Imaginary numbers

When I was in high school, a professor from the local university was invited to deliver a guest lecture to the nerdiest of the math students. I sat in awe as Professor Sherwood introduced imaginary numbers and showed how they could be used to solve second-order differential equations. Could something this bizarre, outlandish and fascinating actually be true? As it turns out, yes. Three decades later, I use imaginary numbers to solve the differential equations that allow me to design cellular telephones.

The awestruck feeling I got in high school is still alive in me today. Now I get this feeling in the presence of the most brilliant philosophers. Material things, they say, are almost entirely irrelevant to the pursuit of wisdom, virtue and happiness. Could something this bizarre, outlandish and fascinating actually be true?

Bourgeois blindness

Both the theologian and the physicist recognize that behind visible things lie invisible things (God in one case, the laws of physics in the other). The bourgeois, on the other hand, shows no enthusiasm for understanding the invisible. He is fully consumed with the visible. Power and wealth are what he sees wherever he looks. It never occurs to him to look for things which require sustained intellectual effort to see. He is capable of sustained intellectual effort only if it is placed in service of things about which he is already enthusiastic: power and wealth. He wants more and more of the things he can already see. He has no interest in learning to see the things he cannot yet see.

I find it helpful to distinguish two conceptions of God. In the first, God is an entity that created and rules the universe. In the second, God is a concept that represents the highest aspirations of mankind. I am an atheist with respect to the first God, but not the second.

Is all truth relative to culture and social environment?

We often hear it said that all truth is relative to culture and social environment. In thinking about this claim, I find it helpful to distinguish two interpretations. The first says, "All truth is relative to culture and social environment. We must accept that we are part of a certain culture and social environment. Things too foreign cannot be seriously entertained." The second interpretation says, "All truth is relative to culture and social environment. We must expose ourselves to a variety of cultures and social environments by reading books from a wide variety of times and places. This will allow us to correct for the bias we have for our own." The first kind of relativist accepts our limitation to our own time and place, even celebrates it. The second sort acknowledges relativism only to go on to combat it.

The greatest philosophers are relativists of the second kind. They ask us to take the questions posed by thinkers of the past seriously, and not sanguinely suppose we have answered them. They aspire to be cosmopolitan and untimely, to transcend the merely personal ties, to cultivate a pathos of distance from hour own place and time in order to understand it.

There is no law but the law of love

One of the ideas that interests me most in the New Testament is the idea that I am not bound by any law but the law to love my neighbor as myself. As Paul puts it in his letter to the Romans,

Owe no many any thing but to love one another, for he that loveth another hath fulfilled the law.

In one sense this idea is continuous with the thinking of the Old Testament. In Leviticus, I also find the commandment to love my neighbor as myself. When Hillel was asked to sum up the Torah concisely, he answered, "What is hateful to thee, do not unto thy fellow man: this is the whole Law; the rest is mere commentary." But the Old Testament also contains a bewildering array of laws covering all aspects of human life. The idea that there is no law but the law of love seems to demand, if not an abandonment of all these laws, at least a radical reinterpretation of them.

In John’s first letter, we find an even more radical statement:

No man hath seen God at any time. If we love one another, God dwelleth in us, and his love is perfected in us. He that loveth not knoweth not God; for God is love.

This too is in one sense continuous with the Old Testament, where I find in Deuteronomy the commandment to love God with all my heart and soul. But the Old Testament also tells me God is the creator of the universe. Just as Paul’s statement seems to ask me to throw out all laws but the law of love, John’s statement seems to ask me to throw out all ideas of God but the idea of love. John almost seems to be saying I must be an atheist in regard to God as creator of the universe, whom no man hath seen, and believe only in God as love, whom I have seen. The equation God = love seems to call for a radical reinterpretation of the Old Testament. The greatness, power, glory, and majesty ascribed to God in the Chronicles must now belong to love.

Of course the New Testament is very inconsistent. After telling us there is no law but the law of love, Paul goes on to enumerate many other laws and vituperate against sinners who transgress them. John returns to the idea of God as author of the universe. Do these inconsistencies tell me I should consider the more radical statements as exaggerations? Maybe. Or maybe it is precisely these radical visions, and not the failures to live up to them, that constitute the most important parts of the text.

