The Observer in the Observed:

Fractal Dynamics of Re-entry

Terry Marks-Tarlow
Santa Monica, California
                 

“Do what you will, this life’s a fiction/And is made up of contradiction.” – William Blake

 

Most of us take for granted the ability to distinguish between ourselves as observers and what we observe in the world. Outwardly our skin seems visible proof of a clear boundary that encases and protects our organs. Inwardly our sense of self, when intact, also feels like a relatively clear boundary, at times even to the point of isolation from others. Yet whether we consider our bodies or minds, the subjective experience of closed boundaries rests precisely on the opposite state of affairs – wide-open portals that continually allow transaction between inside and outside, body and world, self and not-self.

 Open portals are evident in our “posthuman” existence (see Hayles, 1999), where the interface between human being and machine presents boundaries which have grown ever more complex over time, with each technological advance. We plug our consciousness into virtual realities, as we augment, even invade our bodies with the presence of machines. This intense exchange between flesh and mechanism demands nothing short of a redefinition of human subjectivity.

 Mystical poets, like William Blake in the above epigraph, allude to life as fiction inherently made up of contradiction. Hinduism offers the concept of Maya to describe the false perceptual veil by which we shield ourselves from an ultimately mysterious reality. At higher levels of cognitive organization, psychologists study related phenomena. For instance, Shelly Taylor (1989) identifies self-deception in the form of “positive illusions”, those overly optimistic attitudes and expectations towards the future that may be entirely unrealistic, but nevertheless her research shows they can help us to beat the medical odds.

 Despite the complexities of our alleged posthuman existence, most of us live as if consistency, certainty, predictability and clear boundaries, especially between truth and falsity, reside at the base of things, from the workings of our bodies and minds, to those of the universe at large. Boundaries are everywhere, yet most are permeable. By focusing on this highly contradictory state of affairs that extends invisibly under the surface, I follow Blake’s lead to explore the paradoxical dynamics embedded in the very fabric of existence.

 This paper traces a line of logic, begun by George Spencer-Brown and continued by Francisco Varela, which puts paradox at the heart and seam of things. I place Varela’s ideas about re-entry within the context of a branch of contemporary mathematics called fractal geometry. I argue that a deep understanding of fractals helps to illuminate the profound yet invisible paradoxes that permeate ordinary life.

 To set the stage historically, I will explain the cybernetics revolution and how reflexivity first entered the social sciences. Into this historical context, I then place the primitive logic of George Spencer-Brown, plus the extensions added by Francisco Varela. Together, their dynamics of re-entry articulate paradoxical foundations not only for logic and but also for the creation of all structure. Next I connect these logical assertions with mathematics of the complex plane, where imaginary numbers are used to model extra or hidden dimensionality. Imaginary numbers provide the bridge to fractal geometry, whose mathematics involves recursive iteration of simple formulas on the complex plane.

Fractals are dynamic process-structures that etch time into space. They are boundary keepers that negotiate spatial and temporal interfaces between different forces and dimensions of being. My thesis is that fractals provide the paradoxical foundation by which different levels of nature both connect and separate. Every boundary becomes a door, every border a portal. Because the same dynamics hold inside as well as outside the psyche, fractal geometry provides a bridge and language for linking inside and outside worlds. Whether they occur in nature, our bodies or minds, fractal separatrices or boundaries reveal infinite, hidden frontiers in the space between ordinary, Euclidean dimensions.

 I conclude this paper by examining the mechanics of fractal production to reveal a new twist in the reflexive march of science. In a world filled with fractals, not only is the observer detectable in the observed, but the observer is also embodied there, in a primordial, concrete way. Natural fractals, like shorelines and mountain scapes, reveal how the embodiment of the observer in the observed paradoxically precedes the presence of conscious observers.  

THE CYBERNETIC REVOLUTION

The period following World War II was a time of tremendous intellectual growth in America. Emerging from technology developed during the war, a number of trends converged to legitimate the scientific merit of psychology, including the birth of cybernetics, the science of information. This new field, spearheaded by the mathematician Norbert Wiener, mushroomed out of the interdisciplinary Macy Conferences held yearly between 1946 and 1953 (See Heims, 1991). Cybernetics brought a new metaphor of the mind as mechanism. Roots of this idea extend at least as far back as Renaissance times, when the natural sciences, one by one, split off from philosophy. As more empirical studies began, the heart resembled a pump, the body a machine, and the whole universe little more than clock works.  

