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ones, contain subsystems that are “fluctuating.” As long as the fluctuations remain modest and constant, relative stasis in the system is the norm. If the fluctuation becomes powerful enough that it upsets the preexisting organization and balance, a major change, or revolution, may occur, at which point the system may become chaotic. This point of sudden change is called the bifurcation point. Necessity takes a system down a certain path until it reaches a bifurcation point. At this time contingency plays an exaggerated role in nudging the system down a new path, which in time develops its own powerful necessities such that contingency is attenuated until the next bifurcation. It is the alloy of contingency and necessity that guides and controls the presence or absence of these bifurcations, as Prigogine notes in similar language: “The ‘historical’ path along which the system evolves as the control parameter grows is characterized by a succession of stable regions, where deterministic laws dominate, and of instable ones, near the bifurcation points, where the system can ‘choose’ between or among more than one possible future.”16

In the language of contingent-necessity, a bifurcation, or “trigger of change,” is any stimulus that causes a shift from the dominance of necessity and order to the dominance of contingency and chaos in a historical sequence. Examples in history abound: inventions, discoveries, ideas, paradigm shifts, scientific revolutions, economic and political revolutions, war, famine and disease, invasions, immigrations and emigrations, population explosions, natural disasters, climate and the weather, and so on; all have the potential for triggering a sequence to change from order to chaos. A trigger of change, however, will not cause a shift at just any point in the sequence. Corollary 5 states that a trigger of change will be most effective when well-established necessities have been challenged by others so that a contingency may push the sequence in one direction or the other. This bifurcation point, or “trigger point,” is any point in a historical sequence where previously well-established necessities have been challenged by others so that a trigger of change (contingency) may push the sequence in one direction or the other.

In like manner the sensitive dependence on initial conditions—the butterfly effect17—has direct application to corollaries 1 and 2 dealing with the point of time in the sequence—early or late—and the chaotic or ordered nature of that sequence. The butterfly effect, or the “trigger effect,” is the cascading consequences of a contingent trigger of change in a historical sequence. The trigger effect is linked with corollary 1 where the earlier in the development of any historical sequence, the more chaotic the actions of the individual elements of that sequence and the less predictable are future actions and necessities, as well as with corollary 2, which reverses the influence of the trigger effect because the later in the development of any historical sequence, the more ordered the actions of the individual elements of that sequence, and the more predictable are future actions and necessities. Therefore the power of the trigger depends on when in the chronological sequence it enters. As stated in corollary 5, change tends to occur at points where previously well-established necessities have been challenged by others so that a contingency may push the sequence in one direction or the other. The flap of the butterfly’s wings in Brazil may indeed set off a tornado in Texas, but only when the system has started anew or is precariously hanging in the balance. Once the storm is well under way, the flap of a billion butterfly wings would not alter the outcome for the tornado-leery Texans. The potency of the sequence grows over time. In human history the trigger effect is quickly erased once the patterns begin to settle in. An individual of great talent may have little effect in regions of stability, while another of modest competence might deflect the entire sequence in regions of instability.