Владислав Педдер – Processual Pessimism. On the Nature of Cosmic Suffering and Human Nothingness (страница 7)

The population distribution of cities, the distribution of incomes, the distribution of firm sizes, the distribution of citations of scientific papers, the distribution of solar flare intensities, and the distribution of earthquake magnitudes all exhibit power-law behaviour. This indicates that the processes generating these distributions are self-organizing and scale-invariant. There is no external regulator prescribing an optimal city or firm size. The system itself generates the entire hierarchy of scales through local interactions and feedback.

This assemblage of feedback, transmission of perturbations, path dependence, and self-similarity constitutes the essence of fractal determinism. It is not founded on a single originating cause as in the classical Laplacean approach, nor does it admit pure randomness as in indeterminism. Everything is subject to necessity, but that necessity is not one-dimensional: it is multilayered, recursive, and self-repeating.

A crucial consequence of fractal determinism is a reconsideration of the relation between quantum mechanics and the macroscopic world. In standard quantum mechanics the state of a particle in superposition is fundamentally probabilistic: the outcome of a measurement cannot be predicted even with full knowledge of the wave function. This appears to contradict determinism. However, the process by which an uncertain quantum state gives rise to a definite macroscopic outcome is described by the theory of decoherence, which proceeds in a fully deterministic manner.

Decoherence arises from the irreversible interaction of a quantum system with its environment. The environment consists of an enormous number of degrees of freedom – photons, air atoms, molecules of the measuring apparatus. These interactions cause a rapid suppression of the interference terms of the wave function, after which the system behaves as if it were in one of the classical states. Decoherence occurs extremely rapidly for macroscopic objects, on timescales on the order of 10⁻²⁰ seconds, which renders quantum superposition practically unobservable. Decoherence does not solve the measurement problem in quantum mechanics. It does not explain why one particular outcome is observed rather than another. That remains fundamentally random in the Copenhagen interpretation. However, decoherence explains why the macroscopic world appears classical and deterministic. Quantum uncertainty does not penetrate the macroscopic world not because quantum mechanics ceases to apply, but because interaction with the environment makes interference unobservable.

In nonlinear and chaotic systems, small quantum fluctuations at the initial stage can be exponentially amplified and lead to observable macroscopic differences in the final state. Here, however, it is necessary to distinguish predictability from determinism. A system can be deterministic – its state uniquely determined by initial conditions and laws of evolution – and yet unpredictable because of sensitivity to initial conditions. In chaotic systems the exponential divergence of trajectories makes long-term prediction impossible even with infinitely precise knowledge of initial conditions, since any finite precision will be exhausted in finite time.

Thus, although the outcome of an individual quantum event – for example, the decay of an atom – is regarded as fundamentally random, its macroscopic consequences can be deterministically predicted once decoherence has turned that outcome into a classical fact. Moreover, for ensembles of quantum events the probabilistic predictions of quantum mechanics become deterministic in the thermodynamic limit. The law of large numbers guarantees that fluctuations in relative frequency diminish as the number of events grows. Therefore macroscopic observables, which average over an enormous number of microscopic events, behave deterministically with precision beyond any practical means of measurement.

Fractal determinism integrates quantum randomness as one mechanism through which necessity is realised at the macroscopic level. But it does not cancel determinism, since macroscopic processes remain determined by decoherence and statistical averaging. Thus quantum mechanics is compatible with fractal determinism, even if it is incompatible with linear Laplacean determinism.

Weather systems exemplify fractal determinism with particular clarity. The atmosphere is a turbulent fluid governed by nonlinear hydrodynamic equations. These equations are deterministic but generate chaotic dynamics because of nonlinear interactions and feedbacks. Edward Lorenz demonstrated that even a simple model of atmospheric convection exhibits sensitivity to initial conditions, making long-term prediction impossible. The famous “butterfly effect,” according to which the flap of a butterfly’s wings can alter the weather weeks later, illustrates this sensitivity.

Unpredictability, however, does not imply absence of determinism. The atmosphere remains a deterministic system in which each state is uniquely determined by the previous one. Unpredictability arises from the impossibility of measuring initial conditions with infinite precision and from the exponential growth of errors. At the same time the atmosphere displays a fractal structure on all scales. vortices of every size interact with one another, transferring energy from large scales to small via the turbulence cascade. The distribution of energy across scales follows Kolmogorov’s power law, which is a signature of scale invariance.

Climatic patterns such as El Niño exhibit self-organized criticality. The ocean – atmosphere system accumulates heat in the western Pacific until a threshold is reached, after which heat is rapidly redistributed eastward. This event affects weather worldwide via teleconnections – atmospheric waves propagating thousands of kilometres. The frequency and intensity of El Niño events are not regular, but they conform to statistical regularities that reflect the fractal structure of the climate system.

Financial markets display the same fractal logic. Prices and volumes reflect the continual operation of feedbacks. Market participants’ actions alter liquidity and sentiment; this changes subsequent decisions, which in turn affect prices. Most trades do not alter the dynamics, but when volume coincides and accumulates, a single signal can trigger a chain reaction and evolve into a global change of trend. Market crashes are lawful, though rare, fluctuations of a system in a critical state. The market constantly balances on the edge between stability and chaos, where the accumulation of imperceptible changes can suddenly produce a reconfiguration and a consequent collapse or rally. Therefore markets cannot be predicted exactly, but the probability of large moves can be assessed from signs of concentration of volume and volatility.

The fractal structure of markets arises spontaneously from the interaction of many participants, each acting on limited information and private aims. The market self-organizes into a critical state without external parameter tuning. This demonstrates the universality of self-organizing mechanisms that operate in systems of different natures: physical, biological, economic, social.

All this composes the logic of fractal determinism. The world is not predetermined in the Laplacean sense. The future is not encoded in initial conditions as an explicit plan awaiting execution. Yet the world inevitably unfolds according to its own internal links, feedbacks, path-dependencies, and scale-invariances. Chance is not the opposite of necessity but a form of its manifestation. Any deviation is built into the overall web of causes as a lawful fluctuation of a self-organizing system.

The synergetic aspect appears here as continuous self-renewal and self-organization. The Cosmos, understood fractally, constantly reproduces its own differences and generates new forms from the interaction of already existing ones.

Thus everything that exists is not merely the result of external causes but an active mode of being participating in its own self-determination. Human beings, like any other systems, are links in a large recursive pattern in which inner and outer, cause and effect, subject and object cease to be rigid oppositions. A choice deemed “free” is the outcome of the most complex interaction of genetic, hormonal, neural, and environmental factors operating across multiple temporal scales. In sum, not only human behaviour but all processes in nature and society are the results of multilayered, recursive causality in which each event is determined by the system’s entire prior history and by the whole network of current interactions.

This perspective naturally leads to a form of cosmic fatalism. Everything happens as it can happen because other outcomes are impossible within the given configuration of causal links. Every possibility is already the realization of one of the fractal directions of a system’s development, and any deviation is a lawful consequence of internal interaction. This fatalism does not exclude novelty; on the contrary, it makes novelty a necessary effect of complex interactions. The new does not arise in spite of determinism; it is its direct manifestation, a form born of the interplay among many causal threads, folds, and irregularities of being.