The Tale of a Comet

How many times have we wondered about the workings of dazzling, magical brains of the likes of Ramanujan? Of the potentially unearthly origins of brilliants intellects like Ed Witten? That perhaps one solution of Fermi’s Paradox is that brilliant aliens are already amongst us and call themselves Hungarians? Well, here is a story all the way from 1870 which explores this, in superb craftsmanship of lyrical language and poignant sentiment…

Professor Canopus Parallax (!!) writes to his friend, Bernard, about an extraordinary young mathematical genius, Raimond Latoile. Barely 20 years old, Raimond is very much a Ramanujan-like figure. He not just an extraordinary calculating prodigy; he is “a born mathematician” and:

“possesses an intuitive faculty for the higher analysis, and possesses it to such a wonderful degree that all of us here stand before him in genuine amazement. He knows apparently but little about our systems of formulation, though every day rapidly advancing in technical knowledge. And yet, by processes not in the books, processes apparently original with himself, and which he is not able to explain, he has worked out with ease results such as have most violently exercised the highest order of mathematical minds. In a word, this extraordinary youth may be said to think in figures and symbols—the ordinary career of his reason is along the pathway of scientific formulae. More than all this, his mind seems to have grasped at processes and solved problems which we cannot compass with all our skill, and which, with his present deficient powers of expression, he is incapable of interpreting to us.”

Raimond, though, is very child-like in all other aspects, having very little knowledge or comprehension of social mores and knowledge which even toddlers possess. As the university President opines,

“he could not seem less than one of our own people had been dropped upon this earth, a full-grown stranger, accidentally snatched from some other sphere where the customary interchange of thought is through the medium of mathematical formulas.”

Professor Canopus wants Bernard to taking Raimond under his tutelage and provide tender care for about a year and train him to fit into normal society so that no harm comes to this “once-in-a-century” flowering of genius. In moving language, he writes:

“for I need not tell you, men like this Letoile are of too fragile and delicate a constitution to endure rough usage. We can send our earthenware to the well, but we must keep our finer porcelains indoors. And if any mental or moral hurt should come to the young man, we could not fail to be deeply grieved. Our Faculty look upon him as the professors of a musical academy are said to look upon a child possessed of one of those rare voices which do not appear more than once in a century—something to be treasured more zealously than the Sibyl’s books.”

For very obvious reasons, the university and its mathematics faculty would like to ensure Raimond’s personal growth, maturity and longevity. In another flight of luminous language, Canopus writes:

“It has been well observed by one of the deepest thinkers of our century, that there is nothing in the nature of mathematical science which prescribes any boundaries to its infinite progress. There is no limit to the applicability of mathematics, for there is no inquiry which may not finally be reduced to a mere question of numbers, as notative functions of quantities and their relations. The limitation that does exist is in ourselves, in the imperfections of our intelligence, and the absence of power in our minds to go beyond certain processes and degrees of comparison and abstraction. It is only by the discovery of new and simpler methods that the human intellect is able to grapple with the overpowering multitude of new relations and conditions which come up as knowledge advances. And this rank growth of strange weeds in the garden of Science will always run beyond our capacity to eradicate them; for it is part of our unhappy constitution that we are more apt at imagining than we are at reasoning. Hence, we do right to look abroad for new methods and better processes of high analysis; for, while these subtler processes will of course open up to us a vast new field of questions beyond our grasp, they will at the same time give us power to solve many problems already presented, but as yet impracticable to our imperfect algebra. I need not tell you that the present advanced condition of mathematical science, as compared with other sciences, has not resulted from a methodical progression, but has been reached per salturn. It is not coordinate with the advancement of the race, but due to the sublime flights of individual genius. Our science has not crept along with common men on the face of the earth, but has leaped from point to point up the giddy heights, under the impulses given to it by the minds of such uncommon men as Euclid, Archimedes, Apollonius, Pappus, Diophantns, Vieta, Descartes, Kepler, Newton, Leibnitz, Napier, Laplace, and the many other illustrious names which we delight to honor. A new genius, therefore, in giving us new methods, may virtually enrich the world with a new mathematics. Hence the sense of responsibility which we feel toward this young man, who seems to have at his control, could we contrive to develop them, new processes in our science of as great utility to us now as were those of Diophantus to the geometers of his day.”

