toward the center of Tao

totally Tao

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

quite Tao

not - Tao

Complex Tao level 0: Synergetic Tao

In searching new methodologies for complex systems which could overcome the difficulties of the classical ones, at physical level 0  Hermann Haken has developed the Synergetics method (from greek "working together"), created in the 70s-80s years in the field of quantum laser theory, specifically to explain the coherence of the emitted radiation, namely how photons into the laser cavity interact all together in a spatio-temporal way to form the high coherence  characteristic of the output laser radiation.
The laser radiation has two peculiar characteristics: the first is its monochromaticity, that is the light emission has a narrow wavelength (one-colored), the second is its coherence, as clear to anyone have seen a laser beam.

While the former is easily explained in terms of electron transitions between higher energy levels to lower, producing a photon energy very definite, the second can not be explained by the characteristics of the emission of photons in the laser cavity, which should emit independently of each other, and then incoherently.

This application example clarifies some key concepts used in Synergetics in a qualitative way. In the gas lasers the emitting atoms are locked in a tube with the ends of the semi-reflective mirrors that act as resonator for the emitted light. The mirrors are designed in order to reflect light in the axial direction often enough so that the corresponding wave remains for a long time within the device and can interact strongly with the atoms through the phenomenon of stimulated emission.

The atoms are excited from the outside, eg by a light pump source. After being excited, each atom can spontaneously emit a trace of light. In the usual case of a lamp, these tracks of light are emitted independently of each other incoherently, and the amplitudes are distributed as a Gaussian. When the pump intensity is increased beyond a critical value, called laser threshold, where it starts the population inversion - or when there are more electrons in higher energy levels than on the fundamental - the current state gives way to a single wave with amplitude stability on which the fluctuations of small amplitude and phase overlap. The pump intensity acts as control parameter. At its critical value, the old state becomes unstable. The emerging coherent wave acts as a order parameter that through stimulated emission forces the electrons of the gas molecules to emit light in a coherent way. This action by the order parameter over single parts of the system has been called by Haken enslavement principle. In this case it can be seen that from 10¹⁸ degrees of freedom, in which any of the 10¹⁸ atoms in the cavity emit independently of each other, and therefore the total sum is incoherent, one switch to a single degree of freedom, the coherent laser mode over thresholdl. If the pump power is still increased may appear further instabilities and a variety of temporal patterns, but even spatio-temporal, such chaotic laser light or very short laser pulses. The laser threshold, where stimulated emission occurs, show typical characteristics of a phase transition of a system  out of thermal equilibrium, such critical damping, critical fluctuations and simmetry breaking.

The high laser coherence is therefore a cooperative effect of self-organization, and the synergetic method of the enslavement principle between order parameters and the  slaved subsystems gives the relationship between macroscopic and microscopic parameters of the complex system.

Haken has expanded in subsequent years the calculation model for synergetic to a range of disciplines from chemistry to biology to economics to the study of brain and cognitive sciences and, more generally, to any form of self-organization in complex systems that exhibit an emergent behavior. Synergetics therefore stands as a new authentic methodology to address Complexity.

 In the Haken words:

"The systems under experimental or theoretical consideration I sistemi in esame sperimentale o teorico are subject to control parameters which can be fixed from the external or generated in part from the system itself. An example for an external control parameter is the absorbed power in a gas laser by the injected electrical current. An example for a internal generated control parameter are the hormones in the human body or the neurotransmitters in the brain. When the control parameters reach some specific critical values the system may become instable and to adopt a new macroscopic state. Close to these instability points, a new set of collective variables may be identified: the order parameters. They have, at least generally, a low dimensional dynamic and characterized the macroscopic system. Since the cooperation of the single parts allows the existence of order parameters which in turn determine the bahavior of the individual partsi, we speak of circular causality. According to the enslavement principle, the order parameters determine the bahavior of the individual parts, the enslaved subsystems, which can be still subjected to fluctuations. At a critical point, a single order parameter may be subjected to a non-equilibrium transition phase (bifurcation), with simmetry breaking,  with a  slowing down of critical fluctuations. 
Synergetic ha several links to other disciplines, such complexity theory"

In general, the abused term synergy may indicate a cooperative effect of reinforcement/stabilization among different internal processes of the system, or among certain internal and other external to the system.

In the  figure, for example, the two recursive closed processe red e blue are coupled by a third process which may habe synergetic effects, making a new three processes set which may have different qualities from those of the individual processes.

 

top Tao is like down Tao

©2009 Hougaard Malan

small Tao beauty Tao

 

SOMETIMES SMALL IS BEAUTIFUL

Perhaps no variable brings the problems of being alive so vividly and clearly before the analyst's eye as does size. The elephant is afflicted with the problems of bigness; the shrew, with those of smallness. But for each, there is an optimum size. The elephant would not be better off if he were much smaller, nor would the shrew be relieved by being much bigger. We may say that each is addicted to the size that is.
There are purely physical problems of bigness or smallness, problems that affect the solar system, the bridge, and the wristwatch. But in addition to these, there are problems special to aggregates of living matter, whether these be single creatures or whole cities.
Let us first look at the physical. Problems of mechanical instability arise because, for example, the forces of gravity do not follow the same quantitative regularities as those of cohesion. A large clod of earth is easier to break by dropping it on the ground than is a small one. The glacier grows and therefore, partly melting and partly breaking, must begin a changed existence in the form of avalanches, smaller units that must fall off the larger matrix. Conversely, even in the physical universe, the very small may become unstable because the relation between surface area and weight is nonlinear. We break up any material which we wish to dissolve because the smaller pieces have a greater ratio of surface to volume and will therefore give more access to the solvent. The larger lumps will be the last to disappear. And so on.

