1/1/13 Fabulous Fractals & the Future? Carl Sagan on the "Pale Blue Dot"

Fractals - The Colors Of Infinity (1 of 6 series)
Magnificent and inspiring, fractals can be 'read' for the future in opposite ways: evidence of changeless circularity; or evidence of motion and change. Matter is endlessly divisible and changing according to the scientific 'law of contradiction, nothing is predetermined, permanently circular. Motion and change are based on the dynamic unity and struggle of opposites'. The emergence and resolution of contradictions is the basis of all existence, in nature, society and human thought. We are capable of consciously 'grasping' and acting on ideas reflecting external reality to change seeming powerlessness over reality and the future. In an overly-simple nutshell, Marxist dialectical materialism in theory and practice is a revolutionary weapon. Also a counterrevolutionary weapon used under bogus pretexts by oppressors & opponents of liberation to distort, revile and attack what most threatens their predatory, and doomed, domination.

Introduction to Contribution To The Critique Of Hegel's Philosophy Of Right, Karl Marx, 1843-44
The profane existence of error is discredited after its heavenly oratio pro aris et focis has been disproved. Man, who looked for a superhuman being in the fantastic reality of heaven and found nothing there but the reflection of himself, will no longer be disposed to find but the semblance of himself, only an inhuman being, where he seeks and must seek his true reality.
The basis of irreligious criticism is: Man makes religion, religion does not make man. Religion is the self-consciousness and self-esteem of man who has either not yet found himself or has already lost himself again. But man is no abstract being encamped outside the world. Man is the world of man, the state, society. This state, this society, produce religion, an inverted world-consciousness, because they are an inverted world. Religion is the general theory of that world, its encyclopaedic compendium, its logic in a popular form, its spiritualistic point d'honneur, its enthusiasm, its moral sanction, its solemn complement, its universal source of consolation and justification. It is the fantastic realisation of the human essence because the human essence has no true reality. The struggle against religion is therefore indirectly a fight against the world of which religion is the spiritual aroma.
Religious distress is at the same time the expression of real distress and also the protest against real distress. Religion is the sigh of the oppressed creature, the heart of a heartless world, just as it is the spirit of spiritless conditions. It is the opium of the people.... The criticism of religion is therefore in embryo the criticism of the vale of tears, the halo of which is religion.
Criticism has torn the imaginary flowers from the chain not so man shall wear the unadorned, bleak chain, but so he will shake off the chain and pluck the living flower. The criticism of religion disillusions man to make him think and act and shape his reality like a man who has been disillusioned and has come to reason, so that he will revolve round himself and therefore round his true sun. Religion is only the illusory sun which revolves round man as long as he does not revolve round himself.

The task of history, therefore, once the world beyond the truth has disappeared, is to establish the truth of this world. The immediate task of philosophy at the service of history, once the holy form of human self-estrangement has been unmasked, is to unmask self-estrangement in its unholy forms. Thus the criticism of heaven turns into the criticism of the earth, the criticism of religion into the criticism of law and the criticism of theology into the criticism of politics..... The weapon of criticism cannot, of course, replace criticism by weapons, material force must be overthrown by material force; but theory also becomes a material force as soon as it has gripped the masses. Theory is capable of gripping the masses as it demonstrates ad hominem, and it demonstrates ad hominem as soon as it becomes radical. To be radical is to grasp the root of the matter...The criticism of religion ends with... man is the highest being for man, hence with the categorical imperative to overthrow all relations in which man is a debased, enslaved, despicable essence, relations which cannot be better described than by the cry of a Frenchman when it was planned to introduce a tax on dogs: Poor dogs! They want to treat you as human beings! ...Will the theoretical needs be immediate practical needs? It is not enough for thought to strive for realization, reality must itself strive towards thought.

Dialectics of Nature, Frederick Engels 1883
"Motion in the most general sense, conceived as the mode of existence, the inherent attribute, of matter, comprehends all changes and processes occurring in the universe, from mere change of place right up to thinking. The investigation of the nature of motion had as a matter of course to start from the lowest, simplest forms of this motion and to learn to grasp these before it could achieve anything in the way of explanation of the higher and more complicated forms."

