Categories: Body of Christ, civilization, decay of civilization, mathematics, Unity of knowledge
Though most of what I write in this essay is applicable to most populations and nations of the West, I don’t pretend to write in a truly general way. It might not be possible to write in such a way without engaging in needless abstractions. Thus it is that I write of the problems of the West from a distinctly American perspective.
We modern men of the West have badly damaged our civilization in part because we’re not really strongly inclined toward civilization, certainly not strongly inclined toward Christian civilization; recent events indicate strongly and sadly that Christianity didn’t really take in Europe or the Americas and we’ll soon be—at most—baptized pagans. I’ll be concerned with matters of civilization in general and leave the specific Christian aspects of Western Civilization to the side though it is arguable that Western Civilization naturally began to decay when we of the West tried to radically secularize most aspects of that Civilization.
The arts and sciences of civilization are what we confront in school and mostly leave behind us when we leave, though some who learn to hate `school subjects’ might retain or acquire in a fresh form a liking for, say, astronomy or even astrophysics at least in the form of better-quality documentaries. If we were less inclined toward equality, this general process of teaching even students of some talent to hate `academic’ learning might end in a class system where aristocrats, or at least surrounding scholars and artists, would cultivate a taste for the finer sorts of music and visual art and knowledge, literary and scientific. As it is, we are inclined toward equality and also inclined to believe that any passing notion which resembles an idea is as good as the ideas of any man, though we do acknowledge the superior technical knowledge of those who design and build airplanes and bridges and skyscrapers and nuclear bombs, if not those who strive to write the deeper sorts of poetry or novels or history books. Einstein pointed out once that we need to generate 99 questionable ideas to produce one of good quality; one way to understand the thinking of Americans is to realize that any one of those 100 ideas, good or questionable, is considered to be the real thing so that we stop thinking and we solidify our opinions as soon as we have any brain activity corresponding roughly to an idea. Americans were perhaps leaders in this process but others in the West have followed us.
We Americans all demand a recognition that our tastes are as good as any who make an effort to cultivate a taste for more demanding sorts of music, not just Beethoven but also, for example, Celtic folk music as found in the hill communities of North Carolina. Anyone who formulates an opinion about Iraq which would be plausible in some possible world think that opinion as good as the opinion of those who learn a little about the histories and cultures of the peoples of Iraq and maybe even the histories and cultures of archaic peoples who left some traces in present times. Though accepting of the gifts of modern technology as we find it in hospitals and at the airport and in the mobile phone stores, we don’t much like the foundational knowledge which can only be gained by disciplined effort and cannot be faked as can knowledge about the motives of Islamic terrorists or the long-standing goals of the Russian rulers from 18th century Tsars through Soviet bureaucrats and on to their semi-capitalistic and authoritarian successors. This is to say it can be at least embarrassing to express some irrational opinion about the meaning of quantum mechanics when a nearby teenager might well have some elementary but solid understanding from documentaries and from books available at many public libraries. Modern Americans feel no such embarrassments when speaking about, say, the irrationality of Iranian leaders who are, in fact, said to be more rational than American leaders by various knowledgeable observers who aren’t inclined to general admiration of those Iranian leaders, to put it mildly.
Largely because we desire a specific sort of failure, oddly consistent with worldly success, and think it to be a sign of our native superiority, our modern educational systems have failed. It hardly surprising that these systems have failed utterly to teach even the most basic skills of literacy and numeracy to those who don’t wish to learn and to those who have serious problems learning; after all, the systems are run by bureaucrats who show truly modern sensibilities by ignoring all inconvenient facts such as those related to the inability of many adolescent males to sit still in classrooms for five hours or more in a day. Our school systems reached a point by at least the mid-1970s where they couldn’t even provide basic learning skills to those who came to school capable of concentrating for more than the length of a television commercial or—more or less equivalently—a skit on Sesame Street. In fact, the school systems teach not the ability to concentrate on a task but rather the cow-like habits of responding to bells and of shaping habits to the needs of bureaucratic managers. (Teachers, including those who desire to do their job, are also subjected to the same conditioning.) The sad thing is that many of those who most readily acquire such habits are exactly the children who come to school with the behaviors which would allow true learning.
