Under Zelkova Trees With John F. Nash Jr. and KAKUTANI Shizuo

Under Zelkova Trees

TANAKA Akio  

                                        

There are many fine zelkova trees in the National Institute of Neuroscience, Tokyo. There a relative of mine had ever worked as a researcher. I heard that he had studied on anti-psychotic agents as one of the typical researchers at the field in Japan. Several years later he went to Canada for the further studies aiming the top circumstance of the field.

Time passed by, and after returning home, in a short time, he contracted a disease. He had worked as the daily study fighting against the disease, but sadly he died as young as only 55 years old in the midst of his research.

Now 20 years already passed away from his death. In front of mine, many zelkova trees have grown so tall and spread their branches widely to the autumnal clear sky with the leaves changing yellow. Ivies on the trunks have become beautiful red.

One of my sons had ever exercised the first bicycle riding at the plaza in front of the research building, in probably his 6 years old days. The place were always calm and enough wide for the son, splendid to training of tottering riding.

Now he is working as a computer science field every day late at night. The time equally passed for all. I also grew up. Or no, became older to  the later years in the life. In those days I have struggled for my aim of study on language as for me. But no results could be obtained with letting satisfied myself. Remembering the time, these zelkova trees have seen all the scenes silently above ours.

What work I have done? What papers I have proposed? The answer cannot be seen for me.  Only some footsteps on the field could not be abandoned. WANG Guowei, Ludwig Wittgenstein and Sergej Karcevskij. From philological intuition to mathematical descriptions.

From set theory to geometry and still more geometrical algebra and after all returning to geometry and topology, at where now I stand with  receiving the deep influence of  the Linguistic Circle of Prague on which CHINO Eiichi perfectly taught me in my age 30s, at last leading me to the present study on language.

Keen Applied achievement, NON-COOPERATIVE GAMES 1950 of John F. Nash Jr. on equilibrium point from KAKUTANI Shizuo's fixed point theorem 1941 has encouraged me sufficiently keeping on reading contemporary mathematics results.

           

                                                Tokyo
                                      12 November 2012
                         Sekinan Research Field of Language