[To know] whether the future caput mortuum of our solar system will once again be converted into the raw material of a new solar system... either we must have recourse to a creator, or we are forced to the conclusion that ...the incandescent raw material of the solar system of our universe was produced in a natural way by transformations of motion, nature inherent in moving matter, and the conditions of which therefore also must be reproduced by matter, even if only after millions and millions of years, and more or less by chance, but with the necessity that is also inherent in chance. The possibility of such a transformation is more and more being conceded. The view is being arrived at that the heavenly bodies are ultimately destined to fall into one another, and one even calculates the amount of heat which must be developed on such collisions. The sudden flaring up of new stars, and the equally sudden increase in brightness of familiar ones, of which we are informed by astronomy, is most easily explained by such collisions. Not only does our group of planets move about the sun, and our sun within our island universe, but our whole island universe also moves in space in temporary, relative equilibrium with the other island universes, for even the relative equilibrium of freely moving bodies can only exist where the motion is reciprocally determined; and it is assumed by many that the temperature in space is not everywhere the same. Finally, we know that, with the exception of an infinitesimal portion, the heat of the innumerable suns of our island universe vanishes into space and fails to raise the temperature of space even by a millionth of a degree centigrade. What becomes of all this enormous quantity of heat? Is it for ever dissipated in the attempt to heat universal space, has it ceased to exist practically, and does it only continue to exist theoretically, in the fact that universal space has become warmer by a decimal fraction of a degree beginning with ten or more noughts? The indestructibility of motion forbids such an assumption, but it allows the possibility that by the successive falling into one another of the bodies of the universe all existing mechanical motion will be converted into heat and the latter radiated into space, so that in spite of all "indestructibility of force" all motion in general would have ceased. (Incidentally it is seen here how inaccurate is the term "indestructibility of force" instead of "indestructibility of motion.") Hence we arrive at the conclusion that in some way which it will be the task of scientific research to demonstrate, the heat radiated into space must become transformed into another form of motion, in which it can once more be stored up and rendered active. Thereby the chief difficulty in the way of the reconversion of extinct suns into incandescent vapour disappears. For the rest, the eternally repeated succession of worlds in infinite time is only the logical complement to the co-existence of innumerable worlds in infinite space - a principle the necessity of which has forced itself even on the anti-theoretical Yankee brain... matter moves in a cycle that certainly only completes its orbit in periods of time for which our terrestrial year is no adequate measure, a cycle in which the time of highest development, the time of organic life and still more that of the life of beings conscious of nature and of themselves, is just as narrowly restricted as the space in which life and self-consciousness come into operation; a cycle in which every finite mode of existence of matter, whether it be sun or nebular vapour, single animal or genus of animals, chemical combination or dissociation, is equally transient, and wherein nothing is eternal but eternally changing, eternally moving matter and the laws according to which it moves and changes...

Could the universality of fractals in nature be a consequence of the dialectics of nature?
Olbers' paradox - the question of why the night sky is not bright... If matter and hence time and space are infinite then the universe has already passed though an infinite number of states. Several of those states, an infinite number in fact, must also have had stars and galaxies that produced light. Following this line of thought, any event that has happened must in fact already have happened before, an infinite number of times, in an infinite number of places, and will happen again. Here we've stumbled into a trap: history is pre-determined and we have no free will.... the contradiction of infinity philosophers and mathematicians have grappled with for thousands of years, from Zeno the Greek to the present day. A simple solution is to deny that the universe has existed for an infinite amount of time, as mainstream cosmologists have done... In another part of the physics department... physicists also faced the contradiction of infinity but with more success than the cosmologists. Through computer simulations these physicists have been able to show that complex non-linear systems - and a universe of infinite extent is a good candidate - can evolve and change for an infinite period of time without ever repeating. The earth's weather, for example, never repeats exactly. It is impossible to predict but it is not random; effect follows cause in every part of the system and in theory for infinite time. As it changes it can come close to states it has been in before; over an infinite period of time it may come infinitesimally close, but it will never repeat. Physicists draw diagrams of “phase space” to analyse this behaviour. These are graphs that show the different states the system goes through; the path that the system goes along in phase space describes how the system is changing over time. In complex systems the patterns made by these paths are fractals - there is more and more detail at finer and finer scales. The system may come infinitesimally close to a position in phase space that it has been at previously but it will never come to exactly the same position. The universe can evolve for an infinite period of time but it will never repeat. History is not pre-determined, and is not determined mechanically at all, but is determined dialectically as a result of the many interactions between earth's billions of inhabitants. But it is not random; the underlying process, development of production and relations of production, now constrained and held back by the capitalism... pushes society forward in the same way that the sun's energy drives the weather.

