still wildly beating, quivering and twitching; there was a dull pain in the tips of my fingers and in my knees. This undoubtedly did happen! And now I am unable any more to distinguish what is dream from what is actuality; irrational numbers grow through my solid, habitual, tri-dimensional life; and instead of firm, polished surfaces—there is something shaggy and rough. …
I waited long for the Bell to ring. I was lying thinking, untangling a very strange logical chain. In our superficial life, every formula, every equation, corresponds to a curve or a solid. We have never seen any curve or solid corresponding to my square-root of minus one. The horrifying part of the situation is that there exist such curves or solids; unseen by us they do exist, they must, inevitably; for in mathematics as on a screen, strange sharp shadows appear before us. One must remember that mathematics like death, never makes mistakes, never plays tricks. If we are unable to see those irrational curves or solids, it only means that they inevitably possess a whole immense world somewhere beneath the surface of our life. …
I jumped up without waiting for the waking Bell and began to pace up and down the room. My mathematics, the only firm and immovable island of my shaken life, this too was torn from its anchor and was floating, whirling. Then it means that that absurd thing, the “soul,” is as real as my unif, as my boots, although I do not see them since they are behind the door of the closet. If boots are not a sickness, why should the “soul” be one? I sought, but I could not find, a way out of the logical confusion. It looked to me like that strange and sad debris beyond the Green Wall; my logical debris too, is filled with extraordinary, incomprehensible, wordless but speaking beings. It occurred to me for a moment that through some strange, thick glass I saw it ; I saw it at once infinitely large and infinitely small, scorpion-like with hidden but ever perceptible sting; I saw the square-root of minus one. Perhaps it was nothing else but my “soul,” which like the legendary scorpion of the ancients, was voluntarily stinging itself with. …