HISTORY AS POINTS AND LINES by Yuri Tarnopolsky and Ulf Grenander Manuscript 1998-2003 Yuri Tarnopolsky and Ulf Grenander, 2006 1 2 Foreword (2006) Most of this manuscript was finished by 1998. In 2001 the world entered a turbulent transition state toward an unknown future. In 2003 we added Chapter 28, A sunny day in September . Facing global uncertainty from many directions—climate change, energy constraints, new forms of warfare, borderless world, incompetence of governments—we need to look for a scientific consensus on complexity, as opposed to the divisive political, moral, and religious approaches. Testing the ideas of this book against the dramatic beginning of the twenty-first century, we feel confident that the pattern view of the world can be an effective way to understand the developing systems of unprecedented complexity. The intent of this manuscript is to attract attention to Pattern Theory as the science of complex systems. Complexity as subject presumes a complex audience. The style reflects our desire to educate, stimulate, and entertain, while introducing the reader to new and little known or forgotten ideas. The manuscript does not reflect the recent developments in non-numerical Pattern Theory, among which Patterns of Thought by Ulf Grenander should be mentioned in the first place. Patterns and Repertoire in History by Bertrand M. Roehner and Tony Syme ( Harvard University Press, 2002) was an important step toward the legitimization of the search for new ways in scientific study of history. Jared Diamond's Collapse: How Societies Choose to Fail or Succeed (Viking, 2004) approaches the subject from a different angle but remarkably close to the spirit of Pattern Theory. Our manuscript is a register of questions rather than answers, but, as the history of science demonstrates, the right question is half the answer. 3 CONTENTS Prologue 3 15. Invisible walls of events 185 1. Post hoc ergo propter hoc 14 16. Generators 200 2. Atomism 25 17. Regularity in myth and history 213 3. E pluribus unum 41 18. Conflict 229 4. Alternatives and altercations 58 19. Testing the Ariadne’s thread 238 5. Three views of the world 74 20. Probability and energy 252 6. Graphs 90 21. Ideas and actions 269 7. The king and the pear 97 22. Three World Wars 290 8. Groups 109 23. The French Revolution 316 9. To Understand the World 125 24. The Fall of the Soviet Empire 343 10. From Augustus to Nero 130 25. The Circuitry of Imperial China 361 11. Syntax and semantics 140 26. Chaos-order, heat-cold 375 12. Geopolitics of Europe 152 27. History and computers 394 13. Two Velvet Revolutions 162 28. A sunny day in September 417 14. Fermentation in wine barrel Conclusion 434 and society 177 References 441 4 PROLOGUE Change must follow a pattern or leave us unaware of its existence. G.J.Renier (Renier, 1965, p. 229). History and mathematics—can they be put side by side in any sense? Well, it is possible: ...some people dislike the study of history, just as others dislike the study of mathematics... (Brinton, 1956, p. 3) What about history and chemistry? History is the most dangerous product developed by the chemistry of the intellect. (Valéry, 1962, p. 114). Taking history and mathematics, do they have anything to tell each other? 5 Wrestling of arguments, clash of opinions, and animosity of contradicting evaluations never end in history. Mathematical proof is either correct or not: a proved theorem is proved for everybody. Since ancient times history has been a captivating reading. Mathematics is a patented source of headache. History seems to be of no immediate practical value—a dynamic society buries the dead and goes on. Mathematics brings to life all modern technology. History is art, with Clio as its muse, and mathematics is notoriously dry. Nevertheless, the serious answer is a firm “yes.” Since Pitirim Sorokin (1937) filled the four volumes of his Social and Cultural Dynamics with numbers attached to events of the past, scores of textbooks and papers on quantitative methods in history have appeared. There are sites on the World Wide Web on the use of computers in history, college courses, software for historians, and scientific societies. More confusing questions arise: what is mathematics in the era of computers and what is history in the era of sociology? What is history—facts? What is mathematics—numbers? Furthermore, what is truth? Isn’t this book an experiment à la Doctor Moreau in creating yet another chimera and more confusion? This book, written by a mathematician and a chemist, is an experiment, as we hope, in fusion rather than confusion. It is definitely neither about history of mathematics nor about chemistry nor about numbers and calculations. We are not going to do any historical research, for which we, due to our backgrounds, are not equipped. Our sources on history are mostly textbooks and selected books for general audience. Our