Nearly all human beings like colorful images, live or captured on the pages of a book—verified by psychologists and somewhat explained by evolutionary theorists as being one possible response to the opportunities and dangers of our environments. One way to disrupt the thinking processes of young students is to show them a lot of videos and to use textbooks with a lot of glossy pictures. While the improper use of images, especially very colorful, has been shown to disruptive of thinking and learning by modern scientists, we should remember that it also reverses the traditional pathway to literacy which begins with big pictures and a few words on each page and moves toward pages with text and only occasional pictures, if any.
This is part of a general problem which has been developing in the West since at least the century of decay (14th) which followed the High Middle Ages. The radical Franciscan theologians and philosophers of Oxford in that period (roughly, the school of Duns Scotus and William of Occam) provide a focus for this view of that general problem—though they weren’t villains in any moral sense. Those thinkers began the process of demoting mind to being subservient to some ghostly entity called `will’. Even the process of intellectual education, of disciplining the individual aspects of mind so that it can take up the greater communal aspects of mind, becomes a matter of will. If we will to be educated, then we can acquire education if we are placed in a building with books and teachers and maybe computers for a sufficient number of hours a day. In fact, those students from communities, Jewish and Chinese and a few others, which intelligently recognize the importance of intelligence in forming a strong and disciplined intelligence are those who can take advantage of even such incompetent educational systems as we have in the United States. Those from other communities are raised with a disrespect for intellect, communal and capitalized intelligence, and are expected to exercise their will and to take something called `knowledge’ into their poorly formed minds so long as they find themselves in one of those buildings with books and teachers and computers. The process is apparently magical, invoked by that strange and mythical entity typically labeled not only `will’ but `free-will’.
I’m mostly concerned about mathematics in this essay, our schools’ inability and unwillingness to teach even an esthetic appreciation for mathematics to either those with some level of talent or those who don’t have such talent but should be educated for their roles, as musicians or carpenters or homemakers, in an advanced civilization in which mathematics is a deep part of our efforts to understand our world, even the entirety of Creation from a Christian or Jewish viewpoint. In fact, there are almost certainly ways to teach at least some serious mathematics to non-mathematicians.
As matters currently stand, some dislike learning mathematics or other demanding subjects and the rest can mostly be trained to dislike learning mathematics. I was in the second category though I was in college before I learned that my liking was for mathematics of a type and at a level which was easy to learn and was tested by way of trivial problems. Even when I learned how to study well enough to get good grades for my junior and senior years of college, I most certainly had not learned how to truly learn mathematics, how to immerse myself in a demanding subject of study and to respond to it in such a way that my mind would be shaped to that subject. In a sense, I’d been Americanized, had learned how to exert some energy by an effort labeled `will’ and had targeted some textbook summaries of mathematics as the region I’d conquer by this will. In fact, the process of becoming a true mathematician, or a true cabinet-maker or pianist, is that of willingly letting oneself be conquered by a specific region of Creation, not a process of conquest but a process of being conquered and shaped to be a true resident of that region.
Difficult subjects in most American educational systems are dumbed-down, emotionally as much as intellectually, in an effort to engage the minds of the students by entertaining them. Literature becomes a series of electives including vampire-stories or romances at the same time that the study of calculus becomes not only the viewing of glossy images but also efforts by under-educated and mostly bored teachers to answer the sorts of questions which can be answered only after many years of intense study—in mathematics, “Why?” can be answered sometime in graduate school or perhaps in the mature adulthood of someone with good skills of literacy. At the high school level and mostly at the undergraduate level—prepare for a zig, mathematics is a game. At a young age, even a mathematical genius isn’t ready to learn the deeper truths which lie underneath the sorts of games which a reasonably talented child, one capable of becoming a serious scientist or engineer or technically-oriented philosopher, can learn at 12 or younger. Entering this game involves desire, not some sort of higher `will’ independent of an organism. See my recent and freely downloadable book, A More Exact Understanding of Human Being for an overview of human nature which considers desires and other emotional aspects of human being as subject to the sort of discipline which forms us into better sorts of social or communal beings.