Love one another and ye have fulfilled the law

Hillel the Elder, when asked to sum up the Torah concisely, answered, "What is hateful to thee, do not unto thy fellow man: this is the whole Law; the rest is mere commentary."
Shabbat 31a

Love one another and ye have fulfilled the law.
Paul of Tarsus, Galatians 5:14

Enraptured in thought as he walked to Damascus, Paul of Tarsus decided to cease persecuting Christians and join their ranks. When disobedience has a higher motive—love, kindness, truth—how can I not stand with those who disobey?

Gay rights radicals once believed that law must be subverted for the sake of love. Now that our movement has succeeded, however, the old rebellious impulses have become superfluous. Our advocacy of the rule of law is as staunch as anyone’s. Paul’s antinomian “Love one another and ye have fulfilled the law” was a useful doctrine before we had achieved our recognition in law. But now, there’s no need for such a radically disobedient philosophy. Our particular form of eccentricity has been accepted. Why should we continue fighting for the rights of others?

The lesson from our oppression, if we would learn it rightly, is this—we must talk with the oppressed. We must try to find out—are they really so base, so vile to deserve their oppression?

The authorities told me heterosexuality was mandatory. I disobeyed in the name of love. The authorities told them abstinence was mandatory. They too claim they disobey in the name of love. They call their parties “Love Parades.” I demand tolerance for my eccentricities. How can I sit idly by as they are persecuted for theirs? How can I not sympathize with their plight? A bright eyed young man told me he never in life felt more love in his heart than he feels at a rave. I suppose I was a fool to believe him. But how could I not? He had shame and fear in his eyes, the same shame and fear I once saw in my own.

The asinine and elephantine contend to represent the bovine

Socrates’ character in the Republic observes that most of those who constitute the demos care very little for the pursuit of truth, so that the relation of truth to a democratic regime must always be “as a foreign seed sown in alien soil”—that interaction with the regime inevitably results in the “perversion and alteration” of truth—and that the most advisable course for the seeker of truth is to remain quiet, mind his own affairs, and stand aside as a man stands “under the shelter of a wall in a storm.”

A physicist who begins his lectures by making reference to the opinions of the majority about physics would not be worthy of our attention. The study of physics requires a degree of dedication and discipline available only to a select few, and it is only the opinions of this select few that are worthy of our attention. We can say the same thing about every other discipline, including political science.

The majority may rule the state to varying degrees, but it is a grave mistake to allow it to rule my mind, to any degree whatsoever. What sense is there in attending to the squabbles between the asinine and elephantine aspirants to represent the majority, when that majority is intellectually bovine to begin with? Watching the day to day movements of those who lack intellectual discipline is one of the many ways I shirk my own.

Introspection, observing the movements of my own my mind, can be done well or badly. I can pay close attention. I can let my attention wander. I can be honest with myself about what I see. I can deceive myself. Whether my introspection is done well or badly no one but I can decide. There's no chorus of approving voices for a job well done. There are no peals of criticism for incompetence. I must rely entirely on my own integrity. This obligatory self-reliance is among the foremost reasons I avoid introspection. I pay lip service to Emerson, but when it comes down to it, it’s hard for me to dispense with the chorus of approving voices. It’s hard for me to engage in any activity that doesn’t have approval as a likely outcome. The soul searching that knows in advance what it will find—admirable sentiments that I can later show off to win nods of approval—this is the kind of soul searching I prefer. The honest soul searching that isn’t looking for something, but observes for the sake of observation alone, this is much more difficult for me.

All my conversation makes reference to my experiences—a book I have read, a place I have visited, a painting I have seen. Shouldn’t I endeavor instead to show how these experiences have profited me, by revealing something of myself? Yes, I have seen beautiful paintings. But isn’t the present moment also beautiful? Shouldn’t I talk, then, about the beauty of the moment, and let the past be past? There is no greater joy than joining hands and giving thanks for the happiness of being alive together in this moment. Yet I always seem to squander the attention of my companions on futile attempts to recreate the past. When I talk about Vermeer, I show only that I didn’t learn what he tried to teach me. The present moment, no matter how ordinary, can be transformed into a magnificent work of art, if only I would devote my full attention to it.

