Extralogical Complexity Part 1: The Nonlinearity of Nature

 

For an environment to evolve into something like Nature, Nature can’t be what people think. 

 

As discussed in other posts, vertebrate cognition’s need to make comprehensible and motivating models of reality leads to a host of fallacies and illusions about Nature, the World, and human beings (see summary intro). Linear change—constant, predictable change characterized by bell curves and straight lines--is too weak to account for the self-organizing, adaptive powers of Nature. Nor can change occur to accommodate neat, satisfying explanations, where initiating events always lead to proportional outcomes (at least outside of people’s cognitively biased minds). This treatise shows the true dynamics of change, which gives rise to the characteristic phenomena of Complex systems theory presented in the upcoming part two.  

 

You’ve heard “the balance of Nature,” “balance in the Force,” and the like. This is almost exactly what Nature isn’t. Some say it’s chaos or disorder. While common, disorder and mathematical chaos don’t characterize Nature, either. Between balance and disorder, there is dynamism. To host life, an environment must persist “out-of-equilibrium” yet maintain recurrent structure. 

 

ER defines a living thing as a system that maintains its approximate identity by persisting in a periodic-like process, especially within a less ordered environment. This includes constituents of other large systems/networks like industries and economies. For a system to qualify as biological life, it must, among other things, organize and consume energy while persisting out of thermal equilibrium with its surroundings. Life forms are, in other words, oases of periodic order. 

 

Within the life-hosting environment, energies and forces must flow, and flows require thermal, electric, and mechanical gradients--or imbalances. Too little disorder also doesn’t give the hosting environment enough shocks to force it to adapt, to evolve. But it shouldn’t be disordered, either; otherwise, oases of periodic-like order don’t have sufficient time to evolve. You need recurrences, emergences of species and their specimen, businesses and industries. You need recurrent patterns—seasons and geochemical, migration, business, and market cycles, which are often entrained or synced. Since these patterns include periods of suboptimal conditions, they give life-hosting environments antifragility--robustness and adaptability--but they remain predictable enough to avoid readily dismantling the environment (antifragility from Nassim Taleb).   

 

Above all, the environment must readily give rise to self-amplification or self-reinforcing feedback: Occurrences, phenomena, and patterns that reinforce and reproduce themselves, which can bootstrap themselves into existence and out of crises. And this can’t happen where change is linear and constant, in environments characterized by bell/Gaussian distributions. Only in places dominated by multiplicative or nonlinear change, environments characterized by power laws and “fat-tail” distributions, can you have life as humanity knows it (to simplify, nonlinear change is change in ever-growing quantities). 

     

 

Preferential Attachment

 

Nonlinearity frequently manifests when a small disparity in ability leads to a much greater disparity in success. A slightly better product leads to more return customers; more return customers lead to more word-of-mouth; more word-of-mouth leads to a social trend; more profits lead to new investments and products, stores, and, perhaps, other businesses and/or public companies. And “success begets success” as readily in Nature as it does in business. If a specimen is slightly better fit than another and survives, it can potentially have far more decedents, which applies to everything from animals, plants, bacteria, viruses, to single strands of self-replicating genetic material. 

 

The formal term for success begetting success is preferential attachment, and it accounts for “hubs” within a network, constituents with an unusual number of connections/interactions. A prolific flower, whether a specimen or species, will initially attract pollinators by smell or sight. Pollinators tend to return to the same sites. Conspecifics (members of the same species) and heterospecific pollinators (different species) often follow, decreasing parity in success and disproportionally increasing heterospecific interactions. The socially successful not only tend to be better at making friends, but also have more chances to them due to meeting more people. A slightly more fit predator species has disproportionality larger population growth and, therefore, disproportional expansion, increasing heterospecific encounters and, thus, interactions. This type of propagation occurs in “normal” periods as well as in crises.      

