SZ: Section 3: Interface Mathematics Part I

Russell’s Paradox and the Cycle of Unity

p213:  Apparently I hadn’t noticed just how clearly Russell’s Paradox mirrors the cycle of unity in its oscillation between immanent-transcendent (holonic/membership) and transitive (non-membership) forms.  It’s something like an abbreviated, hollowed out, or logical form of the cycle of unity, where each axis this time doesn’t need to wait till exhaustion, but instantaneously implies the other.  Back and forth, or round and round…  You can see this clearly in the embryogenesis of dimension, specifically our vision-logic dimensions at this non-dual (2D polar) level.  See the below diagram, specifically in the bottom right corner.  At root, this is how simple this distinction between immanence/transcendence and transitivity is…and such simplicity is typical of the root levels of fractals.

Very simply, the relation of membership is holonic or immanent/transcendent (focus, depth), and the relation of non-membership is a transitive relation, one next to the other…side by side the sets form a line.  And in the embryogenesis of mathematics, as in the diagram above, the transitive is before the integration of identities into holonic form to reach back into originary immanence.  And again this shows just how core level these two relations (and their axes) are for logic and set theory, which is implicit ontology.  They appear to be key to all the paradoxes of the infinite, but an exhaustive treatment (closure) on that subject awaits…

SZ: A Note on the Absolute Relation and Univocity

There is a key truth to the notion of the absolute as (absolutely) free of constructs. Also, this purity that we sense, along with the value or space I feel the distinction holds, is a key function of the univocity framework in SZ. Maintaining this purity in polarity and distinction, is its primary function.

And of course it is also true that for a distinction to be *real* (Spinoza and dependent arising) it cannot be absolute, and must, in some sense, be inter-expressive. There is one voice, and it can only express difference … without limit … because a limit itself is difference. Deep infinity is expressing itself through the relation(s) of I AM. This is really what nondual means, in my view…and the deeper we can *feel* into that, and out from that, by whatever (and all) catalyst(s), the more alive we are.

So, nonduality is convergent with univocity, meaning a polarity and triunity between the relative and absolute, and “Substance turns on its modes” (Deleuze). We get a *feel* into the triunity and interface that we are, with the univocity framework, the cycle of unity, and with Spinoza’s triune infinite, etc. But they are still not it, in the sense that they can’t contain an infinite surface, let alone its depths. They are just ways of peering into its embodied and real form.

That being said, in the exploration of this infinite “boundary” between the absolute and relative which is the nondual itself, how indeed can we make sure not to lose the distinction itself between the absolute and relative? How can we retain the truth in the implicit and emergent or natural meaning of ‘absolute’? What is the truth of the purity that we sense in the word?

In another word, I think it is ‘boundlessness’, or freedom. It’s just a finger pointing at what cannot be contained within our boundary … but it’s always already infinitely full. As well, the finite and infinite are not simply a polarity. They explode into a rich living depth of conscious intelligence and order. And from where they meet, we expand in whatever art or form which resonates with where we are.

So then what is the essence or purity of the absolute which must be guarded… and indeed how can we guard against the guard itself? ;) Firstly, we note that the absolute is the identical opposite of the relative. And we note that it is relation in the first place which *forms* the absolute (concept) in an orientation on its fundamental limits in infinity. We could say that the absolute is the self-consciousness of the field of relation… in a sense. And insofar as self-consciousness hiders the flow of the self, our own ‘non-action’, then this distinction needs to be resolved, tuned and triuned into a seemless flow and integration of the univocal form.

We have an implicit connection to the infinite and absolute, and absolutely no separation from it. We *are* it. And we can’t help but feel it. This is closure and involution for the field of relation. It’s self-defining other, in identical opposition and return to integration.

So what can be the opposition to relation itself? The absence of it, certainly, as there is nothing other than relation at this level of generality of the term to oppose. So then, what the absolute cannot do is relate (and of course it must…shhhhh!!!). It cannot be used in the field of relation itself, but only in opposition to relation, to give it its embodied form in infinite difference.

