Η FRACTAL ΚΟΣΜΟΛΟΓΙΑ ΤΟΥ ΦΙΛΟΣΟΦΟΥ ΑΝΑΞΑΓΟΡΑ

August 8, 2007 at 3:11 pm (Uncategorized) ()

THE CONCEPT OF FRACTAL COSMOS: ANAXAGORAS COSMOLOGY

http://saj.matf.bg.ac.yu/163/pdf/021-034.pdf

Πρόκειται για μια μελέτη του Ινστιτούτου Φυσικής του Βελιγραδίου σχετικά με την κοσμολογία του Αναξαγόρα. Η περίπτωση του φυσικού φιλοσόφου Αναξαγόρα είναι άξια μελέτης γιατί εκτός από το ότι ήταν ένας προσωκρατικός και ασωκρατικός φυσικός φιλόσοφος, επιπλέον διώχθηκε για τις διδασκαλίες του και δικάστηκε επί αθεΐα από τους τότε ταλιμπάν της αρχαίας Αθήνας. Φυσικά ούτε τα βιβλία ΠΕΡΙ ΦΥΣΕΩΣ του Αναξαγόρα έχουν σωθεί και έχουμε μόνο έμμεσες αναφορές του έργου και αφού έχουν περάσει από 100 κόσκινα και πηγές όπως ο Αέτιος και ο Ευσέβιος. Επιπλέον μεταξύ των βλακειών που διαδίδουν κάποιοι είναι και αυτές οι σαχλαμάρες: http://hieratic.astrologicon.org/anaxagoras.htm

“Μετα το θανατο του, εμφανιστηκαν (στη μικρα Ασια) οι λεγομενοι Αναξαγοριτες. Πιστευαν οτι ολα ειναι προκαθορισμενα, ματαια και οτι καμια τους πραξη δεν ειχε σημασια ……………. Οι Αναξαγοριτες επιδιδονταν δε σε ακραιες πραξεις οπως φονους και κατοπιν πτωματοφαγια. Πιστευαν οτι μετα το θανατο, φευγει μια αυλη υποσταση η οποια επιστρεφει στον νου, ενω η υπολοιπη ενεργεια μενει στο σωμα, και οτι μπορουσαν οι ιδιοι να την λαβουν τρωγοντας το (σημειωση: μια φημη στους σημερινους εσωτερικους κυκλους θελει καποιους να προσπάθησαν να φανε το σωμα γνωστης δολοφονηθεισας πριγκηπισσας, πριν απο λιγα χρονια)”

Σαχλαμάρες δηλαδή για να συσκοτισθεί η επιστημονικότητα και ο ενισμός των φυσικών φιλοσόφων τους οποίους κυνήγησαν οι ιδεαλιστές.Ένα κομμάτι της μελέτης για την κοσμολογία των ατομικών φιλοσόφων:

