The benzene ring was discovered in hypnagogia, as a talented chemist stared into a fire: he saw an ouroboros as the solution. Hypnagogic thinking tends to be characterized above all by recursivity: self-referent metaphors, cycles spawned by cycles, a compulsive thought which cannot unravel because its traversal engenders the compulsion. But this is no mere neurological errata, no mere footnote in the history of affliction: my contention is that all holistic reasoning is recursive by nature, because a whole cannot actually be conceived, but a scale-invariant repetition can be inferred. What is a whole? Not merely a bounded surface, not merely an "object" and thus an erasure of depth: that is the influence of the symbolic reasoning of narrative consciousness, and not the full inheritance of our unconscious intelligence. When we understand, we conceive of wholes. A whole implies stability, which implies circular causality: even a dissipative system as simple as a dustdevil testifies to such. An imbalance of force constrained to a boundary such that novel order emerges: tension, compression, and critical resistance are always involved when we see a "whole". Both topdown and bottomup: the ancient habit of seeing "spirits" in everything, was not as neurotic as we like to imagine. There is a deep rationality to animistic thinking: what is a spirit but a recursive function permeating a field? A scale invariance producing the illusion of personage, and thus requiring a mask both as honor and limit? The nomadic attitude toward spirits was generally very wary: they are infectious by nature, because in our language a spirit is a recursive order parameter unconsciously perceived - whether our ancestors spent too many millennia hallucinating wildly under the influence of this newly liberated oversized cranium of ours, prematurely peeking into spatiotemporal secrets which we have only now begun to soberly examine, is a problem I to leave to the reader for now. Our immediate question is: can we responsibly hallucinate?
But what is the productive imagination, if not responsible hallucination? To maintain an intellectual conscience, which means to "show one's work", to be able to converse, to engage wholeheartedly in the ongoing dialogue, to be able to state reasons and elaborate and build something viable over time: just that much requires already a productive imagination... Therefore we're led to the conclusion that an intellectual conscience cannot be nurtured, exhibited, or even exist without its counterpart: a wild enthralling hallucinatory power. Everything else is just monotony, mendacious conformity, and cowering complicitude which wants to pass off its inability to create as virtue: my point is that good science happens in the tension between the excursions of hallucinatory elaboration and the reductions of articulate dialogue. Therefore we, who are interested in developing our powers of knowledge and foreknowledge, who cannot resist the temptations of the bleeding edge, should develop not only a reductionistic habit of expression but a deepening ability of controlled, willed hallucination: for there is no other way to perceive.
There is an intimate relation between topology and multivariate causal reasoning: this leads here, that leads there. It's been my impression that the mathematical power of "statespace" is nothing other than the cerebellar geometric imagination applied to the time domain, and thus the hominid talent for toolcraft is invoked. Consider what it requires to make a fine handaxe from chalcedony: one must constantly conceive of the motion of the tool in time, along with the transmission of lines of force along the semicrystalline structure one has in one's hands at that moment, examining every ridge and valley for weakness and cohesion, channeling force from the leading edge to the grip without yielding to any local congestion, such that the relative brittleness of the material is maximally attenuated while its hardness and inelasticity is maximally exploited. Take the time to examine a genuine Clovis point, you will find in the most masterful pieces nothing less than this topological sophistication and indeed more - for there are many other considerations than I've mentioned: craft is not something that yields up its secrets to language so easily.
I have the privilege to live in an area of high desert where obsidian arrowheads litter the ground, and one cannot know if any one piece is 200 or 14,000 years old. What we're discussing is not a trivial task: try a little flint-knapping if you believe the stoneage to be "primitive", and that word to signify "easy" or "stupid".
What therefore is the importance of Maxwell's surface? Why has topology become so important in modern science?
Because we are finally undoing some of the willful stupidity of postaxial thinking: namely the famous obtusery surrounding linear causal reasoning. We are accomplishing this by a graduated return to the nonlinear, multivariate, and overdetermined causal reasoning inherited from our hindbrain.
In this context, "linear" represents a cluster of philosophical prejudices surrounding causality:
- Uniquely determined
We will have to examine each of these in turn. But it is enough to say that social posturing is the root of the worst causal thinking with which our sciences are still rife: the ape only pretends to be so dumb as to believe in a singular cause for any event, and only when he finds it socially advantageous - the problem is that it's so useful as to be practically indispensable. Thus is blame mobilized, thus is maintenance and adjustment of social hierarchy made fluid, thus is ritual made possible which achieves very real consequences, and thus is histrionic certainty generated which is so necessary to get a loosely allied troop of primates to do anything at all. Our sciences are still ritual: look behind the veil of the more ambitious journal articles, and you will discover many reasons to subtly fabricate, to gingerly omit, to cloyingly exaggerate, to pretend to be stupider than one is - in the hope that your audience has reason enough to join you.
Linear thinking is social and histrionic in origin: it underlies all hysteria, all as-if, all posturing for clandestine benefit, all disguised social maneuvering. The more panicked and lonely the ape becomes, the more it resorts to a pretense of obtuse linear reasoning - even while it practices an even more opportunistic and multivariate unconscious calculation. There is an intimate relationship between the myth of agency, the superstition of free will, the soul, and the assignment of blame on one hand, and the witch-hunt, ritual exclusion, postaxial religion, and the moral disease on the other... But we've been here before, and this time the path will only strafe these lessons.
Tactile, visual, and auditory processing is the root of sophisticated causal reasoning: the reification of shape, the assignment of locale, the inspection of invariance under transformation, the ape specialty in the intelligence of the hands.
I have examined enough arrowheads to discern the degree of craftsmanship involved in any one: some of them are masterworks, and a signature of the quality of mind and body which created it. Some of them are witness to immense patience, care, and observation. The balance between improvisation and exactitude, the even spacing between strikes, the gentle rotation of angle of incidence, and the final sign of mastery: the logarithmic slope from center of mass to edge. But the best way to see this is not with the eyes: you must put away your eyes and use your fingertips. The surface should feel like rippling water, like the sound of rustling silk, like the curvature of a blade of grass: don't doubt that the knowledge of these formulae resides in the human fingers - don't doubt that the core of your intelligence dwells right there, caught in the whorl of the human fingerprint.