1. On Complexity in Contemporary Science

In a series of publications, Scientific American journalist John Horgan ridiculed the movement as being the fourth C among the "failed fads" of “complexity, chaos, catastrophe, and cybernetics”. In 1997, Horgan wrote that the approach had “created some potent metaphors: the butterfly effect, fractals, artificial life, the edge of chaos, self-organized criticality. But they have not told us anything about the world that is both concrete and truly surprising, either in a negative or in a positive sense.”

2. The Puzzle of Complexity: The Variety of Approaches

2.1. Biology

As regards biology, the understanding of its complexity developed over centuries, starting already with Hippocrates and Aristotle, and proceeding to understanding of physiology, developmental biology, and evolution.

2.1.1. Hierarchy

Biology is of a hierarchical nature, based at the bottom in the same material stuff as all other matter we see around us. Thus the hierarchy is

Upwards and downwards causation takes place as indicated [61,66]. The key influences from above L13 are incoming solar radiation, which in combination with a dark night acting as a heat sink sky enables the biosphere to function in energy terms, and the gravitational fields of the Sun and Moon, causing tides. All this is based in the possibilities physics allows at each emergent level [38].

2.1.2. Physiology

The first real studies of complexity were studies of physiology. Circulation of blood by the heart was already discussed by many including Hippocrates (c.460-370 BC), but was first put on a solid footing by William Harvey in 1628.

Physiological systems One by one all the physiological systems of human beings were understood: 1. the respiratory system, 2. digestive system /excretory system, 3. circulatory system /cardiovascular/vascular system, 4. urinary system/renal/urinary tract, 5. integumentary system, 6. skeletal system, 7. muscular system, 8. endocrine system, 9. lymphatic system, 10. nervous system, and 11. reproductive system, working together in harmony to provide our physical being. Each of the physiological systems is in turn of a hierarchical nature related to its function, as in the hierarchical nature of the heart [138].

Cells A crucial discovery by Hooke in 1665 was the way all life is based in microscopic cells , with their complex substructures (cytoplasm, nucleus, ribosomes, mitochondria, etc) being elucidated in following years. This is the first level at which all the functions of life occur. There are 13 different cell types in the human body.

Molecular biology In 1953, James Watson and Francis Crick published the double helical structure of DNA. The first protein structures to be solved were myoglobin by John Kendrew in 1958 and hemoglobin by Max Perutz in 1963. This lead to the understandings of supramolecular chemistry [111,112] regarding how supramolecular conformational change underlies molecular biology. In particular the molecular structure of the nucleic acids RNA and DNA [185] and of many proteins [152] have been determined, and hence the molecular biology of the cell elucidated [2].

Vast numbers Life emerges out of vast numbers of atoms and molecules and cells:

• The number of cells in the human body is ${10}^{13}$,
• The number of proteins in a cell is $4\times {10}^7$,
• The number of proteins in a human body is $4\times {10}^{20}$,
• The number of atoms in a typical cell is ${10}^{14}$,
• The number of atoms in a human being is ${10}^{27}$.

None of this is obvious, because both atoms and cells are so small (which is why it took so long for both the cellular structure of life and atomic structure of matter to be proved).

Stochasticity and Molecular Machines Molecules in air at normal room temperature are moving at between 300 to 400 metres per second. A biomolecule collides ${10}^{13}$ times a second with water molecules. Biology has evolved to use the opportunities at the bottom [75] to thrive on molecular stochasticity, so molecular machines reliably extract order from this chaos [92,148]. Examples are how motor proteins (myosin, kinesin, dynein) are responsible for muscle contraction and move cargo inside cells, DNA polymerases replicate DNA, RNA polymerases produce mRNA, the spliceosome removes introns, and the ribosome synthesises proteins.

Three key principles occur, all involving contextual logical branching:

• Form and function in biology are related by a multi-scale [119] hierarchical structure, forming an integrated whole [89,164] with structure/function relations occurring at all emergent scales [31,139], involving variables relevant to that level [5].
• Metabolism involves a). enzyme-catalyzed reactions converting energy in food to forms suitable for cellular processes, b). conversion of matter in food to building blocks for biomolecules, and c). the elimination of metabolic wastes [73]. These reactions are crucial in allowing growth and reproduction, maintenance of structure, and environmental responses, and take place in the form of metabolic networks [100].
• Homeostasis in biology was discovered in 1865 by Claude Bernard [39] and then rediscovered in an engineering context by Norbert Wiener in 1961 [188] as a concept he named Cybernetics. The common core of both processes is feedback control loops that counteract deviations from a chosen goal state by corrective action, thus acting top-down to control micro-states so that desired macro states emerge (as in a thermostat) and so enabling contextual dynamical branching (e.g. a heater element is on or off). It is a principle of very wide application in biology, with the set points determined by evolution, and engineering and society, with chosen setpoints.

