Paradigms
Our minds are filled with concepts. Templates for conceptual organization are paradigms. It is not that paradigms are in any sense “true” – no more than concepts are anything but convenient fictions. Instead, our minds strike a pose with paradigms and we come to believe that they are true because they are useful. So, we perceive that Nature follows patterns which couple time and space to produce systematic confluences of dynamic and domain which can be concisely conceptualized. Hence, the world before us appears comprehensible.
Systems
One of the basic assumptions of general systems theory embraces the concept of order – an expression of man’s general need for imagining his world as an ordered cosmos within an unordered chaos. ~ Swedish systems theorist Lars Skyttner
Existence appears ordered into systems. A system is a set of interdependent or interacting components that are considered an integral whole. It is the connections or interactions of components within that determine a system’s salient characteristics. Properties emerge from the connections themselves. A clock provides a measure of time; something none of its individual parts can.
A system is a theoretical incarnation of a tensor network. The relations between components in a system are as significant, if not more so, than the components themselves.
Biology is replete with synergies. Proteins interact with each other to form complex modules and express functionality that they individually are incapable of.
Hierarchy is inherent in all systems. While modules themselves may express emergent properties, their connective arrangements produce further novel synergies.
In appreciating that coherent patterns of energy underlie every appearance of physicality, each body constitutes a system. Perception is a system, in bringing order to disparate, disorganized inputs.
Systems are not confined to phenomena. Skills and beliefs are synergistic thought systems, built through conceptualization, which itself is a system.
The hierarchy of systems is endless. The proximate ecologies of bodies produce ecosystems with their own characteristics and dynamics. Thus, all systems are ultimately entangled, with emergent properties at every level.
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Constructal law construes the relation between form and function – the evolution of tangible systems. Gyres revolve around dynamic interactions in systems. Self-organized criticality comes into play when cause and effect come a cropper to threaten and disrupt systems. All involve the appearance of causality.
Causality
Causality lies at the interface between quantum mechanics and general relativity. ~ Austrian theoretical physicist Caslav Brukner
One event occurs, and another after it. The two are related or not; coincidence or cause and effect. Sussing circumstance is the mind’s constant entertainment.
Causality is considered a philosophical concept but it is also an ever-present issue in physics, chemistry, and biology, where its interpretation forms the foundation of science.
Causation can be of many kinds. They form our ways of ordering our scientific understanding of the world, all the way from the reductive concept of cause as elementary objects exerting forces on each other, through to the more holistic concept of attractors toward which whole systems move, and to adaptive selection taking place in the context of an ecosystem. ~ South African logician George Ellis et al
Reductionism is the philosophical stance that even complex systems are simply the sum of their parts. An accounting of a reductionist system may be made solely by reference to its individual constituents.
It is difficult enough understanding something in isolation; comprehending ecology or a dynamic system is practically impossible. Hence, empirical science is inherently reductionist in its approach. Science embraces a methodology of simplification.
There are no reductionist systems in Nature. Hence, the simplification inherent in science is prone to false conclusions, biased by the limits of our perception and mentation.
Emergence embraces ways in which systems and patterns stem from a multiplicity of relatively simple interactions. Emergence is a top-down causality: a perspective of a larger order arising from atomic actions.
Emergence is reductionist only if a dynamic system can be accounted for by a tally of its constituents. That is never the instance.
If something is more than the sum of its parts, its coming into being is emergent but not reductionist. In this case, a cascade of cause and effect create more than the individual reactions involved would produce. Such is life, the ambient world, and the cosmos.
Interactions may occur at the same scale. Otherwise, in sussing the ultimate source of an action, order of incitement determines whether causality is bottom-up or top-down.
To perceive a flow from micro to macro scale is bottom-up. To instead sense a larger force working smaller bits is top-down: a teleology.
You, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behaviour of a vast assembly of nerve cells and their associated molecules. ~ English biologist Francis Crick
If, as Crick claimed, behavior is bottom-up, one cannot assign causality to intermediates. The causal originator would not be nerve cells or their minion molecules, but the fundamental building blocks of matter.
Neuroscientists believe that neurons do indeed do real work. This is only possible if they act to channel and control the flow of electrons in neural axons – that is, if top-down causation takes place from the neuron to the electron level. ~ George Ellis
To admit that matter complexes – intermediates – determine events is to confess that the door of causality swings both ways. If all is bottom-up, quantum interactions determine everything that goes on.