But then again, with the inter-expression of univocity, the absolute and relative are one: the absolute-relation, and the ONE-ALL. This then is our only view of what the absolute can be, dealing at such a degree of abstraction. But it is an omni-non. It is everything, and so it disappears. Nothing we can say about it (including herein) can exclude the very opposite of what we can say about it, because it contains all REAL opposites…and if we are using unreal ones, well then that speaks for itself.

So dealing with the absolute we speak its language and invoke its forms. They emerge naturally from our own absolutely real form. Wholeness. One way to see into wholeness, which has the advantage of mirroring our self-similar form, is through the metaphor of embryogenesis, first through polarity and then on into multiplicity or the ten thousand things. So that’s where SZ hangs out. What scars of our own embryogenesis are left in our embodied intuitions about the core issues of multiplicity, differentiation, and integration as they show up in mathematics? And what can that teach us about embodied conceptuality and ontology, either its limits or capacities?

Unspinning some bitZ: Section 1

To aid in my memory of just what kind of beast I have left to hobble around this universe, I’ve taken to re-reading this book.  I must apologize for the messiness upfront, and I feel great hope in Bonnitta’s initial Recursion.  Such amazing traction, resonance, depth, and reflection in your expansions, Bonnitta!   It’s always exciting to intermingle universes… ;)  And I’m ecstatic that you are digging into this process of translating our wor(l)ds, because I/WE will learn so much!   Con-gea-ling a continent from the archipelago.  Very fun.  I also must say that I take my own map of this space very loosely as it’s really more an art than a science, given the lack of input I had during the writing of much of it.  More intuitive and subjective than inter-objective, perhaps.  But such is philosophy at the (internal) periphery.  For example I hadn’t read “Where Mathematics Comes From,” (Lakoff and Núñez) which you, Bonnitta had pointed me to a few months back.  I really wished I had, however, because our respective works are so complimentary…which just goes to show yet again this massive convergence of disciplines on the horizon now…. reaching a new harmonic.

So, to this end I am going to leave a trail of attempts to clarify points, some new scrawlings on that old ragged parchment.  Watch out for this … or that … kind of thing.  But it will also contain reflections into resonant threads as I process into what’s being said by my former self…and will no doubt, as is always the case, help me flesh out my current tangents in SZII.  This process will take the place of, or perhaps include the questions I was going to provide, as possible things to consider to aid in the orientation, or reflect into.  But I think it makes sense if I scout ahead and provide some harmonics to smooth the waters and give a view on what’s to come as we proceed.  So I will provide a commentary for each section, hopefully, at the beginning of the week, as I go along the voyage with you all.  Here’s the first one, comments to follow as I finish the reading…but please feel free to engage in this thread, if something resonates.

All page references from SpinbitZ I:

~p76 : What is this imbalance in the mathematical ratio here?  I find it rather difficult to see clearly from the rough text.  To give a view from above, it is an attempt to tap into an intuition of the root-level move from implicit immanence to explicit transcendence via transitivity (I will explain more simply below, see emphasis…).  First in the initial closure (transcendence in root-level involution) of the unit-identies, the number ‘1’ (essentially, the mathematical proton) and input-output (iopol) inversion (in the embryogenesis of math, a bit up ahead, you’ll see ;) ).  Involution always precedes a new evolution, because only with new depth can we begin the necessary reconstruction, rooting deeper and deeper into complexity (continuity, not homogeneity) and source.   This is a critical move with interface philosophy, that transcendence and immanence, or evolution and involution are deeply coupled.  This recursive tension between immanence and transcendence is at the heart of complexity, and it shows up all over, but very clearly in software engineering and language games in general.  This is the problem of scope creep and dealing with legacy code.  We are, after-all, creating and reverse-engineering one vast sprawling language game at the same time, and triangulating down to source in the vast complexity (infinite difference in continuity and unity).  But it is a self-similar echo of/as the real, and we are catching glimpses of this cognitive fine structure in cycles of cycles, and recurring patterns, deeper harmonics in slippage and remapping…  And this is what excites me because the ontology and epistemology, the metaphysics and the mathematics, at the deeper “image-space” level (percept-level, embodiment at the sensori-mnemonic interface, where we find intuition, emotion, and qualia), are really coming to convergence.  Science, Philosophy, and Mathematics are coming to reflect one common structure, as we involute through the embryogenetic layers into the pre- and proto-conceptual which they all share.

