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James Gleick

Chaos

Making a New Science


* * *

This edition is published by arrangement with InkWell Management LLC and Synopsis Literary Agency

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 James Gleick, 1987, 2008

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 1974     -,  -,  ,          [1 - , , , , , , , .].          .   ,      ,     .    .             26- .        ,     .         .

  ,    ,         -      ,    -     ,   ,  ,  ,    : , , ,   ,     ,    .         ,       1940- ,      -                    -  .        ,    (          X).             ,          .          ,      .

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         ,     .          . ,      ,          [3 - , , .].            ,     ,       .  -                ;          .

           ,       ,    .         : , , ,   .      ,              [4 - .].         ,    ;   ,    [5 - Browand F. . The Structure of Turbulent Mixing Layer // Physica. 1986. Vol. 18D. P.135.].

   ,   :    ,      ,           ,   .      ,      ,       ,   ,     [6 -            ; . Musha T., Higuchi H. The 1/f Fluctuation of a Traffic Current on an Expressway // Japanese Journal of Applied Physics. 1976. P.12711275.].       ,          .          ,         ,         [7 - Mandelbrot R., Wisdom M., Alvin M. S. Chaos  A Model for the Outbreak of War // Nature. 1984. Vol. 309. P.303305.].

      .      ,    ,        .         ,       -  ,    , ,   . ,           ![8 - .]     ,      ,         .      ,      ,   .    ,  ,           .     ,     ,    .           ,            ,       .  ,     ,             : , , .  ,        .

      ,    XX        ,     [9 - .]. ,  ,    ,        [10 - .].    ,         -,         , ,          [11 - Ford J. What Is Chaos, That We Should Be Mindful of It?, preprint. Georgia Institute of Technology.P.12.].          ,      ,  ,   .          .    ,     ,            .     ,   ,    , ,         ,      .

       .     XX     ,    ,  ,     ,                 .         .  ,      ,      .  ,               .

 1980    ,  [12 -     (       ),      ,   1663     .       ,        .   ,    , . . .]   ,       ,            ?:     ,   ,                  ,              ,   ,      [13 - Boslough J. Stephen Hawklng's Universe. Cambridge: Cambridge University Press, 1980; . : Shaw R. The Dripping Faucet as a Model Chaotic System. Santa Cruz: Aerial, 1984.P.1.].

  ,               ,       ,  .   .    ,     ,     ,   ,           ,  ,     .

 ,          ,   .  ,        ,    , -    .           ,     .          ?        ,  ,         ? ,  ,     ,   XX .     ,    , , .     ,        ,     ,  .

    ,        ,  :   ,   ,   ,             ,   ?  ,    ,    ,    ,       ,       - .   .

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     ,       .    ,       ,      ?  .                .  ,   ,    , ,             ,  ,     ,   ,           .     1960- ,   ,        ,   ,    .                    .           :             -.

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    - .    .    . ,    .  .    .

   ,    .   ,   .    ,     .    . ,     ,  ,   ,     ,             [15 - , , , .  ,     ,   : Deterministic Nonperiodic Flow // Journal of the Atmospheric Sciences. 1963. Vol. 20.P.130141.    : The Mechanics of Vacillation // Journal of the Atmospheric Sciences. 1963. Vol. 20. P. 448464; The Problem of Deducing the Climate from the Governing Equations // Tellus. 1964. Vol. 16. P. 111.        ,            .   ,        , .: On the Prevalence of Aperiodicity in Simple Systems // Global Analysis / Ed. by M. Marsden and J. Marsden. New York: Springer-Verlag, 1979. P. 5375.].

       :  ,       ,     ,    .          .    Royal             ,          .       ,   ,   ,        .     1960    - ,      .       .   ,          ,       .          .       ,      ,  ,       .      .

         -.    ,          , ,    ,      .  ,     .   ,              .    ,         .   ,       .            75   [16 -  24   .].    -                 .      ,         . -    .

