A Journal for Western Man




An Essay on the

Genuine Meaning of Beauty

G. Stolyarov II

Issue III- September 4, 2002


Frederick the Great, King of Prussia, was a man for whom all should hold a renowned spot within their personal pantheons, where examples of right behavior are contained that people may derive from them the necessary actions that will lead to the betterment of their lives. This man seems to have been a dilettante into such a vast array of fields as would instill in cultured persons immense awe and reverence. He was the most capable strategist of his time, with tiny forces defeating combined armies of great powers adverse toward him. He wrote works of philosophy, retained correspondences with other reformers of thought, and could rightly be called one of the most progressive Enlightenment thinkers, certainly the equal of Mr. Locke, M. de Voltaire, Mr. Jefferson, or Mr. Franklin. He was a comrade of Herr Johann Sebastian Bach and composed fugues for the latter to create variations from. Aside from the fields of military strategy, philosophy, and music, Frederick possessed profound interests in ballistics, mathematics, the sciences, architecture, and poetry. His realm was a haven of culture, with impressive minds from all corners of Europe flocking to Prussia to contribute to the treasures of the world in an environment that welcomed such enhancements, for it was governed by one of the most forward-thinking, radiant men that had ever the fortune of treading the surface of our Planet Earth. Berlin became a new Rome under Frederick, and the legacies of our Classical heritage became secured in Prussia in the form of monumental architecture on the outside and the fineries of the mind on the inside. Frederick was certainly one to fit into the category of Herr Nietzsche's "supermen." What caused this remarkable man to flourish? Simply put: he knew beauty.

The following question had puzzled sages for millennia and produced little systematic response:
What is beautiful? Herein the author shall guide the reader toward comprehending what matters may be truly classified as beautiful in order to distinguish between two forces within our society, one, its glory, the other, its downfall, art and savagery. In order to discern true magnificence from the deceitful and illusionary, we must locate a common base, a foundation for all things of high culture.

Let us for a moment investigate the root of Frederick's activities. He was best known for his exploits in the art of war, that intricate science of logistics, formations, equipment, and, of the utmost importance, roles on the battlefield. A strategist must deliberate for extensive periods of time over his tools of the trade, his maps and subordinate reports, constantly presenting himself with probable developments in the campaign or the particular battle, a statement beginning with "If...". From his knowledge of the advantages and disadvantages of every approach and every aspect of his forces and, preferably, those of the enemy, he may devise a "Then..." clause, pondering afterward on whether or not the act is desirable. If so, then the "Then..." becomes an "If..." and another "Then..." will be created as the next link within the logical chain. This is much reminiscent of a direct geometric proof, with the given conditions being the present situation of the conflict. Indirect proof is also a base for a strategist's reasoning. When presented with inconclusive evidence, he analytically attempts to bridge the information gap. "Assume that a circumstance is not present within the matter in question. Then..." If a link in a chain thus begun seems absurd or violates known given conditions, then the strategist may conclude that the circumstance does exist, after which he may establish his course of action, based on the direct proof, in order to gain himself the upper hand. His work involves also numerous arithmetical calculations as to the number of troops, the amount of dead, wounded, and deserters, and the distances traveled by his men as well as the effect of such on their physical state. An able commander must have intimate familiarity with ballistics and topography in order to calculate the efficiency of his artillery and possible uses of the terrain on which the conflict is fought. To summarize, a strategist is one whose work is founded upon mathematical regularities, patterns, and logic.

What of a philosopher? Would a logical coherence not be required for a complex system of thought to be expressed? After all, a philosophy intrigues us by relating itself to our existences and inspiring us to lead our lives in such a manner so as to bring about the greatest possible advantage and the minutest harm. Would the arguments be much compelling had they not made sense, had they been inconsistent or violated known given conditions of the present, or been incomprehensible as the statement, "If a plague befalls a nation, then it is for the best" would be? Thus, in order for a mode of thought to be a mode of thought, not a haphazard jumble of impulses, in must be perceived in a form transformable to that of a two-column proof, a chain of logic, a web of reasoning, or whatever other metaphors one may concoct. And logic is founded, once again, upon mathematics, only addressing the qualitative notions of congruency, similarity, and parallelism instead of numerical, quantitative elements, although such may be involved in its applications to particular situations where exact data is available. In a valuable philosophy one can pinpoint a single clause of logic, a single link in the chain, and follow in one's mind the means by which a plethora of such indivisible arguments may form the grand whole that impresses through its magnitude and profundity.

