controversial monks from Mt. Athos believed that when one invoked the name of God, God was present in that act. God’s presence was connected to God’s names, and so reciting the name of God in the Jesus Prayer brought one in communion with God himself. Their tradition, called the “name-worshipers” or “name-glorifiers”, was more than a little controversial, and ultimately, was condemned by several Orthodox leaders as heretical. Their monastery was stormed, and the monks themselves taken prisoner and brought to Russia, where they were to live out the rest of their lives. Some who tried to support and defend the name-glorifiers, such as Pavel Florensky or Sergius Bulgakov, did so on theological and philosophical grounds, seeing the modern debate similar to the debate between Barlaam and St Gregory Palamas several centuries before. Even though their position did not hold sway with Orthodox officials, those who followed the tradition of name-glorifying continued to do so, with some prominent Moscow mathematicians becoming associated with them, either by becoming name-glorifiers themselves, or by being one of their defenders. They saw the question of how to name sets and various kinds of infinities (making them real) was similar finding a name for God and realizing a communion with God through that name. Because of their theological understanding, they took for granted the ontological presuppositions that their French counter-parts feared, and were thereby free to explore this new mathematical discovery further. Thus was formed a highly influential circle of mathematicians in Moscow, centered around Dmitri Egorok and Nikola Luzin (with Pavel Florensky an important third), a group which, despite the controversies surrounding them, was able to direct and guide the development of Russian mathematicians. It was because of their efforts that Russia would earn a place of prominence in the 20th century mathematics.
It is when Naming Infinity tries to deal with name-glorifying that one finds the authors at their weakest (and most confused; but this is not surprising, since even among the Orthodox, there is a great deal of confusion and continuous debate as to what name-glorifying is or is not, and even how much of it is compatible with Orthodox thought). While they are correct in saying the monks used a prayer known as the Jesus Prayer to bring themselves into communion with God, the reader would be left with the impression that the only ones who prayed the Jesus Prayer were the name-glorifiers (and anyone caught saying it were immediately imprisoned). This is not the case; it is a traditional, well-practiced prayer, central to many an Orthodox prayer life, and just those groups deemed heretical by the Orthodox Church. Moreover, one could read the book and misunderstand the connection between God’s name and his presence for those who were name-glorifiers. It is not that by giving God a name, one makes God real; rather, God’s presence is realized in the name. One has contact with God through the name, and they create that contact by saying the name, but they are clearly not making God himself real. The authors should have explored the thought of St Gregory Palamas and the controversy surrounding the “uncreated energies of God,” to understand the point of the name-glorifiers when they say God’s name is united with God’s presence. There, they would understand why Sergius Bulgakov (mentioned, but not explored in the book) would appeal to Palamas in his own defense of the name-glorifiers: for Palamas saw the experience of the uncreated energies of God brought us in full contact with God, though God in his essence transcended those energies. The name-glorifiers saw God’s name like Palamas saw the energies, and one could say, for the name-glorifiers, God’s names were at least some of his energies.
Naming Infinity is a book with many purposes. The authors want to show how philosophical and religious attitudes affected the development of modern mathematics; they want to show the controversies found in early 20th century mathematics, and explain them to the non-mathematical audience; and they also want to show the human, biographical story behind modern mathematics, a story filled with as much sorrow and hardship as it is with glory. The book is at its best when giving out the biographical information, it does a fair job at explaining the mathematical questions being raised by them (some familiarity with the ideas involved with calculus would help), but its presentation of the Russian religious imagination was more than a little flawed. The authors’ general disinterest in mysticism affected how they read the theological ideas behind Egorov and Florensky’s mathematics, which, if the reader did not have some idea beforehand, would likely cause them to misunderstand Orthodox theology. Nonetheless, they present a compelling book, and one which is worth reading, as long as one does not expect the book to be a thorough examination of Russian theological conflicts. Moreover, for the theologian, interested in discussion about God, there is enough discussion about infinity and the new mathematical insights on it, that they should easily see the need theological studies have to reflect upon these changes and not take a simplistic understanding of infinity to discuss God (or humanity!) anymore.
3 1/2 /5 stars.
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