    ,         .     ,    ,    ,       ,      [17 -        ,  , .: Large-Scale Motions of the Atmosphere: Circulation // Advances In Earth Science / Ed. by P. M. Hurley. Cambridge, Mass.: The M. I. T. Press, 1966. P.95109.         : Richardson L. F. Weather Prediction by Numerical Process. Cambridge: Cambridge University Press, 1922.].             ,        .        .    ,               .       .       .

 XVIII               .     .      .     ,    -   .         ,  ,         ,     .     ,           .

             ,          -,  ,    . ,     ,     .       .       ,   .  ,  ,     , ,     .    , ,    [18 - .         , .: Irregularity: A Fundamental Property of the Atmosphere, Crafoord Prize Lecture presented at the Royal Swedish Academy of Sciences, Stockholm, Sept. 28, 1983 // Tellus. 1984. Vol. 36A. P.98110.].   1938   ,      .     :    .     .         ,      ,      . ,    ,   .     .

                       , ,     .            ,   . ,     ,     ,     ,              .

        1960-           .   ,     ,          .  ,       ,       .          ,       ,   .      ,      ,    ,   ,     ,     ,    .       ,         :   ,        ,   . ,     ,     ,   ,    . ,          ,   [19 -  :  2006       .],    .        ,        .   ,           ,    ,    .    ,   ,       .   :         ?

,     ,      . ,       , ,   - XVIII  ,     ,          ,    ;       ,         [20 - Laplace P. S. de. A Philosophical Essay on Probabilities. New York: Dover, 1951.].  ,         ,     ;        .   XX   , ,       ,   ,  .        . -       ,              ,   1950-              ,  -. ,  ,         .

,       ,      ,  ,       .     . ,    ,    :           ,   ,     .       .        :      ,      ,       ,            .    .     ,        ,      [21 - .].  ,        .         1910        ,    1986 .          . ,   ,          .      ,   ,        .      .

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   1961 ,     ,            ,   .          .     ,       ,    ,    .



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    [23 - On the Prevalence. P. 55.].   ,     ,    .         : 0,506127.   ,    ,   : 0,506.   ,  , ,      .

   .  ,   ,          ,     . Royal    ,      :     ,            .   ,            -    .         . ,          ,      .  -        [24 -      ,     ,        .       :  ,   ,      ,   ,     ,    ,       .             ,            .      ,         ,        .            ,   ,   .  ,    ,    .      ;            .          .   셻 ( .  . .: , 1990.  . .)    XIX   XX    ;    ,       19201930- ,   .  ,            .].

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      ?   ,     ,      ,   ,     . ,   ,      ,   : -    !      , ,           ,  ,      .   :    [25 - ;   .: On the Prevalence. P. 56.].

       ,     ,  . ,  ,        ,       ,    ,     .         ,    , , ,  .    , , ,   ,     ,       ,     , ,      .                .         ,  ,   ,  ,     . ,              ,     :            ?   ,      ,       .   ,      [26 - .].



    XX          [27 - , ; .       : Weather Scientists Optimistic That New Findings Are Near // The New York Times. 1963. 9 September. P. 1.].       ,          ,        .     :      ,       ,     .  ,      ,  ,    .     ,     ,        .

    ,              .           -.        .  ,          ,         ,     ,    .  ,                 [28 - .].  ,        ,    ,         .  !      ,     .

 1980-            ,      ,      [29 - , , , .].       ,    ,  ,    ,     ,   ,  ,    .     ,   ,      . Royal       ,      Control Data Cyber 205        . ,     ,     ,     .             .        . ,     ,  ,   ,    .              .

        ,    ,        .       ,  ,       ,        ,        .         ,      ,   Cray,       .

    ,         .        ,    .        ,      ,   ,    ,  .   ,  19701980-         . ,   ,      ,                .  ,         .                 ,    ,     .    ,     ,      ,     ,   ,   ,      .          ,     [30 - Medawar P. . Expectation and Prediction // Pluto's Republic. Oxford: Oxford University Press, 1982. P. 301304.].                 ,       . ,    ,          , , ,  ,    ,         ,    .    ,       ,    ,      ,     ,      .

