# Optimization Is Teleology

Optimization = Teleology.

This is not an inclusion. This is an equal.

First of all, if you accept teleology then the purpose optimizes
everything. So it obviously induces an optimization.

Conversely:

An optimization problem consists of two things.

1. The objective function
2. Constraints

An optimization is literally just maximizing or minimizing the
objective function with given constraints. For example, you can
maximize your sleep (the objective function) while you don't miss
out your schedules (constraints).

So as you can see, min/maximizing the objective function works as
a purpose. And that's especially teleological if solving an
optimization problem is not to optimize something, but to explain
and to induce the results.


A typical example is the principle of least time. It means that a
ray always follows the path which minimizes the traveling time. It
is clearly an optimization problem. And it is not about "how to
optimize", but about "why the results are true". So it induces
teleology. Similarily, the principle of least action is an optimization
problem that is to explain the results.

Another example is economics. Surprisingly, economics uses Lagrangian
too (!). Since economics assumes that people are rational, people
optimize everything. As a result, if you solve any optimization
problem in economics, the solution will be the market equilibrium.
How magical! So in this case, everything happens to make market be
efficient.

The last example is linguistic economy. It means that people simplify
languages as long as it doesn't hurt clarity. It is an optimization
problem in which the objective function is linguistic complexity
and the constraint is clarity. And it induces teleology. Every
linguistic event happens to simplify the language.


OK. But aren't there still optimization problems that are about
how to optimize?

In fact, the difference between those two types is just points of
view. For example, you can think the maximizing sleep problem
objectively. You can explain your actions as following the biological
purpose. Regardless of points of view, the optimization problems
are mathematically the same.