Pink Noise - Leonid Korogodski [45]
In this light, the above-mentioned defining property of systems far from equilibrium means that many fields of science cannot be reduced to physics. Studying the behavior of dolphins can’t be done by deconstructing them into elementary particles, even if one has an infinite processing power to solve the equations.
This is also why there can be no single Theory of Everything.
COMPLEX NONLINEAR SYSTEMS AREN’T SOLVED EXACTLY—NOT even numerically, in many cases. As described in [18], T. Petrosky, one of Prigogine’s students, ran a computer simulation for a system with one star, a single planet, and a comet. He tried to predict the number of orbits the comet would make before being expelled from the system. If the initial coordinates and velocities were rounded to one part in a million, the answer was 757 orbits. If up to one part in ten million, it was 38 orbits; one part in a hundred million, 235 orbits; one part in 1016, 17 orbits. Yet different results could be obtained by different ways of rounding the intermediate results of calculations. Without absolute knowledge and infinite precision in calculation, the comet’s orbit was simply unpredictable. Yet no randomness was involved. The system operated under the deterministic laws of Newtonian mechanics.
This is an example of the deterministic chaos phenomenon, also known as the butterfly effect. As shown by Henri Poincaré (1854–1912), there always exist chaotic orbits in gravitational systems with more than two bodies. Chaotic orbits never pass the same location twice yet may approach it arbitrarily close. Therefore, even a slight deviation can make a huge difference later on.
The world may be deterministic, but it is not predictable.
DIGITAL SYSTEMS TOO CAN DEMONSTRATE VERY COMPLEX behavior (see [34], for example). Some are even NP-hard, which is a technical term meaning that there exists no better algorithm to predict the system’s state other than simply running it through its paces. But a faster system can simulate it sooner, thus predicting it. With complex analog systems exhibiting the butterfly effect, this is impossible in principle.
For the mathematically advanced reader: The spectra of the Hermitian operators representing the physical observables in quantum mechanics are discrete only in certain cases.
One can argue that the universe is actually not continuous but discrete in space and time, according to quantum mechanics. But this is incorrect, for only simple quantum systems are discrete. And only simple quantum systems are reversible in time. What we call the wave function collapse is the result of interaction between a simple quantum system and a complex nonlinear system, the observer. Therefore, the quantum system ceases to be simple—and ceases to be reversible.
Ilya Prigogine, thus, restored the arrow of time. No, it’s not true that time only appears to be irreversible, as some claim. It is just that our simple systems—our ideal, linear approximations to the much more complex, nonlinear reality—appear to be reversible. The real world is not.
BY THE VERY NATURE OF COMPLEX ADAPTIVE SYSTEMS, THEY experience events when a small quantitative change brings about qualitative changes of enormous magnitude. Moreover, this is bound to happen to any complex adaptive system, given time: the birth of a new species, cancer, epiphany, economic crisis, political revolution, and so on. In general, this is called