From Skeptic vol. 8, no. 3, 2001, pp. 54ff.
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Special Section Introduction:
A Quick & Dirty Guide To Chaos And Complexity Theory
Three Race Horses & Four HobbyHorses
By Frank Miele
Bookies have a saying, "There are three horses who have never come in win, place, or even show. Their names are Coulda, Woulda, and Shoulda." Bookies live, and sometimes die, by the accuracy or inaccuracy of their predictions. Their performance is immediately obvious to all involved.
The same, however, cannot be said of many academics, even less so of pop-science writers. Despite what you've heard about the hypothetico-deductive method being the touchstone of science, it is the exception when predictions by academics are put to the empirical test and they have to live or die by the results. It's all too easy for them to come up with "supplementary hypotheses" to explain their way out. (Try out a supplementary hypothesis on Tony the Crippler when he knocks on your door to collect the two grand you dropped on a pony that finished dead last. You'll soon drop dead). This lack of accountability is further parlayed as one moves from the physical sciences, to the biological, to the behavioral, to the social sciences, reaching the level of a dead cert in literary studies.
The worst such abuses occur when terms that have a clearly defined meaning, usually mathematical, in the physical sciences are imported into literary studies as metaphors. By the time they reach pop books, a good skeptic's baloney detector should be red-lining. Latest to make this transition are the two C-words, Chaos and Complexity, and their hybrid offspring, Contingency and Counterfactuals. Together they are the academic counterparts of Coulda, Shoulda, and Woulda. They are the four hobby horses of Chaostory. What makes this jockeying all the easier is that the restricted, stipulative definitions of these terms, if not the opposite, are certainly a long way from our understanding of them in everyday discourse.
Chaos: It's Anything But Helter Skelter.
Let's start with chaos. The dictionary defines it as: "(1) utter confusion or disorder; (2) the formless matter supposed to have preceded the existence of the universe." Roget's Thesaurus gives ôdisorder, derangement, and anarchyö as synonyms, and "order, uniformity, regularity, and symmetry" as antonyms. But in the world of Chaos/Complexity theory one encounters such terms as "deterministic chaos" which results from "deterministic dynamical equations." Conceptually, we are told, "chaos is intrinsic to the system and clearly distinguished from the effects of random or 'stochastic' fluctuations in the external environment." Therefore, distinguishing deterministic chaos from stochastic ('true') chaos "is one of the principal hurdles that confronts 'chaologists', scientists working with potentially chaotic systems."1 What is the difference between deterministic chaos and stochastic ('true') chaos? The answer is the Attractor, which can be either a Fixed Point Attractor or a Strange Attractor. This all really makes sense within the world of physics and non-linear mathematics (see Pigliucci's article in this issue for definitions and an explanation), but becomes meaningless chaobabble when applied elsewhere.
Complexity: The Search for Simplicity
My dictionary defines complexity as "intricate, knotty, or perplexing." Its use in Chaos/Complexity theory certainly is perplexing, because there it means a search for simple rules that can explain how the universe can "start with a few types of elementary particles at the big bang, and end up with life, history, economics, and literature."2 How can this happen? The answer offered is self-organized criticality (criticality, another C-word), "the tendency of large systems with many components to evolve into a poised, 'critical' state, way out of balance, where minor disturbances may lead to events called avalanches. Most changes take place through catastrophic events rather than by following a smooth gradual path"3 (Catastrophic, yet another C word).
