Holarchies & Panarchies: How much of a difference exists between a complex system and a simple cause and effect relationship?
“Nature has had a habit, in the past, of first tempting us to a euphoric complacency by the power and elegance of the mathematical structures that she appears to force us to accept as guiding her world, but then jolting us, from time to time, out of our conceptual torpor by showing us that our picture could not have been correct, after all! Yet the shift has always been a subtle one which leaves the previous edifice still standing proud, despite the fact that the foundations on which it had stood have now been completely replaced.”
—Sir Roger Penrose, Road to Reality, P. 486
In a highly interconnected world (à la Bohm), a seemingly simple "causal chain" is always part of an underlying "complex system".1 Consequently, such a perspective places no distinction between the relationship and the system—they are inextricably interwoven facets of the same reality. But we don’t always see it that way because it is hard to see.
Whereas the causal chain appears (on the surface level) to be simple (e.g. a → b), the successive events (e.g. b → c, or b/c → d/e) form a small part of a complex nest of interrelated systems, each flush with its own internal dynamics.2 In that moment—that slice of time—before the initial chain a → b is completed, the adjacent possibles of "b" are innumerable, branching out like pathways in an ethereal yet omnipresent neural structure: an adaptive system.3 All adjacent possibles that a system may reach along its present causality chain create one component of the larger “possibility space”.
The adjacent possible is the set of all possible configurations that are one step away from the present state.
High rates of interconnection and interrelation suggest that, to even reach the initial stages of a "simple" cause and effect relationship, multiple other causal chains have formed, broken, and left a lasting wake of causal relation in the process—a stream of adjacent possibles are fulfilled or left behind—invisible currents shaping the visible flow.4
Past, present and future causal chains are not islands; strands of causality do not stand alone.5
Plausible deduction suggests existing causal chains, their present effects and the future possibility space they form, spin a complex web of causality—an interconnected and complex set of nested systems within systems. This arrangement manifests in two complementary organisational principles: holarchy6 and panarchy.7
While holarchy emphasises stable containment relationships, panarchy captures the dynamic juxtaposition between conservation and creative destruction across multiple scales. Both concepts are metaphorically akin to Ezekiel's "Wheels Within Wheels", or the Vedic Yugas "Cycles Within Cycles". This fractal-like quality permeates all scales of reality, from quantum fluctuations to cosmic evolution.
Ezekiel’s “Wheely Good” Vision
Continuing this logic, it would be remiss to view a single causal chain as merely a "simple" relationship—even though from the surface the relationship between "a" and "b" seems linearly understandable.8
But thinking about what chains preceded "a", and what possible chains will proceed "b", makes mapping the possibility space of future causal chains as difficult as knowing what exact links led to our present slice of reality. To reach the causal chain f → g from an initial chain a → b, the underlying process may be more like:
a1 → b1 → c1
a2 → b2 → c2 → d1 → e1 → f → g
a3 → b3 → c3 → d2
a4 → b4 → c4 → d3 → e2
Or:
Causality is like a tree: you can see a lot of components from the surface—the trunk, branches, canopy, leaves—but hiding below the surface is an entire space of even more fundamental components—roots—that allow the surface level structure to be visible. The visible manifestations emerge from invisible foundations.9
Realistic interpretation of tree root structure
(Credit: Peter 2005; taken from: Selvaraj & Ramancharla, 2015)
Cross section of a pearl millet root - systems within systems - “wheels within wheels”
Getting to the “root cause of the problem” - the Ishikawa diagram is a great example of a) how natural causal structures (tree systems) can be used to b) visualise how cause and effect chains act as distinct yet fundamental parts of a more complex whole, c) think about how structure can transcend domain boundaries (enhancing frameworks from botany → business), and d) provides a novel way of thinking about how causal relations lead some systems (e.g. tree) to develop certain structures (e.g. roots) to affect a problem (e.g. survival) by building more structure (e.g. trunk, branches, leaves, canopies), and so on.
Then you zoom out further, up through the crown shyness you go, until the tree far below appears as one mottled verdant blur—a single causal chain in an immense forest of interconnected, nested systems within systems. Now add into the mix embedded, discrete, non-obvious (and sometimes even counter-intuitive) systems with their multitude of context-dependent inputs, outputs, boundaries and general behaviour patterns, and it suggests even the simplest causal chain benefit from being looked at under such an interconnected lens.10
Each apparent simplicity unfolds into remarkable complexity upon closer inspection, exhibiting what Ilya Prigogine called “dissipative structures”—systems moved far from equilibrium that spontaneously develop emergent order.