 

To carry these thoughts over into the more complex world of living things, a fable may be offered:

THE TALE OF THE POLYPLOID HORSE

They say the Nobel people are still embarrassed when anybody mentions polyploid horses. Anyhow, Dr. P. U. Posif, the great Erewhonian geneticist, got his prize in the late 1980s for jiggling with the DNA of the common cart horse (Equus caballus). It was said that he made a great contribution to the then new science of transportology. At any rate, he got his prize for creating - no other word would be good enough for a piece of applied science so nearly usurping the role of deity - creating, I say, a horse precisely twice the size of the ordinary Clydesdale. It was twice as long, twice as high, and twice as thick. It was a polyploid, with four times the usual number of chromosomes.
P.U. Posif always claimed that there was a time, when this wonderful animal was still a colt, when it was able to stand on its four legs. A wonderful it must have been! But anyhow, by the time the horse was shown to the public and recorded with all the communicational devices of modern civilization, the horse was not doing any standing. In a word, it was too heavy. It weighed, of course, eight times as much as a normal Clydesdale.
For a public showing and for the media, Dr. Posif always insisted on turning off the hoses that were continuously necessary to keep the beast at normal mammalian temperature. But we were always afraid that the innermost parts would begin to cook. After all, the poor beast's skin and dermal fat were twice as thick as normal, and it surface area was only four times that of a normal horse, so it didn't cool properly.
Every morning, the horse had to be raised to its feet with the aid of a small crane and hung in a sort of box on wheels, in which it was suspended on springs, adjusted to take half its weigh off its legs.
Dr. Posif used to claim that the animal was outstandingly intelligent. It had, of course, eight times as much brain (by weight) as any other horse, but I could never see that it was concerned with any questions more complex than those which interest other horses. I had very little free time, what with one thing and another - always panting, partly to keep cool and partly to oxygenate its eight-times body. Its windpipe, after all, had only four times the normal area of cross section.
And then there was eating. Somehow it had to eat, every day, eight times the amount that would satisfy a normal horse and had to push all that food down an esophagus only four times the caliber of the normal. The blood vessels, too, were reduced in relative size, and this made circulation more difficult and put extra strain on the heart.
A sad beast.

The fable shows what inevitably happens when two or more variables, whose curves are discrepant, interact. That is what produces the interaction between change and tolerance. For instance, gradual growth in a population, whether of automobiles or of people, has no perceptible effect upon a transportation system until suddenly the threshold of tolerance is passed and the traffic jams. The changing of one variable exposes a critical value of the other.
Of all such cases, the best known today is the behavior of fissionable material in the atom bomb. The uranium occurs in nature and is continually undergoing fission, but no explosion occurs because no chain reaction is established. Each atom, as it breaks, gives off neutrons that, that if they hit another uranium atom, may cause fission, but many neutrons are merely lost. Unless the lump of uranium is of critical size, an average of less than one neutron from each fission will break another atom, and the chain will dwindle. If the lump is made bigger, a larger fraction of the neutrons will hit uranium atoms to cause fission. The process will then achieve positive exponential gain and become an explosion.
In the case of the imaginary horse, length, surface area, and volume (or mass) become discrepant because their curves of increase have mutually nonlinear characteristics. Surface varies as the square of length, volume varies as the cube of length, and surface varies as the 2/3 power of volume.
For the horse (and for all real creatures), the matter becomes more serious because to remain alive, many internal motions must be maintained. There is an internal logistics of blood, food, oxygen, and excretory products and a logistics of information in the form of neural and hormonal messages.
The harbor porpoise, which is about three feet long, with a jacket of blubber about one inch thick and a surface area of about six square feet, has a known heat budget that balances comfortably in Arctic waters. The heat budget of a big whale, which is about ten times the length of the porpoise (i.e. 1,000 times the volume and 100 times the surface), with a blubber jacket nearly twelve inches thick, is totally mysterious. Presumably, they have a superior logistic system moving blood through the dorsal fins and tail flukes, where all cetaceans get rid of heat.
The fact of growth adds another order of complexity to the problems of bigness in living things. Will growth alter the proportions of the organism? These problems of the limitation of growth are met in very different ways by different creatures.
A simple case is that of the palms, which do not adjust their girth to compensate for their height. An oak tree with growing tissue (cambium) between its wood, and its bark grows in length and width throughout its life. But a coconut palm, whose only growing tissue is the apex of the trunk (the so-called millionaire's salad, which can only be got at the price of killing the palm), simply gets taller and taller, with some slow increase of the bole at its base. For this organism, the limitation of height is simply a normal part of its adaptation of a niche. The sheer mechanical instability of excessive height without compensation in girth provides its normal way of death.
Many plants avoid (or solve?) these problems of the limitation of growth by linking their life-span to the calendar or to their own reproductive cycle. Annuals start a new generation each year, and plants like the so-called century plant (yucca) may live many years but, like the salmon, inevitably die when they reproduce. Except for multiple branching within the flowering head, the yucca makes no branches. The branching influorescence itself is its terminal stem; when that has completed its function, the plant dies. Its death is normal to its way of life.
Among some higher animals, growth is controlled. The creature reaches a size or age or stage at which growth simply stops (i.e., is stopped by chemical or other messages within the organization of the creature). The cells, under control, cease to grow and divide. When controls no longer operate (by failure to generate the message or failure to receive it), the result is cancer. Where do such messages originate, what triggers their sending, and in what presumably chemical code are these messages immanent? What controls the nearly perfect external bilateral symmetry of the mammalian body? We have remarkably
little knowledge of the message system that controls growth. There must be a whole interlocking system as yet scarcely studied.