Meditation and infinity

In everyday purposeful use of the mind, a thought is sometimes interrupted by another thought. In order to remain fast to its purpose, the mind must have a kind of stack, where it records its position in one thought as it is interrupted by another. In normal, algorithmic use of the mind, I must limit the depth of the stack in order to avoid losing my place.

In meditation, however, every thought is interrupted by an observation of the thought. And in this case there is no intention of returning to the original thought. In the meditative state I don’t need or want the functionality of my algorithmic mind, so there is really no reason to avoid a stack overflow. In fact, in terms of my customary algorithmic use of my mind, meditation might be described as a deliberate cultivation of stack overflow. As each thought is interrupted by observation of the thought, the stack becomes longer and longer, deeper and deeper. Each subroutine “Observe this.” is interrupted by another “Observe this.”

In the meditative state my mind feels like it is reeling off into infinity. As the stack grows, I worry that I can’t recover my place in my train of thought. And yet, as soon as I open my eyes, there I am, back in the finite world just as before. I can meet the world’s demands for competent pedestrian reason just as well as before. Of course the feeling of moving toward the infinite is illusory. The mind has a finite number of neurons. But in comparison to the limits I place on the depth of the stack in ordinary consciousness, the meditative state seems to traverse a vast span of emptiness.

For me, algorithmic use of the mind is something like a categorical imperative. It feels immoral, or at least irresponsible, to deliberately produce a stack overflow. But why? Just as I can recover from running “100 GOSUB 100” by hitting the reset button on my computer, I can open my eyes any time and return to the pedestrian algorithmic way of using my mind.

When I was a teenager, I found it interesting to see what my TRS-80 Color Computer would do when I used it in ways it wasn’t intended to be used. It was particularly fun to overflow the stack in the less thoroughly policed world of assembly language, where the stack would transgress its boundaries and overwrite video memory, producing colored patterns on the screen.

There is something very political in using the mind in ways it wasn’t intended to be used. When a leader tells me that God intends me to use my mind and body a certain way, I can be sure what he really means is that he intends me to use my mind and body a certain way. Turning my attention inward, and deciding for myself how I will use my mind, even for a moment, is an act of insurrection.

The true end of knowledge

Contemplate the fact that the Earth hurtles through space at a velocity of more than sixty thousand miles per hour. Contemplate how easy it is to forget this fact. Man is distinguished from other animals by his understanding. We claim this elevates us above other animals. But if we were really proud of our understanding, wouldn’t we often contemplate the facts that are furthest removed from sensory experience, the facts that require the greatest exertion of reason to discover and comprehend? Of course we must have food and drink and a warm place to sleep like other animals. But if we were proud of our understanding, wouldn’t we take care of the needs we share with other animals as quickly and efficiently as possible, and then devote ourselves to cultivating the mind?

The seventeenth century philosopher Francis Bacon, whom R. W. Church called the “prophet of knowledge,” aptly predicted how modern man would come to use the faculty of understanding in day to day life. The true end of knowledge, says Bacon, is not pleasure or curiosity, or the raising of the spirit, or eloquence or wit. The true end of knowledge is to invest man with “sovereignty and power.” When man learns to call everything in the universe by its true name, says Bacon, he will finally be able to command and control everything in the universe. Knowledge directed to any purpose other than command and control, knowledge we cultivate merely for the satisfaction of knowing, Bacon likens to a courtesan we use “for pleasure, and not for fruit or generation.” In Bacon’s view, the faculty of understanding elevates man above the other animals only because it allows us to perform our animal functions more efficiently.

The faculty of understanding is now used almost exclusively as an instrument of conquest, whether for conquering nature or conquering men. But, like all victorious causes, the instrumentalization of knowledge has its share of rebellion and dissent. There remains a small minority who have a different answer to the question of how the faculty of understanding is to be used, or for whom the question still remains unanswered.

On prudence, frugality and celibacy

The part which has been affected by the reasonings of this work is not therefore that which relates to our conduct during the period of celibacy, but to the duty of extending this period till we have a prospect of being able to maintain our children. And it is by no means visionary to indulge a hope of some favourable change in this respect; because it is found by experience that the prevalence of this kind of prudential restraint is extremely different in different countries, and in the same countries at different periods.
Thomas Malthus

In a system of private property, those parents who exercise the prudential restraint Malthus recommends, having only the number of children for which a happy life can be reasonably assured, will provide a happy life to their children. And these children, following the example of their parents, will in turn provide a happy life to their children. Families that exercise diligence in their work, thrift in their expenditures, and restraint in their reproduction will, in time, become wealthy and prosperous.

