Monday 24 June 2013

From Cell to Operad

Operad Meaning Theory

From Cell to Operad

24 March 2013

I ever wrote a next paper in which cell and meaning minimum  are defined.
Cell Theory. From Cell to Manifold For LEIBNIZ and JAKOBSON. Tokyo June 2, 2007.
In the paper, through Roman Jakobson's intuitive assist, the concept of meaning minimum is described by the elementary algebraic  geomtry. At the deeper basis, Gottfried Leibniz's Monadologie , 1714 may influence for making this Cell Theory.   
The main target of Cell Theory was in the generation of meaning in word. This target was more clearly described soon later at the next paper.
von Neumann Algebra 2. Generation Theorem. Tokyo April 20, 2008.
But the balance of soft part and hard part in word, that was conjectured by Sergej Karcevskij in 1920s,  is very hard theme to describe. For solving the hardness, trial papers were proposed at the next paper group,  Notes for KARCEVSKIJ.
At the first paper of the Notes, Note for KARCEVSKIJ Sergej, the soft part in word was described by the free group's definition.
There is more difficult theme on the gradual changeable addition of meaning for which language has always efficiently useful in the thus complicated contemporary world. 
For this theme, I ever tried to write some papers related with time shift. The example is the next.
From another view on language, I had thought brane model for the connection of words or construction of language. The example is the next.
Briefly summarising I have thought on language from its freeness, flexibility and changeability against long stern structure of soft and hard magical agalgum.
The gist is as the following.
Language shows many phases from thinking levels and viewpoints. 
Language can be captured more clearly from descreteness but more flexibly thinkable from meaning variation and changeability.
Changeability of language implies the eternity of time, but this eternity cannot be easily obtained probably without loop condition of movement. 
Loop space can capture this eternality, that is shown often by the repetition. I firmly noticed this situation at the Shinto dance perfomance at a shrine festival.
Loop space was also notified early stage of Chinese histiory in circa. 500 B.C. at one of the five classics,Y ijing that is the fortune-telling text of ancient China.
On Yijing, I was taught from philosopher NISHI Junzo.
From Infinite loop space, the concept of operad is lead as the next.
 is the space that has base *.
 is the loop space over .
Theorem (J.P. May's recognition theorem)
 operates all the fold loop space. 
Continuous space  to which  operates is weak homotopy equivalent with a certain fold loop space. 
 is  identified as a operator that has j number input and 1 number output.
Here I think that  is identified as a word that has j number meaning minimums and 1 number compound meaning.

J. P. May. The Geometry of Iterated Loop Spaces. 1972.
Iek Moerdijk, Bertrand Toen. Simplicial Methods for Operads and Algebraic Geometry. 2010. 

♦Here ends the paper.


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