If the butterfly flapping its wings in Brazil and setting off a tornado in Texas has become the mantra of Chaos theory (even though there's no evidence that a gaggle of butterflies has ever so much as generated a zephyr), Per Bak's Child's Sand Pile is the icon of Complexity theory. He describes it as follows:
In the beginning, the pile is flat, and the individual grains remain close to where they land. Their motion can be understood in terms of their physical properties. As the process continues, the pile becomes steeper, and there will be little sand slides. As times goes on, the sand slides become bigger and bigger. Eventually, some of the sand slides may even span all or most of the pile. At that point, the system is far out of balance, and its behavior can no longer be understood in terms of the behavior of the individual grains. The avalanches form a dynamic of their own which can be understood only from a holistic description of the properties of the entire pile rather than from a reductionist description of individual grains: the sandpile is a complex system.3 So taken by the sand pile metaphor was then Senator Al Gore that he cited it in his book, Earth in Balance, and credited it with transforming his view of the world:
The sand pile theory, self-organized criticality, is irresistible as a metaphor; one can begin by applying it to the developmental stages of human life. The formation of identity is akin to the formation of the sand pile, with each person being unique and thus affected by events differently. A personality reaches the critical states once the basic contours of its distinctive shape are revealed; then the impact of each new experience reverberates throughout the whole person, both directly, at the time it occurs, and indirectly, by setting the stage for future change. One reason I am drawn to this theory is that it has helped me understand the change in my own life.4
Bak shows that such seemingly unrelated phenomena as Raup's data on extinctions, Mandelbrot's analysis of commodity prices, and Gutenberg-Richter's on earthquake magnitude all can be mapped to similar graphs. In each graph we see that the number of incidents decreases as the magnitude of the event increases. Bak then argues that this is evidence that we should look for underlying general laws to explain all such behavior, rather than turning to narratives to describe each incident in terms of its unique precipitating characteristics (such as bad news from the Fed or an accumulation of stress in the earth's crust).
But the net worth of Bill Gates and any of 39 other internet tycoons exceeds that of the majority of the earth's inhabitants combined or the Gross National Product of some nations. Is the saying "the rich get richer while the poor get poorer" a fundamental law of nature not to be tampered with? It is unlikely many advocates of extending chaos and complexity theory beyond the physical sciences would buy into that one.
Contingency as Disingenuous Determinism
The dictionary defines contingent as "1. dependent on something not yet certain. 2. accidental or fortuitous" and "contingency" as "dependent on chance, an uncertain event." In everyday discourse the term is associated with the fee arrangements made between lawyers who wait outside hospital emergency rooms for potential clients for whom they can sue the state or a large corporation, hoping they'll collect "walking away money" to settle a "slip and fall" liability case out of court. For present purposes, however, these terms owe their origin to Stephen Jay Gould. The sacred scripture for the doctrine of contingency is his book Wonderful Life, with the proof appearing on pages 48 and 287:
I call this experiment "replaying life's tape." You press the rewind button and, making sure you thoroughly erase everything that actually happened, go back to any time and place in the past. Then let the tape run again and see if the repetition looks at all like the original.5
"...[the] basic principle of contingency, a replay of the tape yielding an entirely different but equally sensible outcome; small and apparently insignificant changes ... lead to cascades of accumulating differences."6
The theme of Wonderful Life is to dispel the notion that we (i.e., Homo sapiens) are the inevitable product of progressive evolution. Gould argues that of the myriad of wild and woolly creatures alive in the Cambrian seas, it was only a matter of bad luck, not bad genes, that so many disappeared, leaving the field open for the evolution of our line.
But how meaningful a concept is contingency and how telling is Gould's analysis? At best, contingency is a non-theory in that it opts for the importance of freak events over general processes. Cosmology, evolution, or history become "just one damned thing after another." At worst, rather than an alternative to determinism, contingency is disingenuous determinism because it argues that the freak event which wiped out one line of evolutionary development foreclosed all the others and forced the remaining one on a rigidly determined course.
