Next, we come to ‘Ba Gua’ diagram or eight states diagram as shown above.

1. King Wen’s Ba Gua Next, we come to ‘Ba Gua’ diagram or eight states diagram as shown above. Ok, what is message that it want to deliver to us? Usually, Chinese people will hang it on the top of the front door of their house saying that it will chase away ghost or bad luck. Really? Will it contains any mathematical concepts which explain our nature? Korean Flag Just an extra information, as we can see that the Korean Flag also having the similar symbols…... Well, not quite. 4 symbols of the Ba Gua have been taken away and the white and black dots of the Tai Ji symbol in the centre are missing.

2. South south-East south-west Pu Yi’s Ba Gua West East North North-East North-West In the original document of I-Ching, we can see that directions have been assigned to each of the 8 symbols. Why is that so?

3. Will these stars belong to this particular direction? Let us begin our discussion from a simple point of view. Please refer to the following slides.

4. By using 3 switches and by performing all the 8 possibilities , we will get an alternative way to understand ‘Ba Gua’ diagram. Low Low Low Low Low High Low High High Low High Low

5. Let High = H and Low =L H L L H L H H H L H H H

6. Switch C Switch B Switch A Switch C Switch B Switch A All the eight symbols in the ‘Ba Gua’ diagram consist of outer-most line, middle line and inner most line. We assume the outer-most line represent switch C, the inner-most line represent switch A and the middle line represent switch B. Remind that the original meaning of these symbols will be different from what we assume here. Remember that we are using scientific approach here.

7. Now, we will try to use the point of view from digital electronics as a stepping stone to understand ‘Ba Gua’ diagram. Switch C Switch B Switch A Low Low Low Let us assume that there is a room which having eight light bulbs which separately attached to the edges. We have 3 switches to control them. When we turn all the switches to the ‘Low’ state, the light bulb at the bottom left corner is turned on.

8. Switch C Switch B Switch A Low Low High

9. Switch C Switch B Switch A Low High Low

10. Switch C Switch B Switch A Low High High

11. Switch C Switch B Switch A H L L

12. Switch C Switch A Switch B H L H

13. Switch C Switch B Switch A H H L

14. Switch C Switch B Switch A Finally, when we turn all the switches to the ‘High’ state, the light bulb at the bottom right corner is turned on. H H H

15. Reference point If we ‘float’ in the middle, we will see eight light bulbs in 8 directions. Only 1 light bulb will turn on each time.

16. Conclusion: We can say that each of the eight symbols in ‘Ba Guo’ diagram represent a particular direction. Switch C Switch B Switch A Low Low Low

17. Light bulb, in off state Switch B Switch A Switch C Digital Integrated circuit We can actually implement this circuit in real life situation by using a digital IC, switches, light bulbs or Light Emitting Diode and wires.

18. A B C Switch C Switch B Switch A We can design ( using Computer Aided Design software ) a combinational logic circuit which have 3 inputs (Switch A,B and C) and 8 outputs (which represent the 8 symbols in ‘Ba Gua’ diagram).

19. Wire C Wire A Wire B Switch C Switch B Switch A We connect wires from the 3 switches to the wire A, wire B and wire C in the circuit diagram.

20. A B C We connect the out, out2, out3, out4, out5,out6,out7 and out8 to 8 light bulbs which situated at the edges of the room .

21. Switch B Switch A Switch C To make the light bulbs work, we need the ‘ground’. We assume the IC is already being powered. Ground

22. Switch C Switch B Switch A Low Low Low We ignored the wiring for clarity purposes. When we let switch A, B and C to be in low state, We can see that only one light bulb turn on. The others are off.

23. Switch A Switch B Switch C These are the timing diagrams that simulate all the 8 possibilities of the switches.

24. Switch A Switch B Switch C

25. These are the outputs that will control the eight light bulbs. Out Out2 Out8

26. Switch A Switch B Switch C Out Out2 Out8

27. on off off off off off off off

28. off on off off off off off off

29. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 To further enhance our understanding, let us take a look to the I-Ching diagram again. Remember the game which shown previously? Here, X can be used to represent ‘Farmer’, Y for ‘Wild dog’ and Z for ‘Chicken’. X=0 y =0 z=0 represent all of them is at the right Side of the river bank. X =1 y=1 z=1 means that they are at the left side of the river bank.

30. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 We can see the one to one correspondence again.

31. 1 1 1 1 1 0 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1

32. 1 1 1 1 1 0 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1

33. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 We can see that the 0 0 0 and 1 1 1 are again can be related to the symbols in ‘Ba Gua diagram’

34. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis X-axis 0 Z-axis Next, instead of representing Farmer, wild dog and chicken, the X, Y and Z are now use to represent dimensions.

35. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis Let us try to relate the direction in the Ba Gua with the coordinate indicated here. North X-axis 0 Z-axis

36. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis X-axis 1 North-west Z-axis

37. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis 1 West X-axis Z-axis

38. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis 1 South-west X-axis 1 Z-axis

39. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis X-axis 1 North-East Z-axis

40. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis X-axis 1 1 East Z-axis

41. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis 1 South-East X-axis 1 Z-axis

42. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis 1 South X-axis 1 1 Z-axis

43. Y-axis 1 X-axis 0 1 1 Z-axis By now, we can slightly understand that why directions have been assigned to the eight symbols in Ba Gua diagram.

44. 1 1 1 1 0 1 X Y Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 Y-axis 1 X-axis 0 1 1 Z-axis Also, we can see that this is like a unit cell. These coordinates are much like indices such as Miller indices in material science. They can also represent the position where the 8 light bulbs attached to.

45. Y-axis West South X-axis North East Z-axis Now, we can also use arrows to point to the particular directions. The four arrows indicate the North, South, East and West.

46. Y-axis south-East south-west X-axis North-East North-West Z-axis The arrows in the square indicate North-west, North-east, South-east and South-west.

47. Y-axis X-axis Z-axis Combining all the arrows together indicating the directions in 3 dimensions. Remind that we are not providing definite answer here since the author had not went through the former education of I-Ching. The results of our discussion might differ with the original meaning. However, after these lengthy discussions we are able to get some clues and start to see the relation between Science and I-Ching. There is a doubt! Please refer next slide.

48. Logically, the north-west, north-east , south-west and south-east directions should be in the following ways as indicated by the green arrows as shown below. South-west North-west South-east X-axis North-east Z-axis

49. South-west North-west South-east X-axis North-east Z-axis North-west Do you see the difference of the direction of North-west in the diagrams above? Let us go through step by step to see whether there are any connection between these two diagrams.

50. South-west North-west South-east X-axis North-east Z-axis