A simple diagram indicating two potential outcomes when an open system is moved away from its equilibrium (E), and into a new set of contextual parameters (P): either E is found in P and a new emergent order follows, or E remains outside P and chaos— disorder—runs amuck.
Oversimplifying for the sake of my own clarity, whilst the “simple” causal chain (c → d) appears to act differently to the more complex chain (c → d → e → f), but when we factor in past context (a → b → c), or hidden, non-obvious and counterintuitive chains (a1 → b1 → c1
a2 → b2 → c2 → d1 → e1 → f → g
a3 → b3 → c3 → d2
a4 → b4 → c4 → d3 → e2)
the latter (c → d → e → f) can be described as a result of the former (c → d), and the former is made up of processes related to the latter (a → b → c, c → d → e → f, a1 → b1 → c1… etc).
In other words:
Both are equivalent.
*Note*11
Woven threads are tempting to unpick; we are always trying to dig down to the root cause. Certainly this can help understand a part of the whole. But to understand the whole you must step back and try to see it, in all its interconnected splendor—a tapestry of causality where each ephemeral thread derives meaning from its relationship to all others.12
A simple relation is never simple; behind surfaces the possibility space is profound.
David Bohm's concept of implicate order in "Wholeness and the Implicate Order" (1980) provides philosophical grounding for this perspective, suggesting reality exists as an unbroken whole with all parts intimately connected.
This reflects what Albert-László Barabási demonstrated in his network theory research—that seemingly disparate systems follow similar patterns of interconnection, and what Steven Wolfram is showing in his hyper-graph based theory of “rulial space”: how complexity emerges from simple rules interacting in vast networks.
See: Kauffman, 2019, Entropy - a detailed overview of the highly complex “economic web” that shows how causal chains can interrelate to such a degree that the causal links become more than a sum total of the individual chains.
This echoes Edward Lorenz's foundational work in chaos theory on sensitive dependence on initial conditions (the "butterfly effect"), which demonstrates how minute changes in starting conditions can lead to vastly different outcomes.
They intertwine, intersect, and inform each other in an ever-shifting dance of influence, forming what Norbert Wiener's cybernetics identified as feedback loops—systems where outputs circle back to become inputs.
Panarchy, as developed by C.S. Holling, describes adaptive cycles operating across different scales, emphasizing how these nested cycles accommodate both gradual and rapid change, order and chaos.
The apparent simplicity masks profound complexity, akin to what Philip Anderson described in his seminal paper "More Is Different" (1972) about emergent properties that cannot be predicted from their components.
Denis Noble's work in systems biology, particularly "The Music of Life" (2006), illustrates this principle by showing how biological causation operates across multiple scales simultaneously, with no single level holding causal primacy.
See: Paine, 1966, The American Naturalist - concept of “keystone species” suggests “jenga” like structure to some large scale nested ecological systems, where “cascading effects” originate from a non-obvious and seemingly simple causal chain (e.g. declining otter (predator) populations causes rise in sea urchins (prey) who overgraze on kelp, causing a decline in the kelp forests which act as complex ecosystems for a host of other flora and fauna).
See: Shiller, 2015, Princeton University Press - case studying economic “market crashes” highlights how reducing personal risk can counter-intuitively increase systemic risk in the same game theoretic sense that obvious rational individual decisions can lead to counter-intuitive irrational group behaviours when scaled (e.g. when investors individually protect themselves through hedging strategies they can collectively amplify market volatility).
See: Steffen, 2018, Proceedings of the National Academy of Sciences - discrete systems create complex, counter-intuitive feedback loops with numerous hidden thresholds where effects suddenly amplify or change direction suggesting linear inputs can lead to non-linear, unpredictable outputs (e.g carbon emissions melting the Arctic ice, whilst decreasing ice decreasing the “reflectivity” of the planet's surface and accelerating planetary warming further as the land and oceans absorb more sunlight).
Alright, equivalence is perhaps not in the strictest mathematical sense, but still valid (e.g. the apparent simplicity of c → d is illusory when we consider its embeddedness in larger causal networks, where more complex chain (c → d → e → f) can be seen as emerging from or being built upon simpler relationships, each type (simple and complex) fundamentally depending on the other (pointing to an innate interconnection).
Brian Arthur's work in complexity economics at the Santa Fe Institute demonstrates how this interconnected perspective applies even to human systems once thought to follow simple cause-effect relationships, revealing instead complex, non-linear patterns of causality that resist reductionist analysis.