The Unification of String Theory & the I-Ching’s Dynamic Binary Structure

Is the Universe Programmed by Strings?

The mathematical system of the I-Ching is a highly efficient and compact shorthand for a kind of mathematics to help us describe the nature of space, time, matter, energy and perhaps even string theory, at a deeper level, paradoxically. The I-Ching is a highly efficient Master Code, with layers upon layers of meaning, both qualitative and quantitative, embedded within its structure.


“The trinity of world principles, however, does come to expression in the hexagram as a whole and in its parts. These three principles are differentiated as subject (man), object having form (earth), and content (heaven). The lowest place in the trigram is that of the earth; the middle place belongs to man and the top place to heaven. In correspondence with the principle of duality in the Universe, the original three-line signs are doubled; thus in the hexagrams there are two places for earth, for man, and for heaven. The two lowest places are those of earth, the third and fourth are those of man, and the two at the top are those of heaven” – Wilhelm’s I-Ching


Chapter 1- I-Ching Trigrams, Hexagrams and “Correlates”

“……………hexagrams should be thought of not merely as made up of six individual lines but always as composed of two primary trigrams,……………” – Wilhelm’s I-Ching

Furthermore, corresponding lines of the upper and lower trigrams are called “correlates”.  This applies to the relation of the first line with the fourth line, the second line with the fifth line and the third line with the sixth line.

If the lines are different in type, (for example a yin/yang or yang/yin pairing), the correlation is deemed ‘proper’ (or in harmony), otherwise, it is ‘improper’ (for example a yin/yin or yang/yang pairing). However, there are cases of harmony with an ‘improper’ correlation.

It is interesting to note that the Standard Model of Particle Physics is replete with examples of particle/antiparticle triple paired “correlates”, some of which are shown below.

Examples of Triple Paired “Correlates” in the Standard Model of Particle Physics

proton = 2 up quarks and 1 down quark

antiproton = 2 up antiquarks and 1 down antiquark

neutron = 1 up quark and 2 down quarks

antineutron = 1 up antiquark and 2 down antiquarks

lepton = electron, muon, tau

antilepton = positron, antimuon, antitau

lepton-neutrino = electron neutrino, muon neutrino, tau neutrino

lepton-antineutrino = electron antineutrino, muon antineutrino, tau antineutrino

Also, six ‘flavour’ of quarks grouped in three pairs – up/down; strange/charm and bottom/top.

As you can see, a distinctive pattern emerges.

Aside Note:

Moreover, this pattern of coding is also evidenced on the 3-nucleotide codon/anticodon sequence pairing of the Genetic Code. For example, CGT codon and its anticodon GCA  (A = Adenine; C = Cytosine; G = Guanine; T = Thymine).  In fact, in the DNA molecule there are 64 codons (4^3 = 64), the same as the number of I-Ching Hexagrams (8^2 = 64).


Chapter 2 – The Bifurcation ‘Tree’ and the Six ‘Flavours’ of Quarks

Diagram 1

As a result of the bifurcation process (see above) the six ‘flavours’ of quark are split into two groups of three representing a trigram in each case. In each trigram the mass decreases upwards from level 1 to level 3 (for masses, see table at end of Chapter 2). A lower mass increases the natural frequency (frequency increases up through successive levels within each trigram). For the hexagram as a whole (composed of two trigrams stacked on top of each other), the heavier quark within each pair is assigned to the lower trigram, its partner to the upper one. Incidentally, the ‘top’ quark has a greater mass than the ‘bottom’ quark and for this reason is positioned in the lower of the two trigrams. [See Chapter 4 – for a further example of how frequencies are superimposed onto the King Wen ‘Later Heaven’ sequence of 8 Trigrams to give all the colours in the ‘Colour Octave’] .

From the diagram above, you can see that the down/up quarks form the only ‘proper’ correlation. A quark is an elementary particle and is the fundamental constituent of matter. Quarks are made up of tiny vibrating strings of energy. Of the three pairs, the up/down quarks are particularly important as they form both protons and neutrons within the nucleus of an atom. Their significance in the composition of atoms is the reason why their correlation is ‘proper’ and not ‘improper’ as is the case with the other two pairings.  Moreover, a yin/yang or yang/yin ‘proper’ correlation is not just exclusive to particle/antiparticle pairs.