Those with mathematical talents have also their developmental patterns which aren’t necessarily compatible with the standard curriculum, which was Algebra I to Plane Geometry to Algebra II to Trig/Calculus or something of the sort 40 years ago. Human being, the human organism in a particular manifestation, is not so easily overruled by a willed submission to the plans of bureaucrats or others. I knew some young men back in the 1970s who learned basic Group Theory on their own, yes!!, because of a book which taught methods for solving Rubik’s Cube. I was never much attracted to games of that sort, not even liking chess much and liking card games for the social aspects. I’m what you could call a metaphysically oriented mathematical thinker. I would have been more inclined, even at a young age, to make a major effort to solve problems asking for the sorts of abstract reasoning that can prove: if an group has property X, then each member of the group has a square root also in the group. Take the prior statement in a naive way if you’ve not learned the basics of group theory, forgive my liberties if you have learned group theory perhaps far more deeply than I have.
Let me up the ante. Mathematics is such an important part of a proper human mind, individual and communal, as defined by the true traditions of the West, equivalently—such an important part of the nature of Creation, that the West can’t survive if it doesn’t appreciate mathematics well enough to recognize its central importance to the Western intellect, the communal and capitalized living intelligence of the West. This is to say that the West came into existence in the work of Augustine of Hippo, Gregory the Great, Benedict of Nursia, and a host of following thinkers who were scientists and artists and politicians as well as theologians and philosophers. For much of the history of Western Civilization, theologians and artists and literary men were educated in the best of mathematical thought as it existed, much of it being inherited from the ancients, the Egyptian designers of pyramids through Ptolemy—at which point most mathematics was frozen for centuries. The West has gone far beyond that as part of an ongoing effort to explore God’s Creation, far distant shores such as the Americas and planets circling other stars as well as mathematical entities such as groups or physical entities such as protons, and to properly respond to Creation as we can best understand it, the working of wood and the management of factories and farms as well as the construction of hydroelectric power plants and the composition of musical works proper to current sensibilities of a higher and more disciplined sort.
From a different perspective, that of a professional mathematician, Edward Frenkel—Professor of Mathematics at University of California, Berkeley—writes of a great mathematician who is off the radar of Western Civilization, such as it is. In this article, An Unheralded Breakthrough: The Rosetta Stone of Mathematics, Professor Frenkel concludes:
The Weil conjectures did for mathematics what quantum theory and Einstein’s relativity did for physics, and what the discovery of DNA did for biology. Alas, we don’t hear much about this story or about the fascinating drama of ideas unfolding in modern math. Mathematics remains, in the words of poet Hans Magnus Enzensberger, “a blind spot in our culture—alien territory, in which only the elite, the initiated few have managed to entrench themselves.” And this despite the fact that math is so deeply woven in the fabric of our lives and is becoming, more and more, the engine of our power, wealth, and technological progress.
Mathematical formulas and equations represent objective and necessary truths, which describe the world around us at the deepest level. And what’s also amazing is that we own all of them. No one can have a monopoly on mathematical knowledge; no one can claim a mathematical idea as his or her invention; no one can patent a formula. There is nothing in this world that is so deep and exquisite and yet so readily available to all. Today, our celebration of the work of a great mathematician serves as a reminder that everyone should be given equal access to this timeless and profound knowledge.
The Weil conjectures, developed first and partially proved by Andre Weil (brother of the philosopher Simone Weil) while in prison for refusing to serve in the French military under the Vichy government, provide very deep and ultimately simple relationships between numbers and shapes. Professor Frenkel’s article begins by noting those proofs were completed by Pierre Deligne, professor emeritus at the Institute for Advanced Study in Princeton, N.J. Professor Deligne, the “great mathematician” in the article, has recently been awarded the Abel Prize in mathematics, a prize intended to make up for the odd lack of a Nobel Prize in mathematics. Of course, Andre Weil was also a great mathematician, perhaps one of the greatest of recent centuries.
I do object to Professor Frenkel’s claim that modern men, at least those with some years of schooling, have some understanding of the meaning of “quantum theory and Einstein’s relativity” and of DNA. In fact, even modern physicists have not been able to gain an understanding of quantum theory which places it the context of some greater whole, Creation to a Christian such as myself, and most non-scientists, even highly literate thinkers, have an understanding of many parts of modern science better labeled as “superstitions” than as “understanding”. See my very short discussion of an insight of John Polkinghorne, theoretical physicist and then Anglican clergyman: Shaping Our Minds to Reality. After talking about the experience of teaching new mathematical truths and attitudes (What is a vector? “‘But what is it really?’ they say.”) to young scientists, he speaks also of the difficulty physicists have in thinking in terms of quantum phenomena: “Perhaps we are in the midst of a similar, if much longer drawn out, process of education about the nature of quantum mechanical reality.”