The cybernetic association between mind and machine made in the mid 20th century proved a boost to the neurosciences, when neural loops in the brain were modeled as logical chains. This association also ushered in the cognitivist revolution, as activity in the psyche was likened to information processing in computers. Initially, the new metaphor of brain as computer was logically derived from the behaviorists, who compared human behavior to machine output based on environmental input. These stimulus-response relationships were both quantifiable and predictable, thereby turning the discipline of psychology into a fully-fledged behavioral science.

The more humanistically inclined raged against the cold, mechanical, and at times reductionistic views being espoused by behaviorists, psychoanalysts, and eventually cyberneticists. Meanwhile, within the Macy Conferences, protests of a different kind began to surface. Lawrence Kubie, a psychoanalyst and recent retread from the “harder” field of neuroscience, stimulated heated discussion among his colleagues by pointing to the problem of reflexivity (See Heims, 1991).

Reflexivity, by which an assertion points self-referentially to itself, e.g., “What I say now is false,” involves a confluence or melding between observer and observer. Reflexivity is inherent in the very subject matter of psychology. It occurs, for example, whenever researchers use consciousness to understand the nature of consciousness, narratives to study the narratives of others, or behavioral repertoires to examine behavioral responses in others. Research in psychology is like the mythical Uroborus, a snake eating its own tail. Despite every attempt to remain objective by sidestepping subjectivity, even behaviorists find little relief from the Uroboric beast of reflexivity.

During the Macy conferences, Kubie objected to the early cybernetic agenda of separating information fully from its material, embodied sources. The psychoanalyst protested that within any theory, even inside the “hardest” of sciences, reflexivity lurks and the observer lay hidden in the observed. Kubie claimed that all theories about the outside world say as much about the unconscious of the subject who espouses them as they do about the outside universe as consciously perceived. When it comes to theory making, no matter what is observed, the observer winds up implicated in the observed. Although Kubie’s protests were dismissed by most of his fellow scientists, his ideas about reflexivity later became ingrained within the history of psychoanalysis. Robert Stolorow and his colleagues (Atwood & Stolorow, 1979/1993), cofounders of intersubjectivity theory, argue that every theory of personality is self-reflexive in that it universalizes the therapist's personal solution to the crises of his or her own life history.

During the early years of the Macy conferences, the notion of science still rested upon the hitherto bedrock foundation of objectivity. By requiring a clear separation of subjects from objects, objectivity was a position that ran contrary to reflexivity. Because early members of the Macy conferences were interested in maintaining science as an explicitly objective enterprise, they chose to ignore Kubie rather than to revise their own ideas. Instead of including reflexivity within the rubric of science, they dismissed psychoanalysis as science.

Generally, during this first wave of cybernetics theory, the problem of reflexivity was successfully avoided by isolating pattern as a separate realm from which all others emanate. When the pattern of information reigns supreme, its material substrate can be first ignored and then eliminated from consideration altogether. According to this view, even without matter the pattern still matters. By removing information entirely from its material sources, the need for observers was also eliminated. We are left with only pattern as a virtual reality with neither observed nor observer. 

This strategy worked temporarily, but only until the whole enterprise of science began taking a reflexive dive. At the cosmic level of grand-scale events, Einstein’s earlier discoveries in physics destroyed the previously immutable framework of space and time. The notion of objective observation stretched and deformed, as relativity theory and the subjective stance of observers took center stage. Meanwhile, at the subatomic level of tiny, quantum events, another field spawned by Einstein’s work, consciousness began pushing its way self-reflexively into the middle. The still controversial Copenhagen interpretation asserts that at the quantum level, the very act of observation is necessary to materialize that which is observed.

Even mathematics was not immune from a reflexive fall. In the 1930s, an Austrian mathematician named Kurt Gödel used recursive methods in order to code numbers and then talk about them reflexively at a higher, meta-level of abstraction. In the process, Gödel proved that no single theory could ever provide a consistent, complete foundation to logic, annihilating any residual hopes for perfect objectivity within the mathematical underpinnings of science.