The problem, however, is that the diligence, thrift and restraint required for prosperity are far from universal. And it is impossible for a kind hearted child to see the impoverished children of less responsible parents without feeling pity and sympathy. Our children can’t be happy if they must cultivate a hard-hearted indifference to the less fortunate. Diligence, thrift and restraint are therefore not sufficient to the happiness of our own children unless they are practiced by all. The wisdom which allows some families to prosper must be advertised to the world.

But in fact what we find advertised to the world is precisely the opposite. Each producer tries to persuade consumers to buy his product. Although each one of these attempts in isolation is innocent enough, their collective effect is to drown out the wisdom that must be passed from one generation to secure the happiness of the next. Messages of diligence are drowned out by a perpetual stream of entertainments. Messages of thrift are drowned out by relentlessly repeated cries of “consume, consume.” Message of restraint are rarely heard, and one suspects this may be because the same enterprises intent on selling their products are intent on having cheap labor to produce them.

By spending money on luxuries today rather than saving for the future, we are compromising the happiness of our children. By watching Elmo instead of Hamlet, we are compromising the intellectual development of our children. I hope I am wrong, but I cannot help but think that we have condemned the next generation to unhappiness and ignorance, and at this point there is nothing we can do. Just as in the atmosphere, where enough carbon dioxide has already been pumped into the air to bake the planet, so also in the intellectual atmosphere we have passed the tipping point, and there is no going back. The destructive policies of this generation have sealed the fate of the next. At every step on our irresponsible path we glibly assured ourselves “everything’s going to be fine,” and at the same time refused to practice and teach the virtues that would, in fact, have made it fine.

On Television

Just as the American diet includes far more calories than the body can possibly assimilate, so our intellectual diet includes far more facts than the mind can possibly assimilate. We fill our idle time with news, cramming in today’s facts before we have understood yesterday’s. “The news we hear,” says Thoreau, “is not news to our genius. It is the stalest repetition.” Instead of a daily dose of news, Thoreau recommends a daily dose of Ossian. “I look down from my height on nations, and they become ashes before me.” We’re all concerned that television takes away time from study, work and family. But what’s far more dire is that television takes reverence from study, work and family. Our attention and reverence are no longer directed to great teachers and great books intent on making us better men and women. They’re now directed to celebrities intent on entertaining us.

I imagine the reason we find celebrities so interesting is that they lack intellectual and moral virtues, and yet nonetheless receive honors, adulation and rewards. This is precisely what we most crave. We want to be honored without being worthy of honor. We want to be important without being worthy of importance. Those honored for great achievements don’t interest us. Those honored despite their lack of such achievements fascinate us.

Hamlet requires more intellectual effort to understand. Therefore it is better. Television requires less intellectual effort. Therefore it is worse. “We know people don’t like to make an effort,” say Hollywood executives, “We wont force them. The last thing we want is to alienate our audience.”

The purpose of education is to elevate myself from a lower to a higher form of existence. Education presupposes that there is an order of rank, with the most difficult things at the top and things that require no effort at the bottom. Each active intellect moves in a different direction. Its progress can be assessed only in terms of its own standard of development, which it alone can decide. But no matter what direction my intellect is going, television is not helping it get there. It’s merely distracting and entertaining me.

It’s hard for me to imagine why people find television relaxing. The Hollywood assault on the hierarchy of values in the Western Intellectual Tradition is disturbing, not relaxing. The mind that seeks to develop itself seeks out challenge. When it’s tired, it looks for a different sort of challenge. Meditation transforms leisure from an opportunity to relax the mind to an opportunity to refine the mind. The best use of leisure is to cultivate a profound mental silence. This requires great effort to achieve, but, once achieved, is far more blissful than television.

Television brings a nonstop stream of enticing entertainment to the world. Unlike the entertainment offered by Tolstoy or Goethe, this new democratic form of entertainment is no longer accompanied by subtle enticements to moral and intellectual improvement. It scoffs at all efforts to improve the mind.

