Владислав Педдер – Processual Pessimism. On the Nature of Cosmic Suffering and Human Nothingness (страница 6)

Parallel to this, the theory of nonlinear dynamics and deterministic chaos developed. Concepts such as strange attractors, bifurcations, multistability, and self-organized criticality emerged. These research directions provided tools for measuring the scale-structure of systems via power laws, autocorrelations, and fractal dimension, and for modelling how simple local rules generate complex global patterns. To disclose the idea of a fractal basis for determinism it is sufficient merely to point to these terms without delving into their technical definitions. Fractal determinism takes these empirical and formal results and builds from them a new ontology of causality.

The first fundamental mechanism of fractal causality is feedback. Any action alters the environment, and the altered environment acts back upon the source of change. This cycle repeats, and through repetition a stable direction of change is formed. A classic instance of feedback is the river channel. The flow of water alters the bank; the altered bank changes the current; the current again acts on the bank. Gradually a stable form emerges, although no single act was precomputed or predetermined by an external force. The form of the channel is the result of continuous interaction between flow and bank, where each state is determined by the previous one and determines the next.

Such cyclical causality dissolves the classical distinction between cause and effect as separate, sequential events. In fractal determinism cause and effect merge into a continuous process of mutual determination. The river-and-its-channel is a single process in which the division into active and passive, forming and formed, is conditional and depends on the viewpoint. This principle applies to any system. Neural networks in the brain are shaped by experience, yet the formed networks determine what experience will be perceived and how it will be integrated. Social institutions are created by people, but then the institutions shape the people who recreate them. Economic systems are produced by individuals’ decisions, but those systems define the space of possible decisions.

The second mechanism of fractal causality is threshold response. Not every perturbation triggers a process of development. To move from an insignificant state to a noticeable one, the cumulative effect must cross a certain threshold. Below the threshold perturbations are damped by the system; above it a rapid redistribution begins, often cascading in character. This property explains why many changes appear random and unpredictable. A system can accumulate tension for a long time without visible change, then suddenly transition to a new state. The concept of self-organized criticality, formulated by Per Bak, Chao Tang, and Kurt Wiesenfeld, describes systems that naturally evolve toward a critical state in which the smallest disturbance can trigger an avalanche of any size. Example: a sandpile onto which grains are slowly dropped. Most grains provoke minor readjustments, but occasionally avalanches of varying scale occur, whose distribution obeys a power law. The system reaches the critical state by itself without external tuning of parameters. This implies that many natural and social systems constantly reside on the edge between stability and chaos, where the accumulation of imperceptible changes can suddenly produce dramatic reorganization.

Earthquakes, wildfires, mass extinctions, stock-market crashes, and social revolutions all display the same fractal structure in the distribution of events by scale. The frequency of events is inversely proportional to their magnitude according to a power law. This means that small events occur very often, medium events less frequently, and large events rarely – yet all are manifestations of the same process. There is no principled distinction between small and large events, between normality and catastrophe. A catastrophe is a rare but lawful fluctuation of a system that resides in a critical state.

The third mechanism of fractal causality is spatial transmission of change. When something happens in a system, its effect is felt not only at the immediate locus but also in neighbouring regions. Change propagates from one part to another as a chain of causes in which the outcome of the first step becomes the beginning of the second. If a patch of ground becomes saturated, water runs downhill and alters the moisture of adjacent patches. If pressure falls in one part of the atmosphere, air moves and changes pressure elsewhere. If an infection spreads, infected individuals contact susceptibles and transmit the pathogen.

A key parameter here is the connectivity of the system. A dense, highly branched network of links facilitates propagation of a process over considerable distances from its point of origin. If connectivity is weak or sparse, the process dies out. Thus a local event can gradually grow into a global change because the perturbation is transmitted step by step through contacting elements. Epidemics spread along networks of social contacts. Financial crises propagate through chains of debt and interdependence. In all these cases the structure of connections determines the dynamics of the process.

The fourth mechanism of fractal causality is historical dependence. Any change leaves consequences: it alters form, distribution, conditions, or behaviour of elements. These consequences do not vanish but enter the current conditions, becoming part of the context for subsequent processes. Therefore the same impact produces different effects at different times because the environment has already been modified by past events. Soil scorched by fire absorbs moisture differently and supports different vegetation. A society that has passed through crisis responds differently to risk and uncertainty. An organism that has recovered from infection acquires immunity or chronic damage.

The concept of path dependence, developed in economic history and evolutionary economics, describes how past decisions constrain future possibilities. For example, the QWERTY keyboard layout persisted through historical contingency11, reinforced by market mechanisms rather than by optimality: its wide adoption created an infrastructure of training and production that made switching to alternative layouts uneconomical. Technological standards, institutional structures, and cultural norms display the same inertia. Once established, they become self-sustaining, even when the original causes of their emergence have disappeared.

Path dependence differs radically from linear determination. In linear determinism the past determines the future through a continuous chain of causes. In fractal determinism the past determines the future through accumulated structure – through the context in which current processes unfold. Evolutionary biology illustrates this with special clarity. Organisms carry in their structure the traces of the entire history of life on Earth. Each adaptation is overlaid upon preceding structures, modifying them but not cancelling them. Hence evolution does not proceed toward an optimum but wanders across a landscape of possibilities, where every step is constrained not only by present conditions but by the whole prior trajectory.

The fifth and most fundamental mechanism of fractal causality is scale invariance, or self-similarity. This is the property whereby the same processes repeat across different scales. Small and large obey the same rules: change produces a response, the response alters conditions, and the cycle repeats. The difference is only in size and energy, not in the principle of organization. Thus microscopic processes, for example turbulence in a droplet, develop according to the same logic as large atmospheric vortices. In economics this is especially striking: short-term price fluctuations are structured the same way as long-term trends, as Mandelbrot demonstrated in his studies of financial time series.

Fractality means that the form of behaviour is preserved when the scale of observation is increased or decreased. Only the level at which it manifests changes, not the structure of the process. This is a deep property of natural systems that went long unnoticed because traditional science focused on characteristic scales and sought specific laws for each level of organization. The fractal approach shows that many systems lack a characteristic scale. They are self-similar across scales, from the microscopic to the macroscopic.

Power laws, which describe the distribution of events by magnitude, are the mathematical expression of scale invariance. If the probability of an event is inversely proportional to its magnitude to some exponent, then changing the measurement scale preserves the shape of the distribution. This contrasts with the normal distribution, which involves a characteristic scale (a mean) and where deviations from the mean decrease exponentially. In systems governed by power laws there is no typical event: small, medium, and large occurrences form parts of a single continuum.