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. Pu Yi’s Ba Gua South south-East south-west East West North-East North
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. Low Low Low Low Low High Low High Low Low High High
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 Low
Low High High

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

6. Switch C Switch C Switch B Switch B Switch A 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 A
Switch B
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. H H H Finally, when we turn all the switches to the ‘High’ state,
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. Digital Integrated circuit
Light bulb, in off state
Switch A
Switch B
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. Switch C Switch B Switch A We connect wires from the 3 switches to the
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. Ground To make the light bulbs work, we need the ‘ground’.
Switch A
Switch B
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. These are the timing diagrams that simulate all the 8 possibilities of
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.

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. X Y Z 1 1 1 1 1 1 1 1 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. X Y Z We can see the one to one correspondence again. 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1
We can see the one to one correspondence again.

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

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

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

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

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

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

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

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

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

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

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

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

43. Y-axis 1
X-axis 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. Y-axis 1 X-axis 1 1 Z-axis X Y Z1 1 1 1 1 1 1 1 1
Y-axis 1
X-axis 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 X-axis Z-axis West South North East
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 X-axis Z-axis south-East south-west North-East North-West
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. X-axis
Z-axis
North-west
South-west
South-east
North-east
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

51. Can we consider this is also a North-west?
South-west
Can we consider this is also a North-west?
South-east
X-axis
North-east
Z-axis

52. Can we consider this is also a North-west?
South-west
Can we consider this is also a North-west?
South-east
X-axis
North-east
Z-axis

53. Can we consider this is also a North-west?
South-west
Can we consider this is also a North-west?
South-east
X-axis
North-east
Z-axis

54. Can we consider this is also a North-west?
South-west
South-east
Can we consider this is also a North-west?
X-axis
North-east
Z-axis

55. Can we consider this is also a North-west?
South-west
South-east
Can we consider this is also a North-west?
X-axis
North-east
Z-axis

56. If we consider in 3-dimensions
South-east
South-west
X-axis
Still a North-west?
If we consider in 3-dimensions
North-east
Z-axis

57. Will these stars situated within this region?
North-west
X-axis
Z-axis
Will these stars situated within this region?
Will this provide an insight to us that is the reasons why the stars are included in the ‘Luo Pan’?
We have to discuss these since we will need these as a foundation to understand the exciting
part 3 which discuss about quantum mechanics, fractal physics, discrete mathematics, essence of Hua Yan
Buddhism and new mathematical structure for DNA and new Boolean simplification methods.