An Essay for Readers of Michigan Post, and the University of Michigan
Dr. Jonathan Kenigson, FRSA
Mathematics is not to be learned with respect to quantities but with respect to their Proportions. The university of today makes a god of number and not of harmony – of expediency and not of Beauty. Consequently, university “education” is a very dangerous thing – and perhaps one that should be avoided by anyone desiring to understand mathematics as opposed to inane, stupid, brute computation. The so-called “great professor” is the one who makes most ardent use of technologies to reduce the craft of instruction to the atoms of memory or the inanities of mechanization. The regent of the university is, then, the professor most inclined to sacrifice Beauty in favor of expediency. Such a professor is a murderer of the Soul, if not the body. I would not wish the title of professor upon any enemy, if reduction and mechanization is the main purpose of the craft. At least commerce makes no effort to portray itself as beautiful. Worship efficiency and technology, if you will, but at least do it honestly. Do not dare portray the craft of mathematics with the vulgarity of animal regurgitation of facts. Indeed, one need not examine history with distinctness and perspicuity to determine that societies tend to make divinities of their regents. As Plutarch opines, the apotheosis of Alexander, Pompilius, and Romulus are some such cases; and it is the sense of brutes, rather than persons invested with such dignities, to worship their leaders despite the privations and faults of empires. If the aspects of the Soul are under the monarchy of the person in Proportion to the person to the civilization, it must be that all so-called mathematical knowledge is that of Proportion. The Proportions of bodies and quantities cannot be distinguished – for both are Harmonies, if not written upon Nature, then inherent in communion with the several parts of the physical, mathematical, political, and theological worlds. As Plotinus reminds, the several emanate from One and the one from several, such that reason is always a fertile field for the reckonings of those things naturally in harmony and Proportion. Only a vain Atomist could dispute the centrality of harmony in semiotics. Neither Lucretius nor Leibnitz nor any Atomist of substance would have propounded absurdity.
If the regent is generous, then the regency must afford all those inclined to inquiries concerning Harmony the opportunity to engage in such. For, in the absence of such an opportunity, the Soul is servile to the political and moral Will and is incapable of participation in the harmonies of the world. The semiotics of Proportion is native to all properly dignified sciences of Nature. Because mathematics is the art and science of Proportion (inasmuch as quantity is Proportion or number), mathemata is the study of Proportion in the economy of causes. In distinction to theology, the study of number in Proportion is the uncoerced participation of minds and bodies in the determination of the signs engraved upon the general commerce of Nature. The valorization of signs in Nature is the progress of Spirit in Philosophy of History, Parts I and II, where participation in history is weighed equivalent to verstand – the understanding of Proportion. After Heraclitus, Aeschylus commences to weigh Nature by understandable signs rather than portents. In Book II of his Prior Analytics, Aristotle establishes Nature as latent with signs, first among a harmonious pregnancy of Causes. Augustine, in Doctrine, renders such signs as intelligible in the history of Israel and the progressive revelations of the Divine Mind. The Summa of Aquinas defends a critique of general and specific revelations vis. Cause.
To fail in grasping the centrality of Proportion is to be deprived of the most noble and sublime of beauties – that of number in motion and number in harmony. This failure is a murder of the Soul that is both Gnostic and Atomistic. In the first instance, the Scholastic and the Aristotelian would demand that the Animal Soul is not properly deprived of study, since only the Rational Soul is capable of such discursive dialectic. This trajectory begins in Parts of Animals, Motion of Animals, and Book II of Generation of Animals with respect to the motivic properties of animal Will in the absence of judgment. The discourse culminates, perhaps most famously, in Book VI, Chapter II of Nicomachean Ethics, in which the Soul is itself described as perfectly (but not exhaustively) modeled by Proportion. The Proportionality of causes and willed actions is the most complete moral expression of Number, and it is in this sense that Pythagoras’ mysticism continues through the entire trajectory of Western thought until the 20th century enshrined mechanism at the expense of Beauty in life and study. The Pythagorean trajectory is preserved in the Enneads. Aristotle’s disregard for the mysticism present in the Third and Fourth Enneads is in no regard a rejection of Proportion in any conceivable semiotics of aesthetics or Nature.
To study matter without semiotics is thus impossible. This perspective can be found even in Aristotle, where the Scholastics could find Nature expressed less sentimentally. The Inertia of matter is entertained in Books I, IV, and VII of Metaphysics, where the science of matter is described as prefatory to the proper understanding of causation in Mechanics. Newton maintains this point in Principia, Book 1 and the Scholia, as well as Book 3 of Optics. A taxonomy of Calculus begins with the origin of Proportion in the science of irregular figures. One locates this reasoning in Archimedes’ Equilibrium of Planes and Quadrature of the Parabola; it is applied to astronomical bodies and their orbits in Book 5 of the Two New Sciences. Kepler maintains Proportion as the central aspect of the study of conics defining orbits in the Galilean and Tychonian astronomical regimes. Galilean and Keplerian repudiations of Aristotle’s astrophysics do not constitute rejections of the centrality of Proportion that remains present in Principia Mathematica (Book I, Lemmas I-II and Scholium 31 and Lemma II of Book II). Pascal’s rationalism is starkly idealist in comparison to the Principia but retains an emphasis upon Proportion in the understanding of understandable change (Geometrical Demonstrations and Equilibrium of Liquids). It is only in the Analytic Theory of Heat that Fourier departs from the Plotinian trajectory emphasizing the theory of Proportion. Like Pascal, Fourier would never have contested that Proportion is a participation in the semiotics of the cosmos – and perhaps the most robust and important one. Let us not forget that, if we are to slay these giants and coopt their works with reckless disregard, we should not ascribe mathematics to theft. Such attribution would be of flourishing with felony.