knowledge of the subject, except for the events of the twentieth century that we personally witnessed, is secondhand. We offer neither interpretation, nor explanation, nor evaluation. Neither do we want to “open eyes” nor to offer “the real thing.” We do not engage in 6 polemics. At this point we are not much interested even in the historical truth itself. The reasons for such an apparently radical statement will be explained gradually. We might have overlooked some sources that expressed similar or same ideas in the past . We might have unwillingly taken liberties with historical facts. We cannot provide any consistent review of the literature, the volume of which enormous. We take fragments of historical knowledge without critical assessment and use them as experimental material. The purpose of our experiment is to place history on the examination table of a certain apparatus which works like an X-ray machine or CAT scan. Our apparatus is mental rather than metal. It is called pattern theory , a new area of mathematics that was developed by one of the authors and accidentally discovered by the other. We want to take a look at history not because we search for any hidden defects, but because we can place under scrutiny of pattern theory literally everything. Here is an excerpt from the list of subjects pattern theory considers: Automatic target recognition, body movements, behavior, mathematical logic, growth and decay, language, human and animal skeletons, grammars, mathematical functions, automata, industrial processes, weave patterns of fabric, molecules, handwriting, spectra, cockroach's legs, human hands, the crust of the earth, genealogy, plots of novels and fairy tales, archaeology, motion of planets, kinship relations, botanical taxonomy, scientific hypotheses, social dominance, language, anatomy, and much more—actually, anything. So, why not history, more captivating than any fairy tale, the greatest and longest novel ever written, full of suspense, tragedy, and hope, with heroes and monsters of global proportions? 7 The comparison with X rays, however vague, is meaningful for us. We can examine with X rays a multitude of totally unrelated objects as different as live human hand, Rembrandt’s painting, Egyptian mummy, horse’s leg, and the suitcase of an airline passenger. What we see in each of them is a black-and-white shadow with very little resemblance of what is seen on the surface. It can be easily scanned and reduced to a long sequence of numbers stored in computer memory, each presenting the darkness or brightness of a certain point. All X ray photos, so put it bluntly, are made of the same black and white stuff, although they are derived from strikingly different objects. They revoke the shadows on the wall of the Plato’s cave. What unites all those heterogeneous objects is that they are complex and have structure invisible by a naked eye. As viewed through the mental imaging apparatus of mathematics, they may look surprisingly similar: like points connected with lines. Not accidentally, the application of pattern theory to understanding medical imaging is one of the fastest growing. Here we are attempting to apply the same principles to the body of historical narrative. What we expect to see is its hidden skeleton in motion. Following this analogy, we will first try to show how to produce the image of the skeleton, and, secondly, speculate on how to understand what it tells us. If it turns out that a historical narrative and events behind it cast the same shadows of the wall of the Plato’s cave as horse, suitcase, and chemical reaction in a test tube, this would mean that history, regardless of its content, joins the world of dissimilar objects built along similar principles. We hope to understand something new about the unity of the world. Of course, history is such a colorful subject that we will not resist the temptation to put some flesh on the mathematical bones. 8 Since our experiment is first of the kind, we cannot promise too much. If, however, it stimulated a historian to repeat it in a professional fashion, we would say that our expectations were exceeded. The general mindset of pattern theory is not alien to modern culture and we believe that the reader will easily recognize its relation to past and current trends. There is a far more general relation, however. The second half of the twentieth century was deeply imprinted by a dichotomy that Charles P. Snow (1959) had attributed to the contemporary culture. He saw an impenetrable divide between people living in two immiscible media—natural sciences and liberal arts. His motto about two cultures is still echoed by polemic responses. We can mention David Edgerton (1997) and John Brockman (1995). The slow process of fusion goes on in the new century and in quite unexpected directions, as the recent The Sociology of Philosophies by Randall Collins (1998) illustrates.