On to the foundation of musical works. It is a well known doctrine of physics that every object vibrates at a fundamental frequency and its whole number multipliers, the "harmonic series." A certain established relationship between two harmonic frequencies of, for example, a string, will produce sounds that vary an octave. Upon this knowledge the Music Theory was devised, a most impressive discovery of the mathematical base of beautiful sounds. Notation was invented to record these relationships and transmit them to other musicians that they may re-enact them on their instruments. Music is a world of pattern and mathematical precision. A sound off-tune, therefore of an irregular frequency in relation to those of the other sounds in a musical piece, is a strain on the mind, a broken link in the chain. The author himself is a player of the piano, and he will with confidence state that works of greatness that he had learned to represent on his instrument all had a logical scheme not only due to the clarity of sounds, inevitable where a properly functional musical tool is concerned, but also because of the patterns present within the piece as a whole, the repetitions of notes, or a "regularity of change", (A certain rhythm may be replicated, for example, with each note a tone higher), the complex but coherent structures of chords, etc. All this has been forged by theorists into a coherent whole. Based on mathematical relationships between various waves of sound, they have been able to determine what is congruent with what else. Any combination that deviates from this mathematical base results in repulsive cacophony.

Having mastered a language, men become capable of doing wonders with it. The novelist is the linguistic equivalent of the symphonic composer, who spins as vast a web with numerous characters to substitute for instruments, moods and settings for particular sounds, and the structure of the plot and its various subdivisions, initiation of problem, development, climax, and solution, amazingly reminiscent of the four movements in a symphony. From the author's personal experience in having read works of literature and undertaken their construction himself, every element, every word of a complex story must contribute to the whole and establish such a purposeful position within it that its absence will lead to the failure of the entire piece. Another branch of beauty from the root of language is poetry. If there is no logical coherence within a poem, then it is not such, for a poet must concern himself with smaller works, but driven to perfection in far many more areas than mere ideological consistency. There must be present a unifying rhythm, or a pattern in the change of rhythms. An ingenious poem will also contain an identifiable rhyming scheme, where the end of one line, and, upon a truly magnificent occasion, even other portions of it, will coincide with the end of another, a perfect mathematical congruency between series of clear and rationally structured waves that are so as a result of frequency patterns. Such a creation is indeed mathematics within mathematics within mathematics, a fitting tribute to the awesome capacities of man.

A most commonly encountered mode of beauty is the building, the architectural endeavor. These are ubiquitous in any civilized setting, and have become works of art instead of mere shields from the elements beginning with the efforts of a radiant mind, Imhotep of Egypt. Ever since this superior thinker devised an eternal monument to King Djoser, a six-step "pyramid", each layer geometrically related to the last, a building of precision surpassed only by the structures that had come afterward, their designs inspired by the ingenuity of the first Saqqara pyramid. Imhotep was of a learned class of Egyptian priests whose engineering skills were unrivaled in their time. His knowledge later spread to Mesopotamia, Palestine, Greece, and Rome, and in those regions were soon constructed edifices as impressive and formidable. What set the Pyramid of Djoser apart from its chaotic precedents? Instead of being a mere haphazard collection of matter, it was planned, its form calculated precisely, every block refined to the intended dimensions, then placed in a pre-determined position crucial to sustaining the structure of the whole. Before the winds of the desert had taken their toll on it, one may imagine the majesty of the building, six squares each piled atop the next that if a corner of every square were connected by a diagonal, it would be of a unified slope throughout. This was but the first and simplest building of mathematical basis, a creation unimaginable and non-existent prior to the advent of intelligent man. It was a threshold into the construction of far more intricate works that, however complex, can be traced down to their simplest elements, everything planned and designed, based upon patterns and regularities of mathematics. Over time physical laws emerged to assist architects in constructing buildings to best suit their purpose. If anything, this merely increased the precision involved, for now formulas of various sorts would be taken into account when assigning particular figures to a certain element of the structure. The beauty and elegance of these works, their appeal to the human mind, emanate from their mathematical correctness. This can be most visible in the column, the crowning achievement of Ancient Greek architecture. From a simple cylinder of marble, the forebears of Classical Culture have sculpted the essence of visual beauty, every crevice and curve and ornament calculated to the most miniature extent possible, every smallest bit of it crucial and magnifying its grandeur.

