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20

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" ", EIE , , .

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ISBN: 960-7998-23-5 Copyright 2004, (EIE) : .: 210 72 73 501, Fax: 210 72 46 618, e-mail: [email protected] , : S&P ADVERTISING 154,114 71 .: 210 64 62 716, Fax: 210 64 52 570 e-mail: [email protected], www.spad.gr

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23

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24

, , ( ). . , , , , , , , (parity), . , , . , , (), (), , -, ... , , , , . , () . , , , , . G. . Hardy, A mathematician's apology, : (patterns) , , , . , (ugly) .

25

20

. . M. Dirac, 20 , [Proc. Roy. Irish Acad. 63A, 49-59 (1962-1963)], : ( ) Hamilton, ' . , . , S. Chandrasekhar (Physics Today, 1979, . 25) : dxe .32 sinh^x sinh 3+ g -*r }-2

_1 VV2*(+D* ( 1 + e-* y7 . ( 1 e''' v3 =

. (j

+ g -*, }-2

[j + ^-(2+1) ^

Michelangelo Giulano Lorenzo, , , . . , , M. C. Escher (1898-1971). , Escher (. 15). , . Escher, .

26

. 15. M.C. Escher () (1946), (6) Mbius (1963)

. Weyl, Symmetry, Princeton University Press, 1952. A. V. Shubnikov and V. A. Koptsik, Symmetry in Science and Art, Plenum Press, 1974. E. P. Wigner, Symmetries and Reflections, Indiana University Press, 1967. M. Gardner, The Amphidextrous Universe, Charles Scribner's and Sons, 1979.

The Graphic Work ofM. C. Escher, Ballantine Books, 1973.

27

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, WWW, , , , , , ( !) , - .*

() ( ).

* . . . : ' '' , . , , EIE : , 1993 .

29

20

(massive down-loading) . , () . (, , ), , . , (hardware and software) power laws, (fractals). , , . , , , ( ), fractal.

. L. Barabasi, Linked. The new science of networks, Perseus Publishing, 2002. M. Buchanan, Small world: uncovering nature's hidden networks, Widenfield and Nicholson, 2002. D. J. Watts, Small worlds: the dynamics of networks between order and randomness, Prinston University Press, 1999.

30

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abstraction, . . () , ' - , , . fractal (). fractal ( ) . . fractals, . ( , , , , , , , , ..) fractal , , fractal ( ) , . fractal ( ) : (.. ~ 0,11t ... ).

33

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: . . fractal , -.. - 2 3, . , () t. fractal tv (>1). , , fractal ( -). fractal : , fractal . () fractal . fractal , , . , [ fractal ~ 500 kg !, ( fractal )]. fractal , ,

34

( ) . . fractal , . fractal - fractal . . 15 , . () . Dr. Any Goldberger QRS ( ) . , , - 1 ( 1/f ) 0,3 Hz - (ventricular fibrillation) ( -1,5, -2, -3,0,...) . ; (, ) ( ). ( ) QRS 1/f-noise ( ) ~ 5,2 ( 1 ).

35

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() fractal () ( HisPurkinje ) ( AV) . ( ) ( ) , , , . , (-) . , ( ) () . , -- hardware ( ) . - , (the "thala mocortical" pacemaker), , ' - . , (relaxation) , ( ~ 3-4) ( ).

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, . - . - 3-4 10, ( ) . , , (petit-mal epilepsy), , ~ 2 . ' . , . , : . , ( -) ( ) ( ).

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, , . ( ) : , ( ). : - ( Zipf). ( ). . . , , . ( ) ( ). - (). -, .

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. (, ) (DNA, mRNA) ( J.S. Bach) . ' , hardware, software . - , .2

, , robots, hard ware ' . : I J. S. Nicolis, Chaotic Dynamics applied to biological information Acadmie - Verlag, 1987. I J. S. Nicolis, , . processing,

, , 1988. I J. S. Nicolis, Dynamics of Hierarchical systems. An evolutionary Springer-Verlag, 1986. [Transi. Into Russian, MIR 1990)]. I J. S. Nicolis, Chaos and information Processing, World Scientific Publishing Co, 1991. approach,

2. - - - , Feigenbaum.

39

20

66 . Stewart Does God play Dice ( ) . , Stewart Henri Poincar - . : ; ( ) ; Poincar ( ) , , : , . , , (, Jack Wisdom MIT Jacques Laskar Bureau de Longitude ) : . Wisdom, ~ 200 . . , ... , , , , ( , ) - . Stewart , , .