Bernard, despite not feeling confident that he can tutor such a giant intellect in the common manners, agrees to host him. Meanwhile, in the background hovers Cherry, the love of Bernard’s life, the rustic back-story described very nicely…

Raimond arrives to be with Bernard. Cherry falls deeply in love with this extraordinary simpleton, to the point of worshipping him with reverence, but Raimond has no sense of requiting such love nor is he aware of matters of human attraction. Bernard knows this and poignantly observes,

“I might indeed have pulled down the altar, but I could not have destroyed the idol, for that was engraven upon a woman’s heart, and so was indelible forever.”

As for Raimond’s mathematical abilities, he writes:

“I have Spoken of Raimond’s mathematical studies—but indeed that is scarcely the proper word. What he did in this way seemed done not by process of reasoning, but by pure evolution of consciousness. […] Raimond Latoile’s lips seemed to be counting off fugues from and variations upon the grand harmonies of the spheres, tern of apportioning the stars into various constellations. He gave them names and number, in their widest and most transcendent generalizations. Now and then, as he advanced in knowledge of our common symbols, he would, by way of exercise as it were, set down fragments from these essentially rhythmical reveries —abstruse developments of the properties of recondite curves, unguessed corollaries and scholia from the general laws of the stellar spaces, and speculations within the profoundest twilight of the Calculus - demonstrations always complete and exemplary so far as I could understand them but often, when most carefully written out, as much too difficult for me, as the propositions of The Principia or the Mecanique Celeste would be to an ordinary schoolboy.”

Raimond always seems to be at his sharpest after twilight, gazing at the night sky and constellations, seemingly able to see far distant stars clearly without the need for any telescope. And one night, when Cherry sings a sweet hymnal song, he becomes enraptured, some memory gate unlocking in the recesses of his mind. He exclaims:

“ There!” he cried, “there is my home, in the cycles of yonder bright wilderness of spheres which you call Arcturus! There is my home; and since I was sent from thence I have had no word from home, until Cherry’s voice uttered it just now, with such a familiar accent. Surely you are one of our denizens, Cherry, wandering, like me, a little while from home.”
“ Cherry’s whole life is a poem, Raimond,” I answered for her; “ and a very sweet one. But it is only set to earthly music, after all, and I do not imagine she understands the language of the spheres.
“ Yet she speaks to me in that language,” responded Raimond, musingly.”

Just as they speak, a comet appears in the sky, “a messenger, intelligent existences with souls of flame and lightning wings, set on to do the bidding of the superior spheres!”. Raimond now knows that he as well as Cherry are children of Arcturus, and that a message has arrived… Sure enough, in a magical moment, an astronomer in Vienna finds that by some mysterious means, the comet has ended up inscribing mathematical symbols, a mathematical rebus.

“to his great surprise, instead of having a photographic image of the comet, his plate contained the representation of a series of strange characters or symbols, arranged in order, in a circumscribed lozenge, very much like the ideographic writing of the ancient Egyptians. How it came there he could not imagine, nor what it meant. The characters are not those of any known language, nor have the works of Champollion or Young or Rawlinson afforded any key to them - if, indeed, they be characters at all, which I am inclined to doubt. But Doctor Cometenbahnen not only claims that they are demonstrably characters, but also that they are mathematical symbols, and that they contain a problem of importance to the world, if a solution can only be found. And, he truly says, the human ingenuity that has deciphered the strange monuments of Egypt and the cuneiform inscriptions of Assyria, need not be staggered before the text of any language, even though it embody the songs of the very stars.”

What the message says, its intended recipient, intent and the final denouement become a mystical weave of poetry, confusion, love and sacrifice which people may find unsatisfactory but I felt was just fine, particularly in keeping with the romanticism of that Victorian period. There are certain mysteries which need not be explained, and there does not always have to be a Klaatu who has arrived to save earth or solve its mathematical problems…