Wednesday, 25 December 2019
This translation has some ambiguity for automatic. So sorry.
JOHN PEABODY HARRINGTON, ROMAN JAKOBSON, FUKAYA KENJI, MAXIM KONTSEVICH, ZHANG BINGLIN AND ROGER PENROSE
14 John Peabody Harrington, Roman Jakobson, FUKAYA Kenji, Maxim Kontsevich, ZHANG BInglin and Roger Penrose
Language Description
The library on the hill offers a panoramic view of the town. The third floor, east side, is the computer room. The Internet is always connected there, and any table can be used freely. I often spent my days off by the window. To the left of the window, to the northeast, a group of tall blue-green buildings stand tall. From here on the hill, they look even taller. They are the only ones that stand up, as if they are pushing up into the sky. Just south of them, A's house must be there. I wonder if the brown-eared bulbul bumped into one of those tall buildings. The glass wall reflected the dull autumn afternoon light in the distance. When I was cleaning the room after a long time without any birds, I found some brown-eared bulbul down in the corner. The soft feathers floated in the air for a while if you let them go. Was it already living in the city at such a young age? I hoped that it was resting peacefully in the grove of trees on the hills. A started making web pages with Dreamweaver, but as the amount of work gradually increased, I switched to Expression Web halfway through. I also used Office at first, but soon switched to Zoho. In this way, I was able to quickly write detailed mathematical formulas using LaTex. By automatically backing up using SugarSync, all traces of A were on the cloud. I wrote the document in English. Regular sentences other than mathematical formulas can be written relatively easily with a limited vocabulary. This way, there is a possibility that someone somewhere will see it. I had a faint hope, but there was almost no response. Of course, I thought it would be nice if there were one or two people in this wide world who could sympathize with me, but I didn't care about that much after a while. I just need to keep writing. There is no guarantee that there is someone like John Peabody Harrington, who continued to record American Indian languages, somewhere. A photograph of him doing field research around 1920, held by the Smithsonian Institution, looks somewhat like a Western pioneer. It would not be bad to wait quietly in a corner of this city for the future Harrington. It was a fun task to think of a language that includes time as a possible form using a model. However, in reality, it is rare to create something original. I could not go beyond ordinary ideas. He gradually established the procedure for the work. First, create a simple model. Select a figure that is suitable for the model. Express the figure in geometry. Following Kenji Fukaya, the geometry was "a pair of a group and the space it acts on." The appeal of Fukaya was that it allowed him to confirm and envision fundamental things concisely. Referring to Jakobson's "semantic minimum," he established a new geometric "minimum unit of meaning," and by moving time t in a closed interval, he defined a geometric word that contains time as a single meaning. He repeated this direction many times at different levels of geometry. It seemed to him that the universality of language was deeply related to the invariants of mathematics. From Fukaya's book, I learned that quantum cohomology rings can be obtained from the Gromov-Witten invariant, and furthermore, the Gromov-Witten potential can be obtained. Language was approaching mathematics and physics. Symmetry, which had long been of concern, could now be examined logically. Under certain assumptions, the characteristics of various languages could be examined as models from a certain figure or manifold. One of the central themes was the homological mirror symmetry proposed by Kontsevich. When I got tired of working in the library, I went up to the roof. The city spread out under the dark, dappled autumn sky conveyed the grandeur of human activities. The sounds of distant cities echoed like echoes. I wonder if people fly through this city just as birds fly through the sky. Just as birds sometimes crash into the blue-green glass of tall buildings and fall to the ground, do people also crash into something on the ground and fall somewhere? I once read a description of birds in Zhang Binglin's book Wenshi. "In the Book of Han, Emperor Xuan's Chronicles, an edict in the third year of the Yuankang era states that tens of thousands of five-colored birds flew through the prefectures." It seems that there was a time when tens of thousands of five-colored birds flew through the sky. Wenshi continues to quote from the Book of Han. An edict in the third year of the Shen Jue era states that on the first day of the New Year, on the day of the yi chou, the phoenixes rained nectar on the capital, and tens of thousands of birds gathered in search of it. This is what the Book of Han says: The phoenixes rained nectar on the capital, and tens of thousands of birds gathered in search of it. It is true that this article in the Book of Han is true. It is not known whether Zhang Binglin believed these descriptions. However, given Zhang Binglin's habits, he might have believed it as a natural thing. Autumn flowers were fluttering about in the strolling garden on the library's roof. White autumn chrysanthemums, yellow round chrysanthemums, and navy blue chrysanthemums. A modest cuckoo and small white alyssum flowers creeping on the ground. Sky blue salvia, red cherry sage, purple rosemary and pale blue basil. Dark blue saintpaulia, white sapphinia, and crimson geraniums in pots and hanging plants. Heuchera, Dracaena consenna, and Sansevieria were ornamental plants. The spathi were also a deep green and the plum blossoms were already turning red. Various camellias with buds beginning to swell, the last cosmos flowers swaying in the breeze, winter clematis that have grown quite tall, the few remaining large leaves on the grape trellis, and large red and white roses swaying in the occasional strong wind. If you look closely, you can also see the pale pink flowers of Japanese quince, which are out of season. The leaves of the Chinese quince have turned beautiful red, and the leaves of the dogwood have turned brown. Next to them, the rhododendrons have already swelled up quite a bit in their buds. Autumn was gradually deepening. I could hear the sound of the city line carried by the wind. How is K doing? That's right, I should dedicate the document. For familiar days with K. I continued writing documents when I got home. The linguistic space, including time, expanded little by little from a straight line to a plane, and then to a sphere. I was attracted to the work of Roger Penrose, so I tried to create a projective model. While thinking about this late at night, I thought it would be beautiful if language danced in the sky like the aurora. Just as all real numbers are mapped to a line, if all complex numbers are mapped to a plane, the complex plane is created. A complex number determined by two real numbers is placed on the plane as a linguistic unit and called a language point. A third coordinate axis is erected perpendicular to the origin of the plane, and a sphere with a unit radius centered at the origin is created. The sphere intersects with the new coordinate axis at a point of radius 1. If a line is drawn between this point and a language point on the complex plane, and the language point has a distance of 1 or more, it intersects with the sphere at a single point. If the distance is 1 or less, the language point is inside the sphere and does not intersect with the sphere. This shows the limits of language. Ordinary language points are projected onto the spherical sky when the distance exceeds 1. This projection is called the aurora. Language points at infinity converge onto a sphere on the Z axis. An infinite number of languages can be incorporated into a finite space. A line connecting two points on the complex plane draws an arc in the spherical sky. Two straight lines on a plane form two arcs in the sky, and when four points are connected, an irregular quadrilateral floats in the sky. If we model the points in the sky as words, the arcs as sentences, and the quadrilaterals as sentences, language will emerge there. Language becomes an aurora and dances in the sky. Language is aurora dancing above us. I wrote this and dedicated it to K.
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