40

: ( ), , ' , ( , , ); , , . ' (individual) ; . Stewart . . - - , , ' . . : - - . , , , - - QRS -

41

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42

: ( ) (hardware) (software) ( , , ). : , . . -- quantum (software) : , ( ) . , , , - - . - (multifractals) , . , "scaling laws" ( -) exponents () scaling laws ( Feigenbaum ).

43

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. 66 , Elementary Panicle Physics ( ) Fundamental Particle Physics ( ). , elementary fundamental , . , , , . . , "High Energy Physics" ( ). , , . .

; . , . , . , , . , , , . , , . : , ,

72

, , ... , , . , . , (.1) 10 0.1 "1 m. . 10.000 . 2 10.000 ("5 m ) . . .

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73

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74

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, . , , .. genus Citrus, , .. genus Malus. genus genus Citrus genus Malus. H : - ( ..) . . ; , () ; , ; , DNA . . genus , .. , genus Citrus genus Malus . genus , DNA , . , Carl Linneaus (1707-1778) .

77

20

Peter Breughel (1525-1564) 9. , (transmutation) , , , . . , , , . , .

. 9. , Pieter Brueghel o (1525-1569)

, Robert Boyle (1626-1691) Isaac Newton (1642-1727) , De Rerum Natura ( ).

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, , . , 18-19 , ( ) 19 65 - .. , , , 6, , , , .. , Prout Dalton 1810. , . . 19 . 1869 Mendeleev . Mendeleev . Cad Linnaeus . , 20 , Rutherford Bohr, , , -

79

20

. 1911 Rutherford, . . , 2000 . . , . , , . : . .

Mendeleev 20 . ,

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. , . . (.. ), (.. ), . . , , . 19 20 . () (Planck-Bohr ..). , , . , . . . . . , , , , , .

81

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, , . .

(1); , . , , . . . , , . , , . , . , . , , . , . , , .

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83

20

, , . . . - , , , 6 .

. (e. 480-420 ..) (e. 460-370 ..) . (e. 384-322 ..), (, , , , , ..). (e. 340-270 ..). .. . (Titus Lucretius Cams) De Rerum Natura ( ). , (e. 428-348 ..) (e. 570-480 ..), , 370

84

.. , ' , . , , . 5 4 .. : . (, , ) ( ) , , . , . , , . -, , , ..- , . . (, ) , , . () . , . . . , 4 .. , -, 20 .., . -

85

20

, . , . ' . , (W.H.D.Rouse-M.F.Smith, Harvard University Press, 1997) De Rerum Natura, 1.599-634.. , , . ; . [...]. , , . (minimae partes, ). . , [...]. , , , . 4 .. (minimae partes) quarks. , plus a change, plus c'est la mme chose!.

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, , . . (7-8.000 ), , . , , , . -creationist , . , De Rerum Natura . , , , (De Rerum Natura, V 826-831, V 855-859): , . , : [... ] , , . , ' , , , , . . , .

87

20

, . . , , 5 .. Memmius, , .

(2); , . . , . , . , , 17 . , . , Isaac Newton (1642-1727), , Christiaan Huygens (1629-1695), . 20 , , . , . 1924 . :

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There are therefore now two theories of light, both indispensable, and -as one must admit today in spite of twenty years of tremendous effort on the part of theoretical physicists- without any logical connections. . , , . (. Einstein, The Compton Experiment, Appendix 3, in R S Shankland (Ed.), Scientific Papers of Arthur Holly Compton, X-Ray and Other Studies, University of Chicago Press, Chicago, 1975). , , . , , 25 . , . . . , , . , , . .

89

20

. , ' , . - - . Richard Feynman (19181988), 1965, : The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, "But how can it be like that?" Which is a reflection of uncontrolled but utterly vain desire to see it in terms of and analogy with something familiar; I will simply describe it [ ].

On the other hand, I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will get "down the drain", into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that. , : " ;" ' . , [...]. ,

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. . . . , , . , " ;" " ", . (Richard P. Feynman, The Character of Physical Law, MIT Press, 1967). 20 1965. , . ' , , Feynman. ... 1950. ... 1950 19 20 . quark flavor (; ;), charm (), strangeness (), beauty () truth ()! . - , , - . , , 19 20 .

91

20

20 , David Bhm (19171992), Feynman . , . Thought tends to create fixed structures in the mind, which can make dynamic entities seem to be static. To illustrate with an example, we know upon reflection that all manifest objects are in a state of constant flux and change. So there is really no such thing as a thing; all objects are dynamic processes rather than static forms. To put it crudely, one could say that nouns do not really exist, only verbs exist. A noun is just a "slow" verb; that is, it refers to a process that is progressing so slowly so as to appear static. For example, the paper on which this text is printed appears to have a stable existence, but we know that it is, at all times including this very moment, changing and evolving towards dust. Hence paper would more accurately be called papering -to emphasize that it is always and inevitably a dynamic process undergoing perpetual change. , , . , . , . , , . , . , , , , ,

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. , , (Prof. David Bhm, Wholeness and the implicate order, London, Routledge and Kegan Paul, 1980). , Feynman Bhm . .

corpus , . , . . . , . (, ..) . . Lyn Margulis (1938- ), 20 , ; "What is life?" is a linguistic trap. To answer according to the rules of grammar, we must supply a noun, a thing. But life on Earth is more like a verb.