Furthermore, on the far RHS of this bifurcation ‘tree’, you can see that the first tier branch forks to form two separate second tier branches. One branch is for quarks, but what about the other?

Supersymmetric particles are certainly elusive – but, is it possible that the ‘squark’ the supersymmetric counterpart of the ‘quark’ may exist after all?!

(Of course, it may be supersymmetry is a symmetry of nature, but realised at energies well beyond the reach of our current technologies).

Note:

For the purpose of analysis, the above bifurcation ‘tree’ should be regarded as subprogram. Its main role being to simply specify the number of quarks/squarks (?) and their corresponding antiquarks/antisquarks, and, also to stress the importance of the up/down ones relative to the rest within each category. On the other hand, the main program will contain the expanded version of the system – culminating in a trigram for each and every particle and antiparticle disclosed within the subprogram.

Table of Masses/Charges (Courtesy of http://www.physics.ox.ac.uk)

Mass Approx GeV/c^2
  GROUP 1 GROUP 2
Flavour of Quark Charge Mass Flavour of Quark Charge Mass
       Up   +2/3   0.04     Down     -1/3  0.008
     Charm   +2/3   1.5     Strange     -1/3   0.15
       Top   +2/3   180     Bottom     -1/3   4.5

Note: the masses should not be taken so seriously, because the confinement of quarks implies that we cannot isolate them to measure their masses in a direct way. The masses must be implied directly from scattering experiments.


Chapter 3 – Bifurcation ‘Tree’ for the Six ‘Flavours’ of Quarks and their corresponding AntiQuarks

Quark/AntiQuark Derivative Bifurcation ‘Tree’

Diagram 2

Step 1: Forming the Quark/Antiquark Derivative Bifurcation ‘Tree’

I have labelled the above diagram according to the King Wen ‘Later Heaven’ sequence of Trigrams which form a family of 8 Trigrams (constituting, Mother, Father, 3 sons and 3 daughters). The quark derivatives are the male trigrams having an odd number of yang lines, either 1 or 3 and the antiquark derivatives are the female trigrams having an odd number of yin lines, either 1 or 3. It should be noted that the quarks don’t usually end up nicely grouped on one side of the ‘tree’ and the antiquarks on the other. Nevertheless, if a quark appears on the on the RHS branch of the ‘tree’ its corresponding antiquark will always appear on the LHS and vice versa. In other words, a quark and its antiquark will never appear on the same side.

The yin/yang constituents are the ‘Parent’ elements (yin = ‘Mother’, yang = ‘Father’). They set in motion this tree-like system or mode of branching by repeated bifurcation. After three forks in the overall process the three quark derivatives and their corresponding antiquark derivatives begin to emerge.

The Six Flavour of Quarks/Antiquarks

Diagram 3

AntiQ = AntiQuark

Step 2:  Forming the Six ‘Flavours’ of Quarks/Antiquarks by Expansion of the Derivative Bifurcation Tree in Diagram 2

Expand each trigram in Diagram 2 according to the definition of the hexagram given at the beginning of the article.

In other words doubling due to duality, so that a yin line splits into two to become yin and yang and a yang line splits into two to become yang and yin, expanding in an upwards direction. Thus the three lines of a trigram metamorphosise into six lines of a hexagram. The resulting six hexagrams which are shown above, are configured by stacking each of two new primary trigrams on top of each other, and are representative of each of the three pairs of quarks, bottom/top; strange/charm; up/down, together with their corresponding antiquarks, antibottom/antitop; antistrange/anticharm; antiup/antidown.

Note: Overall Net charge balances out to zero, as expected.

Lower Trigram Net Charge: LHS = (+2/3) + (-1/3) + (-2/3)= -1/3;  RHS = (+2/3) + (+1/3) + (-2/3) = +1/3: Total (-1/3) + (1/3) = 0

Upper Trigram Net Charge: LHS = (-1/3) + (+2/3) + (1/3) = 2/3;   RHS = (-1/3) + (-2/3) + (+1/3) = -2/3:  Total (2/3) + (-2/3) = 0

Two out of every three pairings, in each Hexagram are ‘improper’ “correlates”, one out of every three are ‘proper’ “correlates”, indicating a weak interaction or a weak force between Top/Bottom: Charm/Strange; Up/Down quarks and their corresponding antiquarks.

