**Time Symmetry Conjecture**

**For GANTSCHEV Ivan**

*THE CHRISTMAS TRAIN*
1 The universe has language.

2 Language has time.

3 Time consists of real time and imaginary time.

4 Time is recognized by square.

5 Time has unit.

6 Unit of real time is expressed by

**t**^{2}= 1.
7 Unit of imaginary time is expressed by

**t**^{2}= -1.
8 Real time goes toward future.

9 Future’s time

**t**is expressed by real number.
10 Imaginary time goes toward past.

11 Past time

**t**is expressed by imaginary number.
12 Unit of time

**t**consists of 1, -1,*i*and –*i*.
13 Unit of time

**t**is expressed on complex plane.
14 Complex plane is objected to Riemann sphere.

15 Riemann sphere has unit radius 1.

16 Point of infinity on complex plane is expressed by the two poles of Riemann sphere.

17 North Pole is expressed by orthogonal coordinate system (0, 0, 1). North Pole is abbreviated to NP

18 South Pole is expressed by orthogonal coordinate system (0, 0, -1).South Pole is abbreviated to SP.

19 NP and SP also express square of time’s infinity.

20 NP is real time’s infinity.

21 SP is imaginary time’s infinity.

22 Real time and imaginary time are symmetrical from the origin of coordinate system.

23 Time objected to Riemann sphere is objected to a diameter of Riemann sphere, NP-SP, by parallel translation against complex plane.

24 Diameter NP-SP has measure from Riemann sphere.

25 Diameter NP-SP is called Time Line. Time Line is abbreviated to TL.

26 TL is folded smoothly at the origin of coordinate system with the form of alphabet U.

27 When the universe time moves from point of infinity to the origin of coordinate system on complex plane, objection to TL moves from Poles to the origin.

28 When the universe time moves over the origin of coordinate system to another point of infinity, objection to TL moves from the origin to Poles.

29 When human being stands on U-formed TL, TL’s real number side moves toward the origin and TL’s imaginary number side Moves toward the Pole.

30 In the above situation, time flows simultaneously toward future and past for human being.

**Tokyo**

**December 24, 2006**

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