As reflexivity was seeping into the physical and mathematical sciences, a second wave of cybernetics arose between 1960 and 1985. Spearheaded by Francisco Varela, among others, information scientists became better prepared to embrace reflexivity (see Hayles, 1999). In fact, the very name of this new trend, “second-order cybernetics,” amounted to the recursive study of observers studying the higher order processes of observation: the observers observed themselves observing themselves.

 

POSTMODERNISM

Second-order cybernetics arose within a broad, societal sea change known as postmodernism. Over the years the use of this term has been stretched so far as to encompass practically everything, while being deconstructed so thoroughly as to mean almost nothing. For this reason, I beg to dismiss its broader definition in order to focus upon a single facet, its inherent reflexivity. In order to symbolize the postmodern imagination, Richard Kearney (1988) offers the recursive symbol of two mirrors reflecting one another. He contrasts this with the premodern imagination, symbolized by a mirror, in which human creativity reflects God’s creation, as well as the modern imagination, symbolized by a lamp, in which human creativity is illuminated from within.

Because of its reflexivity, the posthuman imagination becomes lost inside an infinite regress of imitations, copies and simulacra. With origins deconstructed into dust, the postmodern being is often portrayed as rootless, wandering inside a mechanical, artificial desert of re-production. Within this bleak frontier, on the one hand, the demise of human creativity and originality is decried. On the other hand looms the cybernetic threat of machines usurping the very autonomy, indeed existence, of their humanist creators.

In How We Became Posthuman, English professor Katherine Hayles (1999) details the threatened demise of embodied existence. She analyzes cyberpunk novels with heroes that evaporate into virtual reality, as their consciousness becomes thoroughly enmeshed and encapsulated within machines. The flip side of this futuristic nightmare portrays machines sophisticated enough to take over the evolution of life itself. As artificial intelligence becomes increasingly equipped with emotion, creativity, the capacity to learn, self-repair and self-generate, this sci-fi genre depicts humanoid machines that threaten to extinguish carbon-based evolution as we know it, replacing it with the far-superior, silicon-based life forms. 

As posthuman boundaries have become more blurred and human beings self-reflexively entangled with facets of their own technological production, lines between observers and observed continue to grow more complex. As reflexivity is integrated more and more consciously into cybernetics, one positive outcome is that the door is thrown open for the scientific study of subjectivity. Since subjects can now study their own subjectivity, consciousness itself has recently regained status as a legitimate and serious object of scientific study.

In the postmodern view, reflexivity is often viewed as a by-product of modern technology constructed in the context of particular social and economic trends. Contemporary methods such as neural feedback even allow us to become active observers of our own brain processes. Inarguably, computer-driven, cybernetic extensions of our perceptual and conceptual apparatuses do help us to detect, direct and even create reflexivity with greater ease. Yet I believe that the roots of reflexivity are much deeper and more organic than social and historical trends suggested by postmodernism. I maintain that the discipline of fractal geometry provides evidence that reflexivity is intrinsic not only to human-made productions, but also to nature at large. 

Fractals help us to advance beyond the cybernetic metaphor of psyche as mechanism to the more organic one of nature, including human nature, as fractal. Here mechanistic means of computer simulation reflexively guide us beyond mechanism, as we circle back to a different kind of origins, for both human and machine, in fractal bases of nature. Before turning to fractal geometry itself, the section to come presents Spencer-Brown and Varela’s logical underpinnings for reentry dynamics as they are embedded in the very fabric of creation.

 CONTRADICTION BUILT INTO THE FABRIC

A great truth is a truth whose opposite is also a great truth.

– Neils Bohr

 

When developing his “Laws of Form,” mathematician and logician George Spencer-Brown (1969; 1979) tried to specify how we create “some-thing from no-thing” in consciousness (See Robertson, 1999). Spencer-Brown used a 2-valued system that consisted only of “marked” and “unmarked” states plus two axioms. From these simple bases, he derived a calculus of first distinctions. Although it is commonly believed that George Boole (1958) developed the most basic form of logic, Spencer-Brown disagreed, claiming his own calculus is so primordial as to provide a cradle not only for logic itself, but also for the basic structure of any universe.