2.1.3. Reproduction and Developmental Processes

Existence of individual organisms occurs via developmental processes based at the cellular level in cell division followed by cell differentiation.

Cell division is part of a cell cycle during which the cell grows and replicates its chromosomes before dividing. It should be noted that this process itself is not coded in DNA but rather is built into the inherited cell structure, duplicated when cells divide and developmental systems are reproduced [144]. The process includes duplication of the gene itself in a complex process mediated by various RNAs, and followed by a careful proof reading and correction process whereby DNA replication errors are reduced by many orders of magnitude [156]. Also gene organelles divide by highly complex processes, as e.g. in the case of mitochondria.

Cell differentiation The same genetic information is encoded in the DNA in the chromosomes in every cell. Genes are segments of DNA that can be read to produce proteins, with regulatory sequences controlling transcription of the gene. Which genes are read is determined by binding factors that turn genes on so that they are transcribed into messenger RNA (mRNA) molecules, which in turn are translated into proteins [185]. The issue is which specific genes are read in which cells in which position in the developing embryo at what time [98,129]. This is controlled by gene regulatory networks on the basis of positional information that controls cell fate decision [79,81,166,191]. The resultant proteins then determine what kind of cell emerges at each position [32,33] and so determines embryo and hence adult organism structure.

2.1.4. Darwin and Adaptive Selection

So where does the DNA come from that shapes biological outcomes? As is well known, by processes of variation and selection as proposed by Charles Darwin in 1868 [44], now commonly agreed to on as a key feature of biology [55] explaining apparent design by natural processes [74]: organisms are thereby adapted to their environment [30].

Of course, when Darwin developed the theory, it was a theory of macroscopic variation (Levels L9 and upwards in Table 1), for the concept of a gene was not even known at that point. It has since been recast as a theory of genetic evolution, and many writings represent it as only being such. This ignores the undoubted role of physiology in the process of evolutionary selection [140] (e.g. as in the case of Darwin’s finches), thereby undermining the central achievement of evolutionary theory [76].

In fact evolutionary adaptation takes place simultaneously at all the emergent levels L4 to L12 in Table 1 in an integrated way [66], as has to be the case, because of the way the levels interact with each other (see e.g. [183] for the interaction of physiology, proteins, and genes). Neither organisms nor genes are levels uniquely determining evolutionary outcomes. In particular, selection takes place of developmental systems [149], so there is a strong “Evo-Devo” interaction between evolutionary and developmental processes [32,33]

From a broader viewpoint, evolution is an example of the power of Complex Adaptive Systems [93], a theme we return to later.

Table 1.  The Hierarchy of structure for biology on Earth. Levels L0 to L4 are strictly physical, and their nature is unaffected by biology. Level L5 is the first distinctly biological level, and level L6 the first level where all the processes of life occur. Higher levels are the Earth (the planet as a whole), Sun (essential to life) and Solar System, Galaxy, and so on. The bottom level L0 is unknown (it could be strings, but they are not well defined). The up arrows indicate upward emergence from a specific configuration; the down arrows, downward determination of specific outcomes in particular contexts.

Table 1.  The Hierarchy of structure for biology on Earth. Levels L0 to L4 are strictly physical, and their nature is unaffected by biology. Level L5 is the first distinctly biological level, and level L6 the first level where all the processes of life occur. Higher levels are the Earth (the planet as a whole), Sun (essential to life) and Solar System, Galaxy, and so on. The bottom level L0 is unknown (it could be strings, but they are not well defined). The up arrows indicate upward emergence from a specific configuration; the down arrows, downward determination of specific outcomes in particular contexts.

