1 <Meaning> in word is given by homotopy.
2 <Time> in word is given by continuous map of homotopy.
3 Time is expressed by t of path α(t).
4 In path from x0 to x1 of closed interval [0, 1] , α(0) is called initial point and α(1) is called terminal point.
5 <Time shift> in word given by interval of path
5 When path has α(0)= α(1) = x0, it is called loop. In this case, initial point is called base point.
6 Initial point or base point makes <base meaning> in word.
7 <Meaning variation> is generated from <time shift> of path α(t).
Refer to the following paper.
8 Loop has group’s structure that is called fundamental group.
9 In homotopy, 3 laws are secured. (1) Reflection law (2) Symmetry law (3)transition law
10 Laws in homotopy secures construction of word’s meaning.
11 Loop’s equivalence class makes homotopy class.
12 Homotopy class [α] and [β] has product. [α] * [β] = [α * β]
13 Product makes <meaning complexity> in word.
14 Now 2-dimensional square I2 is presented. Continuous map α to space X is given by the following.
α : I2 →X
α is called 2-loop that expresses dimensional extension of loop concept.
15 2-dimensional sphere is 2-loop.
16 Riemann sphere has information from Gauss plane.
Refer to the following papers’ group.
17 Meaning variation and concomitant time shift in Symmetry Flow Language are testified by 2-loop sphere.
Tokyo May 17, 2007
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