Asymptotic Stability is the only foundational element of the “Ideal Money” of our definition that does have conceptual existence in prior art notions of good money.
In mathematics, asymptotic analysis is a method of describing limiting behavior. In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
The technicalities that the concept of asymptotic stability entail are too complex to comprehend. In simpler terms asymptotic stability means that values that start close enough not only remain close enough but also eventually converge to the equilibrium.
To make it simpler we take a closer look at Newton’s cradle. Although Newton’s cradle was designed to demonstrate conservation of momentum and energy using a series of swinging spheres, it may still provide a little bit better understanding of asymptotic stability. In a non-linear dynamic system values swing just like a pendulum swings, but tend to converge towards the point where the pendulum hangs straight down pointing to its center of gravity. Imagine the peripheral spheres in Newton’s cradle representing the price swings of a currency and the stationary spheres representing stability (although currency will not be as absolutely stable as in Newton’s cradle).
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