Last night as soon as I had gone to bed, I fell momentarily to the bottom of the ocean of sleep like an overloaded ship which has been wrecked. The heavy thicket of wavy green water enveloped me. Then slowly I floated from the bottom upward, and somewhere in the middle of that course, I opened my eyes,--my room! The morning was still green and motionless. A fragment of sunshine coming from the mirror on my closet door shone into my eyes. This fragment does not permit me to sleep, being thus an obstacle in the way of exactly fulfilling the rules of the Tables which prescribe so many hours of sleep. I should have opened the closet but I felt as though I were in a spider web, and cobweb covered my eyes; I had no power to sit up. Yet I got up and opened the closet door; suddenly, there behind that door, making her way through the mass of garments which hung there, was I-330! I have become so accustomed of late to most improbable things, that as far as I remember I was not even surprised; I did not even ask a question. I jumped into the closet, slammed the mirror-door behind me and breathlessly, brusquely, blindly, avidly I clung to her. I remember clearly even now:--through the narrow crack of the door a sharp sun-ray like lightning broke into the darkness and played on the floor and walls of the closet, and a little higher the cruel ray-blade fell upon the naked neck of I-330, and this for some reason seemed to me so terrible that I could not bear it, and I screamed;--and again I opened my eyes. My room! The morning was still green and motionless. On the door of my closet was a fragment of the sunshine. I was in bed. A dream? Yet my heart was 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....