Hierarchy Part 4: Ian Stewart & Jack Cohen and “Complicity”

complicity

We concluded last section by linking Simon’s watchmaker parable to Holland’s multiplier effect to show that reproduction’s inevitable incorporation of error creates an innate bias to increase complexity, as if the watchmaker’s 1000 units were self-assembling when left to their own devices. Self-organization violates our intuition that complexity is something conserved that must be inherited from complexity in the underlying deterministic laws. To ease ourselves into this more elusive account of hierarchy theory, this section presents a different take on it.

Two of my top 10 favorite books ever are written by mathematician Ian Stewart and biologist Jack Cohen. These are “The Collapse of Chaos” (1996) and “Figments of Reality” (1997), which both are sprawling attempts at reformulating debate on our most challenging questions through a sparkling smorgasbord of fanciful neologisms, mathematical curiosities and quirky imagery. While never making the hierarchy-aspect explicit, many of their ideas are eloquent ways of saying the same thing.

The central metaphor is that of the “phase space”, a multidimensional space (that for practical purposes can be visualized as flat) of all possible states that a system may have, each coordinate corresponding to a unique state, surrounded by a cloud of near-indistinguishable others. A system dynamic therefore sees the point wander around in the space, as a result of constraints ranging from the laws of physics and chemistry to basic features of the biosphere. For example, the periodic motion of a pendulum produces a closed loop. If the point converges on a particular path, we call this an “attractor”. Attractors make dynamical systems appear goal-oriented.

If we apply the phase space metaphor to evolution, each coordinate would correspond to particular DNA string. Given how wings have evolved independently at least four times, they would appear as a vector in the matrix, and we may say that wings are an attractor. Creature-space, meanwhile, is the space of all conceivable phenotypes, whether they are viable or not. Evolution does not act directly on the raw DNA string. Instead, movement in DNA space depends entirely upon selection in creature-space (recall that the K/T meteorite that supposedly killed the dinosaurs spared the mammals, regardless of how “fit” a dinosaur may be in non-catastrophic circumstances). This feeds back into DNA space, where changes in the gene pool potentiate changes in phenotype. Evolution therefore takes place in the combined space. It is driven by the organism but operates cryptically through DNA and consequently cannot be reduced to events that happen in one space alone (as neo-Darwinists insist in their emphasis on “the selfish gene”).

In this sense, evolution is like a self-modifying game where the winning strategy – that which allows you to continue playing – is ever-changing. In snooker, for example, a winning strategy is that which produces “breaks”, sequences of shots that reproduce the conditions for keeping the sequence going. Imagine now that the table edge deforms when hit by a ball, so that the break-producing strategy must change accordingly. As the edge and the strategy co-evolve, the game self-modifies.

This process, of two systems feeding off each other, suspending structural rules, combining phase spaces and changing them recursively so that novel behaviors emerge that were not present in either phase space, is dubbed “complicity” by Stewart and Cohen. In a similar vein, the simplicities that emerge as the two spaces combine are called “simplexities”. As they poetically put it, “complicity is like two mingling tendrils of smoke with an identifiable feature rising from it”. The commingling process connecting two levels may be impenetrably complicated, a witch brew of random fluctuations, but the simplexities that collapse it bring reliable order that can be exploited by other systems.

Philosopher Daniel C. Dennett has compared the role of intermediate levels to that of construction cranes: a small crane sets up a big crane to locally speed up the construction of an even bigger crane. There is no need for mind-first “skyhooks” to support it where more mundane apparatus will do.

A computer may deep down be a sea of electrons scurrying about, but from decades of problem-solving complicity, where the introduction of one novelty motivates another to accommodate it, a hierarchical organization of abstraction has arisen that gives a computer the appearance of transparency, “as if the machinery was made entirely of glass”. Stewart and Cohen compare the dynamic to water in a river: while some of the randomly juggling molecules will climb uphill, the landscape imparts a direction towards where the potential energy is lower, quite like how the context of DNA space, via error and natural selection, presses the wandering point towards increasing complexity.

What links Simon’s, Holland’s, and Stewart & Cohen’s accounts together is the discontinuous reality that crystallizes when interacting systems co-evolve to become working components of each other, in a new level that has a greater capacity to ride out external influences. Natural selection is letting the environment fiddle with your DNA in order to adapt; learning about a topic is letting the environment meddle with your nervous system so that it will cease to be disruptive. As a system self-complicates, it encodes more and more information about the environment, trapping within it a series of past instabilities. It is hierarchical, because subunits remain as resting-points to fall back on, albeit held in a state of continuous freefall to serve the higher order relation. For example, bacteria are still alive today, participating in the machinery of the human organism (we consist to 90% of them). Similarly, the product of enzyme pathways is used up to prevent it from reaching equilibrium, and family remains an important unit for social interaction despite the intricacies of modern society.

Just like how system interaction is pervasive, our reality is saturated with hierarchies. Biological evolution for sure is criss-crossed by them. One example is the macro-evolutionary increase in nestedness, from prokaryotes and eukaryotes, to multi-cellular organisms and colonial individuals. To our knowledge, no organisms lower than bacteria have preceded them or arisen from them, and while reversals are known to have occurred at the higher levels, they are out-numbered by instances of higher-level transitions. It took a billion years of protist experimentation to invent eukaryotes, but once it occurred, like the erection of a crane, it was followed by an explosive burst in ecological diversity. Indeed, such discontinuities are the norm also at narrower time scales, as evidenced by the “punctuated equilibrium” debate of Stephen Jay Gould versus gradualists, as well as Thomas Kuhn’s findings about scientific paradigm shifts, and the revolution-ridden advancement of human technology. This way Absolute Ignorance, mechanically churning forth without foresight, tentatively explores the nearest adjacent in the phase space. A vanishingly small set of these paths seems promising, and a few of them soar into a whole new space of potential, opening a new floor in the hierarchy.

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About lovisasundin

I study psychology and computing science in Glasgow but am originally from Sweden. I like drawing and popular science. Please don't hesitate to contact me at lovisafsundin@gmail.com
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