      ,         .    ,        ,    ,  .  ,     - ,   ,        .

    [31 -        ,   ,   , -,     Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?               29  1979 .].                  ,   ,    .    ,      ,              ,      .

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 ,                ,     [34 - The Mechanics of Vacillation.].                            .  ,      ,          ,     ,          .     .

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  ,       :     .      , ,     [35 -  . . .]:

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    ,          .           ,       , .            :   x,   y.    ,      .     :       ,    ,  ,    [37 -     .      ? + x= = a (t) + b (t) + c(t).      ,   a (t), b (t)  c (t) ,     . ,    ,      .  a (t)     , b (t)   ,  ,  c (t)  .      ,       ,          (  ? +  = a (t), ? + x = b (t)  ? + x = c (t)).      ,     .               .].

        ,      .     ,      ,   .   ,           ,    .    ,   ,         ,      .  ,      .     ,      . ,   ,   . -       .         ,     .         :    .   ,   , ,    .   ,        ,             ,       .   ,        ;   ,   .      [38 - Neumann J. von. Recent Theories of Turbulence (1949) // Collected Works / Ed. by A. H. Taub. Oxford: Pergamon Press, 1963. P. 6:437.].  ,             ,           .

                   .    .       ,      .  ,     ,  ,      ,  .    ,        [39 - The predictability of hydrodynamic flow // Transactions of the New York Academy of Sciences. 1963. Vol. 11:25:4. P. 409432.].   ,         ,   , ,  .  ,     ?    ,            . ,   ,            ,   .     ,            ,    . ,     :   ,   ,       .   ,           ,          [40 - Ibid. P. 410.].  ,      ,       .     ,       ,        .

   ,  ,      ,  ,    ,      [41 -               ,     .      , ,   ,   ,        .   ,           ,     . Saltzman . Finite Amplitude Convection as an Initial Value Problem // Journal of the Atmospheric Sciences. 1962. Vol. 19. P. 329.].       ,   .   ,    ,    .              ,     :     .

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         [47 -   ,    ,  :dx/dt = 10 ( ? )dy/dt = ?xz + 28 ? dz/dt =  ? (8/3) z     Deterministic Nonperiodic Flow    ; ., ,   : Sparrow C. The Lorenz Equations, Bifurcations, Chaos, and Strange Attractors. Springer-Verlag, 1982.].          : 0100; 4120; 9200; 16362; 30667; 5411524; 9319274.     ,       : , , 

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     ,          .         ;  ,          .       .      ,      ,      .   ,   ,                  Journal of the Atmospheric Sciences[50 - Deterministic Nonperiodic Flow   1960-         ,           .].




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 . ,       .  .  :     .

       ,     1940- [51 -              ,    ,    ,          .             : The Structure of Scientific Revolutions, 2nd ed. enl. Chicago: University of Chicago Press, 1970;  : The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago, 1977; What Are Scientific Revolutions? // Occasional Paper. No. 18. Center for Cognitive Science, Massachusetts Institute of Technology;    .      ,     : Cohen I. . Revolution in Science. Cambridge, Mass.: Belknap Press, 1985.].           . ,     :     , ,     ,     .

     ,   ,     .     ,      .     ,          .      ,  .   ,    -  ,        .  ,  ,    , -      .

  ,      ,  ,   ,     .    ,     ,  ,     .      ,     ,  . ,    ,      .   ,   ,   ,    .         ,     ![52 - Structure. P. 6265,   : Bruner J. S., Postman L. On the Perception of Incongruity: A Paradigm // Journal of Personality. 1949. Vol. XVIII.. 206.]

 ,  ,     ,         ,    - .      ,      ,    .   ,     .

 1962 ,       ,        ,        ,         .                    ,             .              ,    ,              ,  ,  ,  .         .