Granted, if our great ancestors hadn't drawn the lucky hand and survived the great Cambrian extinction, we wouldn't be here and you wouldn't be reading this article. But can we really be sure it was just a matter of luck rather than some characteristic such as adaptability that led to their survival? Also, the evidence on which Gould hangs his case, the alleged proliferation of 'weird' life forms in the Cambrian, has been subject to criticism. Some of these wildly weird creatures may be the result of reconstructing them upside down. A rightside up orientation produced very normal looking specimens.7 Even if they did exist in their woollier reconstructions, this is not proof that evolution would not have thrown forth and selected for other life forms possessing certain identifying characteristics of ours and other species. Repeatedly throughout the geological record we see different lineages successively evolving similar anatomies and behaviors in order to exploit available niches. Several independent evolutionary lineages (insects, bats, birds, and pterosaurs to name a few) have developed such complex processes as flight, the eye (chordates and cephalopods), or a brain capable of solving some form of logical problem (apes, elephants, and at a simple enough level, even the octopus). Though separated by 80 million years of evolutionary history since their last common ancestor, the Tasmanian (marsupial) wolf and the true wolf looked and lived a lot alike. The Tasmanian wolf actually survived up until 1933, so we have reports of its natural behavior and even films of it in captivity. As theoretical biologist Brian Goodwin explained:
Suppose you reran the Big Bang. What are the chances of getting the same periodic table of natural elements, the same ninety-two combinations of protons, neutrons, and electrons? Pretty good, or so I'm led to believe. I think of a rerun of the Cambrian explosion in the same way, not to the same extent perhaps, but as an image. A rerun of the Cambrian explosion would produce a world much more like the one we know than Steve Gould says. It wouldn't be identical to the one we know, but there may be a lot of similarities, ghosts we'd instantly recognize.8
When the Chicxulub asteroid wiped out the dinosaurs, birds and land and marine mammals arose to exploit similar niches. And if, playing the contingency card, Chicxulub had missed the earth, it's a better than even bet that some line of the dinosaur tree would have evolved increasing ability to extract, process, and use information from their environment (i.e., intelligence) similar to what the fossil record shows took place for mammals and especially primates.9
We can see this clearly in Harry Jerison's data on the evolution of brain and intelligence.10 Figure 3 shows a graph of the brain weight/volume to body weight/volume for living mammals, fossil mammalian ungulates, and for living and fossil reptiles. The polygon formed by the brain-to-body ratio of the living mammals is distinct from that for the living and fossil reptiles. To the extent that brain-to-body ratio measures information-processing ability, these data show a progressive trend in evolution. The gray zone of archaic ungulates shows that they fall outside the range of living mammals, but are closer to them than to either the living or the fossil reptiles. This is evidence of progress across phylogenetic lines.
How did such progress take place? Chaos, complexity, contingency? Figure 4 (in the magazine) depicts a set of bell curves that provide the answer, adaptation brought about by an arms race. Note first that for each era in geological time the predators (carnivores) have larger relative brain-to-body ratios than their prey (ungulates). Then note how the bell curve for the predators pulls the bell curve for their prey to successively higher mean brain-to-body ratios.
Jerison provides further evidence for the arms race effect by examining the fauna of South America at a time when it was an island cut off from the rest of the world. Before more modern predators arrived via the Panama land bridge, the arms race between a separate line of predators (carnivorous marsupials) and their prey produced an identical pattern of progressive evolution as evidenced by increasing brain-to-body ratios (shaded area in Figure 5).
Gould plays the contingency card for two reasons. The first is his desire to have evolution act in sudden jumps, consistent with his theory of punctuated equilibrium, rather than in gradual, ever more adaptive steps, in the Darwin-to-Dawkins British tradition, revolution rather than evolution. The second is that he wants to dispel forever the notion of evolution as a great chain of being, a long, determined process of steady, stepwise progress, from simple to complex, as depicted in Figure 6 from E.A. Hooton's classic Up From the Ape. As Gould explained, "Progress is a noxious, culturally embedded, untestable, nonoperational idea that must be replaced if we wish to understand the patterns of history.... Progress is not intrinsically and logically noxious. It's noxious in the context of Western cultural traditions."10
Arguing that we would not see identical worlds is attacking a straw man, in this case; one that is dead and white. No one today, save creationists in their lampoons, thinks of evolution as some sort of cosmic time tunnel where a bunch of amino acids ooze into one end and Madison Grant, author of The Conquest of a Continent and The Passing of the Great Race, marches triumphantly out the other. The real questions we should ask are: "Just how different would these worlds be?" and "What are the key morphologies and behaviors that are selected for or against?"
