Word Containing Time and 4 Dimensional Sphere
1 Word contains time inside.
Refer to the following paper.
2 Word has construction that is expressed by category.
On category, refer to Categories for the Working Mathematicians by Saunders Mac Lane, 1998 Springer-Verlag New York, LLC.
3 Time has starting point and ending point in word.
4 Meaning has starting point and ending point in word.
5 Generally word shifts meaning from starting point to ending point by time.
Refer to the following paper.
6 Primitive word does not shift time and stays in the same point.
7 In category, the names of language are called by following terms.
Meaning is called object.
Shift is called arrow.
Starting point is called domain or source.
Ending point is called codomain or target.
No shift or stay is called identity.
Arrow can be composed. The composed arrow is called composite.
In category two axioms are presupposed.
One is associativity.
The other is unit law.
These terms are all complied with above quoted Mac Lane.
8 Word with starting point is expressed on Gauss plane.
9 Word with ending point is also expressed on Gauss plane.
10 Shift time from starting point to ending point is expressed by coordinates’ transference.
11 Here Riemann sphere is putted with having the same origin to Gauss plane.
12 Word with starting point is projected toward the North Pole of Riemann sphere.
13 Word with starting point has coordinates ws (xs ys, zs) on Riemann sphere’s surface.
Refer to the following paper.
14 Word with ending point has also coordinates we (xe, ye, ze) on Riemann sphere.
15 Here 4 dimensional sphere is putted with having the same origin to Riemann sphere.
16 A indefinite strait line determined by coordinates ws and coordinates we makes coordinates wt (xt, yt, zt, tt) on 4 dimensional sphere’s surface.
17 Coordinates wt on 4 dimensional sphere’s surface is uniquely reflected in word with starting point and word with ending point.
18 Word containing time is uniquely expressed on 4 dimensional sphere’s surface.
Tokyo April 5, 2007
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