When we root here, we will find (and this is the difficult part of the transmission, because it is the near the peak of this trek)… we will find that this is not occurring with the orthodox ontologies we find in modern physics.  The Strings, GUTs and TOE-nails of the pre-complexity (mythic, classical, and transitive) mathematical physics.  They have radically failed, exploding in the loss foundations in the transition between transitivity and immanence, the post modern vertigo before rooting in rootlessness…recursion and a new harmonics.  Rather as Prigogine intuited, the key component is the integration of radical complexity into a new simplexity.   The classical (Being centered), legal (Laws of Physics), solid-/particle-biased, simplistic and transitive, ad-hoc, and agglomerative “multi-dimensional” black-box trans-linearity of the post-Cartesian mathematical physics, including in essence and orthodoxy Quantum Mechanics, radically failed in an explosion into, quite literally, the giant flying spaghetti monster which is seen so clearly in the failures of String Theory and MWT to reconnect to causation (immanent, this time)…and this is due to the transitivity and linearity at its heart.  Again, this transitivity is really the essence of what I see in Prigogine’s key distinction between the classical and integrative post-classical dynamics.  In the interrim, to deal with the complexity, stochastics and probabilities must suffice, until the new immanent causal metaphors can be seen (as they are in nascent Sorce Theory).

Rather, what’s more telling of the direction here is the return to the infra-dimensional, beyond also the rational solid form of Fuller’s geometry, and into the recursion and integration at this deeper level of dimension itself (this polar level of the vision-logic axes), into yet another iopol inversion (move to immanence) with the integration of the ratio in fractional geometry .  It is no coincidence that the fraction in fractional dimensionality is the mathematical ratio.  Again, the return to immanence precedes yet another explosion into transcendence….this one just beginning to bloom, having barely found its way into physics, but with glimpses as well in the convergence between Sorce Theory and electro-fractal cosmologies.  All these disciplines and arts share and evoke the same recursive, holonic, and embryogenetic structures.

So, back to the mathematical ratio, and the attempt here (~p76) to elucidate the transcendent bias.  This “trans-bias” is seen in the ratio with the simple fact that transcendence and transitivity form the initial couple (invoked occasionally with “trans-trans-bias”).  Increasing numbers at the top are paired with increasing numbers for the whole, while increasing numbers for the bottom (immanence) are inverted with respect to the whole.  There is a hidden “negative” (or pole, namely immanence, with no limit at zero) in the implicit unity in the denominator … which has suddenly appeared with the ratio.  Where did it come from?  It was always there in the original agglomerative (transitive) enfoldment of the finite unity or ‘1’ in every number.  Simply assuming unity in immanence (or in other words at the origin-identity of the implicit immanent-transcendent axis now coming into view), Fuller’s “unity is plural and at minimum two” (our principle of finite unity), is what allowed the unit-identities of number to congeal from “conceptual substance” in the first place (much like a bi-lipid cell membrane, or a root-unit in Sorce Theory, because they are formed of and around this general polarity, the abstract essence of nucleation, the pulsing and cycling, involuting and evoluting membrane of closure).

The rectilinear Cartesian grid is the view from this initial transitive axis (Fuller’s “attic window”), while the immanent pole (and immanent-transcendent (I/T) axis)  has not yet been explicitly operationalized, as we see later, on the periphery with Fuller’s Synergetics.  This initial move into transcendence and then transitivity is the number-line:  The move from implicit to explicit (nothing to something) and on into agglomeration, from zero to infinity.  This is the initial positive infinity, above the solidus, wobbling through the trans-trans instability and into the vestigial imaginaries … and on … until… right now, at the extending cusp of the return of our language game to radical or “pure” immanence…and the return to(wards) actual complexity….from the crumbling upper crust of representation…as we move into the power of recursive harmonics and its ontic-epistemic entrainment … but at the critical point of involution into the virtual in the “singularity”.  Perhaps indeed this holonic fractal entrainment, this coming laser-like focus between our self-same layers in this infinite difference will be our Ariadne’s thread out of the problems of the information explosion and prediction in the looming eclipse at the auto-evolutionary horizon.