When one turns from the evolutionary record to the record of human history, the use of contingency, and what in that discipline are called counterfactuals, lends itself to even greater abuse.
Counterfactuals: From "What If ..." to "If Only..."
I couldn't find counterfactual in the dictionary. This jargon term is a trifecta of Coulda, Woulda, and Shoulda, best captured by George Herbert's ditty:
For want of a nail the shoe is lost,
For want of the shoe the horse is lost,
For want of the horse the rider is lost,
For want of the rider the battle is lost,
For want of the battle the war is lost,
All for want of a horseshoe nail.
While contingency is offered as an alternative to determinism, the small and apparently insignificant changes leading to a cascade of wildly different scenarios, counterfactuals can act as determinism with a vengeance. As Niall Ferguson, one of the better practitioners of counterfactualism, points out in his introduction to a collection he edited called Virtual History, the "What if ..." of counterfactuals all too easily becomes the special pleading "If only." "What if JFK hadn't been killed?" all too easily becomes "If only JFK hadn't been killed, we wouldn't have gotten into that terrible Vietnam war." Or, "What if FDR knew about Pearl Harbor?" becomes "If only the American voters knew what FDR was hiding from them, we wouldn"t have gotten into the Second World War." Oliver Stone"s "historical films" (JFK, Nixon) and Pat Buchanan's recent book on United States foreign policy (A Nation, Not an Empire) are less about what either of them thinks our policy should have been than about what they want our policy to be now and in the future. "Such veiled counterfactualism has been a striking feature of a great many recent 'revisionist' works of history."11
The British Museum has an entire room devoted to counterfactuals, which it politely terms "Imagined Histories." The Smithsonian calls them "Alternative Histories." Gore Vidal has made a career of writing mixes of history (the way he thinks it really happened) and novels. His latest effort in the genre, The Smithsonian, takes place in that very institution. If that's not enough, you can also go to the Uchronia: Alternate History web page (www.uchronia.net) where you'll find an annotated bibliography of novels, stories, essays and other material involving the "what ifs" of history, known in the trade as alternate histories, allohistories, uchronia, counterfeit worlds, counterfactuals, and negative histories.
Counterfactual works abound. Ferguson's edited volume, Virtual History, contains chapters on England Without Cromwell, the world without the American Revolution, Britain 'Standing Aside' in WWI, Hitler's invasion of England, Hitler's defeat of the Soviet Union, the world without the Cold War, Camelot lives (i.e., JFK doesn't die), and the world today if the Soviet Union had survived.12 What If? contains counterfactuals by historians William McNeil (on how a plague saved the 10 tribes of Israel from being carried off by the Assyrians in 701 BC), John Keegan (on how Hitler could have won the war), and Stephen Ambrose (on what if D-Day failed), among others.13 The Hitler Options: Alternate Decisions of World War II presents 10 different scenarios by which der Fuhrer (a perennial counterfactual favorite) could have pulled it off (odd that he didn't employ any of them).
