Initial Conditions

Peter Oye Sagay

October 03, 2022

The Initial-Boundary-Value Problem (IBVP) is an aspect of advanced mathematics and a prerequisite for advanced mathematicians, scientists and engineers interested in examining and modeling physical problems as Partial Differential Equations (PDEs). Three mathematical statements constitute an IBVP:
(1) A differential equation (usually a partial differential equation) that approximately defines the physical problem of interest.
(2) Boundary conditions (BC) because all physical problems have boundaries of some type.
(3) Initial conditions (IC) because all physical problems do have start-times.
I will not delve into the interesting mathematics of IBVPs. Instead, I posit that boundaries and start-times are natural axioms of great importance in problem definition and solution. There are varied consequences for ignoring boundary conditions and start-times of spaces in space governance. The variation is a function of how well a given space has been able to positively reconcile its past with its present.

Conquerors of space shift boundary conditions and start-times of space. For example, the start-time of the United States of America does not include the times of Native Americans and its boundaries have been shifted several times. Nigeria is another example. A space that has been around for thousands of years, recently celebrated its sixty-second year of independence. It did not celebrate thousands of years of existence because its conquerors have shifted its start-time. In other words, initial conditions shift when IBVPs are redefined.

The mindset of re-calibrating old space continuums as new is misguided. Spaces that have existed for a long time cannot be new spaces. They can be improved spaces. It is to the improvement of spaces based on optimal definitions and solutions of the spaces' IBVPs that all should commit.

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