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Theory in Theory and Practice: Truth and Beauty

Mathematics is the quintessential art form of the twentieth century, blooming on vines planted by the Greeks, tended by masters from the centuries before Newton, taking root around the middle of the nineteenth century to burst into glorious colors in the twentieth. Jean Dieudonné calls it the music of reason, but perhaps better is poetry of reason. The quintessence of conceptual art, totally internal, directly communicable from one thinker to another, cognitive processes provide the virtual gallery. As Shoshichi Kobayashi puts it, "All geometric structures are not created equal; some are creations of gods while others are products of lesser human minds." (Preface to Transformation Groups in Differential Geometry.)

Ordinary people recoil from the notion that mathematics is guided by aesthetics. The idea of mathematics as an art form is as alien to the brain of twentieth century Homo sapiens as is thought. It is particularly odious to those who consider themselves artists or writers or musicians, the so-called creative types. These people, ironically, tend to be the least creative and the dullest of all humans as the bulk of their work attests. They lack that most necessary quality of the creative: curiosity. One is less likely to find a mathematician who eschews literature, art and music than one is to find a so-called writer, artist or musician who appreciates mathematics.

But theory is the foundation of all useful and interesting literature, and the utility of theory is a lesson most easily gleaned from mathematics. Think of it like this: Tinkering in some lab is not science. The work of science is building theory. What comes from labs can guide theory in science, but is not theory. And theory is fiction.

The work of mathematics is building theory based on aesthetics, guided by a formal notion of truth akin to a meaningless game played with scribbles on paper, all of it independent of the sensory, existent world. Because of this freedom from here and now, the model of theory adopted herein for literature is from timeless mathematics.

Literature is not the laboratory-based activity that Ballard takes as his model, a silly notion of what science ought to be. Instead it is theory built on experience, and the writer with small experience produces small work. But so does the writer with large experience and little depth of thought, since depth of thought leads to theory. There needs to be interplay between experience and theory. (Exercise: Read chapter 1 of Albert Messiah's Quantum Mechanics. Though technically dated, it tells the story of the beginnings of a fundamental change in scientific thought through experiments. This is the interplay ordinary people do not understand.)

Mathematics: outside the realm of the senses

In lieu of paying credence to experiment, the modus operandi of mathematics for auto-correction relies on what is called proof, the deduction of truths via pure reason using explicit rules with no relationship to the physical world. One can be certain of the correctness of a proof in the same way one can be certain of the outcome of a chess match.

Just prior to the twentieth century many issues regarding mathematical proof were made explicit and coalesced into their own area of mathematics. Mathematicians applied their mathematical methods to the study of mathematics itself, subsuming this into mathematics, calling it metamathematics. (This bears no relationship to metafiction.) In so doing, they developed exact ideas about truth in deduction, different variants of truth, means of verifying these truths, and the precise relationships between these notions of truth.

So mathematics is not a science with an empirical standard of self-correction, but is rather a purely cerebral art form, the only conceptual art. Mathematical techniques and machinery lend themselves to great nonsense built on an edifice of unverifiable superstitious pronouncements like economics or finance as easily as to experimental sciences like physics. One could as well build a mathematical edifice for Ptolemaic physics or the magical systems of Éliphas Lévi or Aleister Crowley.

Precision is the hallmark of mathematics, the facility of exact mental constructs so clear no one who understands them can doubt that they are visualized identically by all who comprehend. Mathematics is so powerful in its descriptive function it leaves no room for doubt regarding what is meant. This is in part the key to its applicability to both experimental and non-experimental approaches to the noumena, as well as to literature. And yet the more precise the delineation potential, the more restrictive the range of the describable. This turns out to be an important precept for literature. Precision is essential, but so is ambiguity. Proper implementation of the theory of the work dictates when each is required.

Most important and worthy of repetition, the guiding principle of mathematics is aesthetics: if the ideas are not beautiful they are likely untrue. This point is crucial for novels and short stories. Truth and beauty are in a very real sense identical.

The case is similar in physics, with aesthetics one light in the search for truth, but not with such deliberation and single-mindedness. As of this regurgitation into words, physics is in crisis, its two major modern theories not meshing. This has bred new concepts with yet another fertile coupling between mathematics and physics.