There a serious problem arises when it comes to causality. Uncertainty pervades the quantum world, including the sequence of events. The best that can be done is to consider correlation a surrogate for cause.
The weirdness of quantum mechanics means that events can happen without a set order. ~ Australian quantum physicist Jacqui Romero
If quantum mechanics governs all phenomena, the order of events could be indefinite. ~ quantum physicist Fabio Costa
Evolution is a process where environmental interaction shapes genetic modification. Its causality is top-down.
As an example of causality, vision is blurry. At first glance, it may seem that photons strike light receptors that lead to mental integration of perceived patterns: a bottom-up approach. Instead, what is in view is mostly mental anticipation. We mostly see what we expect to see: top-down.
Top-down causality belabors the imagination to conceive of the emanating force; which is to say that coherence is at play in having events go a certain way.
Implicit in top-down causality is determinism: the doctrine that all events exemplify natural laws. The idea of scientific determinism led to Laplace’s demon.
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes. ~ Pierre-Simon Laplace in 1814
Laplace’s demon bears more than passing resemblance to the acts of God espoused by sects of Protestant Christians who consider predeterminism de rigueur and free will illusory.
Scientifically, Laplace’s demon was presumed banished by developments in thermodynamics, particularly process irreversibility as exemplified by entropy. But the demon dodged this bullet because of time’s one-way arrow: cause and effect and reversibility are coincidental. Going back in time is irrelevant.
Determinism is damned by chaos theory, which proposes divergent outcomes from an initial condition in dynamic systems, where distributed causality reigns. Entanglement of events makes pinpointing initial cause practically impossible.
The butterfly effect, an example of chaos theory, illustrates distributed causality. The butterfly effect occurs when a small variation at a relatively small scale produces large perturbations in the behavior of a nonlinear system through a cascade of changes. The butterfly effect stems from a sensitive dependence on initial conditions. American meteorologist Edward Lorenz coined the term butterfly effect in 1963 from his study of weather patterns.
We attribute experienced event sequences as having cause and effect. This ambient sense of causality helps us understand how the world operates, and so anticipate events by their harbingers. In contrast, the energy of the universe is interwoven; an entanglement that renders causality a casualty of chaotic complexity. When it comes to causality, what works locally falters globally.
Constructal Law
The Constructal Law is a universal tendency toward design in Nature, in the physics of everything. This tendency occurs because all of Nature is composed of flow systems that change and evolve their configurations over time so that they flow more easily, to create greater access to the currents they move. ~ Romanian American mechanical engineer Adrian Bejan
Constructal law states that flow favors the path of least resistance. Any system, whether inanimate or alive, evolves to optimize efficient transport.
Constructal law is a tenet of all design and evolution in Nature. It holds that form arises to facilitate flow. Essentially, constructal law is a statement of energy economy shaping structure.
Tree structures – from lightning bolts to circulatory systems – are ubiquitous because they optimize the flow of energy or material from source to destination. (The concept of destination involves a teleology when actions have an intended end. Lightning, for instance, seeks an outlet of discharge.) Alternately, as with plants, a tree structure affords ideal access flow – of sunlight and air.
The essential properties of water create the affinity for drops to coalesce and flow together in following gravity. So, streams flow into rivers, which invariably lead to the sea. The flow is more than mere topography.
Constructal law can be construed as a patterning mechanism for gyres. Constructal law is as readily applied to optimizing the arrangement of cells and organs as it is to cosmological components, from planets and star systems to galactic structures.
Constructal law also applies to economic and social systems, providing the basis for viewing exploitative corruption as a natural tendency: that wealth accumulation, and sustained poverty, are Nature’s way of just desserts.
Nested hierarchical networks of systems are pervasive: from cells to ecosystems to social interactions. Hierarchies afford optimization of communication and controlled energy flow.
Both biological evolution and cultural evolution operate under a number of deep constraints. The majority of webs display a balance between integration of multiple signals and control over multiple targets under a bow-tie structural pattern. ~ Adrian Corominas-Murtra et al
In a bow-tie structure, a diversity of inputs (fan-in) are processed via a limited set of protocols, with various resultant outputs (fan out). Bow-tie architectures often appear in complex and self-organizing systems ranging from biology to technology. Bow ties provide heterogeneous stimulus-response via orderly processing. In operation, bow ties often mediate tradeoffs between efficiency and robustness.
