Matrix calculations and determinants

[Zimbali]

Hey Everyone,

I have been looking into the math related to the binary configurations.

I took the trigram names Ch'ien-Tui and numbered them 1-8.

Thus for every hexagram I gave it a vector, say 8,1 =10, 1,2 =34 5,5=8 and so on.

Then I took the relationship with two vectors i.e. 8,1 and 1,2 in a matrix calculation to get the determinant.

So:

8 1
1 2 = determinant 15

So in this example passage 10 with passage 34 gives 15, which I considered as the optimum behaviour.


What is very interesting is that the determinants of vectors in that manner, seems to hold a great deal of consistency with "best outcome probabilities" when combining the to notions.

Has anyone been working on this type of method?

Best
Iain

 

[bradford]

Not that one. I number with straight up binary:

000 = Kun = 0
001 = Gen
etc.
110 = Dui
111 = Qian = 7

Some do this upside down, but I think that's incorrect for several reasons.


I do the same with the Gua. Graphically the relationships are extraordinary,
See the Figures in the First Chapter of my Volume Two, link below.
Any structurally significant relationship show up with bilateral symmetry,
However, all attempts to correlate structure with positive or negative tone
of the auspice failed to show any significant relationship.

 

[Zimbali]

Noted.

However this does work to correlate in the manner you describe, as that is not its purpose, nor its application.

I'm not sure what you mean by positive or negative tone, as I don't see any relevance.

The element chapters that seem to make up the Yijing are like prime numbers. I don't think they are designed to be broken further than the trigram, to the 3 lines, to the 2 types of line, to the absolute.

So each element or chapter is balanced. Danger is a thing, it exists, we can describe it, we can discuss it. In some respects depending on your perspective it can be a positive or negative influence, but that depends on intervention, the context of your situation, and the related probabilities.

Therefore, for example Danger is not positive or negative. Danger is a thing like hydrogen, or oxygen.

In fact danger can be a good thing, if you understand danger, like with adversity. What one needs to do, is to be able to understand the nature of such, as part of the absolute. What is important is what Danger pairs with. By way of example Danger like with Adversity, could in fact be an opportunity.

What is then explored are the probabilities of the situation, and in the above method one can compute the likely probabilities with the other PRIME ELEMENTAL chapters.

However by numbering in the manner I have it makes for ease of calculation in the manner I explained and looking into the determinant product of the matrix illuminates a clear correlation to the product, and where there is no product the determinant computes zero.

What that then allows you to is analyse the combined relationship between any two hexagrams. Which seems to make sense when you look at the outputs.

Therefore :

y x Nature

1 1 1 Creative power
1 2 34 Great power
1 3 5 Calculated waiting
1 4 26 Potential energy
1 5 11 Prospering
1 6 9 Restrained
1 7 14 Sovereignty
1 8 43 Resolution
2 1 25 Innocence
2 2 51 Shocking
2 3 3 Difficult beginings
2 4 27 Nourishing
2 5 24 Repeating
2 6 42 Benefit
2 7 21 Reform
2 8 17 Adapting
3 1 6 Conflict
3 2 40 Liberation
3 3 29 Danger
3 4 4 Inexperience
3 5 7 Collective force
3 6 59 Reuniting
3 7 64 Before the end
3 8 47 Adversity
4 1 33 Retreat
4 2 62 Conscientiousness
4 3 39 Obstacles
4 4 52 Meditation
4 5 15 Moderation
4 6 53 Developing
4 7 56 Travelling
4 8 31 Attraction
5 1 12 Stagnation
5 2 16 Harmonize
5 3 8 Unity
5 4 23 Deterioration
5 5 2 Natural response
5 6 20 Contemplating
5 7 35 Progress
5 8 45 Assembling
6 1 44 Temptation
6 2 32 Continuing
6 3 48 The source
6 4 18 Repair
6 5 46 Advancement
6 6 57 Penetrating
6 7 50 Cosmic order
6 8 28 Critical mass
7 1 13 Community
7 2 55 Zenith
7 3 63 After the end
7 4 22 Grace
7 5 36 Censorship
7 6 37 Family
7 7 30 Synergy
7 8 49 Changing
8 1 10 Conduct
8 2 54 Subordinate
8 3 60 Limitations
8 4 41 Decline
8 5 19 Promotion
8 6 61 Insight
8 7 38 Contradiction
8 8 58 Encouraging

We take y axis first, the x-axis.

If you then want to compute say 51 with 14 = 12, which makes sense Shock + Sovereignty = Stagnation

[This can be done easy with a matrix calculator, you are calculating the determinant

Therefore

2 2
1 7 = gives a determinant of 12.

The output determinant in my view seem to make a lot of sense.]

I could list then for ease of reference if anyone is interested.

What I would suggest is that the people who came you with Yijing were hugely intelligent and well ahead of their time.

The divination aspect was a smoke screen for those that really understood the mechanics of this, as nothing within it is left to chance.

Therefore a true elite sage [for ease of a better description] guided human affairs based on probabilities and did not leave things to chance.

The mystical aspect of divination is a "red herring" in my view. However it has been highly effective in confusing the masses. More importantly the concept has played an important role in confusing western people to dismissing the value of Yijing as mystical non-sense like a horoscope.

In my humble opinion.

 

[Sparhawk]

You haven't explained the logic of how you attached numbers to the trigrams. What Bradford offered is the binary sequence of the trigrams, or what's attributed to Fu Xi, which is the most logical way to order them: as binary numbers, from zero to seven.

Now, about finding 'optimum behavior'... Go here for a bunch of search results on Chris Lofting ideas about "optimum behavior" and much, much more. I'm afraid Chris isn't on this plane anymore to answer any questions about his methods but they were always interesting and overwhelming in amount and detail. Have fun.

 

[Zimbali]

Thanks Sparhawk.

They are ordered in that manner in RL Wing. I assigned the numbers myself.

Ch'ien 1

Chen 2

K'an 3

Ken 4

K'un 5

Sun 6

Li 7

Tui 8

I didn't assign a zero, only sequential numbers from1. I'll read and digest and revert.



Thanks again.

 

[Sparhawk]

I know everyone has their own preferences, and those are mostly dictated by material availability, but, may I suggest you move on from R.L. Wing? IMHO, you'll get nowhere if you get stuck in that source.

 

[Zimbali]

Thanks sparhawk. Then I guess I must read some more translations. I got the links for Bradford's which looks great. He also already gave me some guidance which I appreciate.

I saw LiSe, what others do you recommend.