  ,        [53 - Structure. P. 24.].     ,       [54 - Tension. P. 229.].       ,     .       .       ,    ,         ,       .                      [55 - Structure. P.1315.].          ,      ,    .  ,    ,  -.          ,    ,         ,      .    XX ,   ,     ,          .  ,    ,         .

       ,    ,   .       ,    ,       (    ).    -   .    ,   , ,   ,          ,  [56 - Tension. P. 234.].

   ,    ,       .      :     ,    .         ,   ,     .      ,    ,   .     .     ,                      ,  .             .

,      ,          ,     .        ,       :      . ,    ,    ,     ,       ,    ,        [57 - .].  ,         ,        , ,    .       ,   .  ,     ,     ,     .   ,  1970-      ,     -   .     ,               ,   .

,       ,   ,           ,      .           .            -        .    ,  ,      ,  .  ,     ,     :  ,   ,     ,    ,    ,         ,            ,       ,    , ,   ,     [58 - , ,  : Chaos: Solving the Unsolvable, Predicting the Unpredictable // Chaotic Dynamics and Fractals / Ed. by M. F. Barnsley and S. G. Demko. New York: Academic Press, 1985.].

         . ,    ,   ,     .          .        ,     .

,         ,           ,   .               , ,   ,   .  (   )         [59 -    ,         ,      . Berry M. The Unpredictable Bouncing Rotator: A Chaology Tutorial Machine, preprint, H. H. Wills Physics Laboratory, Bristol.].   1980-        ,            .      ,       [60 - .]




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notes








1


, , , , , , , .




2


, .




3


, , .




4


.




5


Browand F. . The Structure of Turbulent Mixing Layer // Physica. 1986. Vol. 18D. P.135.




6


           ; . Musha T., Higuchi H. The 1/f Fluctuation of a Traffic Current on an Expressway // Japanese Journal of Applied Physics. 1976. P.12711275.




7


Mandelbrot R., Wisdom M., Alvin M. S. Chaos  A Model for the Outbreak of War // Nature. 1984. Vol. 309. P.303305.




8


.




9


.




10


.




11


Ford J. What Is Chaos, That We Should Be Mindful of It?, preprint. Georgia Institute of Technology.P.12.




12


    (       ),      ,   1663     .       ,        .   ,    , . . .




13


Boslough J. Stephen Hawklng's Universe. Cambridge: Cambridge University Press, 1980; . : Shaw R. The Dripping Faucet as a Model Chaotic System. Santa Cruz: Aerial, 1984.P.1.




14


Cray   ,  . Macintosh    ,   Apple.




15


, , , .  ,     ,   : Deterministic Nonperiodic Flow // Journal of the Atmospheric Sciences. 1963. Vol. 20.P.130141.    : The Mechanics of Vacillation // Journal of the Atmospheric Sciences. 1963. Vol. 20. P. 448464; The Problem of Deducing the Climate from the Governing Equations // Tellus. 1964. Vol. 16. P. 111.        ,            .   ,        , .: On the Prevalence of Aperiodicity in Simple Systems // Global Analysis / Ed. by M. Marsden and J. Marsden. New York: Springer-Verlag, 1979. P. 5375.




16


 24   .




17


       ,  , .: Large-Scale Motions of the Atmosphere: Circulation // Advances In Earth Science / Ed. by P. M. Hurley. Cambridge, Mass.: The M. I. T. Press, 1966. P.95109.         : Richardson L. F. Weather Prediction by Numerical Process. Cambridge: Cambridge University Press, 1922.




18


.         , .: Irregularity: A Fundamental Property of the Atmosphere, Crafoord Prize Lecture presented at the Royal Swedish Academy of Sciences, Stockholm, Sept. 28, 1983 // Tellus. 1984. Vol. 36A. P.98110.




19


 :  2006       .




20


Laplace P. S. de. A Philosophical Essay on Probabilities. New York: Dover, 1951.




21


.




22


.




23


On the Prevalence. P. 55.




