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 zerodimensional 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 selfreflective 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 selfcause, 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 nonbeing.
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 zerodimensional 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.
The Point as Zero Dimensional as Cause for Fracturing of Modern Philosophy/Science

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Re: The Point as Zero Dimensional as Cause for Fracturing of Modern Philosophy/Science
I think you are wrong.
The fundamental structure is a 4 dimensional manifold.
In this context "manifold" refers to a "topological manifold." It is just a shorter name.
A topological manifold is a type of topology. Not all topologies are topological manifolds but all topological manifolds are topologies.
A topology is a set and a collection of subsets that obey certain rules.
A set is a collection of elements. The line is a subset. Points are elements of the set.
So the real basis (topology itself) is a study almost like a botany of the types of sets of elements.
How do we know which topology? Experimental results gained from sense experience.
Further, physics does not reduce reality to the mathematical structure. The mathematical structure is referred to sense experience on the experimental side that determines not just the physical sense of the terms but actually the structure of the manifold.
Our universe has an earth etc...
Even the many worlds interpretations of quantum mechanics constrain the many worlds to be a subset of logically possible worlds based on sense experience in the form of the physical observations to support, for example, one form of a Hamiltonian from another.
So the basis is sense experience and that has resulted in a conclusion that what we experience has a specific structure of a topological manifold.
Now you have to be very careful because the uncertainty principle will not allow a measurement and corresponding sense experience to determine the location of a physical entity.
So the physical manifold itself does not have what you might originally think is the relation to sense experience. The notion of particles as points went out with the wave particle duality of quantum mechanics and principles like those devised by Bell even challenge the notions that physical sensed reality correspond to a view that their is a collection of particles with defined locations. Simple logic as seen in Venn diagrams is violated.
Have fun
The fundamental structure is a 4 dimensional manifold.
In this context "manifold" refers to a "topological manifold." It is just a shorter name.
A topological manifold is a type of topology. Not all topologies are topological manifolds but all topological manifolds are topologies.
A topology is a set and a collection of subsets that obey certain rules.
A set is a collection of elements. The line is a subset. Points are elements of the set.
So the real basis (topology itself) is a study almost like a botany of the types of sets of elements.
How do we know which topology? Experimental results gained from sense experience.
Further, physics does not reduce reality to the mathematical structure. The mathematical structure is referred to sense experience on the experimental side that determines not just the physical sense of the terms but actually the structure of the manifold.
Our universe has an earth etc...
Even the many worlds interpretations of quantum mechanics constrain the many worlds to be a subset of logically possible worlds based on sense experience in the form of the physical observations to support, for example, one form of a Hamiltonian from another.
So the basis is sense experience and that has resulted in a conclusion that what we experience has a specific structure of a topological manifold.
Now you have to be very careful because the uncertainty principle will not allow a measurement and corresponding sense experience to determine the location of a physical entity.
So the physical manifold itself does not have what you might originally think is the relation to sense experience. The notion of particles as points went out with the wave particle duality of quantum mechanics and principles like those devised by Bell even challenge the notions that physical sensed reality correspond to a view that their is a collection of particles with defined locations. Simple logic as seen in Venn diagrams is violated.
Have fun
Re: The Point as Zero Dimensional as Cause for Fracturing of Modern Philosophy/Science
Your turn...Justintruth wrote: ↑Thu Nov 02, 2017 1:57 pmI think you are wrong.
Fair enough, thanks for the response.
The fundamental structure is a 4 dimensional manifold.
In this context "manifold" refers to a "topological manifold." It is just a shorter name.
A topological manifold is a type of topology. Not all topologies are topological manifolds but all topological manifolds are topologies.
A topology is a set and a collection of subsets that obey certain rules.
A set is a collection of elements. The line is a subset. Points are elements of the set.
This is where I am going to interrupt, good presentation by the way (I wish more people would follow this setup), as the topological manifold exists if and only if it is composed of sets and subsets. Agree? In this respect the manifold exists if and only if it is composed of lines/points.
These lines/points in turn construct the four dimensional manifold you are referring too. The line exists as a 1 dimensional space which is fundamentally divided by a zero dimensional point.
The point acts as a divider so to speak. It is not a thing in itself as it is zero dimensional and exists as a division of the line only. The point, in these respects may be observed if and only if the the line exists.
This four dimensional manifold imply that the line is strictly not limited to 1 dimensionality but multiple directions if and only if their is a point to divide it.
The line is a multiple dimensional object if and only if their is a zero dimensional point. The line(s) further extend to the zero dimensional point until the structure is reaches its limits.
The problem occurs, as I stated above, is that the line maintains a multidimensionality if and only if their is a dividing point. This point as zero dimensional (as going in zero direction) is not a thing in itself but rather a "seperator".