L13		Biosphere
L12	⇑	Ecosystems	⇓
L11	⇑	Populations	⇓
L10	⇑	Organisms	⇓
L9	⇑	Physiological Systems	⇓
L8	⇑	Tissues	⇓
L7	⇑	Cells	⇓
L6	⇑	Cytoplasm, organelles	⇓
L5	⇑	Macromolecules	⇓
L4	⇑	Molecules	⇓
L3	⇑	Atoms	⇓
L2	⇑	Protons Neutrons Electrons	⇓
L1	⇑	Quarks Leptons Bosons Higgs	⇓
L0		Unknown physics (if it exists)

2.1.5. Networks

Given these vast numbers, interactions often take the form of networks, where simple interactions are combined to give complex outcomes. Their nature is characterised by graph theory, and one can study the statistics of networks, such as existence of hubs and the degree to which they are scale-free, etc [1,17]. One can also determine what network motifs occur [4], with specific functions. Biological networks are of two types:

• Interaction networks with specific functions, particularly metabolic networks [100] [161], gene regulatory networks [105], and cell signalling networks [19]. These occur inside compartments bounded by membranes that keep the interactants from drifting away, so spatial location is a key aspect of their functioning [122]. They reliably produce macro level functions out of the huge number of interactions of specific components at the micro level. One can model their function by Boolean interaction networks, thus distinguishing biological from random networks [184].
• Nervous systems are structural networks [35] which are themselves hierarchically organised [124]. They consist of neurons (cells made of dendrites, a nucleus, and axons) connected by synapses to other neurons, together forming a physical neural network [104]. Action potential spike chains travelling down axons to other neurons convey information and allow adaptive resonant networks to occur. The hierarchical structure of the brain [124] allows hierarchical dynamics to occur [160].

Note that it is not sufficient to give statistics of the roughly ${10}^{14}$ synaptic connections of the roughly ${10}^{11}$ neurons in a human brain to characterise it. It is the specific details of these connections that embodies our unique memories and abilities that make each of us the human individuals that we are.

2.1.6. Perception, Learning and Prediction, Agency

The extraordinary thing that occurs is the emergence of qualia and mental processes out of physical entities, namely action potential spike chains propagating in the physical brain. Indeed there are a variety of emergent properties arising:

• Learning Plasticity at macro and micro scales enables learning on the basis of experience [103]. The brain is altered by our experiences and understandings, and able to recall (or at least reconstruct) associated memories.
• Perception is enabled by predictive processing of incoming data [36], enabled by cortico-thalamic circuits and experienced as qualia.
• Planning Internal models of the world based on past experience and present data allows prediction of outcomes, and so values-based choices between action options [69] and consequent actions.
• Randomness Stochastic dynamics is a principle of brain function [48]. Indeed stochasticity at the micro-level underlies the capacity for higher level processes to select optimal lower level outcomes on the basis of higher level needs [141,142], allowing higher levels to break free of the iron determinism of physics per se.
• Agency and Free Will This amounts to the emergence of agency [45,87,88], and indeed effective free will emerges [69,147].

2.1.7. The Emergent Whole

What emerges in biology are open systems [151] that are consequently dissipative systems [158] for thermodynamic reasons, which form an integrated whole [80] where each part works together to enable the whole to function. All the characteristics of life emerge, including function at every level [139], and agency.

Measures We do not attempt to give a measure of their complexity, out of all the measures proposed [162], as the numbers of particles and molecules and cells and neural connections involved are too large. One needs some measure characterising the extraordinary properties remarked on in §.2.1.6. Perhaps those are the dimensions that should be used as a basis for such a measure.

3. The Role Each Approach Plays When Viewed Today

3.1. The Core

We propose that the following are the core features allowing complexity involving coordination of billions of components so as to attain emergent function, as in the case of life and digital computer systems, to emerge

3.1.1. The Centre

• Non-linearity. The dynamics involved, and their emergent outcomes, are manifestly non-linear. While the basic elements making up a complex system may indeed have linear dynamics, they are assembled in highly non-linear ways [65], for example involving interacting hierarchical feedback control circuits and interaction networks.
• Organisation. These elements are systematically organised so as to achieve desired emergent outcomes [168] [133]. This occurs either via the processes of natural selection in the case of biology [30,76], or by processes of design and manufacture, as in the case of digital computers [43,169], aircraft, and so on.
• Open systems. These are all open systems with well defined boundaries [151], so unpredictable incoming influences influence their dynamics [179]. They can however be structured so as to attained desired goals despite this fact.
• Dissipative structures and metabolism. In terms of their interaction with the environment, they can be characterised as dissipative structures [158], extracting their order at a thermodynamic cost to the environment via metabolic processes that extract material and energy from the environment, transform them to usable form, utilise them for functional purposes, and dispose of waste products and heat.
• Use of information to shape outcomes. All life inherits information, collects it by various sensory systems, analyses it and stores it, and uses it to determine desirable outcomes [143] [72]. Modern technology is centrally based in information collection, storage, and analysis via digital computers so as to make optimal choices [7] [43].