The particular difficulties in truly understanding modern empirical sciences, history or quantum theory or mathematics or genetics, vary but each can be overcome only by a major effort along with a willingness to allow our minds to be reshaped to the knowledge of reality, to be reshaped to reality through the proxy of human knowledge and human understandings of a particular age and civilization.
By 1930 or so, Jose Ortega y Gasset labeled men of the modern West as “barbarian children”. While he was making a brutal assessment of the state of the common folk, he wasn’t criticizing them in a moral sense so much as the leaders. Under his quite plausible interpretation of the recent history of Western Civilization, masses of human beings had been released in the 19th century from parochial lives by modern political and technological developments. The `clerics’ or teachers and leaders of the West were the ones who failed to raise those peasants and other peoples of limited experience to an appreciation of Western Civilization; in fact, those irresponsible teachers and leaders willingly and even joyfully at times fell to the level of those who left behind the social and political order, the moral order, the culture, the generally pietistic forms of religious beliefs of rural areas and villages, to enter a vacuum of sorts where they should have entered the cosmopolis. The novelist Walker Percy should have titled his collection of essays about modern men as Lost in the Cosmopolis rather than Lost in the Cosmos. The Cosmopolis is the human manifestation of the current understanding of the Cosmos. We are lost in the Cosmos, not because we are inherently alien to this world nor because the world is defective in a way meaningful to us in our mortal lives, but because our understanding of that Cosmos, our Cosmopolis, is defective.
Most men and women of the West remain in that vacuum in which they can exist and sometimes even prosper in ways of individual mental development as well as prospering in ways of material standard of living. The failing of modern men is largely in the ways of the intellect, the “communal and capitalized form of live intelligence” as Jacques Barzun called it—see Intelligence vs. Intellect. For a more complete overview of individual and communal human being, download my book, A More Exact Understanding of Human Being. The intellect of a Western man is, or should be, the mind of the Western Cosmopolis as incarnate in Western thinkers and Western libraries and Western techniques of building and manufacturing and growing food and so forth.
Despite the isolation which is often a necessary part of intense mental efforts in such fields as mathematics, theoretical physics, philosophy, poetry, novels, musical composition, and so forth, these fields are as much a part of human communal effort as, for example, the design and construction of great buildings. Even the occasional child genius has a tremendous amount of that “communal and capitalized form of live intelligence.” Mathematics, as Professor Frenkel tells us, “is so deeply woven in the fabric of our lives and is becoming, more and more, the engine of our power, wealth, and technological progress.” I think the point can be made in a still better way by speaking of the deep relationships between mathematics and all aspects of our civilization, not just those aspects which can be labeled `materialistic’ when isolated, but it seems clear that Professor Frenkel does hold the wider and deeper view. It’s not just coincidence that artists were typically engineers or mathematicians during the early Modern period when the West was progressing so rapidly in so many ways. Those artists developed some of their techniques, such as perspective, by way of mathematical insights but their entire understanding of reality and of what it meant to be an artist was shaped by their entire individual and communal human beings, including those aspects of their beings labeled as “mathematician.”
Mathematical reasoning is a part of the individual minds of some and the communal minds of all in an advanced civilization. Even those who have difficulty understanding specific bits of mathematics will have cultural outlooks reflecting modern understandings of numbers, of infinity, of shapes. To be sure, this process of integrating recent mathematical understandings into the West has been slower than it could have been, largely as a result of the problem I discussed above: the failure of teachers and leaders to respond properly to the greater and higher possibilities of our civilization. Besides, it’s awfully hard to integrate something into decaying human communities. This is a problem I’ll be trying to address over the next few years, or more, by trying to develop a moral language drawing upon modern mathematics and other sciences, which language would allow us, for example, to speak of our `moral space’ being bent by large masses of human beings rather than forcing us to try to put everything in the linear and flat terms of Euclidean geometry, the terms which do show up in our moral discourse, “the straight and narrow way” and all of that. It’s our now improper geometric biases which make it so difficult to understand what it means to be a `non-conformist’ and, equivalently, to understand the strange way in which we’ve truly progressed in the growth of the Body of Christ though recent times show events which indicate to shallow intellects that demonic evil has become more powerful.