Within Spencer-Brown's system, in order to distinguish marked from unmarked states, value must be attributed to one state over the other. This act of marking or making a distinction requires an observer. We can readily understand this requirement for logic: in order to make a mark, apply a set of axioms, or distinguish truth from falsity, a conscious observer must be present. But how does this process of valuation apply for more primitive levels of a system that supposedly precedes logic and even people? Is an observer implicated along with the observed there too?  I will return to this issue in my subsequent discussion of fractal geometry.

As Spencer-Brown progressed with his work, he used basic axioms to derive higher degree equations. But then something strange began to happen: anomalies appeared; re-entry of equations back into themselves sometimes resulted in paradox. This occurred when marked states became equated with unmarked ones. Spencer-Brown offered an interesting interpretation. Rather than to view this as the simultaneous presence of contradictory states, he suggested an alternative. Maybe the system was oscillating between opposite states in time. If so, then self-reflexive acts of re-entry, or self-indication, would add the dimension of time to that of space already implied by first distinctions. Given enough time, both marked and unmarked can exist in the same space.

Neuroscientist and researcher Francisco Varela was intrigued by Spencer-Brown’s ideas, especially by his explanation for the dynamics of re-entry. Varela (1975; 1979) developed “A Calculus of Self-Reference” to extend Spencer-Brown’s work. In so doing, he took a bold, if not radical leap. Rather than to conceptualize re-entry as characterizing higher degree equations only, Varela proposed that re-entry be added at the ground floor, as its own term, along with the other two marked and unmarked states.

This simple difference made all the difference, as Gregory Bateson might have said. It signaled Varela’s departure from Aristotelian logic, which had held an iron grip around philosophers and logicians for millennia. Varela abandoned Aristotle’s dichotomous system, where all propositions are either only true or false; its law of identity, where A can never equal not-A; as well as its law of the excluded middle, where the space between truth and falsity is pristinely empty.

By adding reentry as a third term, Varela opened up an infinitely deep, Pandora’s box of middle ground filled with fuzzy grays, lost identity, and unfathomable complexity. Here not only can something be true and false simultaneously, but even more, Varela actually believed that the existence of autonomy in nature depends upon this contradictory state of affairs. Varela and his mentor, Humberto Maturana, coined the term “autopoeisis” to explain how biological systems self-organize (Varela, Maturana and Utribe, 1974). With re-entry dynamics at the core, autopoeitic systems embody paradox at their boundaries, expressing their autonomous functioning through remaining functionally closed, yet structurally open.

By asserting reentry as a third value in its own right, Varela agreed with Spencer-Brown that self-referential dynamics establish the presence of time. But he went even further, to assert that paradox becomes embodied at the most basic level, in the very form itself. Whether in organic or inorganic forms, autonomous systems appear supported by inherently contradictory underpinnings.

[The rest of the essay is continued here.]

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Yes, what you say makes sense, Joel. I've just read too many science fiction books based on aliens have the same mathematics as us, which seems silly.

Joel Morrison said:

I actually think that Dennett is correct here, to a degree.  Not that all alien species will come to the same exact mathematical structure, but that it's very likely that it represents an attractor in the morphological space of mathematical representation... 

In the Preface to WMCF Nunez discusses the “romance of mathematics,” one such notion being that to learn it is “to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe” (xv.) He lists other aspects of the romance but he asserts that all of them appear to be false. My guess is that he might argue that given math is based on empirical observation of nature, and that our sensori-motor facilities and basic metaphors are quite close to nature, that is indeed why it “works” so well. But given an alien sensori-motor system from a planet where they breath not oxygen but something else, where the environment has different challenges, etc. my guess is that their math would be just as accurate but look entirely different. That is, math is enacted and not discovered as a fully formed a prori (i.e. Platonic form) inherent to the structure of the universe. But being a “realist” of sorts Nunez still accepts that there is a “there” there.* (I like the reiteration of the word “there” in that sentence, having three different meanings in the space of five words.)

 

And of course implicit to the above is that both the human an alien are residents of the same uni-verse. This does not take into account possible other and co-existing universes where their physics might be of an entirely different order, thus their “there” is still there but not in the same sense as ours. Such multi-verses are not merely the work of science fiction either, for as I referenced elsewhere it is a viable option among some quantum theorists.

