Updated 20 September1998
In modern physics, primarily exploring ôvery unbalanced conditionsö and chaotic systems, there is a technical term - ôLyapunov time.ö It designates a period, when a certain process (physical, mechanical, quantum, or even biological) moves beyond the bounds of precise (or probabalistic) predictability and enters a chaotic mode. In other words, the tajectory of the process is subordinate to strict laws only up to a certain moment in real time. Beyond this moment, ônormalö time ends and paradoxical ôLyapunov timeö (or, more precisely, ôpositive Lyapunov timeö) takes over. The characteristics of this ôtimeö are very curious. Unlike usual physico-mechanical time, which is regarded in classical physics as an essentialy reversible quantity (this means that time is nothing else but a static axis, adding a fouth dimension to three-dimensional space; refer to the educational Einstein model), ôLyapunov timeö flows irreversibly, only in one direction, and, consequently, consists not of a once-and-for-all defined trajectory (in four-dimensional space), but of ôevents,ö completely unpredicatable movements, which are arbitrary, accidental, irregular. Processes that occur during ôLyapunov time,ö are called chaotic in contrast to processes in classical mechanics.
This can be illustrated with an example from everyday life. For instance, three people are drinking. Until a certain moment, their behavior is quite predictable: they discuss aquaintances, friends, personal problems, sports, women, politics. Gradually, as the level of intoxication increases, ônoisesö (this is how modern physics calls insubstantial interferences in the flow of the process)begin to creep into the conversation. These ônoisesö may be expressed in that certain passages are repeated by drunken people several times, the psychological conditions become tense, arguments and conflicts erupt, the general atmosphere tightens up. At a certain moment, conditions reach the point of bifurcation (this is a key term in the ôcatastrophe theoryö of the well-known physicist Rene Tom). This means that the logic of behavior of the drunken trio as a whole, and of each of its members separately, can arbitrarily take one of two trajectories of equal probability. For example, two of them go to sleep, and the third goes home. Or, one assaults another with fists, while the third calms them down. Or, all three move into the street and scuffle with passers-by over trifle matters. Or, all peacefuly disperse and come back to their families with a guilty conscience.
When everybody gets together to drink, the final result of the booze-up is not known. Up to a certain point, the situation is subordinate to a limited number of psychological factors, varying depending on the cultural and intellectual level of the drunks. But, whatever the preconditions, if the drinking spree progresses, sooner or later the point of bifurcation is reached, and the group unnoticeably enters into ôLyapunov time,ö where all proportions are eroded, where a minute detail may cause an inadequately massive reaction, where every following action is completely unpredictable and lacks motive.
But what is most interesting is that ôLyapunov timeö is not a period of complete disorder, where all movements are absolutely arbitrary. It is something in the middle between a fully structured system and a complete absence of a system. Scraps of trajectories remain, drunk behavior is subordinated to fragments of logical-psychological determined strings. Chaos has its paradoxical structure, which is called ôphysics of unintegrated processesö or ôsystem of fractal attractors.ö Consequently, ôLyapunov timeö is subject to a certain paradoxical measurement, only more flexible and widely understood than determinism of ôintegrated systemsö (in other words, ordinary classical and quantum trajectories). Some contemporary physicists - in particular Ilya Prigogine, believe that processes flowing in ôpositive Lyapunov timeö are the key to the mystery of life. Here, in this transitional state, between strict structure and complete absence of structure, in a chaotic system lies the ômagicö combination of law and freedom, model and event, determination and spontaneity, and it is this combination that is called ôlife.ö
A purely logical, rational model, as shown by Kant, is not capable of ôgraspingöan object in itself, gist of reality, which always remains inaccessible and noumenal. The ônoumenonö itself keeps complele silence. Only in chaotic worlds, during ôLyapunov time,ö occurs the secret transition from silence to speech, from existence to nonexistence, from rational to irrational, and in reverse.
Amazing, but the ideas of Prigogine and other theoreticians of ôunitegrated processesö strictly concur with traditional doctrines of alchemy, holding that the ôPhilosopherĺs Stoneö can be found in a ôparticle of ancient chaos,ö which the creator neglected during creation! This is the ôphilosophersĺ magnesia,ö ôour Cibela,ö ôour Latona.ö
ôLyapunov timeö is a very important concept on two isomorphic levels - individual spiritual realization and social transformations. For an individual, trying to find its true center, ôLyapunov timeö means cultivation of borderline states, between fresh daytime consciousness and nightly (alcoholic, narcotic, etc.) fainting. Only on this brink is it possible to grasp the magical, spectral point, where individual existence borders with extraindividual realities - of infracorporal, as well as purely angelic character. This is the essence of the machanism of initiation. ôLyapunov timeö is a phase of ôinitiational death.ö One who is able to take control of this ôbottleneck,ö goes over the brink of fatal dualism life-death. On the social level - an analogous picture. Every regime, social arrangement, economic-political formation is subordinate to strctly determinational laws, embodied in the power structure, its ideology, its internal standards. But social energy, like any energy in the corporal universe, diminishes in one direction, ôproduces entropy.ö That is why any regime and any social formation function logically and according to laws only for a limited period. After a certain moment, ôLyapunov timeö arrives. Like a group of drunks, upon reaching a certain boundary, society starts to behave unpredictably, chaotically. The peripheral grows to giant proportions, central, axial moves to the margin.
Unquestionably, ôLyapunov timeö began for the USSR in 1985. The current president (note, ôunpredictableö!) is a typical example of a ôparticleö of a chaotic system. In front of our eyes, a new liberal system is born from the ôdissipating remainsö of late degenerate socialism. But it, too, grows older, its entropy increasing terribly fast, it begins to, amazingly, to the details, remind us of last phases of the Soviet society. It cannot be ruled out that the liberal cycle will be very transient, since some systems are, in principle, not viable (in certain conditions).
Another important aspect: the phase of collapse of Sovietism occured with complete intellectual passivity of major players. In other words, there is no social organism, which could ôgraspö the main content of social ôLyapunov timeö in our situation and put this precious knowledge in the basis of a new social order. It appears that everybody slept through the most interesting events. But initiational death is different from ordinary death in that consciousness is not lost completely (being preserved in a special regime). Chaos must be not only outlived, but interpreted. If this does not occur, repetition of chaos is inevitable. Another catastrophe, another phase of social changes, yet another chord of the ôdissipative leap.ö More than that, this will repete (with a faster rhythme) until some social formation takes on the responsibility for a dangerous and exciting scientific and practical work with chaotic structures.
Contemporary ôstabilityö and ôsteadinessö are even more ghostly and deceiving, than the last days of Sovdep (and return to the past is unrealistic).
Our society today - is as much an incorporeal mirage, as the self-confident idiocy of the contemporary man in the street. But we know that ôLyapunov timeö is our time. That is why, the hand is stretching for...(no, not to what you were thinking, yet) books by Poincare, Kolmogorov, Stengers, Tom, Prigogine, Capra, Nichols, Mandelbrot, and other interesting authors.
To our universal doctrine of Revolution, apart from heritage of ôNew Rightö and ôNew Left,ö we add the theories of ônew physicists.ö
Translated by Victor Olevich