The popularity of television is no more evidence that it is good art than the popularity of new-age pseudoscience is evidence that it is good science. The path to enlightenment consists in overcoming and casting off prejudices our peers have imparted to us, taking reason alone as our guide, seeking the most rigorous exemplars of reason from present and past, and hearkening to them and them alone.

The doctrine of laissez-faire, which stipulates that the state may not interfere with consensual private activity, has been broadened in its application. Now we may no longer even criticize consensual private activity. We’re not even sure we should attempt to persuade anyone, even our own children, that books selected by our teachers to educate us are more worthy of attention than television programs contrived to distract, entertain and manipulate us.

The marketplace is exquisite at equalizing supply and demand. But it is indiscriminate in what it supplies and demands. The best we can hope for from the marketplace is the ability to ignore it. To a large extent, we have this ability. But what do we do? We turn on the television. We deliberately invite the primitive and false philosophy of the marketplace into our lives.

That uncomfortable feeling of idleness

Allowing myself to be ruled by duty to my customers and my constituents, I can never surpass them in virtue. Who knows whether that rebellious temptation to do what I will rather than what I'm told may conceal a path to greater virtue? That feeling of idle purposelessness which is so hateful to me may after all be my salvation. It's only by deliberately cultivating purposelessness, after all, that I can hope to find a higher purpose. Aimlessly browsing through books and music, I may accidentally find the poem or symphony that calls my soul to greater dedication to perfect itself, or to greater devotion to helping my fellow men.

Of course if I'm browsing in the wasteland of pop culture, my idleness will be worse than purposefulness. But if I eschew what is easy and comfortable and confine myself to what is difficult, the act of trying to grasp may help me reach new heights. Who knows how many have been called to abandon petty cares and dedicate their lives to virtue by a noble attempt to appreciate a great symphony or a great poem?

asceticism (n): the means by which those who are not aristocrats in fact become aristocrats in spirit.

Are we sure we want a classless society?

In a classless society we would all be in the same class as the greedy shopkeeper. I, for one, would rather resurrect a class society than surrender my entire soul to this class. There must be at least two classes—a lower class which seeks material rewards from work, and a higher class that works solely for philanthropic motives. The ascetic monk who seeks no rewards because his needs are little—the scion of inherited wealth who seeks no rewards because his needs are met—both of these are my equals. The grasping, greedy shopkeeper, whether novice or billionaire, is not.

Those who pursue material rewards become irate when we call attention to their petty avarice. But this should not stop us from calling attention to it. Work without reward is indeed a higher human activity than work with reward. And we should not dissimulate respect for the lower form of work merely to protect its practitioners from feelings of inferiority. Even when we can afford to come up into the pure air of aristocratic generosity, we fear offending avaricious men, we refuse to place ourselves above them, and our souls drown along with theirs in the sea of avarice.

I envision a new class of aristocratic professionals who receive no rewards from work, and advertise this proudly to the world. Those without inherited wealth would take up two professions, one a conventional paid profession (accounting, engineering, etc.) and a second philanthropic profession (medicine, philosophy, art, literature, religion, etc.). Thrift and asceticism would allow us to minimize the time and energy we must devote to the lower form of work. Those who are too consumed with paid work to take on a philanthropic profession would, of course, be pitied. But if they’re wearing designer clothes, perhaps the pity would be mingled with contempt.

We imagine that being paid for work makes it somehow more “professional,” more worthy of trust, dignity and respect. I say precisely the opposite. Of two doctors with the same education, the one who refuses all rewards is more worthy of trust, dignity and respect. She can achieve a degree of integrity not available to the one who must be paid.

The writer who is part of the new aristocratic class will proudly advertise on the cover of her books that all royalties will be used for philanthropic purposes. The professor who is part of the new aristocratic class will advertise at the beginning of her lectures that her salary will be used for philanthropic purposes. We must set ourselves apart from the avaricious class and make it clear that they are false role models, that something better is possible. Will we offend our colleagues? Probably. Are we wrong to be proud? No, I don’t think so. Being content with what we have, we are exalted by our humility. And we need not be humble about that. We must overcome our ridiculous fear of offending the avaricious, and show them the contempt they deserve. Our visible display of contempt is what allows us to teach impressionable young minds that excellent work is the mind’s highest calling, and rewards are only impediments to excellence.