Robert Sobel's For Want of a Nail: If Burgoyne Had Won at Saratoga14 and Niall Ferguson's The Pity of War: Explaining World War I15 fall into a different class of counterfactual. Sobel's For Want of a Nail traces the history of British America from 1763 to 1973. His 440-page tome includes fictitious maps, election results, economic trends, and a 16-page bibliography. A critical afterword, appearing in the (fictitious) North American Historical Association, shows that the book was meant as a thinking exercise to illustrate two major trends in the history and politics of Anglo-America:
It is the author's contention that the peoples of British North America were fairly united prior to 1763. Although he does not say as much and in so many words, he implies that the North Americans of that day had two political traditions. The first of these came from Britain, and consisted of an evolutionary road to a more perfect commonwealth. The second, a child of the Enlightenment, was a utopian view of man and nature, to be found, in differing ways, in such thinkers as Voltaire, Rousseau, Montesquieu, and others of that period. Following the Seven Years' War, some Americans ... held that the nation's future lay with the Empire, with Europe, with tradition, and with the evolutionary development of institutions. A second group, including the Adamses and Jefferson, were utopians, who believed in free will, held that man could be the master of his fate, rule himself, and wash away the abuses of centuries in a generation. These two groups and ideologies clashed in the Rebellion, which saw the victory of the "evolutionists," if we may call them that. The hero of this book is John Burgoyne, first Duke of Albany, who wins the Rebellion and then sets the new C.N.A. [Confederation of North America] along the evolutionary pathway.16
Evolution v. revolution. Sound familiar?
Too Much or Too Little?
Ferguson's The Pity of War is not really an alternative history. It is an all too real account of World War I, not in terms of a military or a diplomatic narrative, but rather in terms of major topics and a discussion of how much effect they had. Chapters examine specific questions about why WWI began, why it was fought the way it was, and why it ended as it did. The book is most illuminating when Ferguson gets down to counting literal "bang for the buck", how much it cost each side to kill one of the other side's soldiers.
The Pity of War only becomes counterfactual in the final chapter, "Alternatives to Armageddon," where Ferguson challenges the reader to consider what would have been the result if Britain had "stood aside" (the British terminology at that time for not having entered the war against Germany). Ferguson's conclusion is that not only Britain, but Europe and the U.S., would have been a lot better off if the Brits had kept out. The war in Europe would have been a stalemate. No collapse of the Tsarist regime means no Bolshevik revolution and all that came with it. No humiliating defeat for the Kaiser's Germany means no Treaty of Versailles, no Hitler, no WWII, no Holocaust, no Cold War.
Again, Ferguson's book is meant more as a thinking exercise on policy options than an alternative history. To that end, he appeared on C-SPAN opposite Harvard professor Charles Maier and Daniel Goldhagen, author of Hitler's Willing Executioners. Goldhagen is so wedded to his thesis that the Holocaust was inherent in the anti-Semitism of the German people he went so far as to argue that even if there hadn't been a Versailles Treaty Hitler would have come to power, in Austria-Hungary no less, because of the world depression of the 1930s. Now there's a counterfactual for you!
In their pro and con in this issue both Shermer and Pigliucci use the famous example of Lee's Order #191 falling into Union general McClellan's hands to illustrate a counterfactual. I'll use one less well known, the service above and beyond the call of duty supplied by an American nurse before the Battle of the Bulge in World War II, to illustrate how I think the concept is limited and how it needs to be refined and improved.
In December of 1944 the Western allies were convinced it was only a matter of time before they crossed the Rhine and conquered Germany. Der Fuhrer, ever the gambler willing to "think outside the box" (maybe that's why he's such a favorite with counterfactualists), gathered together whatever forces he could spare from the Eastern front for one last chance to win der Krieg. He attacked where the Allied forces had left themselves vulnerable, pushing forward to form a thinly defended "bulge." His army and elite Waffen SS troops surprised the Allies by advancing through the lightly defended Ardennes forest. Hitler hoped to split the British and American forces, driving all the way to the port city of Antwerp. This would deprive each army of its supply base and produce a "Second Dunkirk" that he hoped would cause Britain to sue for peace. He could then turn his attention to the Eastern front.
