Those with even a passing familiarity of him know he is famous for the creation of the geodesic dome. The dome was actually created by someone else but Fuller expanded upon and popularized it. The dome is based on the principle of tensegrity: "A structural principle based on a system of isolated components under compression inside a network of continuous tension, and arranged in such a way that the compressed members (usually bars or struts) do not touch each other while the prestressed tensioned members (usually cables or tendons) delineate the system spatially."
It's a highly technical definition. I incorporate a less technical definition of tensegrity into my exploration of the different domains of hier(an)archical synplexity, an offshoot of hierarchical complexity. This brief paper is more of an annotated table of contents for the longer video discussion here. Below I copied and pasted from the former:
Abstract
Metatheory is that which juxtaposes, organizes, and integrates theories. Hier(an)archical synplexity accomplishes this via its principles of same/difference and the tensegrity that separates yet connects in the overlapping boundary spaces within and between a plurality of complementary yet autonomous theories.
Introduction
The following was written as a general outline and summary of ideas in preparation for the Integral Stage video series on Meta-models in the episode focusing on the above topic (Alderman et al. 2020). Please see the video for a deeper dive into the material.
Hieranarchy
John Caputo (2006) coined the term ‘hieranarchy’ and described it as the negotiation between the finite conditional and infinite unconditional. It is not a simple anarchy opposed to hierarchy but rather the relationship and tension between them. They are not strict, clearly defined opposites but rather ideas that are mutually entailing. It’s a difference that makes a différance, i.e. the same difference in the space between them.
Bryant (2014) discussed ‘an-arch,’ which only eliminates an ultimate, transcendent authority on its own deciding the law. It’s similar to Caputo in that the law is decided by the exception within the rules. In a sense that is how US law in theory operates, in that the particulars of each individual case determine how the rules are applied. Again, that tension between the two notions of transcendent and immanent, which is neither in total distinction but both in dynamic relationship. It is only when the transcendent is seen as the hierarchical source of the immanent where a priori metaphysics goes awry.
This is explicated further in Derrida’s examination of Plato’s description of khora. Khora is not a transcendent principle but rather an excess space between heaven and earth where both are negotiated. Once again the term ‘an-arche’ appears as différance, that principle by which complements interact. It is thus a way to keep meaning open so that it doesn't become fixed and rigid. All possibilities reside therein so that different contexts as yet unseen will provide new meaning. It requires that we are ceaselessly pushing our boundaries and testing our limits, boldly going where no one—except perhaps Jean Luc and crew—have gone before (Caputo, 1996).
Mark Edwards’ metatheory
Edwards (2010) takes up the above thesis when he notes that metatheory is not about creating one transcendent super theory that subsumes all other theories, but rather seeing how those theories relate, how they both support and challenge each other. He uses the notion of interpretative lenses to show which lens(es) each theory uses to support its edifice, and how other lenses are missing so thereby incomplete. The categories of his lenses include holarchical, bipolar, cyclical, standpoint and relational, with examples in each category.
Edwards et al. (2015) further explores how these lenses are organized in metatheory via the metaphor of bridges. Bridges exemplify the connecting and overlapping spaces that are negotiated in the tension between them. In this way it avoids the transcendent metaphysics noted above because there is no dominant lens or view that subsumes the others. Instead it’s a metaphysics of tensegrity, or syntegrity as they call it, whereby “the integrity of the structure is determined by the distributed tensile stress of the entire system.”
Edwards noted that his lenses appear so consistently in theories that they likely originate is some embodied mechanisms. Indeed they do, so to that we now turn.
Image schemas and basic categories
Lakoff and Johnson (1999) describe the nature of image schema as spatial and perceptive categories that ground our more abstract concepts. These are qualities that we pre-consciously ascribe to objects as intermediaries between the objective world and our subjective experience of it. Sample schemas include “container, source-path-goal, part-whole, center-periphery, link, cycle, iteration, contact, adjacency, forced motion (e.g., pushing, pulling, propelling), support, balance, straight-curved, and near-far.” One can see the embodied grounding to Edwards’ lenses.
