**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.