Tuesday, March 29, 2011

A Post of Course One on Relative Loci

If two things are next to each other, then these are near. If the same two things are separated by a substantial distance, then these are far. Two things that are near each other are relatively local. Two things that are far from each other are not relatively local. Two things that are made relatively local to each other have become localized. Two things, however, that were relatively local and subsequently became separated have become delocalized.

           
A man who lives by his neighbor is local to that neighbor. The man’s children, you might add, are even more local to that man. Yet the man’s neighbor is certainly more local to him than someone on the opposite side of the planet, at least in terms of physical nearness. As a standard, a locality in America is named by the county or city that that person lives in. You may say, “I live in Pinckney, Michigan, which is in the United States.” Likewise, one may always be able to grunge through more and more detail as to where a particle is, yet the precision of how specific you define your locality is often defined by the need that your specific description is to suffice. For instance, if you wanted to know where a cluster of molecules was, you probably wouldn’t delve down to the subatomic level. Rather, you would only need to search a level or two smaller than what you are looking for in order to find the region in which the thing you are looking for may be found. In this case, maybe searching down to the level of small molecules that may cluster in such a way so as to find what you are searching for.

Loci may mean spots where things interdependently differentiate, or it may mean spots that are near because these are attached. For instance, a uniform is near the body of a baseball player, yet it is not a part of that baseball player’s body. A chair may be near the table that it goes to, yet the chair is not part of the table. You might say, “Well, the uniform is local to the ball player’s body, yet it isn’t part of his body. And the chair is local to the table, yet it isn’t part of the table.” Exactly. So, if you consider certain phenomena as things that are made of parts, and these parts are made up of parts, when is something just local, and when is the object at hand in and of itself? What you need to define is what you are calling a specific thing. If the ball player’s whole body, including his hair, was the definition of a specific thing, then any part of his body would not be considered just local to his body – it would be part of his body. Yet, if the definition of the given specific thing was only the living portion of the ball player’s body, then his hair would be local to his body versus being part of the same specific thing.

The electrons of an atom are local to that atom, while the electrons of another atom are local to that other atom and not local to that first one. This is because we are not treating the atom as a static blob, but as a kinematic interplay of components that are interdependent. So, there is no “specific thing” that defines that entity of an atom, since an atom is the basis of the structure of matter, and matter is energy in static equilibrium. So, if you are talking about anything being local to the neighborhood of an atom, you are talking about a particle or object that is at least adjacent to the field of that atom. Yet if you are talking about something that is local to an atom, you are talking about something taking place within the given atom itself. For instance, anybody in a city is a local resident of that city, and everybody in that city is part of that city. If you were part of a pencil, you are considered localized within that pencil. This is because the members of a city, just as the electrons of an atom, are kinematic at their respective levels, whereas the parts of a pencil are not kinematic at an observers respective level.

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