Basic categories are how we directly and optimally interact with the objective world. It is the level at which a single image can represent the entire category. The category ‘chair’ is an example. It is the easiest image to do so instead of a more particular kind of chair or the more abstract category furniture. When viewed in any given categorical hierarchy, they are in the middle. Unlike hierarchies which have a fundamental smallest thing and/or a fundamental largest thing, the actual fundamental thing is smack dab in the middle. So this turns the typical Aristotelian or Platonic hierarchy requiring a priori necessary and sufficient conditions not upside down but inside out based on empirical perceptual categories.
Once again, both image schemas and basic categories are in a syntegral relationship holding together and redefining complements, in that middle space supporting a metaphysics of the between.
Madhyamaka
The term itself means the “middle way” between essentialism and nihilism. Granted there are disputes between the different Tibetan schools as to the interpretation of what this constitutes, but the one that most supports my thesis is that of Tsongkahapa of the Gelug clan as interpreted by Thakchoe (2007).
Again we see that ultimate and relative truth are mutually entailing rather than diametrically opposed.They are of a single ontological status, that is, they are both empty of inherent existence, which means they are both dependently arisen and don’t exist in and for themselves. However, epistemologically they can be differentiated in that conventional cognition tends to see both as having an independent nature (samsara), whereas ultimate cognition sees them both as empty and dependently arisen (nirvana). Once one has experienced nondual equipoise through disciplined, meditative practice then one can realize both conventional and ultimate knowledge in the dynamic tension of their mutual relation.
Batchelor (1998) is also of the Gelug persuasion. He reiterates that the two truths are ontologically dependently originated and mutually entailing, nonetheless through the illusion of samsara one does not apprehend this truth. That can only be discerned through the equipoise and non-dual meditative discipline, which transforms convention thought into nirvana.
Garfield (2003) agrees. Conventional truth applies to the empirical world, which can cloud the perception of the ultimate truth as empty, co-dependent arising. Ultimate truth does not deny the existence of conventional existence and its properties, only that it can misinterpret those properties an having independent existence. So ultimate reality is in effect just as empty of independent existence as conventional reality. Paradoxically, the ultimate truth is that there is no ultimate truth, if by the latter we mean a strictly transcendent truth completely distinct and separate from the conventional. Per above, we again see their mutual entailment via the tension between them.
Tai Chi Chuan and Dance
According to the Tai Chi Classics (Barlow, 2020) one can "use four ounces to deflect a thousand pounds." To do this one must "distinguish clearly between substantial and insubstantial." Both are accomplished via compression and leverage, both within one's body and by applying them to another body. Compression and leverage are accomplished by maintaining 4 ounces of resistance or pressure between complements at all times and through all changes. Without this resistance our biomagnetic and biomechanical energy does not flow with enough force to move much of anything, much less a thousand pounds.This is also critical in partner dance connection/communication.
For example, the fundamental premise of same-difference and connection-separation exemplifies the relation between any 'two.' This could relate not just a philosophical axiom but practically to one person or two people (or more). In practicing tai chi alone one is always playing with this ever-changing 'balance' between active and passive parts of their body-mind, or substantial and insubstantial. And there are several of these balances going on at the same space-time, like between the two hands, the two feet, the head and feet, the front and back, etc. These complimentary parts are connected yet "clearly distinguished."
Where the resistance or pressure comes in is in the dynamic tension between them. Note the preposition 'between.' It is what glues them together yet also keeps them apart like a generative (en)closure (Alderman, 2013). I.e, they are adjacent, not one and not two, at least not exactly (Pascal, 2013). This 4 ounces of resistance is strongly akin to any permeable boundary that is both open and closed, that not only separates one from another but also allows connection and communication with another. Hence the practice can also been done with another(s), which experience of working with another feeds back to working with oneself and vice versa. The ongoing training requires both. Hence this practice is also a non-dual, embodied syntegrity.
