Horgan and Kauffman: Duelling Banjo's?

December 11, 1996

Any images of "duelling banjo's" that might come to mind re the Kauffman - Horgan debate dissolve rapidly in reading "On Complexity and the End of Science". What one "hears" instead, is two "artists" playing in totally differing keys and rhythms.

While Horgan is a skilled fabricator of Aristotelian phrases; e.g. "... proponents [of Complexity] must tell us what, exactly, complexity is and how it can be measured." and "... as rigorous and precise as physics", Kauffman brews up imagery with enough self-referentiality to choke a Goedellian horse; e.g. "Work creates constraints on the release of energy that itself then constitutes work." and "The structure of the organization is also the record of the embodied know-how ...".

Kauffman's latter phrase, reminiscent of McLuhan's "the medium is the message" strikes one as being relevant to the discordancy. Does Horgan see the new scientific paradigm, should it "arrive", being delivered through the constrained medium of Aristotelian logic? What is the extent of Kaufmann's implicit redesign of hypotheses, symbolics and measurements for domiciling the new paradigm?

The liberating of physical experience from logical frameworks was accomplished in the early twentieth century, opening the door for a new rational design paradigm. In "La Science et l'Hypothese" (1903) Poincare observed [1]; "induction applied to the physical sciences is always uncertain..."; Wittgenstein, in "Tractatus Logico-Philosophicus" [2] (1921) pointed out that logic and mathematics were "content-free" and incapable of guaranteeing tomorrow's sunrise. Einstein said in "Geometry and Experience" (1921); "So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality."

Given the limits of traditional logic and the opportunity for revision, do Horgan and Kauffman accept Bohm's proposition [3] that rational law applies to complex order extending well beyond causal law, and that hypothesis may therefore include propositions of the nature; "As things are related in a certain idea or concept, so they are related in fact."?

R. D. Laing, a Scottish psychiatrist [4] pointed out that this latter type of rational formulation, applied recursively to behavioral interactions, is what "bootstraps" our "experience" and our view of "self". Does the reality modelling paradigm "shared" by Horgan and Kauffman allow the exaction of more certainty as to "what's out there" from our rational models than as to "what's in here" (i.e. "who" we "are"), rationality being a foreground process spawned by our background consciousness, or "self"?

And, in terms of symbolics to convey hypotheses, there appears to be substantial historical precedent to give us guidance. Amongst the pre-Socratic (pre-Aristotelian) philosophers, Heraclitus' proposition that "being" and "becoming" were systemically interwoven within nature (a "wave" oriented view), lost out to Parmenides' opposing view that the most elemental aspect of nature was simply "being" (an "object" oriented view). That Heraclitus' ideas did not prevail can perhaps be related to a deficiency of symbolics in phonetic Greek script.

What would have been useful to Heraclitus (and to Kauffman?), to explain a nature composed of dipolar opposites which self-unify through a "hidden [self-determining] attunement", is "ideographic" symbology incorporating both "real" and "latent" meaning. Such a capability was inherent in Egyptian hieroglyphics [a], Minoan "linear B" and other pictographic scripts of the mythopoetic tradition which were superceded by phonetic Greek, due to its superior trading-transaction attributes. Hieroglyphics took their final bow at the same time as Heraclitus, at the end of the reign of Darius I [5, 6], c. 480 BC, in the pre-Socratic epoch (Socrates lived from 469-399 BC, Aristotle from 384-322 BC).

A significant challenge is involved in conveying the message of "autonomous co-evolution" of Kauffman, Laing and Heraclitus using a linguistic medium such as English or Greek which was evolved to serve the needs of material-causal transactions. Analysis of Heraclitus' work by Kahn [7] indicates that this challenge is met by linking form and content through the coordinated use of "linguistic density" (meaningful ambiguity) and "resonance" (the echoing of specific imagery). Such "bootstrapping" or "holographic" techniques are in direct opposition to Horgan's Aristotelian pursuit of unambiguous clarity.

How Would the Horgan - Kauffman playing field tilt if the communications medium was not constrained to a lowest common-denominator rigid-body transactional-language orientation? And instead, employed "fractal pictographs" (hologlyphs?) to convey not only behavior but the latent experiential potentials (i.e. "know-how") of nonlinear systems such as those which "autocatalytically enhance nonergodic coevolutionary expansion of the biosphere into the adjacent possible."?