Fractional Charges

The fractional charges pertaining to each of the six ‘flavours’ of quarks and the six ‘flavours’ of antiquarks are derived as follows:

Quarks:  Count the number of yin lines, if one, charge is negative, if two charge is positive

Antiquarks: Count the number of yang lines, if one, charge is positive, if two charge is negative.

Quarks

‘Bottom’ Quark = 1 yin line = charge -⅓

‘Top’ Quark = 2 yin lines = charge +⅔

‘Strange’ Quark = 1 yin line = charge -⅓

‘Charm’ Quark = 2 yin lines = charge +⅔

‘Down’ Quark = 1 yin line = charge -⅓

‘Up’ Quark = 2 yin lines = charge +⅔

Antiquarks

‘Bottom’ AntiQuark = 1 yang line = charge +⅓

‘Top’ Antiquark = 2 yang lines = charge -⅔

‘Strange’ AntiQuark = 1 yang line = charge +⅓

‘Charm’ Antiquark = 2 yang lines = charge -⅔

‘Down’ AntiQuark = 1 yang line = charge +⅓

‘Up’ AntiQuark = 2 yang lines = charge -⅔

Step 3: Analysis of the Hexagram formed from the ‘Up’ Quark Trigram (Lower) and ‘Up’ Antiquark Trigram (Upper) [refer to trigrams in Diagram 3]

Lines 1 & 4: yin/yang ‘proper’ correlation

Lines 2 & 5: yin/yang ‘proper’ correlation

Lines 3 & 6: yang/yin ‘proper’ correlation

All three pairs are ‘proper’ “correlates” indicating a strong attraction between the ‘Up’ quark and its corresponding antiquark.

This strong ‘proper’ correlation extends to the other 5 ‘flavours’ of quark/antiquark pairs as well.

If quarks and antiquarks collide, it is possible that they undergo what is called mutual annihilation; both particles are converted entirely into energy. When ‘adding’ a quark trigram with its corresponding antiquark trigram you will always end up with three yang lines, this being the trigram for the ‘Father’. As a matter of fact, the ‘Father’ trigram is symbolic for ‘White Light’, which is the pure energy of Creation.


Chapter 4 – The Colour Octave

In humans there are 3 different types of cone photoreceptor cells in the retina of the eye, distinguished by their pattern of response to different wavelengths of light. The 3 types of cone respond to light of short, medium and long wavelengths. They operate using the principle of resonance and and are tuned for frequencies Red (R), Green (G) or Blue (B). In fact, the entire technology of colour on earth is trying to create music from 3 tones only, just by varying their relative intensity.

Within the colour spectrum the 3 ‘additive’ primary colours of Red, Green and Blue have their complementary ‘subtractive’ primary ‘anticolours’ of anti-red, anti-green and anti-blue, respectively known as Cyan, Magenta and Yellow.

Furthermore, Yellow (Y), Magenta (M) and Cyan (C) are produced by the equal intensities of two ‘additive’ primary colours of light, to give the combination R+G = Y; R+B= M and G+B = C.

The colours R, G, B, Y, M, C together with Black and White form a cluster of 8 colours or a ‘Colour Octave’. As demonstrated below, a one-to-one correspondence exists between these 8 colours and the I-Ching King Wen ‘Later Heaven’ Sequence of Trigrams. There are 2^3 = 8 permutations of yin and yang taken 3 at a time, giving 8 possible Trigrams, representative of all colours in the ‘Colour Octave’.

Note: ‘Octave’ as in a set of 8 not a musical ‘Octave’.

I-Ching King Wen ‘Later Heaven’ Sequence of Trigrams

In terms of colour Trigrams, the long-range (i.e. low frequency) waves are set in the bottom position, the medium-range (i.e. medium frequency) waves in the middle and the short-range (i.e. high frequency) waves at the top. The strong, unbroken lines are yang lines and are numbered 1 for ‘On’. The weak, broken lines are yin lines and are numbered 0 for ‘Off’.

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