The problem occurs as their is not fully symmetrical structure available except the sphere. In this case it would have to be composed of infinite multidimensional objects.
The problem occurs in that the intersection of these objects results in a center of point zero requiring all the lines to "progress from nothingness back to nothingness". The sphere may then be equivalent to infinite 1 dimensional lines steming from one point and going outward to an infinite limit.
0 dimensionality reflects infinite dimensionality, however 0 dimensionality is not a thing in itself therefore the lines must reflect eachother.
The next problem occurs as the line must reflect upon itself to maintain itself as a 1 dimensional object. This in turn equates it to a 1 dimensional point, or a point reflecting itself back into itself.
The point reflecting back into itself in turn makes it a one dimensional object which forms further points as extensions of itself through a negative dimensional line connecting them.
In this respect the point can be viewed as 1 dimensional and a stable space from which further shapes develop or a dual zero dimensional space from which everything divides.
Considering math and geometry form the sciences, the emphasis on a measurement system requiring a 1 dimensional point or zero dimensional point is the foundation through which we view reality.
I hope that was clear, as I skipped a few steps for convenience.
So the real basis (topology itself) is a study almost like a botany of the types of sets of elements.
How do we know which topology? Experimental results gained from sense experience.
The nature of sense experience as a foundation for geometry will reflect in the geometry itself. Considering all matter is in a constant state of flux, no fully symmetrical geometry structure may be established as a one dimensional linearism (continual flux) is the biproduct...this results in the point as a divider or zero dimensional.
A point reflecting back into itself is immovable and therefore stable and in this respect give a different picture as to the nature of movement as simply "an absence of structure".
Further, physics does not reduce reality to the mathematical structure. The mathematical structure is referred to sense experience on the experimental side that determines not just the physical sense of the terms but actually the structure of the manifold.
All physics is the study of matter. Matter at its core, and you may disagree with me on this, is strictly space perperpetually folding/curving upon itself (movement). The observation of a pure mathematic or geometric is an observation of an unmovable space from which nothing changes.
Our universe has an earth etc...
Even the many worlds interpretations of quantum mechanics constrain the many worlds to be a subset of logically possible worlds based on sense experience in the form of the physical observations to support, for example, one form of a Hamiltonian from another.
So the basis is sense experience and that has resulted in a conclusion that what we experience has a specific structure of a topological manifold.
You emphasize sense experience/empiricism alot. There is not empirical argument for empiricism, just an abstract one. Just like the scientific method itself is an abstract argument, the understanding of reality requires an abstract stable measurement system with the system itself providing the order or perception.
Now you have to be very careful because the uncertainty principle will not allow a measurement and corresponding sense experience to determine the location of a physical entity.
The uncertainty principle is an abstract principle observing the nature of particle movement being unpredictable. It is unpredictable because matter, and you may correct me if I am wrong, moves towards "point zero" as a constant state of flux. As I said above, a geometry founded in sensory experience is founded in the uncertainty principle and by default has to manifest the point (the must symmetrical and fully understandable of all the spaces) as a zero dimensional object because it is a "divisor" or "absence of structure"...with all absences of structure being equivalent to a degree of instability (ie flux/movement). The line as one dimensional object in turn manifests as a continual "progression" or movement as it is directed away form its origins.
So the physical manifold itself does not have what you might originally think is the relation to sense experience. The notion of particles as points went out with the wave particle duality of quantum mechanics
Quantums mechanics could not argue for the particle as a point because its measurement system reduced the point to a zero dimensional construct. If the point is a zero dimensional construct of course the wave particle duality is the only way to observe reality considering the line is continually reflected through itself in this manner.
and principles like those devised by Bell even challenge the notions that physical sensed reality correspond to a view that their is a collection of particles with defined locations. Simple logic as seen in Venn diagrams is violated.
Have fun
The point as a zero dimensional object was determined in the 1700s, if I remember correctly you might want to fact check that, and provided the foundation for the progessive movement we see today as all reality was reduced to a 1 dimensional linear form of measurement. The problem occurs in that this mode of measurement, as an extension of the physical world, manifests a continual flux through division. In simpler terms reality must be continually "divided" in order for it to be measured.
The problem occurs that the line cannot exist on its own merit without a point dividing it. Otherwise it goes out "adinfinitum" thereby equating 1 to infinity (which modern mathematics is strictly against).
The point as a 1 dimensional object whose direction is inward maintains the requirements for a fully formed foundation for both math and geometry as it is 1 in quantity and unity in quality. The point reflecting upon itself in turn forms all geometry shapes as strictly a reflection between points, with the line being an absence of structure itself as it exists as an extension of the point reflecting upon itself.
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