Regarding the relationship between physics and mathematics, Eugene Wigner published an essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, wherein he points out that the two edifices evolve independently, with mathematics entirely untouched by the physical world. Yet they overlap and concur in remarkable synchronicity. Mathematics provides the vehicle for precision. New concepts arise in mathematics with no relationship to physics or the physical world; yet they eventually clothe new visions in physics. Wigner wonders if perhaps there is some underlying truth for them both, though one might do better to consider them as constrained by the same mental constructs and the same filters on the noumena.

In fact, mathematics can couch any fiction with precision, as pointed out just above. And in truth there is really no more ceremonial magic in Crowley than one finds in the standard curriculum of Business Administration, with such rites as the business plan or market research to appease the invisible hand, incantations based on branding and logos and words related to the ceremonial recitation of the business plan to minor deities who provide money for reasons no one can divine, but which seem to have no relationship to the success of the enterprise.

More to the point, however, mathematics provides the most cogent lessons and training for novelists and story tellers in the twenty-first century.

Aesthetics in mathematics: fundamental example

In lieu of explanation, a simple theorem exemplifies the aesthetic principle in mathematics. At the heart of what may be the most elementary of mathematical topics, Isaac Newton's and Gottfried Wilhelm von Leibniz's basic mathematical theory called calculus, it provides the foundation for a major portion of the edifice of mathematics. Without an understanding of calculus, a cornerstone of the modern worldview, one is constrained to a pre-eighteenth century mentality, living with a worldview imposed without active participation. Moreover, not knowing the theory of calculus implies an incomplete liberal arts education, not to mention missing one of the great artistic achievements of all time, indeed one of the crowning achievements of human thought. Those certified as college graduates and not knowing this theory are as likely to be certified in an engineering curriculum as a liberal arts curriculum. The reason for this striking similarity in seemingly disparate disciplines is left as an exercise for the reader to ponder.

The fundamental theorem of calculus expresses a startling relationship between the derivative and the integral, unifying two seemingly disparate concepts into a cohesive form that brought about revolutions in mechanics, geometry, and philosophy. Not only does it surprise thinkers with its non-intuitive relationship, but also with deep, direct connections to a vast hierarchy of concepts reaching into higher dimensions, leading to such profound ideas as cohomology in algebraic topology.

For those not acquainted with this fundamental artwork, an outgrowth of the beginning of modern thought, it may be time to study mathematics to the level of this theorem, a high school topic in advanced nations, before blindly writing novels or short stories. After all, without a modern viewpoint you can't possibly write about your own century. And note that it is impossible to appreciate twentieth century philosophy without an understanding of mathematics, no matter how much you read the popularizations of Gödel's theorem or Wittgenstein. This may not seem significant to those wishing to continue to rehash the passé detective writers, romance writers, chick lit, or similar pap, but for those hoping to step up and present something new and meaningful, it leaves a gaping ideational maw.

Back to Ballard: precision, truth, beauty, lies

Given that the reader has some inkling of aesthetics beyond the media variety implanted in the collective consciousness, a dangerous assumption to be sure, this section progresses on to the relationship between truth, beauty and precision via a dissection of Ballard's The Concrete Island.

Ballard clearly has a theory in mind in this short work and he presents it in such a manner that the reader bridles against an ending forced to fit. This seems to be Ballard's idea of providing a thought experiment, in keeping with his insistence that science is lab tinkering and the novelist apes scientist.

Notice that until this paragraph, the word lie has not found its way into the text. A lie is interesting in that it can be something not generally taken as fiction, something delivered in the style of nonfiction and certified nonfictional with official blessing and yet meant to deceive. The intent to deceive is what distinguishes the lie within the general world of fiction.

Politics is full of such lies. The lie is the meat of politics. And because the lie is blessed with the ceremonial virtue of truth, even though it is a lie the politician can claim to have not lied. This is even after the intent to defraud is clear, since the biggest lies are certified truths. In other words, lies in politics are truths in fiction.

Ballard's The Concrete Island is a lie.

That said, understand when some word is modified with an adjective without being carefully detailed, as in rambling without saying in what sense rambled, or liberating without saying the effect on the liberated, or any of a seemingly endless list of jingoistic keywords, defined with opposite meaning in opposing cultures, such as glorious for the old Soviet or Chinese Communists or freedom for the US and Britain and much of Europe, it is always a lie in the sense given above. The same is true when a central character is described as pretty, for example. Unless the reader decides if the character is pretty, this is a lie.