A painter is the amplifier of yet another recognized category of artistic accomplishment.  When creating a visual masterpiece, he must utilize principles of perspective, scale, and the size of objects relative to their distance from the foreground. For all these, mathematical principles have existed since the times of Ancient Greece, rediscovered by the masters of the Renaissance. Without their careful implement, a painting is grotesquely skewed, hurtful to the eyes due to the distortions present within its image, the whimsical irregularity that is neither precise nor identifiable in its essence. But if we examine such works as those of Signor Masaccio, Signor Leonardo, Signor Titian, Master Vermeer, and Master Rembrandt, we shall spot wonderful consistencies. These artists had so mastered mathematics that they had obtained the capacity to accurately represent the precise interactions between light and shadow. This leads us onto another aspect of paintings, color. Every color is, like a sound, a wave of a certain frequency, and the relationships between these have been structured into a theory as intricate and astoundingly precise as the Music Theory. The Color Theory provides the already commonly encountered reason for aesthetic merit,
patterns in the quantitative relationships between frequencies. A proper painting is as comprehensible and possesses the same repetitions and "regularities of change" visibly as a commendable musical composition does audibly. This is also evident in the logical bonds between every small speck of color that combine them all into one scene, one depiction of far greater accuracy and appeal than nature can ever furnish. A painting is to the wilderness of reality that is untouched by man, as a Classical sonata is to the distorted cries of an aesthetically untrained seagull.

There exist other far more complex and perhaps less conspicuous examples of beauty that must nevertheless be taken into account when creating our definition. For example, it may seem odd at first glance to classify a game of chess into the same category as a song, but, in actuality, both are founded upon the same elements. A song is a combination of musical and linguistic intricacy, the extrapolation upon frequency manipulation by the voice. It possesses the same underlying root of the tree of beauty and is an offspring that begins where the above two branches merge once again into one. A chess game is the art of military strategy condensed into a board with circumstances far more fortunate than reality thus granting the player definite ability to accurately judge every circumstance given sufficient expertise. Every piece possesses precise capacities, and its commander must construct lengthy mental proofs in order to determine the logical benefit that these aspects would bring him. This bears an obvious similarity to the activities of a war leader, and numerous geniuses of battle, including Saladin, Napoleon, and our most esteemed mentor, Frederick the Great, utilized it to assist them in developing their talents. In recent times the emergence of another technological wonder, the computer, has permitted for the creation of games of ever-increasing complexity and style, yet all possessing the same essence as those of Chess, Backgammon, Checkers, Battleship, and others, contributing to the amplification of the thought abilities of an ever greater number of individuals. A well-played game, with the long-term and short-term consequences of every move toward the grand whole is a complex web of logic, similar to the overall qualitative structure of the song. It can be related to every other of our previous examples. This web is spun by a philosopher, a novelist, a composer, and an architect. These recognized persons of artistic prowess have brethren whose work is of the same base, the students of the sciences. This foundation is far more easily recognized in their efforts, and therefore identifying it is not as difficult a task. The mathematician, obviously, produces works of beauty in his theorems, postulates, and formulas, the mechanical engineer in his machinery, the chemist in his compounds, the physicist in the discovery and formulation of precise natural laws, the medical professional in his cures, the chef in his intricate dishes. Now, the author may with confidence state that the unifying element of our term of discussion is evident.
Beauty may thus be defined as a creation of man composed of precise quantitative mathematical relationships united by qualitative mathematical concepts.

