“Ancient science was based like that of today on number … (they) regarded numbers as symbols of the universe, finding parallels between the inherent structure of number and all types of form and motion … the canon of number was venerated as the source of all knowledge.”
John Michell The Dimensions of Paradise
Mathematics offers a systematic and logical approach in the search for a truthful explanation of the nature of reality. It provides a tool of commensurate power, a descriptive language that can both transcend linguistic boundaries and suggest universal, communicable routes into the intuitive.
“Number is the Word but is not utterance; it is wave and light; it is rhythm and music, though no-one hears it. Its variations are limitless and yet it is immutable. Each form of life is a particular reverberation of Number.
The oldest book in the world, the Chinese oracle of divination the I Ching or Book of Changes, is in a sense a mathematical treatise laying down the ground rules in the interpretation of number. It contains sixty four – two to the power of six – hexagrams, one for every number in base two – i.e. using only the numbers 0 and 1 – between ‘000000’ and ‘111111’, ‘0”s represented by the broken ying line and ‘1”s by the solid yang. The Shuo Kua or Eighth Wing of the Commentaries to the I Ching begins with these words:
“In ancient times the holy sages made the Book of Changes …. in order to lend aid in a mysterious way to the light of the gods. To heaven they assigned the number three and to earth the number two; from these they computed the other numbers.”
Elaborating on these words Richard Wilhelm writes:.
“The fundamental principles of the world are heaven and earth, spirit and matter. Earth is the derived principle; therefore the number ‘2’ is assigned to it. Heaven is the ultimate unity; yet it includes the earth within itself, and is therefore assigned the number ‘3’. The number ‘1’ could not be used, as it is too abstract and rigid and does not include the idea of the manifold.”
The I Ching
On consulting the I Ching one is forced to subjugate ones actions to a seemingly random process, to become the confederate of a chance interplay between the two conditions of ying and yang …. representative of the binary states of ‘0’ and ‘1’. By these means the rational mind is not thought to have relinquished its power to make calculated, thoughtful assessments on the basis of genuine probability, quite the contrary. The ritual abandonment of conscious control to hidden, unknown forces was thought to open up direct communication with the suprahuman intelligence that underlies every chance configuration and situation, that only on the level of appearance appears so random and devoid of meaning. Once the ritual splitting of yarrow stalks or tossing of coins has been completed the mind is considered refreshed and able to re-engage with the ‘problem’, the analysis of the resultant ‘answer’ to ones ‘question’ being subjectively invested with the appropriate ‘solution’.
The I Ching offers only a limited matrix of responses to an unlimited potential for query. The premise therefore is that beneath the apparent infinitude of unique scenarios there lie basic, universal patterns. On being consciously put into touch with descriptions of general application, the dynamics of a particular situation can come to lose its mystery and becomes comprehensible. The ‘answer’ triggering off a consciousness of the ‘solution’ already pre-existant in the mind of the enquirer by virtue of universal, numerically based patterns.
Information, as every school kid will tell you, is not the same as data. Data can contain information but only after it has been identified, extrapolated and invested with meaning. It is to view chaos as intrinsically the product of a hidden order that has yet to be made cognisant. For the Chinese however, the relationships between cause and effect are dialectical and asymetrical, where the effect may also be the cause, and the cause the effect.
“Counting that which is going into the past depends on the forward movement. Knowing that which is to come depends on the backward movement.”
The Shua Kua – Eighth Wing of the Commentaries to the I Ching
Similar thinking informs contemporary scientific enquiry. The second law of thermodynamics for instance, states, roughly speaking, that in any change the Universe becomes a slightly more disorderly place, meaning that once, at the dawn of creation, the primal source point must have been a very orderly place indeed.
“As entropy goes up, so the information content goes down. This natural tendency towards disintegration and chaos is evident all around us: people grow old, cars rust, houses fall down, mountains erode, stars burn out, clocks run down. we are therefore presented with a curious question. If information and order always have a natural tendency to disappear, where did all the information that makes the world such a special place come from originally?” ……
Or as another ancient Chinese proverb would have it:
“Confluence is the approach of nothingness. In total confluence, presence stirs.”
It seems the high entropic, low information Big Bang, as visualised by Cosmologists, may contravene the second law of thermodynamics.
“We now know that the second law has statistical validity only. It is permissible merely to say that there is an overwhelming probability that entropy will rise. A decrease of entropy (growth of order) can happen, but is exceedingly unlikely. For example, the random wash of the waves on the seashore could, but almost certainly would not, arrange the sand into the shape of a castle, in reversal of its more familiar obliterating tendency. Does this then suggest that some sort of gigantic miracle has occurred against all imaginable odds?”
The key to understanding lies not only in the backward motion. Consciousness arises out of biological processes but itself can’t be explained by them. Similarly life itself is the product of chemical reactions, the qualiative effect in the overview evading explanation in the specific. The reductionalist methodology whereby the lower one descends in the hierarchy of order the closer one approaches the blueprint upon which everything above has been built is a falacious and much discredited approach. The clever and ingenious technique that it is, ultimately any truth in the matter must also take into account the forward motion. That on rising up the hierarchy new, higher levels of order transpire.
