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An Author's Musing Memoirs About his Work

Reflections, Retractions, and Retracings

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Taking a second look at some of what I wrote

Dear Reader,

Years back, when I was a math grad student, I wrote a short essay entitled, Why study mathematics? The basic thought was connected with the general education math class I was taking, and it is not really an article for why to specialize in mathematics through intensive study, but why a more basic knowledge of math can be a valuable part of liberal arts education. Much like how I taught my class, I did not speak favorably of memorizing formulas—pejoratively called "mindless symbol manipulation" by mathematicians—but spoke of the beauty of the abstractions, the joy of puzzles and problem solving, and even spoke of mathematics as a form of weight lifting for the mind: if you can do math, I said, you can do almost anything. I was sincere in these words, and I believe my obscure little piece captures something that a lot of math students and faculty sensed even if they did not explain their assumption. Since then, there are some things I would say differently. Not exactly that I was incorrect in what I said, but I worked hard to climb a ladder that was leaning against the wrong building.

One famous author in software development, who wrote a big book about "software engineering", had said, "What gets measured gets improved," and began to express second thoughts about his gung-ho enthusiasm for measurement. He didn't exactly take back his words of, "What gets measured gets improved," but he said that the most important things to understand are rarely things that are easy or obvious to measure: the mantra "What gets measured gets improved," is a mantra to ruthlessly optimize things that often are less important than you might think. His second thoughts went further: the words "software" and "engineering" have been joined at the hip, but however hard software developers have tried to claim to be engineers, what they do is very different from engineering: it's an apples and oranges comparison.

I would pretty well stand by the statement that if you can deal with the abstraction in math, you can deal with the abstraction in anything: whether chemistry, analytic philosophy, engineering, or sales, there isn't much out there that will call for more abstract thinking than you learn in math. But to pick sales, for instance, not many people fail in sales because they can't handle the deep abstraction. Sales calls for social graces, the ability to handle rejection, and real persistence, and while you may really and truly learn persistence in math, I sincerely doubt that mathematical training is a sort of industrial strength preparation for social graces and dealing with rejection. And even in engineering, social graces matter more than you might think; it's been said that being good at math gets you in the door, but social influence and effectiveness are what make a real superstar. I would still stand by a statement that if you can handle the abstraction in math, you can probably handle the abstraction in anything else. But I'm somewhat more wary of implying that if you have a mathematical mind, you just have an advantage for everything life may throw at you. That's simply not true.

There are some things I have written that I would like to take back, at least in part, but even where my works are flawed I don't believe mass deletions are the best response. I would rather write what might be called "Retractions and retracings" and leave them available with the original works. Why study Mathematics?, whatever its flaws, gives a real glimpse into the beauty that draws mathematicians to mathematics. I may be concerned with flaws here, but they are not the whole truth. However, there are some things I would like to comment on, some flaws to point out. In many cases, I don't believe that what I said is mainly wrong, but I believe it is possible to raise one's eyes higher.

HOW to HUG

Mathematics may be seen as a skill, but it can also be how a person is oriented: jokes may offer a caricature, but a caricature of something that's there. One joke tells of a mathematician who finds something at a bookstore, is delighted to walk home with a thick volume entitled HOW to HUG, and then, at home, is dismayed to learn he purchased volume 11 of an encyclopædia. And I mention this as a then-mathematician who wrote A Treatise on Touch, which may be seen as interesting, may be seen as deep, and may have something in common with the mathematician purchasing a book so he could know how to hug.

Part of what I have been working on is how, very slowly, to become more human. This struggle is reflected in Yonder, which is at its most literal a struggle of philosophers to reach what is human. There is an outer story of disembodied minds set in a dark science fiction world, who are the philosophers, and there is a story within a story, an inner story, of the tragic beauty of human life. When I showed it to a science fiction guru, he suggested that I cut the philosophical dialogues down by quite a bit. The suggestion had a lot of sense, and quite possibility a traditional publisher would want to greatly abbreviate the sections that he suggested I curtail. But I did not follow his advice, and I don't think this was just author stubbornness. When literature builds up to a success, usually the path to success is filled with struggles and littered with failures. This is true of good heroic literature, and for that matter a lot of terrible heroic literature as well. (Just watch a bad adventure movie sometime.) Yonder is a story that is replete with struggles and failures, only the failures of the disembodied minds have nothing to do with physical journeys or combat. They begin stuck in philosophy, mere philosophy, and their clumsy efforts to break out provide the failures, and therefore to greatly abridge the philosophical discussion would be to strip away the struggle and failure by which they reach success: a vision of the grandeur of being human. Like much good and bad literature, the broad sweep was inspired by The Divine Comedy, opening with a vision of Hell and building up to a view of our painful life as a taste of Heaven, and you don't tell The Divine Comedy faithfully if you replace the Inferno with a brief summary stating that there are some gruesome images and a few politically incorrect ideas about sin. The dark science fiction world and its mere philosophy provides the vision of Hell that prepares the reader to see the humanness of Heaven and the Heaven of humanness. The inner story can be told by itself; it is for that matter told independently in A Wonderful Life. But there is something in Yonder, as it paints the stark, dark, disturbing silhouette of the radiant, luminous splendor and beauty of human life.

