Insights from a carp ensuring complementarity of radically distinct perspectives?

Constrained, Unconstrained and Surprised in a Global Context (Part #13)

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Allegedly Chinese small-scale farmers -- those keeping a single carp in a small pond -- have recognized that the tendency of the fish is to remain stationary in the centre of the pond (without exercise) thereby rendering it far more vulnerable to disease. The situation would seem to be reminiscent of the problematic condition of the frog in the well as perceived from a Zhuangzist perspective. The solution allegedly adopted by farmers is to place a rock in the centre of the pond. The carp then swims continuously around the rock -- seemingly responding to the illusion of swimming around the bend in a stream. The tale of the carp has been charmingly represented by Tomás Fülöpp (Hubert's Voyage, Vacilando, 19 April 2022).

Arguably the Confucian insight of li -- finding the rhythm in the everyday to ensure a life of harmonious ease -- can be compared with that of the carp circling the stone.

Rocks and holes constraining comprehension: The challenge to comprehension has been remarkably clarified using the mathematics of q-analysis as developed by Ron Atkin (Multidimensional Man; can man live in 3-dimensional space?, 1981) and separately summarized (Comprehension: Social organization determined by incommunicability of insights).

Atkin illustrates the challenge of comprehension in relation to experience "within" the geometry of a triangle whose centre is experienced ambiguously as either a rock or a hole. For humans constrained to an understanding of the distinctive colours of its edges alone (see below), the form of the triangle as a whole remains incomprehensible -- as represented by white. If the person's colour vision is 0-dimensional, then it is restricted to the vertices. It can only see one vertex colour at a time and never a combination (as represented by an edge). If vision was 3-dimensional, it would allow traffic throughout the geometry, but would perceive other colours as well, calling for a fourth vertex (forming a tetrahedron) in order to contain the full range of combinations.

Comprehension through transcending the plane (as indicated by the q-analysis of Ron Atkin)
Conjection as recognizing "white"	Relative orders of comprehension
	0-dimension: Red, Green or Blue 1-dimension: Yellow (=Red/Green) Purple (=Red/Blue); or Turquoise (=Blue/Green) 2-dimension: White (=Red/Green/Blue)

As with the Sun, the rock-hole effectively "bends" the light of communication around it. The carp swims around through a cognitive tunnel -- without being aware of its circularity.

Mysterious nature of a hole: The rock-hole ambiguity to comprehension can be explored further through the work of Terrence Deacon with regard to what is missing:

The problem is this: Such concepts as information, function, purpose, meaning, intention, significance, consciousness, and value are intrinsically defined by their fundamental incompleteness. They exist only in relation to something they are not.... The "something" that each of these is not is precisely what matters most. But notice the paradox in this English turn of phrase. To "matter" is to be substantial, to resist modification, to be beyond creation or destruction -- and yet what matters about an idea or purpose is dependent on something that is not substantial in any obvious sense. So what is shared in common between all these phenomena? In a word, nothing -- or rather, something not present. (Incomplete Nature: how mind emerged from matter, 2012, p. 23, emphasis in original)

Basically, it means that our best science -- that collection of theories that presumably comes closest to explaining everything -- does not include this one most defining characteristic of being you and me. In effect, our current "Theory of Everything" implies that we don't exist, except as collections of atoms. So what's missing? Ironically and enigmatically, something missing is missing. (p. 1, emphasis added)

What is the "well" or "hole" of ignorance that underlies conventional knowledge and inhibits fruitful reconciliation in the light of conventional model building? (cf. (Unthought as Cognitive Foundation of Global Civilization, 2012; Nicholas Rescher, Ignorance: on the wider implications of deficient knowledge, 2009). As discussed separately, what is the implication of the provocative insight of Ambrose Bierce: The small part of ignorance that we arrange and classify we give the name of knowledge. (Cognitive mystery of holes, lacunae and incompleteness, 2014). Given the influential role of ignorance, a case can be made for reversing the current focus of universities in seeking to eradicate it, as separately argued (University of Ignorance: engaging with nothing, the unknown, the incomprehensible, and the unsaid, 2013).

Of particular relevance is the remarkable exploration by Roberto Casati and Achille C. Varzi (Holes and Other Superficialities, 1994) -- with respect to the borderlines of metaphysics, everyday geometry, and the theory of perception (reviewed by Steven A. Gross, What's in a Hole? The Harvard Review of Philosophy, 1994). They seek to answer two basic questions: Do holes really exist? And if so, what are they, as queried in an extensive entry on holes in the Stanford Encyclopedia of Philosophy.

Turtle as embodiment and bearer of a hole? As described above, the turtle is seen as carrying a magic square upon its back. The form of that square can be thought of as an eightfold circuit of distinctive conditions with which various sets of labels are associated, whether numbers, BaGua trigrams, orientations, or topographically related. Speculatively these can be seen as centred on what might be reframed as a hole of some kind -- with which the number five is associated in the square. This offers an association with the classic Chinese pattern of the Wuxing, presented here as rotating around the centre of the magic square (below left).

The corresponding trigrams might then be presented as rotating within a torus (below right) -- with the suggestion that the two animations are comparable in terms of their cognitive significance as sustainable processes (Memorable dynamics of living and dying: Hygeia and Wu Xing, 2014).

Animations suggestive of sustainable comprehension as a cyclic rotation
Magic square with the 5-fold Wuxing pattern rotating around its centre	Rotation of 8-fold BaGua pattern of trigrams (also .mp4, .wrl and .x3d versions)

Arguments relating to the development of the animation on the right are developed separately (Zen of Facticity: Bull, Ox or Otherwise? Herding facts and their alternatives in a post-truth-era, 2017).

Cognitive complementarity of turtle and frog-in-a-well: The animations above, together with the triangular framing by Atkin, are together indicative of the entanglement of contrasting modes of comprehension to which the extremes of the fable point.

Each invites consideration in terms of the tale of the carp in the pond in that cognitively both Confucians and Zhuangzists circle a subtle central insight which apparently eludes them -- but nevertheless holds them captive. Paradoxically it is the dynnmics of the turtle's magical pattern which engenders the well by which the frog is "trapped", but both frog and turtle are constrained to circling the hole-stone whose nature eludes them.

The arrows of the 5-fold Wuxing pattern of the animation offer a useful indication of the perspective of the carp at any one time, namely of the extent to which it can see around the stone to the new condition with which it might next engage by moving. This suggests a degree of anticipation integrating the attraction of surprise.

Understood as a toroidal tunnel of experience, as implied by Atkin's triangle and the configuration of trigrams in a torus, this invites speculation on the nature of the "toroidal experience" exemplified by the circumnavigating carp (Imagining Toroidal Life as a Sustainable Alternative , 2019).

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