The Big Bang gave rise to a universe comprised almost entirely of hydrogen, the smallest of atoms and one with a built-in urge to form molecular couplets – a function that I suspect is inextricably allied to the force of gravity, a contractive force to counter balance the outward, expansive momentum. In fact the moment the creative surge moved up to the production of helium, the next largest and far more stable atom, the process of creation switched itself off. The existance of the ninety or so other higher elements are entirely attributable to the entropic principle, being the product of stars undergoing decay, death and dispersal. Like flowers shedding seeds on the approach of winter, the process recommences with a return to the beginning that in the fullness of time gives rise to evolutionary forces.
For some cosmologists solace resides in the Anthromorphic Principle. Rather than accept the notion that our existance is the result of some grand fluke of chance or “gigantic miracle”, the emergence of order, life and intelligence are understood to be an intrinsic, immanent quality within the very fabric of reality, a form of inner programming if one likes. For Pythagoras and his ancient forbears, as with the I Ching and today’s scientists, the key to this enigma lay in the logic and form of number.
“All that has by nature with systematic method been arranged in the universe seems both in part and as a whole to have been determined and ordered in accordance with number, by the forethought and the mind of him that created all things; for the pattern was fixed like a preliminary sketch, by the domination of number pre-existant in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and eternal essense, so that with reference to it, as to an artistic plan, should be created all these things, time, motion, the heavens, the stars, all sorts of revolutions.”
Nicomachus a Pythagorean writing in the 1st Century A.D.
For Pythagoras the number ’10’ held particular significance. In comprising the sum of the first four integers ‘1’, ‘2’, ‘3’ and ‘4’ he considered it the number of divine materialisation, the Tetratys or Quaternion, portrayed in the manner of the pins in a modern day bowling alley . In contemplation of this structure not only could one perceive the ‘Euclidean’ axioms of dimensional increase and the sacred harmonic intervals of 1:2. 2:3 and 3:4 – the octave, fifth and fourth respectively, but ultimately reveals ‘the source of nature that perpetually rolls along’.
The Holy Cabbalah likewise places emphasis on the number ten, the Tree of Life containing ’10’ Sephiroth or letters. These were divided into three groups of three atop of which presided Ain-Soph that ….
“… has a form and yet has no form. He has a form whereby the universe is preserved and yet has no form because he cannot be comprehended.”
Moses ‘de’ Leon The Zohar
These ’10’ Sephiroth spell out the constituent elements of the ‘Tetragrammaton’ – ‘the name of four letters’ – which spell out the true, unutterable and sacred name or ‘Word’ of God. The utterance of which gave rise to the creation, being not a name in the sense of a title but a description of the process of creation itself.
In the beginning was the Word.
And the Word was with God.
And the Word was God.
The same was in the beginning with God.
The Gospel according to St John Chapter 1 verse 1
A further level of resonance connects the Pythagorean and cabbalistic models. The Tetratys was thought of as the perfect ‘form’ within an evolutionary progression of four sacred geometric structures beginning with just ‘1’ triangle deliniated by three points, followed by a triangle placed above two triangles, deliniated by six points – that contains within its frame ‘4’ triangles in all – the fourth implied at its centre, hidden and reversed. The third ‘progressed form’ is the Tetratys itself, the ten pins of the bowling alley, deliniating layers of one, two and and three triangles, containing three hidden or reversed triangles, making ‘9’ in all. The fourth state, following on from the Tetratys, comprised tiers of one, two, three, four and five points deliniating a structure containing ten upright triangles and a further six reversed, making ’16’ in all. The progression, therefore, corresponding to the point, line, plane and solid, is one of a squaring of the value of the level used to produce them, resulting in ‘1’ – (‘1’ x ‘1’), ‘4’ – (‘2’ x ‘2’), ‘9’ – (‘3’ x ‘3’) and ’16’ – (‘4’ x ‘4’) triangles respectively.
The third element, the Tetratys itself, corresponds to the ‘plane of juncture’ that links knowledge with understanding, being associated within the fourth stage with the line of four points that divides the figure into three tiers of triangles above and one tier below. The corresponding level on the Holy Cabbalah being the hidden, missing, conspicuous in its absence, non-Sephiroth of “Daat” – the ‘Abyss’, ‘void’ and ‘great transmutator’ – out of which flowed all God’s creation.
The drawings, my “forbidden fruit”, applies the motion of pushing the ’16’ – (‘4’ x ‘4’) to the ’25’ – (‘5’ x ‘5’) state; and then allowing it is fall or return to a state of unity ‘0’ – (‘0’ x ‘0’). Neither of which are tenable of course. The ebb and flow causing transmutational effects prefigured by a process of fission and fusion. The forward movement leading to ever more ordered focus to the spiral motion of wave and particle, towards the portrait of a double helix. The backward motion seeking ever more simplicity as it draws the double helix back into itself. A spring, so to speak, ever vibrating.
Pictorally speaking, God is not outside and exterior to his creation but an intrinsic property within, infusing the very fabric of the universe. Furthermore, consciousness is not conceived as an after effect of motor functioning or even an agent responsible for the program that governs our behaviour. It is a fundamental property immanent in the physiological processes themselves. Beneath the infinite orders of surface reality resides substance. And the spirit of this substantiality is appearance multiplied in the manifold – through invocation, evocation and manifestation to materialisation, which in turn is no more than the beginning of the next stage in the process of invocation. It is the quality of consciousness pulling itself up by its own bootstraps – the universe engaged in a continuous process of making itself known to itself – each death in the steady march of entropy opening up the potential for form on a higher order. The line now a plane, the cross-section of an infinitly large solid, ephemeral and devoid of substance and time.