Ballard neglects to delineate his theory. His character and his setting do not implement the theory. He does not detail with appropriate precision what is essential to support the theory. A work that could have bristled with life and authenticity falls flat and empty and is, in the end, unconvincing. He never convinces the reader of his character's original plight. The protagonist's desire to remain in his prison to escape what might be taken as a meaningless, facile existence is a lie, certified true by the fact of being the conclusion of a novel. It remains arbitrarily decided by Ballard, not a natural outgrowth of the protagonist's previous life. It is forced because he does not detail his characters and their role in the theory except as pawns to his point. It is a lie.

To be more specific, an initial problem with The Concrete Island is the description. The locale and the circumstances of the protagonist being trapped there without anyone noticing is so poorly described it is not possible to get any idea of how it could happen. Were a careful locale and circumstance constructed early on, the idea would gain plausibility. Instead, the reader is asked to suspend disbelief and it lingers as an impossible situation.

Nonetheless, readers will either forgive this and accept the premise or shut the book. For those who slog along, the protagonist's life experiences are thrown out as offhand remarks when necessary to move the experiment along. His injuries are not clearly delineated, so the extent of the injuries are never apparent, and miraculous healing occurs as needed. The woman and her companion on the island are not detailed sufficiently to make the experiment anything less than a blatant manipulation. Only those pieces that seem interesting to Ballard for the sake of his experimental result matter, and the book reads as a fudged lab notebook. In the end, the assumption made by Ballard about his protagonist qua experimental subject doesn't hold water.

Beyond Ballard: operational meaning

Examples of not providing specific detail abound in news reporting. For the sake of irony, consider here the joyful example provided by the mathematician probably better known to US citizens than any other mathematician in the world, Theodore Kaczynski, the so-called Unabomber. Of course, the reader likely never read one of Kaczynski's papers in function theory, or even has the vaguest idea of what they concern. Nor has the reader likely read his manifesto, though it is widely available on the web and is probably his best read work. But recall that the media labeled his manifesto rambling. No one said in what sense it rambled, though they implied it was the incoherent ramblings of an anti-technology madman.

In fact, if you read it you will find it to be more coherent than most of what appears in the popular press. A man who wrote such cogent mathematical papers as Kaczynski would not ramble. And in fact, the style in his manifesto puts him ahead of nearly all journalists and essayists in the US. He knows grammar and he knows how to punctuate, something found in very few journalists. His work is more coherent than almost anything one will find in any newspaper in the US.

In reality, what the word rambling tells the reader is something about the user of the word, not the noun which it modifies syntactically. That is a problem with language. Just because a word exists does not mean it refers to something in the world. And just because someone modified a noun does not mean that the reader is being told something about the noun being modified. In fact, unless it is explicitly explained how that noun merits such a modifier, the reader is being told something about the user of the adjective. For example, John Grisham uses the adjectives pretty and nice almost exclusively in lieu of description in his novel Runaway Jury, as in He had a nice smile, She had pretty eyes, She had a nice, pretty ponytail. This tells you that the author seems to admire certain smiles, eyes, and ponytails, but is too lazy or too unskilled to describe them. He hopes you will manufacture your own. And when journalists wrote that the Unabomber's manifesto rambled, they told the reader that they, the journalists, had not the wherewithal to understand it. If they bothered to read it all.

Operationally defined words. Not freedom, but what is meant by freedom operationally. Or democracy. Or pretty. Better to describe and let the reader decide if free, democratic, or pretty.

Consider JR, an almost perfect novel by William Gaddis. An outrageous story of a schoolboy building a paper business empire which he is unable to survey because he cannot get to the city on a field trip, it sneaks up on the reader via deft prose style and form, without bluntly presenting its theory. Written purely in dialogue without identifying the speakers, it forces the reader to concentrate on who says what until catching the rhythm of the language well enough to identify the speakers. By this time, the wild comedy has engrossed the reader in a tale many would otherwise abandon as too stupid.

The fundamental beauty of this work shines through in its amazing prescience. The novel presages the irrational internet bubble led by shallow children fed massive allowances masquerading as venture capital by adults with more money than sense. Perhaps this event was symptomatic of a decaying culture in which adults strived to live, through their coddled children, lives put off for a future that never came.

If it had not happened, no one would have believed it possible. If Gaddis had stated his theory in an essay detailing the irrationality and childishness of business, no one would have paid attention. If he had chosen to tell his tale in the style of Toole's Confederacy of Dunces, it would have failed with the same resounding thud as Toole's Pulitzer Prize-winning dud. By choosing the form dictated by theory, his beautiful satire became comedy in the highest sense. And it came to pass in "real life," demonstrating the truth of the work.