1 Now define sentence and word.
Differentiable manifold M has space V that has transformation group G.
G contains transformation function g.
g(x) =a/b
Point x makes Vx
In upper conditions,
M is sentence.
{Vx} is word.
2 Here M is given by klein bottle.
Refer to the following papers.
Obi Theory Universe 19, 20 and 22 Tokyo May 5, 2006
Obi Theory Time E 32 and 33 Tokyo May 6, 2006
M is gauge field.
M has twist when goes around.
M has vanish twist when goes around twice.
3 M is finite.
Language is finite.
M’s section is finite.
Twist is finite.
4 M breaks continuous symmetry.
M has discrete symmetry.
Twist is discrete symmetry.
5 Here M is filled with super fluid substance such as liquid helium.
In M, helium is quantumized.
Circulated quantum that is treated as element of language, is generated.
6 M’s section is vocabulary.
Vocabulary makes fiber bundle.
When vocabulary is quantumized, language becomes quantumized discreteness.
7 Vocabulary is in differential situation that is called world.
World is continuous and finite.
Language is discrete and finite.
8 Language’s minimum unit, namely root of word, is treated on quantumized substance that is in discrete, finite and probably entangled situation.
Because entangled situation is regarded as one of the most basic situation of quanta.
Tokyo June 14, 2006
Sekinan Research Field of Language
www.sekinan.org
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