Model of hierarchical complexity
It is partly in response to the above model (MHC) that I came up with the phrase hier(an)archical synplexity. So let’s take a look at it.
Commons et al. discuss its Platonic and Aristotelian roots, which both arise from transcendent, idealistic and a priori axioms. Both operate on the dichotomous logic of the law of the excluded middle and set categorical necessary and sufficient conditions, i.e. something is either in the set or it isn’t. Also the orders of hierarchical complexity are fractals and scale-free, meaning the repetition of self-similar patterns at different scales. Yet Broido and Clauset, after examining a variety of a thousand networks, determined that models based on MHC principles do exist but are rare. And that other mathematical models are necessary to describe most other networks (Berge, 2019).
Lakoff and Nunez argue that there is no one correct or universal math. There are equally valid but mutually inconsistent maths depending on one's premised axioms. This is because math is also founded on embodied, basic categories and metaphors, from which particular axioms are unconsciously based (and biased), and can go in a multitude of valid inferential directions depending on which metaphor (or blend) is used in a particular contextual preference. They dispel this myth of a transcendent, Platonic math while validating a plurality of useful and accurate maths (Berge, 2019).
Hence the HMC is metaphorical blend with a consistent and coherent inferential structure and useful when applied to networks with which it is applicable. But its premises are not founded in a priori, transcendent Platonic or Aristotelian idealism but rather embodied image schema and metaphor. And it isn’t applicable for networks outside of its purview. It is one of a plurality of valid and useful models to be taken into account and organized into an overall metatheory by the principles of hier(an)archical synplexity as noted above.
Bibliography
Alderman, B., Pascal, L, Berge, E. (2020) “Hier(an)archical synplexity.” Integral Stage video series on Metamodels. https://youtu.be/-j9__VKUkKE
Alderman, B. (2013). “Magic circles, generative (en)closures and kosmic foam.” Integral Postmetaphysical Spirituality forum. http://integralpostmetaphysics.ning.com/forum/topics/magic-circles-generative-en-closures-and-kosmic-foam
Barlow, G. (2020). “The Tai Chi Classic.” Blog post. https://thetaichinotebook.com/2020/02/25/the-tai-chi-classic-part-1-a-new-interpretation/
Batchelor. S. (1998). “Letting daylight into magic.” Blog post first published in Tricycle: The Buddhist Review. https://www.stephenbatchelor.org/index.php/en/letting-daylight-into-magic
Berge, E. (2019). “The root of the power law religion.” Integral World. http://integralworld.net/berge11.html
Bryant, L. (2014). “Anomalous communism/anarchism.” Blog post. https://larvalsubjects.wordpress.com/2014/03/14/anomalous-communismanarchism/
Caputo, J. (1996). Deconstruction in a Nutshell. New York: Fordham University Press.
Caputo, J. (2006). The Weakness of God. Bloomington: Indiana University Press.
Edwards, M. (2010). Organizational Transformation for Sustainability: An Integral Metatheory. New York, London: Routledge.
Edwards, M. et al. (2015). “Inter-bridging: Bridges and bridging as metaphors for ‘syn-integrality’ in organization studies and practice.” Integral Review 11;3, September.
Garfield, J., Priest, G. (2003). “Nagarjuna and the limits of thought.” Philosophy East and West, 53:1, pp. 1 - 21.
Lakoff, G., Johnson, M. (1999) Philosophy in the Flesh. New York: Basic Books.
Pascal, L. (2013). “Principles of adjacency (draft).” Integral Postmetaphysical Spirituality Ning forum. http://integralpostmetaphysics.ning.com/forum/topics/principles-of-adjacency-draft
Thakchoe, S. (2007). The Two Truths Debate: Tsongkhapa and Gorampa on the Middle Way. Somerville, MA: Wisdom Publications.
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