Mathematics is the most fundamental set of tools in the human effort to explore, analyze, and understand the world in which we live. In Professor Frenkel’s words: “Mathematical formulas and equations represent objective and necessary truths, which describe the world around us at the deepest level.” Again, I argue often and repetitively that mathematical understandings underly and provide many of the concepts and terms even for our moral discourse, which remains inadequate and even improper largely because we haven’t yet learned how to speak of our moral lives, individual and communal, by use of our far richer mathematical knowledge. We speak of our moral lives in terms of mathematics, such as Euclidean geometry, as understood in the ancient Mediterranean world and, as a consequence, our moral understanding has not advanced from those ancient understandings. To say, that moral realities haven’t changed over the centuries of human advance in technology and political systems, and the huge growth in population and in the complexity of human communities, is to take up a strangely inadequate form of conservative thought.
Despite all that can be said about the importance of mathematics, and other fields of human endeavor, to the greater human understanding of reality which is civilization in a true, if limited, way of speaking, most of those blessed with chances to attend the well-funded if mostly dysfunctional school systems of Western Civilization consider all that culture stuff, the great novels and great visual art of various national traditions in the West as well as science and mathematics and engineering, to be so much stuff to leave behind when handed their diplomas. We are barbarian children. That stuff we don’t like comprises many of the various aspects and parts of civilization; what we like are violent sports and disordered music and other entertainments which are the stuff of barbarian tribal life.
In contrast, Puritan divines, clergymen and theologians, such as Cotton Mather and Jonathon Edwards devoted part of their leisure time to the study of the great science of their days, including the work of Newton which was presented in the very demanding form of Euclidean geometry instead of the more sophisticated but simpler form of Newton’s own calculus. Many of the great, multi-volume works of serious American history and biography from the Gilded Age and a little later were produced by men who were insurance brokers or lawyers or the like and were read by a variety of middle-class Americans who wouldn’t have thought themselves to be particularly intellectual.
I return to mathematics to note that it takes some effort to learn the calculus but then many arguments of modern physics can be presented in a few lines in terms of that calculus instead of pages of involved arguments in terms of Euclidean Geometry. In part, this is the genius of mathematics, a genius shared with many fields of study and practice: put in the effort to build a vocabulary and set of techniques which can be applied in efficient ways to very complex and complicated problems. In metalworking, it shows up in the use of the best current machines being used to manufacture current products and also future machines which are better in some desirable way. This is one major way to view a civilization under development: ever more wisdom is being encoded in more compact and more usable forms.
We pretend to recognize the importance of the mind and yet we glorify mostly those who develop extreme skills in sports, those who are ruthlessly successful (or lucky) in politics and business, those who invent gadgets we enjoy. This isn’t to deny the perceptual intelligence and quick decision-making skills of a Tom Brady or the similar intelligence and skills of an experienced catcher guiding a young pitcher. Yet, we should realize that it was Shakespeare who gave us so much of our beliefs about what a modern, Western nation is and what its leaders should be like. Can you name the great athletes alive at the time of the Bard of Avon? We remember Plato as a great thinker and moral presence and know only vague rumors of his accomplishments as a wrestler.
Many of us can’t engage in mathematics to be sure. One rejoinder is that few Americans can run fast enough to play wide receiver in the NFL but many Americans sit in front of the television each Sunday watching NFL games. If we better form ourselves as images of God by being NFL fans than by engaging in efforts to understand God’s Creation, then we Americans are in good shape for our final judgments. If God would prefer that we devote some serious effort to understanding His thoughts as manifested in Creation, we might be, at best, headed for a long stay in a remedial education program before entering Heaven. The prior statement should be understood in terms of human communities and not in terms of human individuals, many of whom aren’t gifted with mathematical abilities and won’t be held responsible personally for not understanding, or even knowing about, the work of Andre Weil or its completion by Pierre Deligne.
My guess is that we better serve God, Western Civilization, and future generations by understanding the work of those mathematicians than we do by gawking at the achievements of Tom Brady, though—to be fair—sports is a part of human civilization as well as mathematics. Tom Brady has his place also, along with those forgotten great athletes of the Elizabethan Age.