This day he did not dwell or elaborate on the accident itself and only brought it up with but a hint of reminiscent melancholy and a repressed sigh as the turning point in his life. While he was laid up for months, some books on mathematics fell into his hands. They must have been well written or his condition may have made him susceptible to their contents, because for the first time in his life he became feverishly interested. It proved a revelation. He had considered himself fairly intelligent until then, but he felt now like a child in arms as compared with the men who had thought up these things or when considering what they could do with them. The satisfying generalizations, the logical conclusions and unexpected demonstrations which, once understood, appeared so simple as to make one feel like a fool; the embracing concept of function and the formidable tool of transformation. All these things reaching conclusions that transcended the very minds which had discovered or perhaps created them. That was the slightly maddening thing about it. Were these things discoveries or creations? Or could one not settle by concluding that they were the system of discovering the workings of one’s own mind?
He remembered his delight when analyzing the general solutions of equations. The practical quadratic was a sonnet with two possible endings; the cubic was an ode to ingenuity and perhaps a monument to the controversial perfidy of an unscrupulous mathematician, its irreducible case a hint of irritating suggestiveness; the quartic, a drama in which three unknown victims are enlisted, two of them liquidated to zero only to be exhumed later to yield the solution with their identity; the quintic, the pillars of Hercules, a stimulus to generalizations and conquests which far surpassed the original problem and a profound humanistic lesson which tells us that we should always question whether the solutions we seek to our problems really exist.
During his university days he had swum in a small part of this ocean, or rather, had floated like something impermeable and stationary, without understanding, or venturing to see what lay beyond the horizon, or sinking to find what was in the depths, or even considering whether it might be at times a reflection of the sky. Perhaps it had been his youth, more concerned with immediate and mundane things, perhaps his teachers or the books he read had not been inspiring. The fact remains that while he lay in bed he had been visited by this revelation that changed his attitude about life. Forgotten were all thoughts of serious music, changed completely his sense of values. These were the boundless perspectives to explore, the great game of the mind. He did not regret at all his protracted confinement to bed, but would have prolonged it, nor did he regret being lame for life and thus having lost the fickle love of that wonderful girl who sat in a box the memorable night of Faust, basking vicariously in his glory, and whose corsage he still treasured, withered and disintegrated, in a beautifully inlaid coffer carved like a miniature mosque.
When he finished, he was playing something very sentimental and put on a comically contrite look which came unexpectedly to life with his characteristic laugh. I realized that he had been amusing himself at our expense. What a character!
I still held his notes in my hand and turned my attention to them again. For the first time I noticed that many of them were written in the style he talked. There were several dashes in between phrases which probably stood for his derisive laughter:
Those who attack relativity perhaps have never understood it fully, but those who disregard Euclid perhaps have never understood him as simply as schoolchildren do. But possibly this comes from boredom at confronting the same thing over and over again or from a desire to save the profession or put it on a paying basis. Cast doubts, create new things, and your customers come flocking back. Give them something so solid that it lasts forever and soon you have no more customers— The system of the guild. Stand together and protect it at all costs. Nothing as decisive as this final step of higher dimensionalities — and they have on their side the average man. Who can believe such a radical assumption that denies all evidence of our senses, our intuition of flowing time, of real motion? Who indeed? So, one must propagandize the collapse of reason and flood the market with startling revelations. It is a carnival with fireworks and all. Take a group of sightseers who don’t know what it’s all about, disguise them brilliantly through an ingenious transformation and make them dance on tensors over nets of matrices to the syncopation of covariants and contravariants and they are at your mercy. When they hear that the addition of velocities has a limit and that infinity has been clocked at three hundred thousand kilometers per second, they don’t realize that while they have been stood up with the intuition-cuddling assertion of the reality of time and motion, their reason has been knocked down with the absurdity of a limiting velocity, so long as it is considered a velocity to which nothing can be added and from which nothing can be subtracted, and they have been swindled out of the very ground from which they were contemplating the mental pyrotechnic display. They are all yours. The implied flattery has won them over, and you are back in business again.
Yet, this concept of a limiting velocity becomes simple when considered as an extension where all inclinations which appear as velocities from zero to infinity take place within a quadrant beyond which they only appear as motion in the opposite direction with less than ninety degrees as the difference between an explosion and something that stands still and endures, for the conversion of static mass into energy, or more properly speaking, for an observer to experience mass as energy or vice versa — curiously enough, a multiplication by the square root of minus one. It is by viciously interpreting this graphic representation that a sophistic proof of a contraction, instead of an elongation, is spuriously obtained, thus contradicting the very premises of the argument. Anything in order to explain the inescapable negative results of an experiment which was doomed to failure because it was no experiment at all.
In the light of our concept, we have a type of infinity to which something can be added and from which something can be subtracted, contrary to the relativistic viewpoint The fundamental concepts are the same, but the conclusions are very different These conclusions appear in both cases as paradoxical, but while in one system they become understandable, in the other they defy reason.
I should have known better, but I allowed myself to be dragged into the discussion. Not being at all sure of my ground, I tried to advance behind a shield of generalizations and demagogy. This was, I said, being iconoclastic and unfair to the great men of science — and the world does not applaud or sanction people for nothing — who had achieved such remarkable conclusions and contributed so many things to our modern world. I did not go into what conclusions or what things, because even if I did not know them well, I felt certain that I must be speaking the truth, but the Moor turned the tables on me and said that I had chosen the wrong word when I said “iconoclastic” because modern science was certainly a specialist at laying low idols and old tried and respected truths. He was sponsoring the movement of back to neo-Euclidianism and the tautological neo-Newtonism and I think I caught something of his perennial phrase “don’t know what it’s all about.”
I contented myself with saying that even a dumb clock is right once every twelve hours, but he looked at me with the eyes of a hypnotizing fakir and emitted in a stage whisper:
“Right every moment while stretched out, taking a nap, on the fourth perpendicular, but don’t tell anybody.” He held his pose pointing his fingers at me and then went: “Boo!”
This time I gave up.
He pursued his line of reasoning as if there had been no interruption and, temporizing with Dr. de los Rios, who had argued some of his implications, he conceded that perhaps modern science is only endeavoring to avoid boredom at the repetition of the same old postulates and redundant formulas, perhaps scared by a frightful suggestion of futility once tossed off by Poincare, by creating a novel mental game whose price lies outside an imaginary vicious circle and befuddles the main issue with the razzle-dazzle of surprising apparent contradictions: “To take the decisive step, to lift the frame of the little machine, would be exhibiting paradisiac innocence. The oversimplification would be intolerable — anybody could understand it. No more inner sanctum or chosen few.”