What’s the difference between G-d and Prime Numbers?
The Former has causal agency and absolute simplicity; the latter share the essence of permanence itself. Humankind will morph into something worse and vanish altogether. The sun will devour the earth and turn to ash and the motley caravan of days will journey no more, but an infinitude of Primes will remain, irreducible, imperishable, pulsing with life like bioluminous creatures in a dark sea, not contingent quirks in a vale of tears but omnipresent passageways to all possible worlds, their properties impervious to the warp of dreams and the solvent of Time.
The Ishango bone from 23,000 BCE with its nineteen and seventeen and thirteen and eleven notches, is it not a baton handed to us by Paleolithic kin, a magic wand brandished by apprentice sorcerers? When they weren’t drawing bison or sharpening spears they were tantalized by the same riddles that obsessed Euclid. They may not have discovered the causal relation between sex and pregnancy, obvious only in retrospect, but they knew some numbers are more powerful. Some numbers are magic.
Go back further. Do you see him? Seated on his haunches in the brush waiting for creatures you couldn’t find on Wikipedia in a month. Do not let the grandiloquent names of eras fool you. In the way a finite number of sunsets separates you from childhood, a longer orange and black chain of days connects you to him playing with rocks. He gathers six and puts them in two groups of three then three groups of two. Six disappears like a patch of water on the horizon that fades when he goes to inspect. He adds a stone. He adds a stone and mixes them into groups of three and four, two and two and two and one, six and one. They defy all attempts at destruction, possessing some intrinsic cohesion as though consisting of persistence itself, which they do.
Furrows distort his pronounced brow. He has no sounds to affix to the visions and sensations flooding the cave behind his eyes. An antelope wanders past but he does not see it. A cloud of dust arises over his futile attempt to reduce the stones. The sun spreads his shape over the concoction, creating the first blackboard. Which discovery is greater, his or Newton’s? He picks up the stones* and holds them to his chest to share their indestructibility? Perhaps man’s longings for everlasting life arose thus.
Standing upon his shoulders, mathematicians savor a vicarious taste of immortality, interacting with Beings who will endure, the sole survivors, the ultimate hombres. Space and time will expand and explode like some cheap balloon, leaving a puff of quantum dust, but Primes will endure undiminished, glowing with life in a sea of Nothing, unbound by the chain of days. They never weren’t and always will be. You weren’t, barely are now, and soon won’t be. You jelly?
This mystery religion demands sacrifices, but not of blood. Men sell their souls. Why not their sanity? Maybe the erosion occurs naturally. After glimpsing the Foundation of things, jeweled pillars in a secret kingdom sought by philosophers and poets and scientists alike, the return to this stockyard of flux is more desolate than Lazarus’s homecoming.
Mathematicians are watchers in a sacred garden, observing fauna more fantastic and elusive than gryphons or centaurs. And you can never join them. Ever. Your C+ in Algebra did not equip you for this expedition. You are a paralytic separated by a canyon from Riemann’s forest, its august splendor cloaked in the bewitching haze of twilight. Even for the Elect who can enter the hidden paths it soon becomes too dense. Many do not find their way out.
If the summum bonum is contemplation of the divine, how indescribably cruel to predestine most to ignorance. Surely some approach is possible, some humble veneration. Making up in vigor what it lacks in precision, an analogy suggests itself. Few Catholics understand the philosophy of Aquinas. Neither do they need to. Salvation comes from faith and good works. And ritual. Ritual sustains everything else. Unfortunately the asceticism of the Pythagoreans makes their reverence difficult, not that you didn’t try. There were fewer temptations in ancient Greece. Vegetarianism is easy when there isn’t a Burger King on every corner. A new faith is needed. When in doubt: WWMLD? (What would Martin Luther do?)
In The Temple of 1,234,567,654,321,234,567 There Are Two Divisors
The disciples of Pythagoras lost their way due to doctrinal entropy. Latter-day secularists (“mathematicians”) spend their days scribbling hieroglyphics, discussing Star Wars and Far Side cartoons and disdaining the reverent awe of the simple devout. The wielder of the Ishango bone would have clubbed them. They need an empiricist monk to ground their work and offer it as a sacrament to the faithful. They need a Temple where the incorporeal suffers the contortions of Existence to join the common man, that doomed but defiant twinkle of statistical glory who always turns to iconic representations to focus his mind on what he venerates but cannot see, to deflect his attention from the motley caravan of days. And Temples need keepers
The 3,370,501 paper clips in your storage Pod are as tangible as the bones of the martyrs enshrined in the Otranto Cathedral. The Rubbermaid totes in the garage, decorated with glow in the dark stars and filled with assorted screws, nuts, and bolts, need to be counted on a regular basis. You would not pray the rosary only once. (The Tic Tacs were a bad idea; foolish even. The ants could not be quantified and the Tic Tacs decreased.)
