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many competing keyboard arrangements, the QWERTY system. As the school became well known her teaching methods became the industry standard, even adopted by Remington, which also began to set up typing schools using QWERTY. In 1888 a contest was arranged between Longley’s method and that of her competitor Louis Taub, using a different typing technique on a non-QWERTY keyboard. Longley’s star pupil, Frank McGurrin, apparently thrashed the competition by memorizing the entire QWERTY keyboard and typing by touch alone—an innovative technique for the time. The event generated much publicity and touch-typing became the method of choice for American typists. The Sholes-designed and Remington-manufactured typewriter with the QWERTY keyboard became necessary to the point that it would take a typing revolution to reshuffle the keyboard deck. Unless the major typewriter and computer companies, along with typing schools, teachers and publishers of typewriter manuals, and a majority of typists, all decided to change simultaneously, we are stuck with the QWERTY system indefinitely. An informal version of the model of contingent-necessity is what might be called the QWERTY principle: historical events that come together in an unplanned way create inevitable historical outcomes.

Beyond Chaos: Self-Organization, Antichaos, Simplexity, and Feedback

Sensitive dependency and bifurcations are only two aspects of chaos to be considered. “The straw that broke the camel’s back” provides another metaphor of nonlinear dynamics. As the straw is piled on piece by piece, the camel’s legs do not slowly bend lower until belly meets ground; rather, the camel maintains its straight-up stature until a critical breaking point is reached that causes the legs to suddenly buckle. Such is the nature of earthquakes, avalanches, economic depressions, ecological disasters, and quite possibly wars, revolutions, paradigm shifts, and other catastrophic historical events. Per Bak and Kan Chen describe this phenomenon as self-organized criticality, where “many composite systems naturally evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system.” They note that large systems such as geological plates, the stock market, and ecosystems “can break down not only under the force of a mighty blow but also at the drop of a pin.” This one-pintoomany, when dropped into a system in a critical or delicately balanced state, starts “a chain reaction that can lead to a catastrophe.” Calling self-organized criticality a holistic theory, Bak and Chen claim: “Global features of the system cannot be understood by analyzing the parts separately. To our knowledge, self-organized criticality is the only model or mathematical description that has led to a holistic theory for dynamic systems.”20

Their metaphorical model and experimental test of a catastrophe is a pile of sand in which single grains are dropped onto a flat, circular surface. The pile grows slowly and gradually into a gentle slope, and can be described by linear mathematics. But “now and then, when the slope becomes too steep somewhere on the pile, the grains slide down, causing a small avalanche.”21 This avalanche, or catastrophe, is triggered not by a major event or necessitating force, but by a minor contingency. (The avalanche, of course, could be triggered by a major event, but not necessarily.) The point at which the avalanche occurs Bak and Chen call chaotic. As the pile grows larger and larger, it “evolves on the border of chaos. This behavior, called weak chaos, is a result of self-organized criticality.”22 Because the actions and locations of the early falling grains affect the actions and locations of later falling grains, “the dynamics of a system are strongly influenced by past events.”23 In other words, history determines the system.

This action is what the model of contingent-necessity and its corollaries predict. The fall of the grains will be chaotic in the early stages and more ordered in the later, until reaching a critical point