Hierarchy Part 6: Conclusion


The unreasonable ubiquity of hierarchies should be suspect. Is the fact that you need a B to get from A to C – the fact that any accomplishment stands on the shoulders of giants – so trivial and arbitrary so as to be practically worthless?

We have seen that hierarchies are the source of structure and discontinuities in nature, of system boundaries – what constrains the undifferentiated flux in which our reality truly wallows, to produce statistical patterns that may be exploited, the way a bee may exploit the emergent phenomenon of flower color as a cue for food. If patterns are what psychologist James Gibson called “affordances” – invariances we may rely upon to further our goals – then the underpinning hierarchies are the joints we seek to carve Nature at. Hierarchies, in some modest realist sense, therefore exist independently of the observer.

Meanwhile “understanding”, which explanations serve to induce, is a cognitive state in the observer. The orgasmic phenomenology indicates a biological reward system meant to favor this type of thought processes over others, even though the depth of understanding mostly is illusive. Rarely are we capable of performing clear, mechanistic “clockwork” simulations in our mind’s eye of how phenomena in our life come about, and a need for explanation seems satisfiable by religious myths and physical formulae alike. Most of the time, our understanding is shallow, schematic and shadowy in nature, reliant on that information is just a Google-visit away. Moreover, we can predict, based on statistics, without insight, and we can explain without the ability to predict, so the interdependence of prediction and explanation is tenuous. So why would one type of thinking be preferred over another, and from where does this strong intuition of “depth” derive?

Cohen and Stewart describe the mental model of many working physicists as a reductionist “tree of everything”, with a putative theory of everything at its base and explanatory arrows twirling upwards, ramifying indefinitely and impenetrably, occasionally collapsed by an emerging simplicity. This way, sociological phenomena are ultimately explainable in terms of quarks. Two influential philosophers of science, Hempel and Oppenheimer, idealized the scientific pursuit as subsumption under more fundamental laws, the way Newton’s law of gravity can be subsumed under Einstein’s, or like how theorem can be derived from mathematical axioms. Is it a coincidence that they all have a distinctive hierarchical quality?

Recall that “near-decomposability” – the fact that different levels behave at frequencies that vary in order of magnitude – entails that any level can be described, with a good degree of approximation, independently of others. This is why academia can untroubled specialize into cell biology, molecular biology, and organic chemistry. In the words of information theory, the lower and higher levels carry information redundancies, and the state can be described by compressing their information. Thanks to the statistical properties, we can describe a cell without reference to sub-cellular events, or a problem-solving process without reference to neuronal firings. By putting it in terms of building blocks, we trim the description to make it lighter to carry, and if we are lucky we can even mathematize the state at one level into what econometrics call a “reduced-form equation”. But a sense of understanding upon doing so is unlikely to obtain, for an organism is concerned with means-end analysis and not concision for concision’s sake.

Now emphasize the “near” in “near-decomposability” and recall that in a hierarchy, subsystems are held in a state of freefall and actively participate in the higher order relation as a functional component. Cells, for example, are constantly exchanging material with the extracellular environment. Equilibrium of one individual cell equals cell death, and equilibrium of many cells equals organismal death. Even though the de-individuating transition from single-cell organisms to multi-cellular organisms evolutionarily was continuous, in hindsight it appears discontinuous and thys invites comparison with human artifacts where each component has an intended function. By metaphorical transfer, a certain cell has a “function” in the organism. If a certain neuron population responsible for breathing is blocked, for example, then the organism may die, i.e. the flux of all cells eventually settles into equilibrium with the environment. In this sense, a change in a subsystem is amplified through positive feedback, causing a cascade of changes in the higher level system. Correlating a subsystem to an “effect” or “function” therefore allows one small change to cause a lot of change. Understanding complexity is therefore this connection between fine-grain and large-scale behavior.

This kind of knowledge makes economical sense and imparts more power than correlating one change to a change of the same magnitude.  Hierarchies, in other words, provide opportunity for piggybacking on levering mechanisms for the thinking organism to achieve his pragmatic goals of changing the existing state of affairs into the desired state of affairs. It is like a financial investment – harder to attain (cognitively demanding), but with a greater payoff (in the predictive ability it affords).

Explanation then, is about framing a question in a way that appropriately links fine details to large effects, and the focal entities – the hierarchical levels – are arbitrary only insofar as they are determined by our pragmatic goal. Explaining an organismal behavior through molecular biology does therefore not conflict with an explanation in terms of evolutionary past – both are useful explanations in their own right. The hierarchical frame is self-consciously shifted as we see fit, either definitionally (a priori) or empirically (post hoc). The biology textbook hierarchy extending from cells to biosphere is a logical exercise useful as an analytical framework, but which does not reflect aspects like material flows and says nothing about spatial extent (a tree can be both an organism and a landscape). It is about usefulness of characterization, not ontology. Realizing this prevents any scientific debate from degenerating into semantic arguments spoken at cross-purposes due to over-commitment to names and labels, causing inconsistencies that do not reflect true competitiveness between explanations of the data available.

Towards the end of his essay, Simon acknowledges the chicken-and-egg flavor of his theory: are we able to understand the world because it is hierarchical, or does it appear hierarchical because those aspects are the only ones that could conceivably contribute to our survival precisely because of their stability? After all, scientists are interested in an infinitesimally small subset of all events in the world: the phenomena. The life of an individual gas molecule does not interest them. Phenomena are salient behaviors, salient due to an underlying invariance that makes them understandable, useful, and capable of sustaining themselves as thoughts in our minds. If there are complex structures that are not hierarchical, we would probably have no way to know them.

The conclusion is that the concept of “explanation” simply makes no sense in the absence of Nature’s penchant for hierarchies. Wherever there is an interaction and a reproductive mechanism at work, there is a slender, hopeful thread of hierarchy to latch onto and guide you towards the levering mechanism underneath. Nature handed down to us a wastepaper basket. Barely discernible in this vast pile of crumpled paper lay delicate pieces of origami craftwork. If you unfold them, you will find traces of a hierarchical past.  Carrying them around by flattening around the joints of these folds is the key to becoming a master origamist and what allows you to fold Nature as you wish.

Now that’s something to wrap your head around, if ever there was.


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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