 

* Which gives me an idea for a postmetaphysical bumper sticker: There is a there there, but...

And now I'm hearing it sung to the tune of Ole McDonald Had a Farm: "Here a there, there a there, everywhere a there there..."

Though I agree with Nunez and Lakoff on the post-romance of mathematics, I do feel that the closure-centric attractor (the attractor our own mathematics is orbiting) will be a big one, universally, and in this sense there is a truth to the romance (though not an absolue one).  Mathematics is the language of nature simply because it is generalized relation, but this generalization makes it a language for much more (and less) than merely the physical universe.  It makes it a language for art as well (simulation of mental worlds), and the difficulty is in the post-romantic separation (and integration) of the two.  This is where modern physics is currently stuck, having a pre-rational understanding of its own trans-rational mathematics (much of which still hasn't made it into quantum physics).  This is also why it's so easy to generate and take for science such artistic theories as Multiple Worlds (Universe) Theory (MWT). As an artist I'm not saying that art has no merit, certainly, nor that there is nor should be no overlap between art and science.  The overlap is fundamental and healthy, but it's simply not an identity.  Art has freedoms that science does not, being entrained to the empirical and pre-representational world as science must be.  That empirical entrainment gives science its value, and so it's critical to understand the key differences between art proper and the art of science, where they overlap, and how they must differ.

 

We could discuss the merits of MWT at length, but I will say this. In my view physics and cosmology lag both philosophy and mathematics by a long way, in terms of deeper tacit metaphysics.  Complexity science (and biology) is rapidly caching up, but this is because it is born from trans-rational mathematics, and it has yet to make its way into physics. In my view physics is still foundational and hence pre-rational in its deepest metaphysical substrate (the pe-rational (also in my view) is where we find the confusions of post-modernity, with the absolutization of relativity---absolutization and categorical thinking being the hallmark of the mythic modes).  

 

So in the post-modern loss of foundations (e.g. causation), in the transition to the nondual-rational (integrated or whole rational) emptiness/fullness (complexity) view there was a corresponding implicit semantic drift in the meaning of "Universe" from ONE-ALL to one of many, and from the absolute scope to the relative, but this was made possible only with a loss of the understanding of what a "Universe" is.  Instead of simply being the ONE-ALL integration of all possible physical manifestations (including all possible emergent laws, etc) a Universe is now just defined loosely as a set of laws (membership or set-theoretical criterion), with no understanding of how such 'Universes' (sets of laws) interrelate and differentiate (holarchy).  The original meaning behind the old word 'Universe' was simply replaced with either Multiverse or Omniverse.  But the original meaning, still somewhat intact under the switch in name has still not integrated the truths of the rational regarding the nature and nondual logic of "Substance" (Spinoza-Deleuze), not to mention the key differentiation and integration of the ontic and epistemic.  And having lost the causal thread in this transition, Quantum physics is desperate to rationalize the classical (in the sense of pre-complexity) mathematics it used to replace it. Having invented the "single particle approximation" (linear/singular point at the heart of the nonlinear trajectory, as opposed to massively parallel/continuous/immanent infinity) and extrapolated it into a "singlet wave function", both of which are pre-complexity forms of mathematics (you can tell because they contain no arrow of time, and no real complexity (see Prigogine's "active matter"), they were surprised when these classical mathematical approximations failed to explain the post-classical empirical complexity.  So in the "collapse" of these wave functions, which are now taken for the causation itself, instead of being recognized for an approximation and generalization, there is a dilemma and the need to explain the mathematical inadequacy of the model.  And thus the invention of MWT, which is essentially a con-fusion (conflation of a pre-fusion) of the distinction between ontic and epistemic aspects of real holarchy, or in other words an absolutization of the relativity of perspectivism (categorical and mythic).

 

Sorry, I know this is a bit confusing on its face, and there are more optimal ways of explaining it.  But I hope it makes some sense.

"In my view physics and cosmology lag both philosophy and mathematics by a long way"

 

But the very reason that mathematics is leading the way in terms of development is due to this "platonic" (in the post-romantic sense) aspect of generalized relation.  Following the laws of general relation (e.g. closure transcending through 'violation' (immanence) onto the core vision-logic axes), it is forced into unfolding into the general embryogenetic structure of the evolutionary cosmos, regardless of whether it understands what this structure is.  And hence it is always on the bleeding edge in front of the empirical sciences.