Constructal design applies at every scale. Hence, constructal law stipulates a hierarchy of coherence at every level of existence.
For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it. ~ Adrian Bejan
Gyres
Most systems in Nature are not in equilibrium; they exchange fluxes of matter or energy with their surroundings or undergo chemical reactions. ~ French physicist Jacques Prost & French biophysicist Jean-Francois Rupprecht
In the 5th century BCE, Greek philosopher Leucippus developed a theory of atomism. Less than a century later, Greek philosopher Democritus posited vortex motion as a law of Nature.
Copernicus’s cosmic heliocentric model had a gyre flavor. In the mid-17th century, French philosopher René Descartes proposed planetary motion as occurring in whorls. At the smallest scale, Descartes declared that no empty space could exist, and so it must be filled with matter, in vortices of aether.
A conceptual convolution that kept coming around, the notion of gyres as explaining fundamental physical dynamics kept reappearing. Lord Kelvin’s Vortex Theory had atoms swirling about in an aether soup. Maxwell used the gyre in formulating different theories of electromagnetism. Feynman correctly predicted quantum vortices in 1955.
In 2011, American microbiologist Erik Andrulis reintroduced the gyre as a paradigmatic framework for understanding the basic mechanics of Nature at every scale, from quantum to organic to cosmic.
The gyre appears, a posteriori, to be a prime candidate for a core model of natural systems. ~ Erik Andrulis
A gyre is a vortex that forms a system interacting with its environment. A gyre is characterized by its structure, qualities, thermodynamics, and interactions.
A gyre’s core is the position about which its matter and energy revolve. The shape of the swirl about a core may be various: spherical, conically cylindrical, or disk-like.
Gyres possess chirality: a handedness or certain direction. Chiral gyres may be observed at the quantum level, in various organic molecular structures, and at the galactic level. DNA is a chiral helix. Chirality is significant in several facets of biology.
Andrulis attributes organic qualities to gyres, including spontaneous self-organization, and a life cycle which originates when conditions are favorable. As an interacting thermodynamic entity, a gyre consumes matter and energy and exudes it in turn. A gyre selectively attracts and repels. If it can, a gyre self-regulates, adjusting itself to an internal balance (homeostasis).
Any cycle that exists in Nature – in physical, chemical, or biological systems – may be viewed as a gyre. ~ Erik Andrulis
Unlike the physical models preferred by physicists, gyres are inherently nondeterministic in their reliance upon environmental interaction; hence, not given to modeling, though facets of a gyre can be mathematically characterized. There are too many variables flowing in vortex behavior for a gyre to be entirely predictable. Mathematically, any set of equations with more than 3 independent variables yields unpredictable results.
Self-Organized Criticality
Consider a collection of electrons, or a pile of sand grains, a bucket of fluid, an elastic network of springs, an ecosystem, or the community of stock-market dealers. Each of these systems consists of many components that interact through some kind of exchange of forces or information… Is there some simplifying mechanism that produces a typical behavior shared by large classes of systems? ~ Dutch economist Henrik Jensen
Self-organized criticality (SOC) is a property of dynamic systems where a threshold exists that when passed sets off a substantial reaction. In having a critical point that unleashes a cascade consequence, SOC demonstrates the butterfly effect.
Self-organized criticality showed itself to researchers who looked at growing piles of rice grains in 1995 experiments at the University of Oslo (Norway). A rice pile was made by dropping grains of rice one on top of another.
In long-grained rice, SOC was shown by a single dropped grain triggering a sudden avalanche. Just before, the rice pile had reached a stationary critical state: stable, but on edge. That grain that launched an avalanche was the proverbial straw that broke the camel’s back.
In a pile of short-grain rice, with a smaller aspect ratio than longer grain, SOC was not apparent. Thus, SOC is sensitive to system features. Systems with SOC tend to be slowly driven, without fixed equilibrium, but extended degrees of freedom, and are highly nonlinear.
Avalanches of snow show SOC. Layers inside snow form a fragile network of ice grains with lots of space in between. Some arrangements are an avalanche waiting to happen.
A key element of SOC involves power-law distributions. When the frequency of an event varies as a power of some attribute of the system, the frequency follows a power law, which is a consistent mathematical relationship between system attributes or behaviors. A growing rice pile follows a power law by having far fewer large avalanches than small ones.
SOC is scale-invariant: the laws that apply to a system’s behaviors are not dependent on system size. SOC systems have a fractal aspect, of self-similarity in dynamic regardless of scale.