To those who comprehend not why beauty must be a creation of man, the author presents the following deliberation. Does nature create functional organisms? Yes, but it is unable to construct them with precision. There exists a reasonable explanation for why the human being in a savage wilderness is hideous and shall remain hideous until achievements of culture do not cloak or mend his “pristine” state. Every man is, essentially, randomly generated by combinations of the genetic codes of his parents. Chance selects which parent will donate which gene of theirs for a particular trait of the child at hand. What results is a smorgasbord of functions that may well not be the workings of an ideally healthy Homo sapiens, certain defects present within every creature, none of the greatest possible efficiency or a mathematical perfection. To add to this, no natural portion of the human organism can truly be classified as a geometric shape nor have concrete principles and formulas determine the means of measuring its smallest elements. And this may be said of the human being, the most advanced and least repulsive of the natural creations. The lower an organism is on the food chain, the more disgusting its exterior and interior workings. From the erratic fur covering the animals and feathers coating the birds, to the repulsive, slimy forms of the insects, to the randomly twisted carcasses of plants (A note to the reader: the only flora considered beautiful is that cultivated by humans in gardens, where, with the correct tending, they become geometrically proper and worthy of exhibition. Indeed, man mends these natural resources as he does to conceive any other work of beauty, yet the fact remains that man alters them in such a manner that nature cannot.), to the terrifying disfigured structures of microbes, the hideousness culminates in the semi-living, devastation-wreaking blob of chemicals that is the virus. The further from human control a matter is, the more repulsive and irregular, the more erroneous and flawed it becomes. There is a line that hideousness eventually crosses into danger. Among the examples in our "hierarchy of ugliness" for life, that line begins with a majority of insects. The less advanced a structure, the more it lacks the stability of precision, the more it is willing to inflict harm to "compensate" for its fallacies. But a treatise against parasitism would be too far a deviation from our original topic. The author simply means to clarify the hideousness of anything parasitic. Parasitism breaks down, degrades, severs. Beauty connects, constructs, restores. Two opposites cannot be one. Wilderness creates to destroy; man creates to create further. Wilderness dooms to oblivion; man seeks to fathom, preserve, and utilize. Thus, Wilderness, being, in essence, the more parasitic the further it becomes detached from the willful accomplishments of man, cannot be beautiful unless tamed, sculpted, and enhanced by humankind.

But what has man created for himself in order to conceal his natural errors and render himself beautiful? Let us begin with the matter of greatest ease, the covering of our deformed exteriors, clothing. True clothing aims to mend the erroneous form of the human body into one of significantly greater geometric precision. In its evolution over time, the Western suit for males and the gown for females have been the most recent advancements on the path toward mending the human form into an ideal state consistent with our mathematical doctrines. Our limbs have now increasingly begun to resemble cylinders, and our upper organisms, from the shoulders to the waist, parallelepipeds. This is, of course, a crude oversimplification that neglects the aesthetic enhancements offered by such precise accessories as ties, collars, pockets, buttons, all adding intricacy and appeal to clothing, building upon simple shapes as the Greeks had done with the column. A clothing designer producing works of such correctness is a developer of beauty. And by wearing these articles, we ourselves become far more beautiful and demonstrate our understanding of genuine aesthetic grandeur. What physical deeds do we perform concerning our heads? We groom our hair, place various artificial coloring on our faces to conceal deformities, tend to our teeth and skin, style or remove facial hair, provided we have any. Technology has even permitted such techniques as plastic surgery to correct inborn defects and slow the decay that aging inflicts on one's exterior, granting it greater geometric precision. With prospects of genetic alternations just over the horizon, we may live to encounter humans engineered by humans to a perfection that an absence of innovation would be unable to furnish.