 

This is why it is called the "queen of the sciences".  Mathematics follows the female/yin-intuition of the evolutionary embodiment with relation itself, as it unfolds into the implicit axes (freedoms, dimensions) of the percept-concept, the vision-logic axes at the heart of mathematics.  (These are your circle and line archetypes, Tom, at the heart of the integrated fractal, and they are also seen all over, such as with Peter Collins' Integral Holistic Mathematics). 

 

*[MODERATOR'S NOTE:  I have added a link to Peter Collins' site above.  Looks really interesting!]

I just thought about this in relation to Khun's incomenserability thesis.  Given that we all seem to agree that an alien mathematics would not be under any obligation to look like ours, would any difference be completely untranslatable?  Or would it be fairly easy to understand, like translating binary into hexidecimal?

 

I don't have any good reason for this, but for what it's worth, I lean towards realism on this issue; I suspect that Dennet has it right.

I agree with you.  I think there are deep tacit attractors (beneath the selection of base) here that would allow a ground for translation.  This is just because of what mathematics is, as the self-similar generalization of the deepest forms of embodied contact with and as relation.  If we can connect in any way with an alien species we de facto live in the same universe, and the same relational attractors will unfold.

infimitas said:

I just thought about this in relation to Khun's incomenserability thesis.  Given that we all seem to agree that an alien mathematics would not be under any obligation to look like ours, would any difference be completely untranslatable?  Or would it be fairly easy to understand, like translating binary into hexidecimal?

 

I don't have any good reason for this, but for what it's worth, I lean towards realism on this issue; I suspect that Dennet has it right.

 

Joel, Le t me consider mathematics as the language of  generalized realtion to  structural openness beyond the finite/infinite divide. Does the integrated /vision logic axes and self similarity of fractals relate to open ended structures ?

The architecture of fractals as boundary keepers at the functional level is clear enough. Between mountains and rivers and coastlines. And chaotic forces like water, heat and the weather and space. At this interface they are functionally closed and structurally open . but unless structurally open means a movement beyond the finite/infinite and conscious/unconscious divide there maybe a self inflicted reductivity in the dynamics of recursions.

self similarity of fractals is a neat perspective of dimensional entry and how non linearity informs a domain.  Structurally open suggests flowing both ways into content and emptiness . speaking of going places.  rewires the location for apriori

Since open endedness naturally relates to all levels – organic, cosmic, embryogenetic, ecological  (I guess its like what you say in math as aside from a focus on closure) -  If higher math or cybernetics represent what is not cognitively available (at least to some extent if not more) to the organism , they should also address the gap between functional closure and functional revolution .

probably from experience to event , structure has dynamics. open also implies post structure, and beyond the identity of the self similar fractal . the idea of re-entry allows this view as well, authenticates the direction .  mapping this fuzzy  area may be a moot point, but if theres a path as a prelude to a jump – I could be led out there as infinity disappears to be discovered on reentry….

Many of the same issues here--including recursive dynamics, hierarchical inclusion, boundaries, parts and wholes etc.--have been discussed in other threads, particularly this one on theories of everything and theories for anything. If one has the time and/or interest it might make for relevant background for this thread?
valli said:

Does the integrated /vision logic axes and self similarity of fractals relate to open ended structures ?

The term axis could be substituted for the words 'freedom', 'dimension', or 'infinity', and all of these are inherently open and polar, in nature.  I chose axis because I wanted it to not be confused with our everyday conception of dimensionality because in my view these core 'dimensions' or axes are the very core of both ontic and epistemic dimensionality.  And so they are at the vision-logic level of understanding, rising up out of dimensionality and the common perspectives thereon by digging beneath it (transcendence through immanence, as per usual).

 

At this interface they are functionally closed and structurally open .

 

Yes, this is what is meant by an "aspect infinity", aspect being the finite component as revealing, like a lens or quality, the infinite or open directionality (in a sense) of the motion.

 

but unless structurally open means a movement beyond the finite/infinite and conscious/unconscious divide there maybe a self inflicted reductivity in the dynamics of recursions.