Another intrinsic facet of systems subject to self-organized criticality is interdependence: one feature dynamic may affect another. Whereas SOC is an observation about a system, interdependence is the inherent nature from which SOC arises. A cascade event can only occur because a system possesses interlocked features. Whereas the degrees of freedom a system has characterizes its malleability, interdependence creates conducive conditions by which a critical point may be exceeded via feedback loops.
Physics, geology, biology, and sociology are all entrenched with SOC systems. In a vast variety of contexts, complexity in structures and behaviors emerge from roots bound by relatively simple rules, however difficult discerning those rules may be. Self-organized criticality pervades Nature in myriad forms, as well as in complex man-made systems, such as economics and politics.
While prediction is an elusive oracle to find, mathematical models can give insights into the workings of SOC systems by correlating crucial factors, which can give a rough idea as to how close a system may be to a tipping point. Critical points are often presaged by behavioral changes that indicate a phase shift coming.
Stable systems tend to quickly recover after minor turbulences. There is a robustness that tends to equilibrium: homeostasis in organisms or biological systems/populations. Recovery is engendered by intrinsic compensatory mechanisms awakened by feedback. But exceeding criticality in multiple facets can result in systemic stress, where recovery becomes problematic.
Animal social groups are complex systems that are likely to exhibit tipping points – which are defined as drastic shifts in the dynamics of systems that arise from small changes in environmental conditions. ~ American ecologist Jonathan Pruitt et al
Species populations can experience catastrophic collapse in response to small changes in environmental conditions. Recovery can prove impossible.
A notable example of self-organized criticality in Nature is overfishing: the collapse of sardine stocks in California and Japan in the late 1940s, and Canadian cod in the 1990s. At low population densities, group dynamics falter. Difficulty in finding mates, and the breakdown of cooperative behaviors, such as forming schools for hunting or predator avoidance, can preclude recovery.
SOC in ecosystems is often broad-based, as populations of different species interrelate in a network of interactions, most obviously the local food web.
Climate change often leads to local extinctions and declines by influencing interactions between species, such as reducing prey populations for predators. These shifting interactions may make even small climatic changes dangerous for the survival of plant and animal species. ~ American ecologist John Wiens
Symmetry
A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before. ~ Hermann Weyl
Aristotle argued that the stars were pasted on celestial spheres which moved in circular orbits. He was wrong, but the assumption behind the idea pervades physics: symmetry.
Through meticulous observation in the early 17th century, German astronomer Johannes Kepler discovered the elliptical orbits of planets about the Sun, albeit moving at varying speeds: faster closer in, slower further out. Yet all balances out. An imaginary line connecting planets to the Sun traces out equal areas in equal times: what is now called the conservation of angular momentum.
Newton explained why this happens with his universal law of gravitation; a behavior grounded in symmetry: the force of gravity acting equally in all directions. Einstein’s refinement of gravity was also founded upon a symmetry: the equivalence principle.
The cosmological principle and all of physics’ conservation laws are built upon an assumption of symmetry within a closed system; something for which, in both instances (symmetry and system), there is no evidence.
In the 1960s, theoretical physicists Sheldon Lee Glashow, Abdus Salam, and Steven Weinberg independently discovered that they could unify electromagnetism with the weak force through a symmetry which became a keystone of quantum physics’ Standard Model. But that Standard Model is reliant on violation of symmetry, not on its adherence. Breaking electroweak symmetry produced a prediction of the Higgs boson, which was discovered nearly a half-century later.
In producing quantum color charges, the symmetry of the strong force is what makes particles of matter possible. Yet all particles in Nature exist in colorless states: effectively white. Such equanimity breaks symmetry.
Symmetry underlies causality: that an action produces a reaction. Newton’s 3rd law of motion – of equal and opposite reaction – applies as much to psychology and politics as it does to physics. Yet such symmetry is belied by the butterfly effect, from which great movement may be had from the most minuscule initial fluttering.
Chemistry is rife with butterfly effects and other asymmetries. Handedness plays a vital role in molecular interactions and associations. All organic molecules are chiral. Life depends upon asymmetry.
The basic laws of physics supposedly do not vary over time or space. Forces emanate with energetic equanimity. Yet such equality is not the story of existence.
Symmetry may give order to the universe, but breaking it is essential to anything happening. With matter ruling the roost, spacetime is defined by distortion – such is the gravity of the situation in Nature.
