You start walking toward them, but, strangely, you walk in what looks not to be a straight line but rather an arc, curving in towards the center of the circle before curving outward again to meet your friends. You wave to one another, and your friends beckon you over. Maybe you will never reach the edge after all? What is happening?Īt some point, you see your physical self notice some friends, standing some distance away in the circle. When you are 3/4 of the way to the edge, you are moving at only 7/16 of your original speed. By the time you are halfway to the edge, you are moving at only 3/4 of your original speed. It initially looks like you will reach the edge in a surprisingly short amount of time, but, as you continue watching, you notice yourself getting smaller and slowing down. You watch yourself walk towards the edge of the circle. As you rise, everything seems perfectly normal at first, but, when you reach a sufficient altitude, you notice something strange: your body appears to be at the center of a perfect circle, beyond which there is simply…nothing! You’re out for a walk one day, contemplating the world, and you suddenly have an out-of-body experience, your perspective floating high above your corporeal self. On my return to Caen, for conscience’ sake I verified the result at my leisure. I did not verify the idea I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. Having reached Coutances, we entered an omnibus to go some place or other. The changes of travel made me forget my mathematical work. Just at this time I left Caen, where I was then living, to go on a geological excursion under the auspices of the school of mines. Greifswald and the M… on Ultrafilters VII: Large C… September (1): How D… on Dante, Einstein, and the Shape… Circles 3: Building Everything out of Nothing.Greifswald and the Mathematical Sublime.Follow Point at Infinity on Search for: Pages
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