Now I am Enough Old for Remembering the Past
Recently I read Susan Sontag's WHERE THE STRESS FALLS, 2001. The impression is a little different with the other books.
I was never the good reader of her, but her existence was always strong and had glittered.
The time was Sixties that contained the infinite things in it.
Now I am enough old for remembering the time.
She wrote a fine essay on the time, Thirty Years Later ... , 1996. The pages are short but sufficient to describe the time that was infinite and endless.
If her life was able to be shine, while my Sixties was always under the tiny dim light.
At the place where I was, the long view never could be seen. I never thought on the things as I was very coward and was fluttered even at the very tiny event of the time. I was infirm and timidity.
What I could do at that time was read or turned pages of the text books of some foreign languages.
How little and shallow heart I had, pitiable and poor existence. Probably till now.
Reference
Under the Dim Light
Tokyo
27 September 2012
Sekinan Research Field of Language
From Cell to Manifold
Cell Theory　
Continuation of Quantum Theory for Language
For LEIBNIZ and JAKOBSON
1
Cell is defined by the following.
n-dimensional ball Dn　has interior that consists of cells. Cell is expressed by Dn - δDn and notated to en that has no boundary.
δis boundary operator.　
Homomorphism of Dn is notated to Ä“n.
ēn - δēn = en
2
Set of no- boundary-cells becomes cell complex.
3
Some figures are expressed by cell. hn is attaching map.
n-dimensional sphere Sn = ē0 ∪hn ēn
n-dimensional ball Dn = ( ē0 ∪hn-1 ēn ) ∪ ēn
Torus T2 = ( ē0 ∪h1 ( ē0 ∪ēn ) )∪h2 ē2
3 Grassmann manifold is defined by the following.
Grassmann manifold GR(m, n) is all of n-dimensional linear subspaces in m-dimensional real vector space.
S1 = GR( 2, 1 )
4
Canonical vector bundle γ is defined by the following. E is all space. π is projection.
γ= ( E, π, GR(m, n) )
5
Here from JAKOBSON Roman ESSAIS DE LINGUISTIQUE GÉNÉRALE, <semantic minimum> is presented.
Now <semantic minimum> is expressed by cell Ä“3.
6
<Word> is expressed by D2.
7
<Sentence> is expressed by Grassmann manifold’s canonical vector bundle γ1 ( GR(3, 1) ).
Tokyo
June 2, 2007