Finally, on the issue of measurement, there is once again good historical precedent to provide a base for current debate. The aphorism "the devil is in the detail" was not lightly dismissed by scientists such as Johannes Kepler, whose belief was congruent with Heraclitus' that "Geometry existed before creation, is coeternal with the mind of God,is God himself [9]". It was not treated lightly because Kepler's mother would most certainly have been burned at the stake for witchcraft had not Kepler strenuously interposed himself in her defense. Kepler himself narrowly missed being tried for witchcraft (prosecution papers were drafted but never served).

The problem with measurement in the domain of complexity and order, is a cultural one which stems from Aristotelian reality modelling and its interwoven ethics [b], as implied in Aristotle's statement that "Goodness is simple, and evil takes any shape.".

In the physics of rigid bodies, the most significant measurements are the easiest to perceive, thus measurement in the Aristotelian framework presents us with a common view of reality at low levels of consciousness. In the physics of geometry and order, however, the most significant features of the reality model are extracted from the detailed patterns in our observations. For example, a crude look around us suggests that the earth does not move. A more detailed look suggests that we are moving around the sun in a circular, frictionless orbit. A still more detailed look suggests that we are moving in an elliptical orbit around one of the foci which is close to coincident with a wobbling sun (an indication of interfering geometric-harmonies), and that tidal friction caused by the gravity of the moon and planets is converting some of the earth's dynamical energy into thermal energy, changing the earth's (our) trajectory in a time-directed, non-periodic way.

Thus, as we add refining detail to our rigid body measurements and approach the least significant end of the measurement spectrum, so emerge the most striking features of complexity and we appear to approach the most significant end of the geometric measurement spectrum (i.e. the "attractors" characterizing the system progress from simple circles, to complex multiple attractor geometries, to ???).

This measurement problem wouldn't be so bad if the most significant features of this complexity were available at low (i.e. common) levels of consciousness, as with rigid body physics. But, as Einstein has pointed out in "Geometry and Experience" (1921); "A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To "visualize" a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement." The connection to Kahn's work on Heraclitus is clear.

So, clarity in Aristotelian terms, is impossible in the higher measures of geometrical complexity. Clarity and resolution are drawn from a most ambiguous but resonant "holographic" view of multiple interfering systems; i.e. from an "expanding consciousness". In Aristotelian ethics, interference-based supposition comes too close for comfort to the "evils" of "suppositition" and should be eschewed rather than embraced. Thus while Kepler provided a geometric-harmonic theory for the solar system, he came close to being burnt to death for it while Newton's invention of a "field" to facilitate a more mechanical, or Aristotelian philosophy-conformant framework, made him a popular hero [c].

In conclusion, "discordant harmonies" appear in the Horgan - Kauffman debate as a result of incomplete specification of implied, but possibly radically differing, modelling and cultural paradigms. The nature of hypothesis, the symbolics deemed meaningful, and the measurement and theory validation approach might profitably be made explicit by Horgan and Kauffman so as to eliminate confusion as to whether any differences of perspective emanate from the model or the modelling tools.

As Ian Stewart observes in "Does God Play Dice?", an approximate solution to an exact problem is not the same as an exact solution to an approximate problem. Where Horgan would sacrifice precision in problem description to gain simplicity and clarity in the solution, Kauffman would sacrifice simplicity and clarity in the solution to preserve precision in problem description.

"Complexity" is doing its readership a valuable service in sponsoring the Horgan- Kauffman debate. And if the debating behaviors can be supportive of the purpose of "unification of opposites through harmonic attunement", rather than of a discrete linear true/false judgement, everyone stands to "win".

Ted Lumley

[1] Poincare, Henri, "Science and Hypothesis", 1903

[2] Wittgenstein, Ludwig, "Tractatus Logico-Philosophicus", 1921

[3] Bohm, David, "Wholeness and the Implicate Order", 1980

[4] Laing, Ronald, D., "The Politics of Experience", 1967

[5] Budge, E. A. Wallis, "The Rosetta Stone", 1929

[6] Chadwick, John, "The Decipherment of Linear B", 1958

[7] Kahn, Charles H., "The Art and Thought of Heraclitus", 1979

[8] Budge, Wallis E., "The Gods of the Egyptians: Volume I", 1903

[9] Bernstein, Jeremy, "Experiencing Science: Profiles in Discovery", 1978

[10] Eaton, Ralph M. editor, "Descartes Selections", 1927


[a] The decipherers of ancient pictographic scripts, such as Michael Ventris, used the term "combinatory" to describe the independent conveyance of meaning through the employing of "the same words in different combinations". This mode of "signifying" meaning supplemented the two direct "signings" of meaning through groupings of pronounceable units of sound (syllables) and single letters (partly pronounceable abstractions). In languages designed to serve material transactions (i.e. rigid body based reality frameworks), such as phonetic Greek and English, combinatory effects are very diffuse and difficult to pick up (except in poetic or humorous renderings which do not honor the scientific constraint of self-consistency).