The idea that the paradox can be resolved by a fractal distribution of the stars is discussed by the mathematician Benoit Mandelbrot in his book “The Fractal Geometry of Nature”. Since Mandelbrot's work in the 1960's there has been an increasing awareness of how prevalent fractals are in nature, and in society. They can describe rock layers in the earth, leaves on trees, river beds, income distributions, even the coast of Britain. (A famous paper from Mandelbrot is titled “How long is the coast of Britain?”, and he concludes that because coastlines are fractal the coast of Britain is infinitely long. Having walked part of the coastal path I can believe it.)
If the stars and galaxies have fractal geometry we could expect clusters of galaxies, then clusters of clusters and so on. Similarly there would be voids in which there would be almost no stars or galaxies, some of which could come together to make bigger voids and then still bigger voids and so on. Mandelbrot points out that in that situation it is possible to find “a large proportion of directions that go to infinity without encountering any star”. So the sky will be dark at night. Plasma physicists say the scattering of light by plasma clouds causes the background radiation. Strictly speaking this is different from the subject of Olbers' paradox, which talks about light from stars and not light from scattering...Scattering by fractals (infinite scattering by infinite numbers of discontinuities at all scales) is a difficult topic and... only recently looked at in fields such as solid-state physics or geophysics where there are similar scattering problems. There does not seem to be anything in the scientific literature about Olbers' paradox and scattering by fractal clouds of plasma. Given the nature of fractals, it seems possible that a similar statement might apply in that case for the scattered light as for the direct light, but this is only a guess.
Possible support for the fractal idea... is that the universality of fractals in nature is a consequence of the dialectics of nature. The scaling behaviour of fractals in nature, which links processes at many different scales, a symptom of the underlying general laws of change and motion - the universality of the dialectical laws of change and development. Widely different processes can occur at different scales (the erosion of a small pebble from the sea-shore compared to the formation of bays and deltas), but a common geometry emerges because of the common dialectical behaviour. Take the rocks in a cliff face for example. From a kilometre away it is possible to see a number of rock layers, and walking towards the cliff more layers will become visible. But the pattern of the layering (which could be quantified using suitable measurements) is the same at all scales, from the very large scale when viewing the layering at a large distance down to the scale of a few millimetres when close-up. (This is a controversial subject amongst geologists but does appear to be supported by the evidence.)  How can this happen, when the small scale layering in the rocks was produced by completely different physical processes compared to the large layers? This is another example of the complex dynamical problems that physicists have begun to study in the last 20 years or so. What the physicists are finding is what Hegel discovered several centuries ago - that changes in nature occur according to the general dialectical laws of motion. The small layers in the cliff face might be caused by changes in sedimentation rates; tectonic processes might cause the larger layers. But these different processes all produce layering with similar patterns because all processes obey common dialectical laws of motion. Punctuated equilibria occur - at all scales. There is an accumulation of quantitative changes that produces sudden qualitative changes - at all scales. Necessity is expressed by chance - at all scales.  
A paragraph from the article “Crisis in Cosmology” mentions this:

“The reality of most physical phenomena is that there are many interlinked features, all of which interact. And increasingly physicists are beginning to find that it is the interaction that is more important than the details of the physical laws. Transitions occur that are determined by the complexity itself regardless of the details of the physics; this is why a fractal model can work over many scales and different physical mechanisms. The physical axioms and their deductions not only become inadequate, they become irrelevant. More general laws emerge - the dialectical laws of quantity and quality, of the union of opposites and the negation of the negation.”
There is now only limited evidence the universe may have a fractal structure. Time will tell.

Carl Sagan brings life, humanity & science alive - as he subtly at points contradicts his conservative host!
Extension 720 Classic: Carl Sagan in a discussion with Milton Rosenberg on space & beyond as outlined in his book, "Pale Blue Dot." (12/13/94)
Audio: http://media.wgnradio.com/media/mp3file/2011-04/wgn-x720-sagan_60676133....