While I was a math undergrad, I read and was deeply influenced by the Tao Te Ching; something of its influence may be seen in The Way of the Way. That work has its flaws, and I may have drunk too deeply of Taoism, but there was a seed planted that I would later recognize in fuller forms in the Orthodox Way. I had in full my goals of studying and thinking, but I realized by the way that there was some value to be had in stillness. Later I would come to be taught that stillness is not an ornament to put on top of a tree; it is the soil from which the tree of life grows.

After I completed my studies in math, and having trouble connecting with the business world, I took stock, and decided that the most important knowledge of all was theology. I had earlier planned to follow the established route of being a mathematician until I was no longer any good for mathematics and then turning out second rate theology. My plans shifted and I wanted to put my goal up front and, I told my pastor, "I want to think about theology in community." (If you are wincing at this, good.) So, in this spirit, I applied to several schools and began the study of academic theology. If you are an astute reader, I will forgive you if you ask, "But isn't this still a mathematician looking for a book on how to hug?" The goal I had, to teach at a university or even better train Orthodox priests at a seminary, was a laudable enough goal, and perhaps God will bless me with that in the future. Perhaps he wants the same thing, but perhaps God first wants to free me from the chain of being too much like a mathematician wanting to learn how to hug by reading a book.

During my time studying theology at Cambridge, I was received into the Orthodox Church. I am grateful to God for both a spiritual father whose lenience offered a corrective to my legalistic tendencies, and for a godfather who was fond of reading Orthodox loose cannons and who helped me see a great many things that were invisible to me at the time. For instance, I asked him for help on some aspect of getting my worldview worked out correctly, and I was caught off guard when he explained, "You aren't being invited to work out the Orthodox worldview. You're being invited to worship in the right glory of Orthodoxy, and you are being invited to walk the Orthodox way." In that sense Orthodoxy is not really a system of ideas to work out correctly that, say, a martial art: there may be good books connected to martial arts, but you learn a martial art by practicing it, and you learn Orthodoxy by practicing it. And in that response, my godfather helped me take one step further away from being a mathematician trying to find a book that will teach him how to hug. (He also gave me repeated corrections when I persisted in the project of trying to improve Orthodox practices by historical reconstruction. And eventually he got through to me on that point.)

Becoming Orthodox for me has been a matter of becoming really and truly human, or at least beginning to. There is a saying that has rumbled down through the ages in different forms: in the second century, St. Irenaeus wrote, "For it was for this end that the Word of God was made man, and He who was the Son of God became the Son of man, that man, having been taken into the Word, and receiving the adoption, might become the son of God." I have not read this in much earlier sources, but I have read many later phrasings: "God and the Son of God became Man and the Son of Man that man and the sons of man might become gods and the sons of God." "The divine became human that the human might become divine." "The Son of God became a man that men might become the sons of God." And one real variation on this has been quoted, "Christ did not just become man so that I might become divine. He also became man that I might become a man."

If Christ became man that I might become human, this is manifest in a million ways in the Orthodox Church. Let me give one way. When I was preparing to be received into the Orthodox Church, I asked my godfather some question about how to best straighten out my worldview. He told me that the Western project of worldview construction was not part of the Orthodox Way: I had been invited to walk the Orthodox Way but not work out the Orthodox worldview. If there is in fact an Orthodox worldview, it does not come from worldviewish endeavors: it arises out of the practices and life of the Orthodox Church, much in line with, "Seek ye first the Kingdom of God, and his perfect righteousness, and all these things shall be added unto you." Not just corrections, but being caught off-guard by effectively being told, "Here are some of many rules; there is no need for you to know all of them. They are important, and you need to strive for strict excellence, but you are not treating them in the right spirit if you hold them rigidly and legalistically. (Work out with your priest how you will best bend them.)" The Orthodox Church's nature as essentially an oral tradition has helped cure me of silly things like meticulously studying ancient texts to put my mind to an antiquarian reconstruction and answer the question, "How should we live?" (The Orthodox Church is ancient, but it is not really infected with antiquarian reconstruction efforts.) The rhythm of the liturgy and its appointed seasons, the spiritual housecleaning involved with preparing for confession, the profoundly important community of the faithful: all of these are part of how it works out in the Orthodox Church that God became man not only so that I might become divine, but also so that I might become more truly man.

Part of this becoming human on my part also has to do with silence, or as Orthodox call it, hesychasm. Part of the disorder of life as we know it is that our minds are scattered about: worrying about this, remembering that pain, and in general not gathered into the heart. Mathematical training is a training in drawing the mind out of the heart and into abstract thinking. The word "abstract" itself comes from the Latin abstrahere, meaning to pull back (from concrete things), and if you train yourself in the habit of abstraction you pull yourself back from silence and from what is good about the Tao Te Ching.

In Silence: Organic Food for the Soul, I all but closed with the words, "Be in your mind a garden locked and a fountain sealed," which speaks about having a mind that is gathered together and is in the fullest sense mind: which is not when abstract thinking is its bread and butter. Perhaps some of the saints' wisdom is abstract, but it does not come from building an edifice of abstractions.

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