The offensive was initially successful, especially against those sectors defended by relatively inexperienced American troops, and because bad weather kept Allied air forces grounded. Eventually it was halted far short of Antwerp. The Americans refused to surrender the vital crossroads of Bastogne, with which two names are forever linked. The first is that of the defending commander, General McAuliffe, who replied "Nuts" to the German request for surrender. (He may actually have uttered another four-letter word, but these accounts were written in the 1940s when "trash talk" was not in vogue.)
The second hero is General Patton, whose 3rd Army eventually lifted the siege of Bastogne. (Who can forget actor George C. Scott in his Oscar-winning role ordering the military chaplain to provide a weather prayer so that he would have air cover for his advance?) But British military historian Sir Basil Liddell Hart discovered a third hero, actually a heroine, on whom I shall build my counterfactuals. When he interrogated the Wehrmacht commanders after the war one of them told him he could have taken Bastogne early on, but he had "dallied with a young American nurse, 'blonde and beautiful,' who held him spellbound."17 Surely this unsung heroine was worthy of, if not the Purple Heart, at least some appropriate honor. In any case, let's consider what would have happened if the Panzer commander hadn't wasted vital time playing doctor.
Counterfactual #1. The plan goes exactly as Hitler hoped. The British troops are cut off in a second Dunkirk and Otto Skorzeny's commando troops produce widespread panic among the inexperienced American troops. The Churchill government falls and King George VI abdicates. A successor government with the Duke of Windsor restored as Edward VIII releases Rudolf Hess from prison and sues for peace. The shock causes FDR to die of a heart attack. He is succeeded by Vice President Henry A. Wallace, who was elected with him in 1940 but was denied renomination at the 1944 Democratic Party convention. The military ignores all orders from the hapless pro-Soviet Wallace and waits until the anti-Soviet Harry Truman assumes the presidency in January of 1945. Listening to his generals and admirals, Truman turns America's war effort to defeating Japan and blocking any Soviet drive in the Pacific. Now fighting on only one front, Hitler outmaneuvers the Soviet army as he did in 1941 and wins back the Eastern front. As in Robert Harris' novel Fatherland, an aging Hitler eventually shakes hands with American president Kennedy, the also aged Joseph Sr., the non-interventionist. The big debate among future historians is when, where, and how the European Jews disappeared.
But even supposing that the officer-nurse tryst didn't take place, would all (or any) of these events follow inexorably? It's just as likely that after his victory in the West, Hitler would have once again gambled in the East and this time lost big. With Britain and the U.S. out of the war, victorious Soviet armies would have eventually taken all of Germany, and the "Iron Curtain" (a term Josef Goebbels used before Winston Churchill by the way) would have been the Atlantic Ocean. Rather than Harris' Fatherland, the result would have been more like Orwell's 1984.
Counterfactual #2, #3. Any number of other scenarios might be imagined. Fearful that the war would now drag on forever, a successful officer's plot might have killed Hitler and sued for peace with the West (thus putting the Iron Curtain on the Vistula, rather than the Elbe) or, if rebuffed, with the Soviet Union, or with Russian generals inspired to eliminate Stalin (thus putting it on the Rhine). Or it could have made very little difference at all in the grand scheme of things and just meant that more lives would be lost and cities ruined. Especially when we are dealing with human beings who make conscious decisions, often based on past experience, events do not flow inexorably.
Counterfactuals are useful as thinking exercises that help us understand how events are interconnected. They become more meaningful as they become more mathematical and therefore testable. Tetlock and Belkin18 and Schroeder19 describe methodologies for determining what constitutes reasonable and unreasonable counterfactuals. The best examples to date are the cliometric (measuring Clio, the muse of history) work of Robert Fogel. His analyses were at first disputed, largely because his new methodology challenged two sacred cows of historians and economists (particularly those on the American left): Fogel concluded that without the Civil War slavery would have continued to be economically profitable, and that railway construction was not a sine qua non for U.S. industrialization. (Fogel got the last laugh, receiving the Nobel for economics for his work in 1993.)