But the greater impact of beauty has been and must continue to be on the human mind. We are born to be tainted with natural impulses that, however a proper end of survival they may seek, utilize obsolete and improper means to achieve it. In the author's previous works we had discussed how the inability of instinct to evolve alongside culture has produced such abominations as drug and sugar addictions, censorship of progress, and violent emotionally-guided sentiments. Yet to remain at the level of development of one's “animal instincts” is an even greater folly. Given a proper education, one may avoid the above miseries caused by an obsolescence of our natural systems, but without development one is forever bound by the dreadful fallacies of an uncultivated subsistence, namely, disease, susceptibility to the elements, vulgarity, transience, and oblivion. Thus, the greater aim of beauty, of culture in general, is to civilize the mind, to update it to the system of thought most fitting to the progress of humankind, its only guarantee for long-term survival. While instinct contradicts its intended purpose, beauty seeks to accomplish it. This is precisely the reason for our establishments of learning, which must liberate the human thought processes from the self-destructive script of instinct and instill in it an appreciation for the wonders of logic, pattern, and quantitative relationship that had made possible the very existence of both the arts and the sciences, which are, in truth, one; that, which is beautiful. Of the various systems of learning that had thus far come into existence, none, the author must admit, had fulfilled that purpose ideally or even remotely close to such, else we would have inhabited a utopian society where the will of man is omnipotent and self-directed. However, any systematic process of learning has been able to free at least portions of our selves from the parasitic, suicidal grasp of nature. Any man educated is infinitely more a human than one who is not. Diogenes Laertius relates to us this moment in the life of one of Greece's most profound thinkers: "When asked how much educated men were superior to those uneducated, Aristotle answered, 'As much as the living are to the dead.'" Indeed, if anywhere has life a foothold, 'tis in learning, for learning is growth without destruction, and such is life. This, then, the means of passing on beauty to the hideous, culture to the uncultivated, life to the subsisting, knowledge to the ignorant, is the ultimate beauty, founded upon the same logical and numerical (referring to a grading system for performance measurement) base as its previously addressed counterparts.

The purpose of this deliberation has been to create a definition of beauty which the reader may then be able to apply to all matters in order to grant them either the presence or absence of such a distinction. Every portion of this definition has obtained justification enough for one to be able to safely state that a crooked structure, a contradictory thought pattern, a losing strategy, a cacophonous piece of music, an incorrect use of language, a haphazard blob of paint upon a canvas, a dysfunctional machine, and a harmful medicine are not beautiful. Furthermore, one possesses the capacity to state that an even greater degree of hideousness is evident within that, which has not seen even the most futile attempts of men, the disordered plant, the microscopic parasite, the cry of a seagull, the droppings of geese, the genetic jumble of contradictory schemes for suicide within human beings, and an ignorant mind. What is it that renders existent all genuine accomplishments of beauty? 'Tis work, a relentless labor of hours, days, years, centuries, and millennia by men who love both themselves and their species, fulfilling the essential need of humankind to survive and perpetuate itself by committing itself to the finalization of the resolve to remain on the path of development. Nothing comes by itself but degradation. And it is degradation that true beauty would halt and reverse for the boundless benefit of all. The author doubts that a work of utter perfection had yet been achieved, but numerous individuals for whom we must hold an eternal remembrance, including Frederick the Great, that delightful expansionist of righteousness and civilization, have come remarkably close to attaining this goal. And work, thought, and knowledge shall someday lead us to ascending to that divine peak of humankind's pyramid of gold, a metaphorical marvel that would have made Imhotep proud. It is proper to summarize our findings in the following quatrain:

The path is long, the slope is steep.
Man yet may fruits of triumph reap.
He must, survival to retrieve,
The turn of beauty into truth achieve.

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, Le Quebecois Libre, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. His newest science fiction novel is Eden against the Colossus. His latest non-fiction treatise is A Rational Cosmology. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.

This TRA feature has been edited in accordance with TRA’s Statement of Policy.

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Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.

Read Mr. Stolyarov's new comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, at http://www.geocities.com/rational_argumentator/rc.html.