Symmetry Flow Language 1 Premise for Symmetry Flow in Language 2007

Symmetry Flow Language

1

Premise for Symmetry Flow in Language

TANAKA Akio

1 On Boltzmann’s principle, entropy S is expressed by the following.

S = k_BlogW

k_B is Boltzmann constant.

W is thermodynamic weight. On Newton dynamics, W is expressed by measure of set satisfied needed conditions in phase space.

2 H-theorem is presented by the following in accordance with Boltzmann’s principle.

Probability that gases has velocity v = (v_x, v_y, v_z) is expressed by f (v, t).

H(t) = ∫f (v, t) log f (v,t) dv    d H (t) / dt ≦ 0

Thermal equilibrium is expressed by the minimum of H.

3 On symmetry flow language, abbreviated to SFL, the followings are supposed.

1*    Language has energy.

2*    Language regulates position r = (x, y, z).

3*    Language regulates momentum p = (p_x, p_y, p_z).

4 SFL is supposed to satisfies Boltzmann’s principle.

5 Word of SFL has structure. The structure consists of meaning and time of beginning point abbreviated to m_b and t_b, meaning and time of ending point abbreviated to m_e and t_e. The succession of meaning from t_b to t_e in word is called flow.

6 Here flow is expressed by {φ^t}.

Flow has equation solution when vector field X is defined.

dφ^t(r) / dt = X_φ^t_(r)  (1)

7 Now on oriented closed surface, Riemann metrics g_ij and Ricci curvature R_ij is presented.

Ricci flow on manifold is expressed by the following.

d g_ij / dt = -2 g_ij  (2)

Ricci flow (2) can be seen as a better form of equation (1).

8 SFL is considered by equation (1) and Ricci flow (2), especially (2) in relation with Thurston conjecture.

Tokyo May 5, 2007

Sekinan Research Field of Language

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