in Bak, Tang, and Wiesenfeld’s “self-orga-nized criticality” (9). In an essay entitled“More Is Different,” Anderson (10) describedhow features of organization may arise as an“emergent” property of systems. An exampleof this point of view is given by work oncomplexity “phase transitions” and accompa-nying speculations that various aspects ofbiological systems sit on a critical point be-tween order and complexity (11).The next few years are likely to lead to anincreasing study of complexity in the context ofstatistical dynamics, with a view to better un-derstanding physical, economic, social, and es-pecially biological systems. It will be an excit-ing time. As science turns to complexity, onemust realize that complexity demands attitudesquite different from those heretofore commonin physics. Up to now, physicists looked forfundamental laws true for all times and allplaces. But each complex system is different;apparently there are no general laws for com-plexity. Instead, one must reach for “lessons”that might, with insight and understanding, belearned in one system and applied to another.Maybe physics studies will become more likehuman experience.References and Notes1. U. Frisch, B. Hasslacher, Y. Pomeau, Phys. Rev. Lett.56, 1505 (1986); J. Hardy, O. de Pazzis, U. Frisch, J.Math. Phys. 14, 1746 (1973); Phys. Rev. A 13, 1949(1976).2. Early work on the derivation of hydrodynamics fromconservation laws can be found in S. Chapman andT. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, Cambridge,ed. 3, 1970).3. A. R. Kerstein, J. Fluid Mech. 291, 261 (1997); S.Wunsch, thesis, University of Chicago (1998). Forexperiments, see, for example, B. Castaing et al., J.Fluid Mech. 204, 1 (1989). For theory, see E. Siggiaand B. Shraiman, Phys. Rev. E 49, 2912 (1994).4. B. Mandelbrot, Fractals and Scaling in Finance: Dis-continuity, Concentration, Risk (Springer-Verlag, NewYork, 1997).5. A. Katchalsky and P. F. Curan, Nonequilibrium Pro-cesses in Biophysics (Harvard Univ. Press, Cambridge,MA, 1967).6. G. Nicolis and I. Prigogine, Self-Organization in Non-equilibrium Systems ( Wiley, New York, 1977).7. A. Turing, Philos. Trans. R. Soc. London Ser. B 327,37(1952).8. For example, L. Kadanoff, A. Libchaber, E. Moses, andG. Zocchi [Recherche 22, 629 (1991)] discussed thedevelopment of interlinked structures in a Rayleigh-Benard flow.9. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381(1987); J. M. Carlson, J. T. Chayes, E. R. Grannan, G. H.Swindle, ibid. 65, 2547 (1990).10. P. W. Anderson, Science 177, 393 (1972).11. S. A. Kauffman, The Origin of Order (Oxford Univ.Press, Oxford, 1993); At Home in the Universe (Ox-ford Univ. Press, Oxford, 1995).12. Supported in part by NSF grant NSF-DMR-93-14938(N.G.) and by the ASCI Flash Center at the Universityof Chicago under U.S. Department of Energy contractB341495 (L.P.K.).VIEWPOINTComplexity in ChemistryGeorge M. Whitesides* and Rustem F. Ismagilov“Complexity” is a subject that is beginning to be important in chemistry.Historically, chemistry has emphasized the approximation of complexnonlinear processes by simpler linear ones. Complexity is becoming aprofitable approach to a wide range of problems, especially the under-standing of life.“Complexity” is a word rich with ambiguityand highly dependent on context (1). Chem-istry has its own understandings of this word.In one characterization, a complex system isone whose evolution is very sensitive to ini-tial conditions or to small perturbations, onein which the number of independent interact-ing components is large, or one in whichthere are multiple pathways by which thesystem can evolve. Analytical descriptions ofsuch systems typically require nonlinear dif-ferential equations. A second characterizationis more informal; that is, the system is “com-plicated” by some subjective judgment and isnot amenable to exact description, analyticalor otherwise.In chemistry, almost everything of interestis complex by one or both definitions. Con-sider the design and synthesis of a simpleorganic substance (,102covalently bonded,first-row atoms) as a candidate drug—a rep-resentative activity for organic, medicinal,and biological chemists. A single step in themultistep synthesis of such a substance mightinvolve 1022molecules of several types (eachcomprising as many as 102anharmonicallyoscillating bonds) and several times this num-ber of interacting nuclei and electrons, allimmersed in 1024molecules of solvent. Thesynthesis itself might proceed by perhaps 10different strategies (that is, sequences of re-actions) for making and breaking bonds andfor generating the intermediate compoundsthat ultimately result in the final compound;each strategy might have many thousands ofpossible variants differing in synthetic detail.The design of a molecule that has the rightproperties (shape, surface properties, and as-sociated electrostatic fields) to interact spe-cifically with one part of the surface of atarget protein molecule presents yet anotherset of complicated challenges (Fig. 1) (2).Faced with the impossibility of handlingany such real system exactly, chemistry hasevolved a series of approaches to the treat-ment of complex systems, which range fromreasoning by analogy, through averaging, lin-earization, drastic approximation, and pureempiricism, to detailed analytical solution.The study of complexity in systems of reac-tions (or of processes or of properties) thatcan be described by nonlinear equations hasbeen limited to the few that are both complexenough to be interesting and simple enoughto be tractable. The emphasis in thinkingabout complicated systems has been to findmethods that are predictive, even if they arenonanalytical. Philosophically, chemistry is abranch of science that attempts to predict andcontrol rather than simply to observe andanalyze: A large industrial reactor that pro-duces heat in unpredictable bursts is moreimmediately terrifying than interesting. Theoptimization of combustion for the produc-tion of work, the understanding of mecha-nisms of drug action, and the development ofstrategies for organic synthesis are all prob-lems of great complexity. They are also prob-lems of sufficient urgency, which must besolved as best as possible, even if analyticalsolutions for them are not practical.Chemistry is now evolving away from themanipulation of sets of individual moleculesand toward the description and manipulationof systems of molecules,