24


     ,     ,        .       :  ,   ,      ,   ,     ,    ,       .             ,            .      ,         ,        .            ,   ,   .  ,    ,    .      ;            .          .   셻 ( .  . .: , 1990.  . .)    XIX   XX    ;    ,       19201930- ,   .  ,            .




25


;   .: On the Prevalence. P. 56.




26


.




27


, ; .       : Weather Scientists Optimistic That New Findings Are Near // The New York Times. 1963. 9 September. P. 1.




28


.




29


, , , .




30


Medawar P. . Expectation and Prediction // Pluto's Republic. Oxford: Oxford University Press, 1982. P. 301304.




31


       ,   ,   , -,     Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?               29  1979 .




32


.




33


, .




34


The Mechanics of Vacillation.




35


 . . .




36


 ;    . : Wiener N. Nonlinear Prediction and Dynamics // Collected Works with Commentaries / Ed. by P. Masani. Cambridge, Mass.: The M. I. T. Press, 1981. P. 3:371.                  .  :       ,       ,       .




37


    .      ? + x= = a (t) + b (t) + c(t).      ,   a (t), b (t)  c (t) ,     . ,    ,      .  a (t)     , b (t)   ,  ,  c (t)  .      ,       ,          (  ? +  = a (t), ? + x = b (t)  ? + x = c (t)).      ,     .               .




38


Neumann J. von. Recent Theories of Turbulence (1949) // Collected Works / Ed. by A. H. Taub. Oxford: Pergamon Press, 1963. P. 6:437.




39


The predictability of hydrodynamic flow // Transactions of the New York Academy of Sciences. 1963. Vol. 11:25:4. P. 409432.




40


Ibid. P. 410.




41


              ,     .      , ,   ,   ,        .   ,           ,     . Saltzman . Finite Amplitude Convection as an Initial Value Problem // Journal of the Atmospheric Sciences. 1962. Vol. 19. P. 329.




42


         ,         . .    . : , 2010.




43


     : Cook A. E., Roberts P. H. The Rikitake twodisc dynamo system // Mathematical Proceedings of the Cambridge Philosophical Society. 1970. Vol. 68. P.547569.




44


;           ,        ,        ,   ,    .    ,    ,    , .: Robbins . A. A moment equation description of magnetic reversals in the earth // Proceedings of the National Academy of Science. 1976. Vol. 3. P.42974301.




45


.




46


     : www.youtube.com/watch?v=Gu50alrmzNA.




47


  ,    ,  :

dx/dt = 10 ( ? )

dy/dt = ?xz + 28 ? 

dz/dt =  ? (8/3) z

     Deterministic Nonperiodic Flow    ; ., ,   : Sparrow C. The Lorenz Equations, Bifurcations, Chaos, and Strange Attractors. Springer-Verlag, 1982.




48


.  :  .    //  . .: , 1981. .88117.  . . .




49


, .




50


Deterministic Nonperiodic Flow   1960-         ,           .




51


             ,    ,    ,          .             : The Structure of Scientific Revolutions, 2nd ed. enl. Chicago: University of Chicago Press, 1970;  : The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago, 1977; What Are Scientific Revolutions? // Occasional Paper. No. 18. Center for Cognitive Science, Massachusetts Institute of Technology;    .      ,     : Cohen I. . Revolution in Science. Cambridge, Mass.: Belknap Press, 1985.




52


Structure. P. 6265,   : Bruner J. S., Postman L. On the Perception of Incongruity: A Paradigm // Journal of Personality. 1949. Vol. XVIII.. 206.




53


Structure. P. 24.




54


Tension. P. 229.




55


Structure. P.1315.




56


Tension. P. 234.




57


.




58


, ,  : Chaos: Solving the Unsolvable, Predicting the Unpredictable // Chaotic Dynamics and Fractals / Ed. by M. F. Barnsley and S. G. Demko. New York: Academic Press, 1985.




59


   ,         ,      . Berry M. The Unpredictable Bouncing Rotator: A Chaology Tutorial Machine, preprint, H. H. Wills Physics Laboratory, Bristol.




60


.


