As I’m out of town for a few weeks, I thought I’d invite my good friend Percy Plumtwiddle to be a guest blogger. He is an ardent enthusiast of geometry, and we have had many animated discussions on the geometry of three and higher dimensions.
But he has his stubborn side (don’t we all?). And yes, his language is flowery and over the top, but well, we all have our eccentricities, too. Nonetheless, he makes some interesting points — just how interesting, I’ll have to let you decide.
Also, his essay, while not too long, is a bit long for just one post — so I’ll break it into two installments. I’ll return to my keyboard in a few weeks. In the meantime, enjoy Percy’s unique perspective on geometry, and more broadly, life in general….
On Threeness
Were I God — and I assure you, dear reader, that such is not remotely an aspiration; and were it, even my dear friends and those who hold me in highest esteem (those that there may be) would chortle audibly at the consideration of such a prospect — and were it incumbent upon me to create a sentient being or two (admittedly, I would be somewhat embarrassed, were I God, to admit to the creation of many such beings which presently spoil an otherwise hospitable planet) — and had I the necessity of establishing a place of residence for the aforementioned sentient beings (not that it would be required, matter being at times inconvenient, especially when taking the form of a piece of chocolate cake hidden under one’s outer garments at the precise moment when a head-on collision with a rotund nephew is imminent) — I would not hesitate for a moment in making such a domicile, in dimension, three.
Lest the frivolous reader imagine such a dimensionality to be merely the whim of a somewhat eccentric, although omniscient, Supreme Being, or lest the pious reader imagine that such a dimensionality foreshadows the fairly recent (according to even the most conservative of cosmological estimates) doctrine of the Trinity popular in some Western religions, and lest the banal reader imagine that this third dimesion would be, as goes the cliche, a “charm,” and lest the reader of belles lettres be tempted to make a thoroughly trite reference to MacBeth — apply the cerebral brakes forthwith! I intend to provide sound reason to dispel such imaginations, should the reader find it bearable to forage among slightly less green pastures.
I appeal not only to the reader’s intellect — being, unfortunately, acquainted much more intimately with self-proclaimed members of the cranially elite than I presently desire — but also to the reader’s aesthetic sensibilities, as potentially volatile as such an appeal may be. But I have profound faith in this universal Threeness, so I proceed, fully cognizant of the perilous quagmire in which I may soon find myself immersed, should the fates allow.
Indeed, my argument is entirely geometrical, being of the school of thought that such argumentation is lacking in no essentials. Should the reader be otherwise disposed, I urge an immediate cessation of the perusal of this document, the administration of a soothing tonic, and perhaps the leisurely reading of a light novella.
Several remarks of the Euclidean persuasion present themselves. Oh, indeed, we are all familiar with the usual formulae for distance, angle, etc., etc. These pose little difficulty, even in thirty-seven dimensions, once we are introduced to our good friend the Greek capital sigma.
But let us turn our eyes to the imaginitive world of polyhedra, a subject quite dear to my heart. Another discussion entirely! It is within this discussion that the force of my words comes to bear. For indeed, I should be greatly surprised if when, upon strolling through the Pearly Gates and bidding good-day to St. Pete, I find that God did not have amongst his cabinet (a gaggle of geese, perhaps, but the precise nomenclature for an approbriation of Archangels momentarily eludes me) one for whom polyhedra are a consuming passion.
And what would give cause for raised eyebrows? Follow along. Examining your regular polyhedra of dimension two, we find squares, triangles, etc., etc., and, while these are no doubt pleasing to the eye, one might find oneself a trifle bored after pondering a polygon of forty-six sides. For next comes the all-too-exciting forty-seven sider, and while one might appear to the casual observer nonplussed, the more astute attendant of human psychology would undoubtedly sense a consuming ennui. Hardly worthy of God, or even a lesser member of his cabinet. Of course, one may counter that I have neglected the likes of five-pointed stars, nineteen-pointed stars, and eighty-five-pointed stars, and one would be correct. But these, too, soon become tiresome.
This ends the first installment of Percy Plumtwiddle’s essay, On Threeness. Be sure to catch the second (and final) installment next week!
Creativity in Mathematics 