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It is a material process, surfing over matter like a strange slow wave. It is a controlled artistic chaos, a set of chemical reactions so staggeringly complex that more than 4 billion years ago it began a sojourn that now, in human form, composes love letters and uses silicon computers to calculate the temperature of matter at the birth of the universe. ' ;' . , . . . , , , . (Prof. Lynn Margulis, Lecture in the IIASA "Evolution and Complexity" series, Luxemburg, Austria, 13 September 1995).

, , , : . , - , , , 1954. , , . . , , , 1980. , -, - . -. , , , 2000. , , - . , , A.A. , 1993.

94

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99

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100

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, , , . , , . , , - - , , . , . ' , . . a posteriori a priori . . , , . : ) a posteriori , ) a posteriori , ) a priori ) a priori . a priori . a posteriori . . a posteriori . , a priori . a priori ; a priori , a priori-a posteriori -.

109

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( , ). . , . , , . , . . ' 19 . , characteristica universalis, , . . 19 ' , , . . 19 , . , , , , , : , . . , , . .

110

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111

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113

20

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114

, ,

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115

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, . , . , . Gaston Bachelard. Le matrialisme rationnel, o Bachelard : . , . Maurice Merleau-Ponty. , Ponty : . - . , , . - - , , . , , . ; ; , , . . . . . -

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, . , . , , , , cogito , , cogito. . , , . . . . ; , Bachelard, ; ' , ; . : , , , . 1927, Martin Heidegger Huserl . , Werner Heisenberg

117

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. ; 66 Heisenberg , Heidegger , . , , . , , . ; Huserl ' ; , Hans Wagner, , , . , , ( ), , . , , ' , , . ' , , Ernst Cassirer, ,

118

, . / , . [...]. , , , (F.S.C. Northrop). , , , . . D. Abro, , , , , . : . . , / . . .

119

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121

20

, , . - - , Dummett (1982) Putnam (1981, 1990). , , . , , , .. - - . . . - , , . , ( ) . , , : . , . , , ( ) .

122

- - (6. van Fraassen 1980). ( ) , . - : , , . . ( ) . , . , , . , : , Carnap (1939, . 64), . , , ( Wright 1992, . 1-2) , . - - , . , , -

123

20

, -, , (, , ) . , ab initio . : , ; : .

, Popper (1982). (), ( ) . ( ), . Popper ( ) , . Popper Popper ,1 ' . Musgrave (1996, . 23) ( ) : . : , , , (.., . 21). -

1. Miller (1974) Tichy ([1974]).

124

, Musgrave . ( ) .2 , , . ' , . (. Laudan 1984). , () , . , . , , : , . , ( ) .

, Putnam (1981). , -

2. van Fraassen (1980, . 8) (-) , .

125

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( ) . Ellis (1985) Jardine (1986). Ellis, , , (1985, . 68). , (. Psillos [1999], . 253-55). . Jardine (1986, . 35), . , . , : . , , , () , . , Putnam (1990, . viii) (, C. S. Peirce) , , . Putnam ( ). , Putnam, -

126

, / . : , ( ) ; , . , : , . . . . . , , . , . , . , . , , . ; , - - . , ( ) . ' , Wright (1992) , . , , -

127

20

( ). , : , a priori , , . , , , . , , , ( ) .

' , . , , , . Fine (1986, . 151) . , , . . - , , , .

128

( ) , : (, ) . . , , , . , (. Rorty [1991], . 46 ..), (Fine 1986, . 151), ( ) - ( ) ( ) . . . 3 , , , : a priori . , (. Boyd 1981). , ( ) ,

3. Psillos (1999, . 245-46) Niiniluoto (1999, . 94-95).

129

20

- . , ; . : ; , , , ( ), ; , . . ( ) . , . Leplin (1997). (.., . 102). Leplin (. 121), . - . , , Boyd .4

4. , 6. Psillos (1999, . 4).

130

; ( ). . , , , , , . ( ), . , . , . . . , . , , ..

Seilars 1960. , , . , Smart (1963, . 39) Maxwell (1962, .

131

20

18) , . , , . Putnam (1975, . 73) : . . . : ) ) , , . , , , . . , , Pierre Duhem,

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