"Chaos breeds life, when order breeds habit."
In the late 1700s, the eminent work initiated by the English mathematician and physicist Sir Isaac Newton was carried forward by the French mathematician and physicist Pierre-Simon Laplace, also known as the “French Newton.” Laplace firmly believed in determinism, the idea that the past completely determines the future, that given enough information about a system, it is possible to make completely accurate predictions about the future state of that system.
The two simulations matched each other closely at the start, but after several model “months” they wildly diverged, not even remotely resembling each other in the longer term. Upon completing an extensive analysis, Lorenz realized that his assumed inconsequential round-off error was in fact highly consequential, that given enough simulation time even the tiniest round-off errors produced massive changes in the entire system.
Dx/dt = P(y-x)
This is now known as the Lorenz attractor, a model of rolling fluid convection so simple that it can be described by three basic equations, yet even given all the information about the system it is not possible to make accurate predictions about its future state - the rolling fluid convection system never enters the same state twice, and as such the plotted line that gives shape to the Lorenz attractor never intersects itself. It is not possible to make accurate predictions about the future state of such a system. Yet it is clear to anyone with eyes that the Lorenz attractor contains an orderly pattern.
The observations of Lorenz and his description of the Lorenz attractor embody the phenomenon of chaos, a phenomenon that is difficult to pin down with words. That said, a chaotic system contains at least two core features:
Many people today prefer predictable things over unpredictable things; they want to know what they will be doing at work before they actually go to work, or where they will be going before heading out for the evening, or where they will be staying before going on a vacation. For a variety of reasons, there exists a strong urge to predict future events before those future events are actually experienced.
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