A

1 Tube-ring expresses 3 dimensional space.

2 Tube-ring and [cut-glue] operation makes 4 dimensional space.

3 Generally cut-tube-ring and 1 [cut-glue] operation adds 1 dimension.

4 Inductively tube-ring and

*n*[cut-glue] operation makes 3+*n*dimensional space.
5 Now minus 4 dimensional space is made by -7 [cut-glue] operations.

6 Minus 1 dimensional space makes what is called imaginary lineation. Minus 2 and minus 3 make imaginary plane and imaginary cube.

7 Minus 4 dimensional space makes imaginary generating cube with time, abbreviated to imaginary time-cube.

B

8 Here lineation expresses the shortest one determined distance in the space. Plane expresses free distance in the space. Cube expresses free crossing in the space. Time-cube expresses free generating crossing in the space.

9 Raising a dimension give a freer operation in a space.

C

10 Now minus dimensional spaces are also supposed to be given freer operations in spaces.

11 Minus dimensional spaces are difficult to describe concrete image. By freer operation, minus dimensional spaces are distinguished.

12 Minus 1 dimensional space has no freedom in the space.

13 Minus 2 dimensional space has no crossing freedom in the space.

14 Minus 3 dimensional space has no generating freedom in the space.

15 Minus 4 dimensional space has no freedom that is capable in minus 5 dimensional space.

D

16 Now space is expressed by string that is capable of stretch, bending and knotting.

17 1 dimensional space only can stretch string.

18 2 dimensional space can bend string.

19 3 dimensional space can knot string.

20 4 dimensional space can generate knotted string.

E

21 Inductively minus, abbreviated to -, dimensional spaces are expressed by the situation of string that is what is called to imaginary string.

22 Now imaginary string is abbreviated to

*i*string.
23

*i*string is supposed to be given same operation in minus dimensional spaces.
F

24 Space is supposed to be expressed by freedom of string and

*i*string.
G

25 Now dimensional space is called world. Minus dimensional space is called anti-world.

26 World and anti-world become symmetry with regard to structure that is expressed by freedom and string.

Refer to the following paper.

27 Here string and

*i*string are impartially called string.
28 By freedom of string in 4 and -4 dimensional spaces, the very same figured string at the very same place can happen to emerge. Because in 4 and -4 dimensional spaces, two same figured strings can freely exist at the same time by definition of freedom.

29 If adequately raising dimensions, separate two knots of strings are combined each other.

30 In high dimensional space, planes, cubes and so on are freely combined each other.

31 String’s freedom in dimensional space is linked with topological transformation.

H

32 Freedom and its concrete expression’s string interpret world and anti-world.

**Hinoemata July 16, 2006**

**Post script**

**[Reference February 10, 2008]**

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