It has been widely accepted that the atomistic teachings of Leucippus and Democritus was conceived as a response to the Eleatic school. For our subject the most relevant philosopher of Elea was Zeno and two of his antinomies. The first we mention is his assertion that the plurality as a notion appears incomprehensible to human mind. It includes the question of (in)divisibility of objects, which appears pertinent to both the Abderian and Anaxagoras’ solutions. The second is the Stadium aporia, which denies the possibility of motion, basing its argumentation on the continuous structure of the space and time. The latter antinomy will be shown relevant to an interpretation of the kinematics that Anaxagoras’ differentiation of the primordial cosmic matter implies and will be discussed in the next Chapter. Here we analyse briefly the question of the (in)divisibility, regarding either purely mathematical or material objects, which appears relevant to both Anaxagoras and Abderians. From Parmenides, whose radical monism rejected even a possibility to consider non-existence (on epistemological grounds), to Zeno, whose aporias may be interpreted to be construed in order to discourage any attempt to criticize his teacher on rational grounds. In one of his antinomies concerning the (im)possibility of plurality Zeno states: ”(i) If there are many things, it is necessary they are as many as they are,…But if they are as many as they are, they will be limited [in size]. (ii) If there are many things, the things that are unlimited, for there are always others between the things that are, and again others between those. And thus the things that are are unlimited.” As with other Zeno’s aporias, it is not clear whether by things mathematical objects are meant only, or they refer (also) to material objects. This antinomy is quite intelligible if one restricts himself to densely packed sets, with cardinal number of the continuum, in modern parlance. In fact, all Zeno’s paradoxes may be interpreted as mere transcription of properties of mathematical objects into the material world. In any case, later thinkers understood them to refer to the latter. The thesis that there exists only One has been challenged by atomists by postulating a number of binary divisions, in a sort of a (extending) chain diversifications. The primary division is that of the overall reality into two elements (στoιχ_ια): full (πληρ_ς, matter) and nothing (κ_νoν, void), the latter by following Melissus.Void was conceived as a limiting case of rarefication of something, with the air as paradigm. In the final analysis void reduces to the (modern) notion of space, emptiness, but its existence was thought by ancient thinkers as (epistemologically) independent of something, i.e. not conceived as a negation of the latter. In the modern (positivistic) analogue, vacuum, the concept of nothingness appears as elusive as it was in ancient times. The existence of nothing is not only contradictio in adjecto, but may be considered an empty notion both in ontological and epistemological sense. In the former aspect, we have evidence that massless fields, like the gravitational one, penetrate any part of the space (or, in a stronger sense, even create the latter), whereas the assertion that a part of a space contains absolutely nothing is not a scientific statement, in Popperian sense. As the next step Leucippus conceived the material world as appearing on two levels, microcosmos and macrocosmos. The first level of this binary multiplication scheme consists of indivisible objects, atoms, which by their aggregation form macroscopic, everyday reality. Atoms are thus embedded into void, and move freely in it. As for the indivisibility (or indestructibility) of these elementary entities, one should note that this property does not imply atoms must necessarily be deprived of any (internal) structure. Modern physics knows many instances where an ”elementary particle”, like neutron, is endowedwith internal structure, more precisely, may be conceived to contain a number of other ”elementary particles”, like quarks, for instance. The latter may be unobservable from the point of view of the same theoretical model to which quarks owe their existence. This analogy has, of course, a limited significance, however, since the notion of destruction (or division) has different meaning today from the simple mechanical picture of the ancient, due, mainly, to the mass-energy equivalence. Atoms share the same property of unobservability with the void, but unlike the latter can not be deprived of the logical consistency. They appear unobservable due to their smallness, which makes them exist beyond our perception. Abderians conceived the universe as consisting of a plurality of worlds (cosmoses), formed by innumerable atoms, the latter being also of any conceivable shape. This property, however, moves atoms further from the concept of pure element, in the traditional sense of α_. By assuming a morphological, as well as in respect to the magnitude, unrestrained plurality, the elegant picture of the original idea is much lost. Such atoms resemble our concept of organic molecules, rather than modern atoms themselves. The structure of atom fits better our notion of elementary particle, like electrons, protons, mesons, etc. Another point of interest here is the mechanism of world creation as conceined by Leucippus (and presumably Democritus) (KRS, p. 17). Leucippus holds that the whole is infinite ”… part of it is full and part void… The worlds come into being as follows. Many bodies of all sorts of shapes move ’by abscission from the infinite’ into a great void; they come together there and produce a single whirl, in which, colliding with one another and revolving in all manners of ways, they begin to separate, like to like. But when their multitude prevents them from rotating any longer in equilibrium, those that are fine go out towards surrounding void as if sifted, while the rest ’abide together’ and, becoming entangled, unite their motions and make a first spherical structure. This structure stands apart like a ’membrane’ which contains in itself all sorts of bodies; and as they whirl around owing to the resistance of the middle, the surrounding membrane becomes thin, while contigous atoms keep flowing together owing to contact with the whirl. So the earth came into being, the atoms that had been borne to the middle abiding together there. Again, the containing membrane is itself