math [1.00-01] the philosophy of points



math points page graphic


 


All mathematics can be explained, and, perhaps, axiomatically grounded, as well as anything can be, in points. All mathematics can also be axiomatically grounded in other ways but this is the mode of progression I have chosen herein.

Perhaps circles or numbers could also serve as a baseline example in some axiomatic form to begin with but I think points are perhaps one of the most simple yet perplexing things (or non-things) that can be pointed to (for lack of a less humorous way of phrasing this).

This is a philosophical treatment of points and how we can derive all mathematics from them.

Axioms are primary assumptions that are made because they, to someone, appear self-evident and they can be used to develop a particular system.

What is a point in space? Does it matter if there is time? If we are to observe the point and posit new points and draw lines, then, yes, time must exist also. We can imagine that a point exists as a marker in space or in time, in whatever dimension we choose.

A spatial point could be the bullseye of a target and a temporal point could be the drum beat of a song.

A point can be a beat of sound, a child's ball, an abstract concept with no spatial dimension itself, or any part of the world [PoW] that we can isolate as something behind a backdrop or amongst its contrast of nothing or that which is not "it".

What "it" is, in fact, is not important. (For more details on a linguistic concept of [PoW] meaning in language, see my language page.)

A mathematical point need have no empirical existence in terms of extension or volume. The word "point" or a point like a period "." exists in space and time as markers for that which need not have any substance.

A point then, exists as a concept in the mind, but, nowhere in empirical reality, does a point exist because a point has no width, length, or height.

Often, in mathematical notation, the point is denoted by a small dot "." and the reference letter, capitol "P" as in [ . P ], read "Point P".

Even if nothing but the emotional state we experience existed and changed in time, we would be at least capable of developing an understanding of points.

It is only important that something has been isolated from everything (or nothing) else in the world.

When we think of a single point existing in infinite space, we think of a single thing or idea against nothing. Nothing, being the space in which possibility, even the possibility of space, has not become actualized.

One may consider space a thing but, at least conceptually, this is only a contingent metaphysical assertion concerning space. Space need not be something in itself but, I think, we are best to understand space precisely as the substrate of and relationship between that which exists in forms of being, which, on a scientific reading, would be energy.

Although we say that nothing does not exist, we still have a referent for nothing, namely the number "0" or the word "nothing". The empty set is not nothing, it is a set with no elements.

Points may occur in space or time or both but they must be isolated. More than one point is the simple addition of a single point to a new point in space or time.

As soon as we conceptualize the addition of points, mathematics, in space and number, has been born in the mind. I imagine this birth takes place well before we become aware of it enough to talk about it like this.

A new conceptual point is "2" and a new point in space or time is said to have a distance between them. A line can be drawn between two points in space and time and then we have a single dimension between them. This, the numbers and the points that can make lines in multiple dimensions, are the basis for all mathematics.

Variables hold numbers and functions perform calculations on these numbers. All numbers can be made to correspond to points in space associated with numbers in multiple dimensions.

The distances between intersecting lines can be measured in degrees that correspond to one or more forms of referencing. The manipulation of points in space and numbers, conceptually, through input into functions, can create all morphologies of lines and shapes and topographies.

The collection of all points equidistant from a single point where the distance is greater than nothing is at least one definition of a circle. Any three points that are in different places, and, to be a different point, one thing must not be in the same place as another.

In the next section, on numbers, there will be a further discussion of how mathematicians have grouped types of numbers (like even or odd) into sets of numbers with particular properties.




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