 

Social giants are society’s hubs. Throughout the country, people are connected by an average of six degrees of separation, with a single degree being the friend of friend. In Earth’s biosphere, species are connected by ten degrees. Resulting from their nonlinear propagation, connections are unevenly scaled, leading to disparity. Disparity ensures that at least a few constituents are strong enough to survive most crises, increasing an ecosystem’s antifragility. At the same time, excessive hub-orientation can lead to nonlinear runaway extinctions. As confirmed by Complexity experiments, cataclysmic events, like asteroid collisions or hyperactive volcanos, aren’t required. Nor are the economic equivalents required for economic crashes. 

 

Belief propagation in society can work this way if each person convinces more than one person on average. Since they’re composed of entangled packages in an interconnected network, propagation in a personal pool of beliefs is similar. Personal and societal belief propagation may be comparable with information cascades, as well (see Ubiquity by Marc Buchcanan). Everyone has at least some tendency to conform--some more, some less, some different. A conformity threshold is the number of people that need to conform to a given behavior (e.g., a riot, the purchase of a new product) before a given person succumbs. A person with a threshold of one conforms after the first person conforms; a person with five succumbs after five conform. This has resulted in entirely unexpected behavior, such as riots. Of course, cascades aren’t completely reliable because the absence of a single threshold at the wrong time can stop the trend dead in its tracks. Information cascades, unsurprisingly, tend to be accelerative: begin slowly, increase at an ever-increasing rate, slow down, then end quickly. 

 

But it’s more than this. Take a system of five variables, say the constituents of an ecosystem. Since how two constituents interact can be influenced by others they interact with, they can undergo up to 26 interactions. When a new species is dragged into the ecosystem, you add just one variable, but you get a total of 57 possible interactions. Add another, you get 120. 10 is over a thousand; 20 is over a million; 30 gives you over a billion. It’s true that if general interdependences become too high, the system will veer toward acting as a single entity, but even if a fraction of these possible interactions occur, interactions will still vastly outweigh the number of variables. This heightens network activity, further empowering feedback and self-amplification. 

 

The perpetual change of numerous related variables and subnetworks acted upon multiplicatively leads to positive and negative amplification and reinforcement, including self. ER calls this Complex feedback and Complex causation, producing effects that vastly exceed initiating events. Thanks to Complex causation, small “causes,” like the flap of a butterfly’s wings, lead to large effects, and preventing small causes prevents large effects. This is the self-amplification that life requires. It allows a lot to manifest from little, including during crises that create opportunities.

 

In extralogical Complexity:

Network flux, the birth and death of fragile parts that the force of self-organization acts upon, is modeled as random variation and is sometimes called the “lifeblood” of systems; Complex causation, which acts upon network flux, is modeled as natural selection; and Complex feedback, resulting from the dance between the latter two, is evolution. This makes evolution and Nature nonlinear phenomena. 

 

The laws of causality and energy conservation still apply, of course, just as the flap of the butterfly wings would be better described as a trigger. Complex causation means that “small” planned or unplanned events—human, environmental, animal, institutional, etc.—can have unexpectedly “larger” consequences. Physical laws are satisfied only after accounting for intermediary events, ones unlikely to be ascertained for accounting. Complex causation and feedback can merge with other feedback; mutual dependencies develop; and feedback loops stabilize--resulting in organized self-perpetuating phenomena. 

 

From this comes sensitivity to perturbations and initial conditions, and, therefore, intractability and minimal predictability. Because initial conditions are so sensitive, so isn’t the precision and quantity of information necessary to predict large systems/networks, which put to shame any hypothetical human database. But since networks obey certain laws—economic, biological, ecological, etc.--and maintain their approximate identities for extended periods, they do have guess-ability. Complex causation contradicts the intuitive view of causation: Assumed proportionality in cause and effect is part of the causation bias, the assumption of satisfactory explanations.

 

The result: 

Scaling relationships, exponential formulas such as power laws, relationships between the frequency of magnitude of events like earthquakes, extinctions, and economic crashes; power law distributions like Pareto’s law of the distribution of wealth; exponentially scaled connections between constituents of large systems/networks such as connectivity and interactions between species and businesses. Power laws emerge in computational experiments exactly as they do in the real World. 

 

Most importantly, Complex causation and feedback are the sources of the self-organization and synergy of Complex networks--the Complex system. This will be introduced in part two.