increased, owing to the attraction of bodies outside; as it moves around in the whirl it takes in anything it touches. Some of these bodies that get entangled form a structure that is at first moist and muddy, but as they revolve with the whirl of the whole they dry out and then ignite to form the substance of the heavenly bodies.” If atoms constitute primordial cosmogonical material, the concept of whirl appears the primitive construct of the initial cosmic kinematics. From the modern perspective it is not clear what sets atoms into this sort of motion, in the absence of any concept of (universal) mutual attraction and interaction at distance in general. The vortex as a primordial motion was needed to explain the celestial kinematics, which was circular. But the whirl appears an archetype which goes beyond such a rational explanation. We meet this picture in the ancient mythology, like that beautiful tale of Eurinome and the serpent Ophion emerging from the Chaos in the form of a whirl (Graves, 1966). Vortex appears the only sort of motion that can create a structure out of chaotic matter. It is not the most primitive kind of motion, the translational one being simpler. But the circular movement is an absolute motion, unlike the translational one, owing to the homogeneity of the chaotic matter, which is tantamount to the homogeneity of space in modern parlance. The circular motion is observable from any (inertial) reference frame, and thus may be regarded as a (stationary) structure. It is interesting here to note that experiments with superfluid helium have reproduced vortex structures that simulate kinematics of modern cosmogonical models. The concept of membrane is also significant for a modern physical morphology. It implies a sort of ring around the bulk of the matter, with the latter attributed to Earth. The ring augments by ”attracting” (κατατην_π_κρισιν) the objects from outside, but the term ”collect” would better describe the process. Abderians assumed a many-world universe. Democritus holds the same view as Leucippus about the elements, full and void (see KRS, p. 418) ”… he spoke as if the things that are were in constant motion in the void; and there are innumerable worlds, which differ in size. In some worlds there is no sun and moon, in others they are larger than in our world, and in still others they are more numerous. The intervals between the worlds are unequal; in some parts there are more worlds, in other fewer; some are increasing, some at their height, some decreasing; in some parts they are arising, in others they are missing. They are destroyed by collision one with the other. There are some worlds devoid of living creatures or plants or any moisture.” The idea of many-worlds universe was not exclusively Abderian property and was in the air at the time. This may be regarded as an enormous endeavour of the human mind, that can not be overestimated. Conceptually, it implied a jump from finite to infinite, psychologically a turn from anthropocentrism to a true cosmopolitism (more exactly universalism). With the risk to succumb to Whigish concept of history, it is tempting to ascribe to a number of above assertions corresponding modern interpretations. Which worlds Democritus might have thought of? According to the quoted literal testimony, the most appropriate candidates for those ”worlds” are galaxies, which fit best the above description, both with regard to their transient lives and variable separations. In particular the possibility of the worlds collisions appears interesting from the point of view of the modern observational evidence. But such a conjecture would hold only if one could ascribe to Abderians a heliocentric system, instead of then reigning geocentric picture of our planetary system. To them, sun and moon followed the same kinematics and were to be treated on the same footing, apart from the difference in brightness. Hence, Democritus could conceive a planetary system without sun (ie a central star), which in our time would be impossible to do. Anyway, the ancients had no reason to conceive the MilkyWay as a three-dimensional celestial structure, instead of two-dimensional star distribution over the celestial sphere. It will come only with the advent of telescope that Kant could afford to speculate on the extragalactic nature of the then observed, ”nebulae” (Kant 1755). The speculation that the worlds are scattered with unequal density within the universe appears interesting in view of Anaxagoras’ ideas, as we shall discuss later on. It is all the more interesting since this goes, at first sight, against the principle of isonomy, which implies, among other things, the homogeneity of the space. On the other hand, isonomy postulates equivalence of all possible variations, in the absence of acceptablerestrictions on the mutual distances, shapes and contents of ”other worlds”. It seems that Democritus was not satisfied with the infinite universe as a collection of world replicas, but insisted of diversity, as a necessary prerequisite of plurality. The latter, in its turn, was to complete the entire concept of universe, which ought to be infinite both in quantitative and qualitative terms. In fact, his concept of atomic shape and magnitude diversity points in the same direction. Democritus’ universe appears a three-level entity. The first, fundamental level belongs to atoms, sibility of nesting one cosmos into another, i.e. formation of a fractal cosmos. There is no possibility of under- and over-structure, no hypercosmos unless one allows for an internal, hidden structure within atoms, still indestructible, as is the case of hadrons in modern high energy physics, whose constituents, like quarks and gluons, appear beyond the reach of a direct experience. To summ up, Abderians conceived an infinite universe, both in respect of spacetime and matter content. Out of these infinities, as well as of the infinite diversity of atoms regarding their shapes and magnitudes, arose an infinite collection of (different) worlds, scattered all over the universe, in a random manner. The worlds further come into being and disappear, like living creatures. It is the latter analogy that justifies the maxim of many Greek philosophers that microcosmos is equivalent to macrocosmos. And it is this thesis only that resembles, albeit in a rudimentary form, the principle of selfsimilarity, that was the central dogma of Anaxagoras.

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