One of the most important concepts in Physics is that of state: a list of intrinsic properties which may or may not change without "disrupting" the state; the changes are indicated by measures specified as functands of the state function.

The concept of physical state is homologous to number system in arithmetic. We generate the natural numbers by recursion on the successor function. And we generate the operation of addition of naturals by a recursion upon the previous recursion; and we say that naturals are closed under addition, that is, "all in the family", without "leaving its naturalness". But when we define an inverse to addition in terms of this operation, called "subtraction", we discover than naturals are not closed under subtraction, which require a "new number system", called "integers".

Similarly, we are concerned with operating upon the state properties and enquiring as to when these are closed operations (remain within the state), and when not. Dealing with this last question, and how to answer its various subquestions, generates all of Physics, or more correctly, a particular Division of Physics, such as Mechanics or Electromagnetics or ....

The notion of state also acquires a topological aspect, when state becomes the special form known as "frame". The division of Mechanics began to "mature" when the notion of "inertia" was developed as a state, and even more so when there developed the concept of inertial frame.

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Science developed out of tribal religion and a theological notion that may have motivated the concept of inertia was that of state of grace. Common as an expression, it is not Biblical (although comments of "grace be with you" or "grace and peace be with you" are plentiful). As best I can determine, it may have first appeared in the monumental work of the great scholastic, St. Thomas Acquinas (1225-1274?), Summa Theologica. A passage of approximately two pages contains the phrase, "state of grace", 11 times.

Acquinas asks, "Whether the gift of understanding is in all who are in a state of grace?" And, after fielding three negative "objections", Acquinas finds a positive answer to his question. But this does not give us the understanding we need for the present.

Rather I find this in an ONLINE Sermon, "A State of Grace", delivered in 1994, by The Rev. David E. Bumbagh of The Unitarian Church in Summit, NJ. Saying that "grace is a freely given gift", Bumbagh tells us, "We live in a state of grace, in which hidden gifts lie waiting to be discovered within us ..."

One might paraphrase, "part of mechanics lives in a state of inertia, in which hidden gifts lie waiting to be discovered". Grace is a state of spiritual security from all demands, troubles, temptations of the secular world. Inertia is a state of physical security from all forces of the dynamical world. The latter repertorially reflects the former.

Hence, it is not surprising that some historians of science believe that the Franciscan friar, William of Ockam (1300?-1349?), anticipated the notion of inertia long before the usually accredited Galileo. (In the 1986 film, "The Name of the Rose", the character played by Sean Connery was modeled on William of Ockam.)

Being "inertial" is comparable to equivalence in arithmetic, congruence in geometry, equilibrium in statics, symmetry in art and physics. An inertial frame must be of such sensitivity that any departure from it, any exception to it, would be readily detected, readily recognized. It provides ground for detecting the exceptional figures of reality. Dually, (as in De Moivre curve between upper and lower controls), it can become a figure, for "showcasing outliers".

In physics, at least since Galileo, a state has geometric description and geometric variations are typified as translational, rotational, reflectional. So inertia needs to be explicated for all of these.

First attempts to explicate it led to pre-relativistic mechanics, essentially translational; extended in special theory of relativity to more rotational scope; extended in quantics (through spin) for reflection.

Thus, much of physics can be subsumed under the explication of inertia ("physical grace") -- a goal not yet reached.