From Being to Becoming: Time and Complexity in the Physical Sciences by Ilya Prigogine (review)

Books 319 worst, one of his compatriots may have contributed most of it. But the association is interesting, and because it sparked Cook’s imagination it has been refreshingly fruitful. As for the use of the Golden Section, a theme which is an undercurrent of Cook’s writing, this also cannot be proven. Use of the Golden Section was apparently a trade secretamong architects and artists -if they knew it at all, they kept the knowledge hidden from the public. Beforethe timeof precisearchitectural drawing, only a written statement to that effect could prove the deliberate use of Fibonacci’sseriesin proportion, let alone the Golden Section. Butgreat artists have usually been people of great intellect. To them, the almost magical properties of the Golden Section would be mathematically intriguing as well as stimulating to use in their works. That it was esoteric would add to the fun of using it.. .but never slavishly. This, perhaps, is the secret that Cook uncovered. That delight in nature leads to imitation of nature; that imitation of nature in novel and extended ways can be pleasurable, that nature is exceedingly economical and elegant in combining form with function, that nature is never quite mathematically perfect and the artist knows how subtle these approximations to a mathema and departure from it can be, allof which he can produce intuitively. This is the ‘Art which conceals the Art’, as Oscar Wilde has said. Incidentally, Bramante did nor build his spiral staircase in the Belvedere in 1444 (p. 346). Cook’s book is indeed a classic. It deserves to be reprinted and to be on the shelves of every humanist-biologist and every nature-loving artist or architect, regardless of whether one accepts its theses. References 1. DArcy Thompson, On Growth and Form. J. T. Bonner. ed. (Cambridge: Cambridge University Press, 1966). 2. Leonardo da Vinci, The Unknown Leonardo, Ladislao Reti, ed. (London: Hutchinson, 1974). From Being to Becoming: Time and Complexityin the PhysicalSciences. Ilya Prigogine. W. H. Freeman, Oxford, 1980. 272 pp., illus. Paper, E6.40.ISBN: 0-7167-1108-7. Reviewed by George Agoston. Those who havefollowedthe articles and letters on the subjectofart and entropy in Leonardo (3, 351, 353, 354 (1970); 6, 29, 76 (1973))will be particularly interested in Prigogine’sbook. The subjectof entropy isone of the principle subjects treated, yet the dominant thrust is toward a concept of time. The author’s first words in his Preface point this out succinctly: ‘This book is about time.’ The book is written at an intermediate level, requiring familiarity with the basic tools of theoretical physics and chemical kinetics. In classical mechanics, no distinction is made between the future and the past. The equations can be used to describe motions, reversibly forward and backward in time.(Timeplaysa two-way role.)Thesameis true in quantum mechanics. The author describes both domains as ‘physics of being’, characterizing a static universe. Both can be applied only in certain types of problems. Classicalmechanics,for example,can be used to determine the path of a satellite in space. But both are inadequate without supplementary tools to deal with processes‘withina vaster formalism’ wherein time can be taken to pass only forward, for examplein the decay of a ripple in a pool of water, the heating of an iron ball thrust into boiling water or the dispersion of a drop of ink inwater. Such processesareirreversible; they donot return spontaneously to their initial state. In accordance with the second lawof thermodynamics such change is accompanied by an increase in entropy -and, clearly, time plays a one-way role during such one-way processes. These processes belong to the ‘physics of becoming’ in a changing universe. ‘Irreversibility starts where classical and quantum mechanics end’ (p. xviii). The author’s aim is to describe the relation between ‘being’ and ‘becoming’. He discusses first classical and quantum mechanics, pointing out their basic concepts and limitations. He then continues with irreversible processes as described by the second law of thermodynamics . In equilibrium processes in isolated systems, order, such as in an ice crystal, may be produced spontaneously at low temperature and low entropy. But order may be produced also in nonequilibrium irreversible steady-state situations-processes close...