In hieroglyphics, however, combinatory effects rich in "latent" as well as literal meaning were concentrated within the pictographic groupings. The following example describing a hieroglyphic pictograph grouping for the Goddess Net [8], the "Lady of the West", may help to illustrate this point. Net "... appears in the form of a cow with eighteen stars on one side, and a collar round her neck from which hangs (image); on her back is a ram-headed lion with horns and plumes, (image), upon his head. The cow stands in a boat, the prow of which terminates in a lion's head with a disk upon it, and is provided with wings; the stern of the boat terminates in a ram's head, and by the fore feet of the cow, which is described as "Net, the Cow, which gave birth to Ra," (image of group) is an utchat (image).

Such "combinatorial" characterization of the latent qualities and experience of just one of the many (metamorphosing) faces of Net would necessarily be far more diffuse in written English text. The extensive use of combinatorial effects by Heraclitus and Wittgenstein, so diffuse and difficult to render in English, made these philosophers very difficult to understand. The "linguistic management" of metamorphosing imagery, an essential requirement of reality modelling in the Egyptian and other mythopoeic cultures, appears next to impossible in English, since the diffuse combinatorial meaning would overlap and intermingle in an inseparable way. Written communications of meaning associated with systems which metamorphose (i.e. in which "being" is interwoven with "becoming", or which are in a state of "autonomous coevolution" is therefore extremely tenuous without exploiting symbology accommodating locally dense combinatorial meaning conveyance, such as an appropriate pictographic or visual medium.

[b] The following excerpt from Aristotle, "The Doctrine of the Mean", Nichomachean Ethics II., 6-7 illustrates some of the origins of this cultural problem in which "virtue" is associated with simplicity and stability of form, while evil is associated with complexity and metamorphosis;

"Virtue, then, is a kind of moderation inasmuch as it aims at the mean or moderate amount.

Again, there are many ways of going wrong (for evil is infinite in nature, to use a Pythagorean figure, while good is finite), but only one way of going right; so that the one is easy and the other hard--easy to miss the mark and hard to hit it. On this account also, then, excess and deficiency are characteristic of vice, hitting the mean is characteristic of virtue: "Goodness is simple, evil takes any shape.""

[c] Newton would have been aware that Descartes destroyed his work "Le-Monde" which broke with Aristotelian tradition, in 1633, after hearing of the burning of all copies of Galileo's "Dialogue Concerning the Two Chief World Systems" in Rome and Galileo's punishment by the Inquisition. Eaton [10] cites Bossuet on this as follows; "'But 'M. Descartes,' remarks Bossuet, 'was always afraid of coming under the notice of the Church, and we see him taking precautions in this matter which go to excess.' He had before him 'the fate of the philosophers of the preceding century, who had ventured to question the accepted physical doctrines [Aristotelian]. Ramus, Bruno, Campanella, Vanini, had suffered for their opinions, and Descartes did not propose to join their company.'"

In 1637, four years after his suppression of Le Monde, Descartes published his classic Aristotelian thought-conformant work, "Discourse on the Method of Rightly Conducting the Reason and Seeking for Truth in the Sciences", introducing the four simple and terse logical propositions with the religio-cultural apologetic; "And as a multiplicity of laws often furnishes excuses for evil doing, and as a State is hence much better ruled when, having but very few laws, these are most strictly observed; ...".

Newton, a secretive man who studied alchemy as well as the "natural philosophies", would have known the dangers of working on the "harmonies" side of the fence. As Bohm points out, Newton's illuminating insight on the universality of gravity (Kepler had apparently understood this universality also but got hung up on Aristotle's flawed notion of inertia) appeared to come to him from the geometrical harmonies side; "as with the order of movement of an apple in fall, so with that of the moon, and so with all". Presenting it in this mythopoetic form would likely have raised the hair on the back of the neck of even the most conservative of witch-watchers. Newton's introduction of the abstract notion of a "field" (action at a distance) although raising protests from Leibnitz, Berkeley and others, intentionally or coincidentally provided the means of "laundering" his discovery so that he could express it in Aristotelian "rigid body" terms, F = g*m1*m2/d**2 and avoid expressing it in geometric-harmonic terms, beautiful as that would have been to the pre-Aristotelian mythopoetic cultures.