A QuinellaùChaos and Complexity, or
Contingency and Counterfactuals
Chaos and complexity are important concepts in mathematics and physics, but we should look skeptically at their introduction into other fields, especially in books with titles that sound like a cross between a drive-in movie from the 1950s and a self-help seminar: Complexity: Life at the Edge of Chaos; The Collapse of Chaos: Discovering Simplicity in a Complex World; Frontiers of Complexity: The Search for Order in a Chaotic World. Rather than an alternative to determinism, contingency can be a disingenuous form of determinism when it is applied in counterfactuals as some sort of 19th century railroad switch, diverting the train of history to one and only one "entirely different but equally sensible outcome." A better metaphor is to think of events, in either evolutionary or historical time, as cars swerving between the fast and exit lanes during rush hour traffic. Odds are the total traffic flow will be affected in all the lanes, with lots of fender-benders and crashes as the lanes accordion in and out. Drivers in many, but not all lanes will make adjustments. Most will make it home safe, if delayed. Some will come home bandaged. And some will end up toe-tagged and body-bagged. Which drivers make it and which ones don't will depend on their individual driving ability, the performance of their car, and luck as well. But tomorrow there will be another rush hour (Figure 7).
Michael Shermer likes to point to his huge file of "Theories of Everything" articles submitted to Skeptic, to illustrate how theories that attempt to explain everything usually explain nothing. Outside of the physical sciences and mathematics, chaos and complexity may be just analogies and metaphors, theories of everything that are little more specific than the daily horoscope or the messages in fortune cookies. But uttering the words "chaos" and "complexity," especially in the right tone of voice and at the right time, can get your way paid to an academic conference in some fashionable part of the world (where the most important conversation will go on over drinks), or land you that management job (that requires only meeting the minimal qualifications). And you can make book on that!
References
1. Conveney, P. and Highfield, R. 1995. The Frontiers of Complexity: The Search for Order in a Chaotic World. New York: Fawcett, 174.
2. Bak, P. 1996. How Nature Works: The Science of Self-Organized Complexity. New York: Springer, 2.
3. Ibid., 2.
4. Quoted in Ibid., 63.
5. Gould, S. J. 1989. Wonderful Life: The Burgess Shale and the Nature of History. New York: Norton, 48.
6. Ibid., 287.
7. Cohen, J. and Stewart, I. 1994. The Collapse of Chaos: Discovering Simplicity in a Complex World. New York: Viking, 132.
8. Lewin, R. 1992. Complexity: Life at the Edge of Chaos. New York, NY: Macmillan. 74.
9. Russell, D. 1992. An Odyssey In Time. Toronto, Canada: University of Toronta Press.
10. Jerison, H. 1972. The Evolution of the Brain and Intelligence. New York: Academic Press.
11. Lewin, Op. cit., 139-140.
11. Ferguson, N. 1997. Virtual History: Alternatives and Counterfactuals. New York: Basic Books, 19.
12. Ferguson, N. 1997. Op. cit.
13. Cowley, R. (ed.) 1999. What If? The WorldÆs Foremost Military Historians Imagine What Might Have Been. New York: Putnam.
14. Sobel, R. 1973/1997. For Want of A Nail: If Burgoyne Had Won at Saratoga. London: Greenhill Books.
15. Ferguson, N. 1999. The Pity of War: Explaining World War I. New York: Basic Books.
16. Sobel, Op. cit., 405.
17. Liddell Hart, B. H. 1970. History of the Second World War. New York: Putnam, 651, n.2.
18. Tetlock, P. and Belkin, A. 1996 Counterfactual Thought Experiments in World Politics. Princeton, NJ: Princeton University Press.
19. Schroeder, P. 2000. Embedded Counterfactuals and World War I As An Unavoidable War. Paper presented at the 2000 Annual Meeting of the American Political Science Association to appear in Tetlock P., Lebow, R., and Parker, (eds.) Unmaking the West: Counterfactual Thought Experiments in History.
