The Point as Zero Dimensional as Cause for Fracturing of Modern Philosophy/Science
Posted: Tue Oct 31, 2017 5:23 pm
The Point as Zero Dimensional as Cause for Fracturing of Modern Philosophy/Science
Presented Argument:
All understanding of Philosophy and Science has originated with the study of geometry or "space" under Pythagoras. The modern concept of mathematics and science as rooting the point as a zero-dimensional entity has been one of the primary causes for the observable division and "confusion" we observe today.
1) The standard interpretation of the point within geometry has been that the point is fundamentally dimensionless, or is directed in not direction at all. In this respect it is not a "thing" in it self, however is used to "quantify" and "qualify" all existence.
2) The problem occurs as all geometric structures exist if and only if their is a point. The line, triangle, square, etc. exist if and only if there is a point. This point in quantity is equivalent to 1 and quality is equivalent to Unity as it exists on its own terms.
3) The line is strictly a point reflecting a point and in this respect is a deficiency in structure of the point and not a "thing" in itself. It's one dimensionality is synonymous with "direction" in and this respect implies "movement" towards an end point and not towards itself. In this respect the line is a deficiency in stability, therefore structure, as it cannot exist on its own terms without a seperate point.
In this respect it is equivalent to a deficiency in structure as disunity/randomness or -1. It is equivalent to a deficiency as a negative is not a thing in itself but rather a deficiency in structure, in this case Unity and 1.
4) The circle exists as an "infinite" number of points, stemming from one center point. This center point, as 1 in quantity and Unity in quality, reflects upon itself to form infinity through the circle. In this respect 1 as Unity (for quality exists only if their is quantity, and quantity exists only if their is quality) reflects "Infinity" with "Infinity" existing if and only if there is unity.
In this respect all number exists if and only if their is infinity as all number (whose qualitative dual is a geometric solid) is strictly one reflecting upon itself. One reflecting one in turn reflects 2, one reflecting one reflecting one in turn reflects 3, etc.
The point must therefore continual reflect unto infinity in order to maintain itself as stable, other wise it becomes finite and unstable. In this respect the point reflects all number as fundamentally numberless. Infinity is numberless number and in this respect is All number, with all being equivalent to Unity.
5) The problem occurs as to how the point can reflect without being a dimension, and in this respect it is fundamentally self-reflective or moves inwards toward itself. In this respect it never moves and is 1 dimensional in movement. The corresponding points that result as this act of reflection are structural extensions of the point itself with these structural extensions being bound through "approximation" or "deficiency" in structure through the line.
The line is an approximation of points and can be equivalent to effect as "approximate causes", for an effect is strictly an approximate cause.
6) In these respects the point is the causal unit of all space as it is both 1 and Unity. As a self-cause, the point manifests itself through approximate points as extensions of itself, through the line. The line, as approximation, exists if and only if their is a point and in itself is equivalent to -1.
The point reflecting upon the line, or 1 reflecting -1, in turn results as zero as it is an absence of reflection and non-being.
7) In this respect the point is equivalent to an ethereal space and is universal, however not observable in a physical sense for it binds reality and does not flux in this respect. The concept of the point as zero-dimensional is fundamentally wrong in these regards as all reality is fundamentally a reflection of points.
This is probably one of the reasons why modern science and mathematics has a problem finding aggreeable foundations. It inverted the nature of geometry from 1 to 0. In these respects we can observe why many of the sciences continually fractate with no common median of language...all because of the definition of the point.
Presented Argument:
All understanding of Philosophy and Science has originated with the study of geometry or "space" under Pythagoras. The modern concept of mathematics and science as rooting the point as a zero-dimensional entity has been one of the primary causes for the observable division and "confusion" we observe today.
1) The standard interpretation of the point within geometry has been that the point is fundamentally dimensionless, or is directed in not direction at all. In this respect it is not a "thing" in it self, however is used to "quantify" and "qualify" all existence.
2) The problem occurs as all geometric structures exist if and only if their is a point. The line, triangle, square, etc. exist if and only if there is a point. This point in quantity is equivalent to 1 and quality is equivalent to Unity as it exists on its own terms.
3) The line is strictly a point reflecting a point and in this respect is a deficiency in structure of the point and not a "thing" in itself. It's one dimensionality is synonymous with "direction" in and this respect implies "movement" towards an end point and not towards itself. In this respect the line is a deficiency in stability, therefore structure, as it cannot exist on its own terms without a seperate point.
In this respect it is equivalent to a deficiency in structure as disunity/randomness or -1. It is equivalent to a deficiency as a negative is not a thing in itself but rather a deficiency in structure, in this case Unity and 1.
4) The circle exists as an "infinite" number of points, stemming from one center point. This center point, as 1 in quantity and Unity in quality, reflects upon itself to form infinity through the circle. In this respect 1 as Unity (for quality exists only if their is quantity, and quantity exists only if their is quality) reflects "Infinity" with "Infinity" existing if and only if there is unity.
In this respect all number exists if and only if their is infinity as all number (whose qualitative dual is a geometric solid) is strictly one reflecting upon itself. One reflecting one in turn reflects 2, one reflecting one reflecting one in turn reflects 3, etc.
The point must therefore continual reflect unto infinity in order to maintain itself as stable, other wise it becomes finite and unstable. In this respect the point reflects all number as fundamentally numberless. Infinity is numberless number and in this respect is All number, with all being equivalent to Unity.
5) The problem occurs as to how the point can reflect without being a dimension, and in this respect it is fundamentally self-reflective or moves inwards toward itself. In this respect it never moves and is 1 dimensional in movement. The corresponding points that result as this act of reflection are structural extensions of the point itself with these structural extensions being bound through "approximation" or "deficiency" in structure through the line.
The line is an approximation of points and can be equivalent to effect as "approximate causes", for an effect is strictly an approximate cause.
6) In these respects the point is the causal unit of all space as it is both 1 and Unity. As a self-cause, the point manifests itself through approximate points as extensions of itself, through the line. The line, as approximation, exists if and only if their is a point and in itself is equivalent to -1.
The point reflecting upon the line, or 1 reflecting -1, in turn results as zero as it is an absence of reflection and non-being.
7) In this respect the point is equivalent to an ethereal space and is universal, however not observable in a physical sense for it binds reality and does not flux in this respect. The concept of the point as zero-dimensional is fundamentally wrong in these regards as all reality is fundamentally a reflection of points.
This is probably one of the reasons why modern science and mathematics has a problem finding aggreeable foundations. It inverted the nature of geometry from 1 to 0. In these respects we can observe why many of the sciences continually fractate with no common median of language...all because of the definition of the point.