Time Flow in Word For KOHARI Akihiro and His Time

Time Flow in Word For KOHARI Akihiro and His Time

Language and Spacetime

Time Flow in Word

For KOHARI Akihiro and His Time

TANAKA Akio

1

Word is expressed by phase space in the situation on dynamical system.

Phase space M has a point x.

Continuous time t is expressed by group R that consists of real number.

Homomorphism φ^t(x)expresses the system.

φ^s+t(x) =φ^s (φ^t(x)), φ⁰ (x) = x

2

In thermodynamics, equilibrium is presented.

Equilibrium situation is expressed by (U, V, n).

U is energy in the system. V is volume. n is material.

Here new equilibrium is expressed by (U’, V’, n).

3

Now a category is presented.

(U, V, n) →^f (U’, V’, n)

f is function of entropy.

Here (U, v, n) is expressed by P. (U’, V’, n) is expressed by P’.

The situation of equilibrium is expressed by the following.

f : P → P’

4

The situation of equilibrium is rewritten by phase space.

Each situation of equilibrium is expressed by a point x.

After time t, point x and x’ is presented by the following.

φ : φ^s(x) →φ^s+t(x)

5

Now equilibrium system is expressed by {φ^t} that is called flow.

Here phase space M can take tangent vector X.

Point x has tangent vector X_x = dφ^t(x)/dt_t=0

The flow has solution as equation φ^t(x)/dt = X_φ^t_(x)

6

Here set {φ^t(x) | t∈R } is presented. The set is called orbit.

7

In word, meaning is expressed by flow and time is expressed by orbit.

Tokyo May 3, 2007

Sekinan Research Field of Language

www.sekinan.org