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Drawing as a Random Walk Through Pascal’s Triangle. From Space/No Space to Equilibrium/Non -Equilibrium

24 February 2025

6 mins

Edwin VanGorder


Consider Leading order gap space of the convective space quanta and sub -atomic levels relative photonic spectra. The state of preservation within the atomic nucleus of the ideal kernel is in non-equilibrium contrast to the orthogonal status equilibriums.
Self -composing and self- distribution over distortions and the relation of compound figures to composite space in complex narratives as relative to equilibrium and disequilibrium counter tensions give a window on the doors of these perceptions. Matisse for example with negative space narrative frames the collective integral over the objects shaping space , Escher provides directions of compounding entities or metamorphosis as presenting of co-chains and cohomologies while the space/no space of Smithson grants a module the dimension of normalizing as a thing in itself dimension. We might best follow these paradigms then with “equilibrium /non Equilibrium” to approach the elusive quantum critique and in which the progress made over the Langlands conjecture as relating spectral to automorphic groups can be followed via all its own resonance patterns and Finnegans Wake like hyper punning sorting upon dimensions of language dream, art, thought and physics mathentos.(Mathentos for Greeks the dawning awarenes of that of which you speak…)…
The drawing builds on the Leading I Orders or recursive ten fold magnitude bracket as as in scientific notation of n base ten which correspondingly attend to the square root of ten and its reciprocal as control axis over a three tensor ie zeros bracketing (which could of course be altered in the simplex status extending the string) and in doing so creates a catastrophe like self reference when the second zero bracket has digit two this a mod transference to next level thus while 31 is 3.1 x 101 32 is .32x 102 In harmonic terms this transference has resonance in the proportion 2.764 (where .764 = 1.309 and .309 times 2 is golden section) which has reciprocal 3.618 while .3618 has reciprocal .2764. in relation to this it interests me to pose a variation on transposed matrix by relating succeeding primes added and subtracted from one of the nearest adjacent perfect squares of which one will produce in sum of the difference another square root with some exception at other singularities such as the primes adding to a square or the creation of the values 5 or 1. One thus para hypothesis the Reimann conjecture as an intuition that the mathematical and geometric means are in tension to place a relation between equilibrium and disequilibrium. It is intriguing that the creation of a prime must also be its editing from any repetition towards creating another prime and the information seems ensconced in the square values which together are as “image” analogical to 1.1 as it were… this number has been termed a kind of “magic number” in setting the offset of thin material matrices towards hyperconductivity and along these orders one senses better why this is so… It interests me to create irregular gap spaces in the log… comparable say to the “mirror displacements of Robert Smithson who in creating spaces between mirrors in landscape opened up ones rationalization of the experience in a way prescient to the quantum event in which is concealed a form of history one in a sense produces.
Drawing as a Random Walk Through Pascals Triangle :considering the webs and winds of reflexive orders of flux momentum building over leading orders to compare in simulacra the staging of orbital and s pin counter dynamics to emergent nemacity or fuzzy number bifurcations and indices
Returning to the idea of leading orders, as in the simplex levels of Pascals Triangle and a random walk as placing turns to a Monet Carlo… the extended simplex gates then are behavior axis notes which in recent physics has emergent paradigms in the realization the black hole accretion disc is rather then flat instead multileveled and pulled as it were into the orders of cosmic web structure indices upon form while in hyper conductive materials likewise a new dimension “nemacity” over the spin of light and polarity of atomic structure binary opposition lends as mentioned the channels of fuzzy number transitive’s or alternate oscillation constructive routes available to an electron preference of gateway upon the gap space.
The gap space mathematically then as the remainder overlap or underlap of repletion’s is a transport to center view as it were of the condition of the gnomon or gamma complement area which stages the complement strip as simultaneously the dimension of the square to oblong distortion of the figure in the square space. 
The drawing then considers in its construct these aspect of leading orders migrating from gamma -Gnomon to gap space with views to contrast of structure naming fragments t to unity as ration and then again mod, or fragmentary forms as themselves the whole units upon which are named next order fragments as it were : in relation to a paradigm of consecutive adjacent primes summed and subtracted from the left or right square number which will then provide another square analogical to the number 1.1 upon the recursive structure of the number line and its base ten referent to 3.168 the square root of tent of which the tenth part is also the reciprocal of Pi.

Properly speaking then the gnomon/gamma edge determined space of complementary function might be termed non gap and the centered lap/overlap as a conductivity region resonant to projection as gapped… thus I condition the axes of the octonian as “loaded to independent function widths to midline bundle crossing which then as a focal length continued in a linear mode towards the gnomon planted regions in opposing quadrant space as that mathematical space derivative. In my next paper I will go into plotting specific harmonic values of constants in more direct analytic.
Hypothesis: over a primus of symmetrical structure log and bilateral devolved of the numbers of perception two and three, embedding Pi within the square root of two as a signifier of manifold give a fundamental paradigm of octonion spinor axes loaded to meet gnomon/ gamma parameters linking the piecewise construct to dependent and independent functions, derivatives and tangents bundle integrated via that model. Linking then as well the One Way diagonal construct to its parallelogram model with analytic continuation to Complex number fields and the mirroring kernel carrying the information of the pull back and pull forward motif over dual spaces and the tangent and cotangent bundle upon which to meet at outset the time dilating priming which accrues to the smash products or function transforms iterated within the DeRham Complex as so far intuited and outset of considering the Langlands conjecture as our effective Finnegans Wake. Up along the way compare the structuring an initial derivative in base ten unity to translation in derivatives towards a mod form. In this case one is effectively posing the square root of two and the square root of ten as a simulacrae upon which a kind of oversight function exists as the golden section mean is that of the square root of ten and square root of eleven added. Accordingly multiplying the roots by 1.1 modifies the recursive base ten reference to another mapping as it’s simulacra

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