3.1.2. Symmetry, Broken Symmetry, Topology

From a physics viewpoint, what underlies emergence, in addition to coarse graining, is one of three features:

• Symmetry, such as gauge groups [97] that characterise the basic physics itself, and in many cases symmetries characterising emergent structures [28], for example crystal symmetries leading to Bloch’s Theorem and related emergent properties.
• Broken symmetries. More complex emergence is based in broken symmetries, as pointed out by Anderson [5]. This is key inter alia to biological emergence through the immense complexity of macromolecular shape [111,112], and to technological emergence through the structure of transistors [67].
• Topological effects [120,174], which by nature are non-local: you cannot determine topology from local quantities without determining how they fit together at emergent scales. This occurs particularly in the case of topological insulators, feedback control loops, and physical and interaction networks.

3.1.3. Modular Hierarchical Structures, Multiple Realisability

Biological and technological, systems are modular hierarchical structures for very good reasons explained by Herbert Simon [169]. The basic principle is to break up a complex task into simple operations, design modules to carry out the simple operations, and then combine the outcomes to produce the desired result. This involves abstraction, labelling, information hiding and multiple realisability, as explained clearly by Booch et al [26]

• The modules are more tightly bound relative to the inter-module interactions, and generically have more rapid dynamical processes than those between modules.
• The modular structure comes into being by developmental processes (biology) or manufacturing (technology), and possibly by self-organisation in the right context where all the components in a contained space have the necessary nature.
• Upwards effects in the emergent structure take place by contextual coarse-graining or black boxing, depending on context.
• Downwards effects occur via interlevel time-dependent constraints on the one hand, and by higher levels creating, modifying, or deleting lower level elements on the other.
• Through these effects, new properties occur at every emergent level that were not present at lower levels. They are characterised by effective theories at each level [64,139] in terms of emergent variables appropriate to that level [5].
• Multiple realisability takes place whereby higher level functions or adaptations can be realised by many different configurations at lower levels [21,82,110]. This means that effective laws characterising functions at higher levels, such as homeostasis or natural selection in biology or a computation in a digital computer, cannot be described in any simple way at relevant lower levels (genes, molecules, electrons) because at that level they are characterised by billions of possible alternatives.

3.1.4. Function, Adaptation

The key difference between physics per se and both and biology and technology is that the latter centrally embody function and purpose at every emergent level in the hierarchy (Table 1) above the physical levels L0-L4 [67,71,90,128].

In order that they can successfully do so, they must

• Continually adapt to the environment in which they operate so that they can meet the challenges it represents, thus they must be Complex Adaptive Systems [13,93,193].
• This occurs through evolutionary processes whereby characteristics of a class of entities are determined by adaptive processes, as in the case of Darwinian evolution in biology [44,76] and in technological evolution [7]. In each case, branching dynamics takes place via selection of best outcomes from a set of alternatives
• This adaptation takes place consistently at every emergent level simultaneously; it has to do so in order that system functionality is maintained all the time.
• It also occurs through developmental processes [80,191], whereby individual entities come into being and then continually adapt to the environment on an ongoing basis.

3.1.5. Stability via Feedback Control

They must be stable under the kinds of perturbations they are likely to meet on an ongoing basis, and so must be homeostatic systems [89,127] (in the case of biology, the setpoints being determined through evolutionary processes) or cybernetic systems [9,188] (where the setpoints are either set by design, or are adjustable on an ongoing basis). Branching dynamics occurs via contextual use of information [72,143].

3.1.6. Causal Closure, Stochasticity

Because of the meshing together of upwards and downwards causation, causal closure involves the whole set of interacting levels [63,130]; any smaller set of levels will contain dynamic variables whose evolution is undefined. Because of this, every level of the emergent hierarchy (Table 1) adapts to context simultaneously during both evolutionary and developmental processes.

It is crucial that the vast numbers of components involved in a cell at the micro level are moving at high velocities and colliding millions of times a second, so molecular stochasticity is a key feature of biological dynamics at those levels [92,137]. Because of this, stochasticity provides freedom whereby lower levels can be adapted to higher level needs, thereby enabling the possibility of agency [141,142]. Lower level outcomes can be selected as needed from the myriad of options that occur every microsecond.

