## Pleasure of Mathematics

**TANAKA Akio**

Thinking about language by mathematics is one of the most fantastic time for me, ever and probably from now on. Now I remember that the days of writing Stochastic Meaning Theory and Energy Distance Theory showed me the new visibility to language from ambiguous intuitive situation.

Stochastic Meaning Theory

Energy Distance Theory

- Energy and Distance
- Heat and Diffusion
- Energy and Functional
- Finsler Manifold and Distance
- Word and Meaning Minimum
- Geometry of Word

Especially Stochastic Meaning Theory was a fresh entrance to writing on my physical image of language. Energy and Brown motion are both purely the themes of physics. But in those days about 2007, I thought that if language have energy or language have free movement like Brown motion and in the space described by mathematics language generate words or sentences. Stochastic approach is enough strong to my uninhibited desire. In those days what I really wanted to get was the universality definitely described on language.

One day I was admonished from my teacher CHINO Eiichi,"You should not take those course that were not for our ordinary people's study, we were not Wittgenstein. " CHINO taught me almost all the linguistic information from the utterly beginning. I was surely not Wittgenstein, or did not want to become him. But what Wittgenstein pursued in his life time was also able to pursue in my life time, I have thought it over and over. At this situation, Roger Penrose wrote quite exactly as the following.

- In 2005 Roger Penrose published
*THE ROAD TO REALITY A Complete Guide to the Laws of the Universe*. At the preface he wrote, ""**We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics.**

I ever wrote on CHINO with deep gratitude after his death in 2002.

- If C live, he also may ask me, "What are you researching now?" And I also will answer him as same as ever. I have pursued universals, never done facts, without repenting. Oh C, if you live, will we also talk on language at the table facing each other under the low ceiling of the shop, going up the steep stairs. The name of the shop is
*California*. For the memory of our daily forgetful life, its never miserable though poor all over, I will write down our delight.

For me, mathematics is not a tool to think but pleasure to think. If there be not mathematics right before me, how I describe language's Brownian motion to the others in the complexed and gotten entangled situation by historical deepness and areal wideness.

I wrote at the paper, "Language as Brown Motion" as the following.

Abstractive space

*Ω*

*σ*additive family that consists of subset of

*Ω*

*F*

Measure that is defined over

*F*

*P*

*P*satisfies

*P*(

*Ω*) =1.

Probability space (

*Ω,*

*F*,

*P*)

Stochastic process defined over (

*Ω,*

*F*,

*P*) (

*Bt*)

*t*≥ 0 =(

*Bt*(

*ω*))

*t*≥ 0

(

*B t*)

*t*≥ 0 that satisfies the next, it is called

**Brownian motion**.

(i)

*P*(

*B*0 = 0 ) = 1

(ii) For ∀

*ω*∈

*Ω*,

*B t*(

*ω*) is continuous on

*t*.

(iii) For0 =

*t*0 < ∀

*t*1 <…<

*t n*, ∀

*n*∈ N , {

*Bt i*-

*Bt i*-1 }satisfies the next.

a) {

*Bt i*-

*Bt i*-1 } are independent each other.

b) {

*Bt i*-

*Bt i*-1 } are followed by mean 0 and variance

*t i*-

*t i-*1 of Gauss distribution.

Random variant of 1-dimensional Brownian motion starting from the origin

*B*

*σ*(0, ∞ ) : =inf {

*t*>0;

*B t*∈ (0, ∞ ) }

*A*= {

*σ*(0, ∞ ) = 0 }

*A*∈ F 0 *

*P*(

*σ*(0, ∞ ) = 0 )= 0 or 1

*t*↓ 0

*P*(

*σ*(0, ∞ ) = 0 )= 1

From symmetry of Brownian motion

*B t*= -

*B t*

From these premise, the next assumption is led for us.

Language that has Brownian motion

*L B*

*L*

*B*has actual language and imaginary language.

At this process mathematics is not definitely a tool for thinking. By the very mathematics, I could first get the clear notion of actual -imaginary relationship as the style to the others. It is a great pleasure to get difficult theme after long times. And also pray all the people, thinking complexed intuitive notions and hoping to describe clearly, step up one or two levels alike me.

**Tokyo**

**13 December 2014**

**Sekinan Essay**

Weaving products for bed cover

Ome, Tokyo

The exhibit of festival at Autumn 2016

Read more: https://srfl-essay.webnode.com/news/pleasure-of-mathematics/

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