Mathematics of Local Optimism
The theory of Local Optimism assumes that there are many possible worlds; most are virtual, not lasting long enough to be observed; a few last long enough to be observed, and are called real.
Local optimism states that any real world is a local optimum; it is the best of all sufficiently similar possible worlds. Call such a possibility-neighborhood the “circumstances”; meaning “that which stands around”; then local optimism says that this is the best possible world, under the circumstances.
This resembles Leibnitzian Optimism, which states that this is the best possible world of all. Leibnitz says that this world is a global optimum; whereas Local Optimism says that this is a local optimum.
According to local optimism, there may be many local optima, some better than ours, some worse. This leaves open the question of what is being optimized. Call any system of world-evaluation a “value field”. Real worlds exist at peaks in the value field.
Local optimization is a proven principle in physics and biology. Biological systems naturally evolve to maximize reproductive fitness; and physical systems obey the law of least action; so optimization can be a maximization or a minimization.
Local optimism has these mathematical consequences:
Let the rate of change of value be called ‘progress’, and the rate of change of progress be called ‘uplift’. Then at any local optimum, in every direction, progress is zero, and uplift is negative. That is the “Frown at the Peak”.
Any path from one local optimum to another must at first decline.
Any path from one local optimum to another must meet a Path Pessimum; the worst of all possible worlds along the path.
At any path pessimum, progress is zero, and uplift is positive. That is the “Smile in the Valley”.
A world ceases to be a local optimum when an ascending path appears, leading to a sufficiently different world. Such paths can appear or disappear when the value-field changes. Therefore revaluation can create and destroy local optima.