Removing the fourth step to your front door left a big drop, but the top is now a magnificent throne overlooking seventy-nine pink flamingos spray painted gold. Judiciously chiseled off the walls in the living room, missing portions of crown molding create 101, 103, 107, and 109 arches respectively. Added to the first floor, a seventh door leads to a tiny cave of crumbling plaster, but its absence was intolerable. In the aquarium across from you, Hardy and Littlewood the Oscars hover like prehistoric genies, incredulous witnesses of a bygone time. Segmented amber eyes separated by fist-thick foreheads watch you watch them watch you watch them. Out of their line of sight, a community tank of Tiger Barbs flanks the fridge. The unexpected demise of the thirty-first necessitated feeding one to the Oscars to preserve the tank’s harmony.
Unlike a Mandela** representing the impermanence of things, the 444,449 marbles covering your basement floor signify persistence. How many nights have you spent scooping handfuls, rolling in them, marveling at the certainty that no smaller assemblage can infiltrate and disband them, that they constitute a perfect unity despite their multitude. If only your mammoth-hunting forbear could join you. Rest assured, he is here in spirit. So is Goldbach and Euler and Gauss and Ramanujan and perhaps we are not distinct minds but manifestations of a Great Monad pondering the eternal. Death will not extinguish your flame. It will rejoin those who have partaken of these mysteries, which means your self or ego or whatever they’re calling it this week is an illusion. You do not exist independently of thoughts about the Primes.
No faith is bereft of tribulation. The presence of the Truth increases knee-trembling questions. Pascal was a featherweight when it came to angst. And gambling. The number of irreducible particles in the universe either is or is not prime. Can you live without knowing? If not, the competing option poses interesting problems. The Taurus Raging Bull in your dresser can hold six. For all numbers other than three, if a prime gathers you unto the Great Monad, a non-prime is your epitaph; if a prime remains, you were felled by a feeble, reducible assassin. The 15,683rd day of your life approaches. Decide by then or you’ll have to wait for the 15,731st.
Caution is required when adding bottle caps to the collection in the attic. How could you think 22,333 is prime? Your status as a simple monk does not absolve you from the responsibility of thought. Count them the day after you open them.
Hose the bird droppings off the bronze address numbers affixed to the back of the garage. 6,666,666,666,666,666,666,666,666,666,666,666,666,666,641 mocks the insubstantiality of physical reality. That many grains of sand would not fit inside the universe. So much the worse for the universe, this botched concoction, this hodgepodge of waves and particles seen through a glass darkly.
6,666,666,666,666,666,666,666,666,666,666,666, 666,666,641 exposes the shadowy stuff of which you consist. Kneel before it and raise your arms. Squint and see how they are misty outlines. Behind them 6,666,666,666,666,666,666,666,666,666,666,666,666,666,641 catches the light, not dependent on it for illumination, gleaming like some golden bridge over the stream of Heraclitus. Sixes do not secede from this union. They do not reveal themselves as circles and arches and squiggles the way letters in a word do if stared at too long. Run your fingers across it. Feel it pulse with the heartbeat of Reality. Ignore your Gladys Kravitz-like neighbor’s incredulous stare. The ravenous indifference of Reality will soon devour her. And other things.
Note well: if G-d is not free to make square triangles, married bachelors, alternatives to modus ponens, or give 6,666,666,666,666,666,666,666,666,666,666, 666,666,666,641 more than two divisors He is as powerless before them as you. The Supreme Mathematician’s workshop was built to fit the anfractuous corridors of an a priori labyrinth. Perhaps He spends His days soaring past zeros on Riemann’s critical line, approaching omniscience since no amount of positive confirmations can prove it, exploring the endless beauty of a landscape He did not create. Blasphemy and crazy talk? Then what is the nature of their relation?
Cicadas buzz, having emerged from a slumber of thirteen or seventeen years to mate for a few weeks and die. Who’s the wisest animal again? In your armchair you prepare seven bottle tops for the collection. Hardy and Littlewood shimmy up and down their aquarium, ignoring partially submerged Ping-Pong balls. Through bubble walls they soar like enraged deities defending a crystal cosmos. The enormity of the tank filled with 151 gallons fails to diminish the footballs with fins, as though their significance is not dependent on any relation to a grander scheme, as though their fierce nobility and purpose would endure in the totality of water.
Novels Featuring Mathematicians Afflicted with Great Evil
*Not the band.
**Petronius Jablonski created a Mandela made entirely from colorful bits of Styrofoam, thereby felling the branches of Buddhism predicated on impermanence, hopefully ending their wanton destruction of good art. (They’re worse than Pete Townsend!)
***And how often are primes two apart? Consider 18,407,687 and 18,407,689. The nebulous wisp between them, is it not akin to the dreamlike pasture separating the granite castles of Beethoven’s Fifth and Seventh Symphonies? No one knows if there is a biggest such instance of sibling rivalry or if they continue forever. The largest heretofore discovered contains 300,000 digits. It is not impossible that man will join the shells encased in sedimentary rock without figuring it out. Our digital replacements will be no less stumped but more stoic in its face.