To Winter RI Ko 2015
14  John Peabody Harrington, Roman Jakobson, FUKAYA Kenji, Maxim Kontsevich, ZHANG BInglin and Roger Penrose

From author:This text’s translation by Google translate is a little hard to be accurate at the present, especially on mathematical explanation by usual writing.

You can see the whole city from the library on the hill. The east side of the third floor is a computer room. The internet was always connected there, and I could use any table freely. I often spend my holidays near the window. A group of tall blue-green buildings rises to the northeast of the left side of the window. Seen from here on the hill, it is much higher. Only there is towering above the sky. Immediately south, there should be A’s home. Did the bulbul hit a tall building like that? The glass walls were distant and dull, reflecting the light of the autumn afternoon. 

When I was cleaning the room where the birds were gone for the first time in a while, I found some furrowed flock in the corner. The soft wings floated in the air for a while when released. Have you lived in the city because of your childhood? I wished that I was now resting slowly in the grove of the hills. A created Web pages and Dreamweaver, but since the amount has gradually increased, I switched to Expression Web from the middle. I used Office for documents at first, but soon I switched to Zoho.

In this way, I was able to quickly write small mathematical expressions using LaTex. When Backup was run automatically using SugarSync, all traces of A were on Cloud. The document was written in English. Regular sentences other than mathematical expressions are relatively easy to write with a limited vocabulary. This could lead to someone seeing somewhere. I had little hope, but there was little response. 

Of course, I thought it would be nice if there could be one or two people in this wide world who could sympathize with me, but that didn’t bother me that much. I just keep writing. There is no guarantee that there will be someone like John Pepody Harrington, who continued to record the American Indian languages. 1920 The photographs in the Smithsonian Institution’s collection, which are doing field research around the year, look somewhat like the pioneers of the West. It’s okay to wait quietly for the future of Harrington in the corner of the city. 

It was a fun task to think of a language containing time as a possibility using a model. However, in reality, it is rarely something that can be created, such as an original one. I couldn’t exceed the conventional idea. He arranged the work procedure little by little. First create a simple model. Select the shape suitable for the model. How much is the figure written? 

According to Kenji Fukaya, the geometry was “a group of groups and the space in which it acts”. It was Fukaya’s charm that he was able to briefly confirm and look at the fundamental things. By referring to Jacobson’s “semantic minimum”, a new geometric “minimum of meaning” is set, and the time t is included as a meaning by moving the time t in the closed interval. Defined the geometric word.

I repeated this direction many times with different levels of geometry. The universality of language was thought to be closely related to the invariant of mathematics. In Fukaya’s book, I learned that the quantum cohomology ring can be obtained from the Gromov-Witten invariant and the Gromov-Witten potential can be obtained. Language approached mathematics and physics. It has become possible to logically check the symmetry that has long been a concern. Under certain assumptions, the character of various languages ​​can be inspected as a model from, for example, one figure or manifold. One of the centers was homological mirror symmetry, which was proposed by Kontsevich.

When I got tired of working in the library, I went out to the rooftop. The city, which spreads under the dark maroon autumn sky, conveyed the grandeur of human activities. The sounds of distant cities echo like a chord. Are people flying in this city as birds are flying in the sky? Just as birds sometimes crash into the ground by colliding with the turquoise glass of tall buildings, will people crash into the ground and crash somewhere?

 I once read a story about birds in the book Shorin no Fubun. “According to the poem of the 3rd year of the Emperor Hansho, a bird of five colors, it passes over the prefectures in which it belongs.” It seems that 10,000 birds of five colors flew in the sky. As for the beginning, I continue to cite Chinese books. According to the poem’s third year of honor, he gathered New Year’s lords, Otori, Emperor and Kanro to the Kyoto teacher, and according to the flock of birds, the findings of the Han book were true.

The contents of this Chinese book, in which 10,000 birds gathered in search of it, are true. It is unknown whether Shorin believed in these statements. However, according to Shorin’s habit, he might have believed it as a natural thing. 

Autumn flowers were dancing in the strolling garden on the roof of the library. White autumn Ming chrysanthemum, yellow Maru chrysanthemum, Nozoku chrysanthemum Soothing Hottogigisu and the white and white Arissum flowers crawling on the ground. Sky blue salvia, red cherry sage, purple rosemary and light blue basil. Dark blue Saintpaulia, white sapphinia, crimson geranium bowls and hanging. Huquera, Drachina consenna, Sansevieria houseplant. Spatti is also rich in green, and the red sea urchin is already red. Various sasanqua that began to inflate the buds, the last cosmos flowers that sway in the wind Winter clematis that has been quite tall, large leaves on the grape rack with few remaining, and a large red or white large ball swaying occasionally in the strong wind . 

If you look closely, you can also see the pink bokeh flowers that change the season. Shala beautifully turns red, and dogwood turns the leaves brown. On the other hand, rhododendrons had already inflated the buds considerably. Autumn was getting deeper. 

You can hear the sound of the city line riding on the wind. How is K doing? Well, let’s make a dedication to the document. For familiar days with K. I continued to write documents when I got home. The linguistic space including time gradually expanded from a straight line to a plane and from there to a sphere. Attracted by the work of Roger Penrose, I made a projective model. 

As I was thinking about it at midnight, I thought it would be beautiful if the language danced in the sky like an aurora. A complex plane is created by mapping all complex numbers to planes, as if all real numbers were mapped to straight lines. A complex number defined by two real numbers is placed on the plane as a language unit, and it is called a language point. Establish a vertical third coordinate axis from the origin of the plane and make a sphere with a unit radius centered on the origin. The spheres intersect at a radius of 1 on the new coordinate axes. If that point and a linguistic point on the complex plane are connected by a straight line, when the linguistic point has a distance of 1 or more, it intersects with the sphere at one point. When the distance is less than 1, the linguistic point is inside the sphere and does not intersect the sphere. 

This shows the limits of the language. Ordinary language points are projected on the spherical sky when the distance exceeds 1. The projection is called aurora. Language points at infinity converge on a sphere on the Z axis. You can capture an infinite number of languages ​​in a finite way. A straight line connecting two points on the complex plane draws an arc in the spherical sky. The two straight lines form two arcs in the sky, and connecting four points creates a distorted quadrilateral in the sky. 

If we model the points in the sky as words, arcs as sentences, and quadrilaterals as sentences, the language will emerge there. The language becomes Aurora and dances in the sky. Language is aurora dancing above us.