3.1.7. Interaction Networks

Networks are a key feature whereby simple interactions can combine to produce complex results. In biology they include,

• Metabolic networks [100,161,183],
• Gene regulatory networks [105,183]
• Their interactions with each other [85]
• Neural networks [95] [35]

These have come to be what they are through natural selection. In the case of technology, they include

• VLSI circuit boards with billions of components
• Artificial Neural Networks of many kinds, including networks underlying Artificial Intelligence and programs such as ChatGPT-4.
• The global Internet

the first two having arisen via very careful processes of design, and the third by a rather haphazard developmental process.

3.1.8. Emergent Agency

Agency occurs in all higher forms of life, characterised as any living thing with eyes, ears, feet, or wings (it may well occur in other simpler organisms, but we claim that in these cases it is indisputable: these are all organs associated with agency, so they are evidence it exists in these cases). According to Philip Ball [15],

“ The whole point about agency is that it can be versatile, adaptive and improvisational. Agency evolves precisely because living organisms are liable to encounter challenges that evolution itself is too slow to adapt to.”

That is why it has evolved [99,175]. Ball continues,

“What most distinguishes agents is that they have reasons for actions, which in turn elicit value judgements: a primitive notion of meaning” [15]

It involves predictive processing of possible outcomes via contextual use of information, enabling obtaining desired out comes as contexts change. Agency also occurs also in high level technological systems, such as automatic pilots in aircraft, self-driving cars, and automated factories, which make contextual choices as to what to do next.

Characteristics of agency are stated by Potter and Mitchell [155] as shown in Table 2, where we have for convenience renumbered these items.

Table 2.  The elements of agency: a comparison of [155] and this paper. 

Table 2.  The elements of agency: a comparison of [155] and this paper. 

	Potter and Mitchell [155]	This paper
1	Thermodynamic autonomy	Metabolism
2	Persistence	Homeostasis
3	Holistic integration,	Hierarchy
4	Multiple realisability	Multiple realisability
5	Low-level indeterminacy	Low-level indeterminacy
6	Historicity	Memory
7	Endogenous activity	Endogenous activity
8	Agent-level normativity	Value judgements

These are essentially the characteristics we have emphasized above for both living systems and technology. There is a close correspondence between them, highlighting the properties needed for agency to emerge.

Number 7 is what makes it agency, the others are what are required for it to occur. There are different levels of endogenous activity in that cybernetic systems will attain set goals G reliably, but a higher level of goal-seeking occurs if the goals G in a cybernetic system are themselves selected in an adaptive way according to some selection criteria $C_1$, and a yet higher level if the selection criteria $C_1$ themselves are selected according to even higher selection criteria $C_2$ [58].

Number 8 emphasizes that agency is always connected with function associated with some purpose (see [67] for the case of digital computers). Low-level indeterminacy, emphasized above in §3.1.5 in the case of biology, occurs also in all technological systems because of the Shot Noise that arises because of the discrete nature of the charges carried by electrons or holes. Reliable outcomes emerge in the technological case because of thresholds associated with coarse graining.

4. Cognitive Limits of Materialism and the Irreducibility of Life and Consciousness

• Cartesian dualism (which would not allow any unitary synthesis between matter and spirit),
• Reductionist materialism (which would claim to reduce the mind to material principles),
• Explicit theism, which would introduce a transcendent agent to explain life and consciousness from outside nature,
• Subjectivist idealism, which would lead everything back to the spirit by considering matter as pure appearance.
• Panpsychism, with an attempt to develop a scientific theory of awareness already present at the quantum level, connected to an emergent psycho-physical hypothesis where the mental is closely connected to physical complexity; this could explain the development required for natural selection, although the mystery of this emergence would remain.

• Physical emergence holds from levels L1 to L3;
• Chemical emergence occurs at level L4;
• Biological emergence from level L5 up, with the first level with all the functions of life being L7
• something completely new occurs at level L10, namely agency; in the case of humans: consciousness, self-consciousness, and the ability for meta-reflection and so morality and responsibility.

5. Conclusion

“Parisi explains why reporters who were scratching their heads about how to explain spin glasses were missing the point of his research. His work isn’t about this system or that – a specific metal alloy, or the flocks of starlings in Rome that Parisi studied as a complex system in the 2000s. It’s about the universality of phenomena, whereby systems of many interacting components that look utterly different – be they flocks of starlings, groups of particles or the magnetic atoms in spin glasses – can be described using the same mathematics.

The fact that you can do so isn’t because there is a loose analogy between these systems but because they are all, at root, the same (collective) thing.”

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