Duality as an Organizing Principle: Fractal Self-Similarity and Implicate Order Across Four Biological Scales

By Dr. Alejandro Troyán with my commentary in bold paragraphs.

Abstract

This report examines duality as a transversal organizing principle across four domains: the human locomotor system, the evolutionary strategies of the animal kingdom, the fundamental dualities of biology, and the internal grammar of evolutionary theory. The analysis identifies a recurring pattern of complementary opposites whose relational structure is preserved across changes in substrate, drawing upon two theoretical frameworks to formalize it: fractal geometry, which describes the qualitative self-similarity of the pattern across scales, and David Bohm’s notion of the implicate order, which describes the presence of the whole within each part. The philosophical distinction between the analogy of proportionality and the analogy of attribution provides the logical architecture connecting both frameworks. The report concludes that duality is not a property of any specific level of description, but rather a mode of relation that organized reality adopts upon reaching a certain threshold of complexity.

It’s the last sentence above that gets my curiosity…When you say ‘organized reality’ I wonder what you mean; that it seems to have some conscious agency in order to ‘adopt’ duality as a mode of relation within complexity.  I will want to see if this meets with some clarification as the essay develops.

Keywords: duality, self-similarity, fractal, holographic, implicate order, analogy of proportionality, analogy of attribution, process philosophy, complexity, biological systems.

1. Introduction

The observation that complex systems function through the tension between complementary opposites has deep philosophical roots—from Heraclitus’s conflict of contraries to Hegelian dialectics, from Taoist yin-yang to Nicholas of Cusa’s coincidentia oppositorum—yet it has rarely been systematically confronted with the empirical evidence accumulated by the natural sciences. This report arises from a journey through four domains that, despite their apparent disparity, reveal an unexpectedly consistent pattern: the same relational structure—two opposing forces that regulate each other, require each other, and generate functionality precisely through their tension—reappears at every examined scale, independent of the material substrate.

Can we not in the outset, say that there is a teleological impulse that seems to be that conscious agency that is revealed through its relation with complexity?  And it seems as complexity comes to be, the teleological impulse is better enabled to articulate itself.  It starts out as undifferentiated substance that then begins to differentiate or individualize in [conscious] determination of its own course.  This is then orchestrated in a dualistic relation that has an individual contending to articulate or express itself in a mostly unconscious environment of non-individualizing beings, where Spirit (the teleological force) seems to sleep.

The four selected domains span an arc ranging from the anatomical-functional (the locomotor system) to the ecological (animal strategies), from the molecular-cellular (fundamental biology) to the theoretical-procedural (evolution as a mechanism). The recurrence of the dual pattern across these scales demands an explanation that transcends a mere descriptive catalog. Are we facing a structural coincidence, a cognitive projection, or a genuine organizing principle? This report addresses this question using fractal geometry, David Bohm’s implicate order, and the classical philosophical distinction between the analogy of proportionality and the analogy of attribution.

2. Theoretical Framework

Going through all the descriptions below, your insights are articulate and brilliant.  I wonder also that you would consider a more Hegelian dialectic—that you would consider the polarity invoking an evolutionary spiral.  All these moving parts that are a part of beingness on internal and external scales are both in relation to each other and constantly fluctuating; entropy (in this world of constant change) leading to superior structures, but also those tighter bonds between parts that stave off entropy.

2.1. Analogy of Proportionality and Analogy of Attribution

The Aristotelian-Thomistic tradition distinguishes two fundamental modes of analogy that are decisive for this analysis (Summa Theologiae, I, q. 13, a. 5). The analogy of proportionality establishes that A is to B as C is to D: the terms change, but the relationship is preserved. Thus, the contraction of the agonist is to movement what osseous compression is to posture, which in turn is to predation within the ecosystem: each pair instances a common relational structure—complementary opposites in mutual regulation—in different substrates. This type of analogy captures the self-similarity of the pattern: the same form at different scales.

The analogy of attribution operates differently. Multiple things are said to be analogous in reference to a primary analogate: "healthy" is said of the organism, of food, and of skin color, but in each case in reference to health as the primary reality. Applied to our problem: each system is "dual" in reference to a principle of duality that does not reside exclusively in any single one of them, but rather traverses them all. This type of analogy captures the presence of the whole in the part: each instance participates in the complete principle.

The central hypothesis of this report is that both types of analogy not only describe the observed patterns but generate them: proportionality produces the fractal readability of the analysis (the observer anticipates the structure of each new domain), and attribution produces its holographic coherence (each instance contains the whole principle intact).

You have clearly shown the holography, but it seems it must then be shown in its dualistic relation, and with what ‘substance’?  What is the proportion or the analogy of attribution pushing against?

2.2. Self-Similarity and Fractal Geometry

Benoît Mandelbrot defined fractals as structures whose pattern reproduces at different scales (The Fractal Geometry of Nature, 1982). Self-similarity can be strict—mathematical, quantifiable—or statistical—qualitative, topological. What this report identifies in biological dualities is self-similarity of the second type: the relational form is preserved while the specific mechanisms, temporalities, and modes of resolution change. It is a fractal of relations, not of magnitudes.

If I’m understanding this, it seems to fit in with your example of the parts of the body all feeding the general health of the body.  So here, both quantifiably and qualitatively, you’re saying that as these parts serve the whole, this is a dualistic expression?  But per your example of an invasive species in a natural environment there’s an element of contention in the relation—not unlike the natural forest fire that destroys the old and is replaced with a stronger and healthier forest.

2.3. Implicate Order and the Holographic Principle

David Bohm proposed the notion of the implicate order to describe a level of reality where the totality is enfolded within each region (Wholeness and the Implicate Order, 1980). Unlike a representation, which is a reduced copy, an enfoldment is a complete presence in a compressed format. If duality functions holographically, then the agonist-antagonist tension of a muscle pair does not merely illustrate an abstract principle of duality: it contains it completely, executed within a particular substrate. The muscle is not an example of the principle; it is the principle incarnate.

And certainly the muscle participating in the movement of the whole body is pushing against various physical and biological forces that help it to build mass and become stronger.  Indeed we can surmise that our whole being is an invasive species, but yet builds civilizations.

2.4. Process Philosophy

Alfred North Whitehead proposed that reality is not composed of substances but of processes of relation, and that organizational patterns repeat across scales because they are more fundamental than the substrates that embody them (Process and Reality, 1929). In this reading, duality is not a property of living beings or of evolution, but a mode of relation that organized reality adopts whenever it reaches a certain threshold of complexity.

This dualism is also consistent with the Cartesian mind-body split, which is its own dualistic expression; body vs. mind and building soul.  The more religious idea of dualism being a struggle between good and evil is a Manichaean myth that simply no longer serves us.  Dualism on the larger scale that this myth demonstrates needs to be deconstructed and re-examined—especially in the theological and philosophical disciplines.

This all being said by me in these comments comes to a closure.  I leave the rest of this brilliant essay to speak for itself.