A NEW LOGIC OF HUMAN STUDIESnby Frederick TurnernConsider the following paradoxes. A welfare systemndesigned by well-meaning politicians guided by thenadvice of the wisest sociologists and economists available,ncosting billions of dollars, whose net effect is radically tonincrease the numbers of the poor, especially women andnchildren, and to deepen their misery, incapacity, andndespair. A stock market which rises because the statisticalninstruments designed to detect similarities with previousnrises are causing investors to make it rise in the same patternnand which helps to generate the financial conditions itnpredicts. A social polity expressly created to ensure thenequality of all citizens, which produces an archipelago ofnconcentration camps across a continent and whose theoreticalndismissal of the concrete eflFectuality of theorizingnunleashes real social forces of unparalleled savagery. Anforeign policy which depends for its effectiveness on thengovernment’s ignorance of its existence and implementation.nAn economy which attracts foreign investment bynborrowing so much money that it is able to remainnpolitically stable and thus economically healthy.nMore and more of our collective life seems now to benpopulated with such logical monsters, such scyllas andncharybdises of reflection and feedback. Yet good as well asnevil can be compounded by the peculiar kind of interestnwhich they offer; unfairly, unto him who has much, muchnshall be given and the kingdom of heaven is like a mustardnseed: something that will grow quite unpredictably all overnthe place.nBut these monstrosities are the despair of any “scientific”nsociology or historiography. And now physics itself seems tonhave caught the plague; and even that purest sanctum ofnlinear logic, mathematics. Those positive knowledges tonwhich modernist history and sociology appealed for a modelnnow seem almost as messy and chaotic as the seething life ofnhuman culture.nThis new vision of the “positive sciences” has emergednfrom the brilliant new studies of chaotic, nondeterministic,nrecursive, fractal, dissipative, catastrophic, period-doubling,nand feedback-governed systems, associated with the namesnof Mitchell Feigenbaum, Ilya Prigogine, Benoit Mandelbrot,nand Rene Thom. Perhaps some of these terms requirena brief (and necessarily incomplete) explanation. Annalgorithm is a mathematical method for doing something—say,ngenerating a geometrical shape in a computerngraphic. A recursive algorithm is one which possesses anninternal loop, such that the solution arrived at by onenpassage through the loop is fed back again into the beginningnof the loop, “adding,” as Benoit Mandelbrot puts it,n”fresh detail to what has been drawn on previous runs.”nMandelbrot also gave the name fractals to a family ofnFrederick Turner, poet and essayist, is Founder’s Professornof Arts and Humanities at the University of Texas atnDallas. His most recent book is The New Worldn(Princeton University Press).nshapes, irregular and fragmented surfaces, curves, andn”dusts,” generated by recursive algorithms based on anrandom or arbitrary numerical “seed,” which repeat theirnown form or type of form at different scales of magnification,nso as to pack into their details at one scale a microcosmnof the next larger scale. The space-filling curves of Peanonare only one example. Mandelbrot sees these forms everywherenin Nature: in trees, cloudscapes, coastiines, thenbronchi of the lungs, corals, star clusters, waves, craters,nand so on. A dissipative system is one which maintains itsnform not despite its tendency to decay but by means of it.nDissipative systems can be self-organizing; I shall discussnsome examples later, such as certain forms of turbulence.nThe term is Prigogine’s. A catastrophe is a discontinuity, asnwhen the gradual increase of some factor suddenly crosses anthreshold in which some entirely different state is precipitated;nit can be observed when a cooling supersaturatednsolution suddenly crystallizes, or when an animal’s behaviornsuddenly changes during a gradual change in the stress itnis undergoing, or when a gradual change in economicnfactors triggers a massive move in the stock market index.nRene Thom was first able to describe such discontinuities orncatastrophes mathematically, in his catastrophe graphs.nPeriod doubling—Feigenbaum’s term—is what happensnwhen certain ordered systems break up into chaotic ones,nlike a smoke-ring dissolving in the air; out of such chaoticnsituations, however, new forms of order can arise spontaneously,ngiven the right circumstances.nThe lawfulness governing such systems is of a radicallyndifferent kind from the rules that govern classical determin-nnnDECEMBER 19871 31n