Well, (assuming I understand you here, which I very well may not) I think the argument could be inverted in that it would be impossible for anything to exist if ever there were no relation between the finite and infinite, ontologically speaking.  But epistemically, I'd say that it all begins in nothingness, which as a self-similar echo is the very root of foundationalism, recapitulating that originary emergence from nothingness (tacit sensory-mnemonic primitives) into form (percept and concept).  But, again, ontologically speaking, as we see in the conundrum of the substance and bundle views of substance in Philosophy, it's an absurdity to take this nothingness as an absolute formless substance, and that's actually a dualistic and pre-rational construct.

 

Structurally open suggests flowing both ways into content and emptiness . speaking of going places

 

OK, so I would say that this structural openness is inherent in the embryogenesis of the concept, in several ways.  Firstly, it originates in "emptiness", but again not as an absolute formless substance, but as a tacit foundationless ground of existence, infinitely formed but just unconsciousness (enfolded consciousness) relatively to the emergent forms in the embryogenesis.  So in this sense of unfolding, emptiness into form.  Also, with every new layer there seems to be a return to the ground of immanence which facilitates the reconstruction of the old structures into the new layers.  THis is common experience with meditation, art, and the like.  There is always a flux between immanence and transcendence, emptiness and form in any openly and healthily evolving, integrating and transcending system.

 

In mathematics this is how closure is constantly "violated" to bring about the transcendence into new order (numbers and operations), and without both closure and its violation none of the embryogenesis could occur.  And this is the very basis of conceptual thought, in generalized form, I argue, revealed simply through the generalization of the simplest conceptual objects and events, the numbers and operations.  It is not the whole of it, but a key window into its heart.

The term axis could be substituted for the words 'freedom', 'dimension', or 'infinity', and all of these are inherently open and polar, in nature.


Joel, that’s a common theme to my arguments across issues the difference between open and polar  – Valera’s autopoesis Terry refers to, that contradiction (polar/paradox) is the underpinning that gives rise to form – and my view of open structures as potential to move past contradiction, what I think of as  transrational. (if polar doesn’t mean a conflict between opposites but could be a coexistence – it in turn implies a shift to an integral mode)

 

in that it would be impossible for anything to exist if ever there were no relation between the finite and infinite, ontologically speaking.


Yes, that’s likely . in fact it's that they are too self similar. Quality markers or uniqueness could be event related and not existence specific (as itself for example) - contradiction being a constituent, and what arises is the movement beyond since there is essentially a simultaneity (not limited to any unit but across them) – the aperspectivism I refer to.

 

OK, so I would say that this structural openness is inherent in the embryogenesis of the concept, in several ways


I ought to have said the other domain instead of emptiness, never liked emptiness. I’ll come back to this, let me resort to metaphors for a bit :) lets  me revel in shades that waver in undercover options, to reframe things . but then frames are signifiers that can turn from flashy to conciliatory – in that sense they exhibit a sensibility that is inventive for a frame.

In the opening post of every page of this thread are excerpts of Terry's referenced paper. Therein she says: “Paradoxical dynamics [are] embedded in the very fabric of existence,” and that Varela asserts the “dynamics of re-entry articulate paradoxical foundations not only for logic and but also for the creation of all structure.” I am not an expert on Varela so not able to refute this, but this is from the Stanford encyclopedia entry on embodied cognition:

 

“Varela, Thompson and Rosch argued that the standard division between pre-given, external features of the world and internal symbolic representations should be dropped, as it is unable to accommodate the feedback from embodied actions to cognition via the actions of a situated cognitive agent.”

 

Joel says something similar to Terry when he said in this thread (p. 6): “Representation...is a self-similar echo of reality itself.”

 

I know that Lakoff, Johnson and Nunez do not see this connection, that “representation,” which is indeed grounded in basic image schemas and metaphors, is not akin to the structure of reality itself. Rather they assert that the representation paradigm is a non-embodied “false” reasoning. And it would seem that Varela might agree, but as I said I'm not sure. We did a thread on Varela and from what I've seen therein there was no indication that he made this leap, even through the eyes of Bitbol. So perhaps both Terry and Joel can help me understand this leap they both appear to make? And how Lakoff et al. are mistaken?

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