As we take our first tentative steps into the wilderness of universal ontology, it is crucial to consider the way in which the scientific establishment "solves" the problem of the ultimate form of matter. This solution comes to us by way of an implicit scalar prejudice, such that "sufficiently small" objects are taken to be practically equivalent with geometric points. There is precisely zero theoretical significance, however, as regards this kind of "practical equivalence."
That is, the fact that there is no possible way to empirically investigate the necessarily space-filling geometries of electrons does not give us sufficient reason to uphold a positive doctrine of the zero-dimensionality of such entities. The philosophical problem with this doctrine is that the difference between a small, three-dimensional form and a point is wrongly taken to be one of mere scalar reduction. But the difference is truly one of negation: not once, but three times! That is, in order to logically move from sensible, space filling reality into the realm of the pure mathematical location, we must in turn eliminate the third, second, and first dimensions from the object under consideration.
Because of these obvious difficulties, physicists will evade the issue by simply referring to fundamental objects with the descriptive qualification: "point-like." It is in this way that they are allowed to be agnostic when it comes to the question of material forms. But this refusal to commit to an answer of such an obviously significant question only serves to shine a light on the particularly un-theoretical (anti-theoretical?) postures of the people that labor under the title of "theoretical physicist."
Whenever it is assumed that "Observations prove theories," then there will never be cause to take a stand on an issue that is so far divorced from the world of visual sensibility.
But apart from this merely negative reason to uphold the non-dimensionality of fundamental material entities, there exists a far more compelling positive reason. For, when it comes to the notion of mathematical solvability, there are no things more "precise" than the simplistic algebraic equations whose results come in the form of point locations. That is, if a thing truly occupies one and only one location at any given time, then it can be rightly said that there is a perfect theoretical correlation between this "easy" kind of mathematics and the real world (even if said correlation can never be truly realized with real world measuring devices).
But if a thing truly occupies three-dimensional space, then the nature of the connection between the existing body of theoretical literature and the actual physical universe suddenly becomes much more problematic. Given, however, that the origin of the current "point based" paradigm can be traced back at least to the time of Descartes (and possibly much further back than that), there will obviously be quite a lot of institutional resistance to any implication that such a fundamental premise must be reconsidered.
But all is not lost. The geometers of the world have at least been able to reclaim the first dimension, in the name of "string theory." The philosophical problem with this new theory is that it is still based upon the same scalar prejudice that makes an ontological distinction between the worlds of the small and the large.
In the realm of pure geometric forms, however, there is no such distinction. That is, there is only one circle and there is only one square. To be a structure whose radius is everywhere equal or that consists of four equal sides and four right angles is to be a singular conception. While it is true that we can easily perform a mental synthesis of the distinct notions of geometric form and relational comparison, the fact is that the former is a priori necessary for any possible experience while the latter comes to us only through our everyday experiences with real world objects.
Whenever we speak about differences in scale, we are truly referring to the problem of the resolving power of our sensory apparatus, which question belongs purely within the realm of engineering feasibility. Keeping this in mind, it becomes necessary that any legitimate universal physical theory deal only with those concepts that are necessary for the possibility of experience rather than being merely derived from experience.
In my theory, the fundamental objects are forms that are defined everywhere within universal space. That is, there is only one scale, and that is the universal scale. In this way, the notion of "empty space" is also abandoned. But while this general notion might garner popular appeal with certain individuals who are always searching for underlying unity (i.e. "holism") in their concepts of physical reality, there is an immanent danger that the crucial benefits of the atomic doctrine will likewise be abandoned.
The crux of the problem is that the everyday notion of the mutual exclusivity of "solid things" does not necessarily deserve a place within the confines of foundational theoretical physics. The phenomenon of [im]penetrability, however, should be explained by our theory rather than reflexively assumed to be self-evidently necessary. In other words, in what way does it make sense to affirm that a circle is or is not penetrable? I would assert that neither of these affirmations make any sense at all.
We must always be consciously aware, therefore, of the vast difference between 1) a theoretical derivation of physical reality that deals only with pure mathematical forms and 2) a method (algebra) for the efficient arrangement of various experimental results. In the case of the former, we are speaking of the act of searching for truth, for no reason other than the satisfaction of the philosophical impulse. In the latter case, however, we start to get into issues that are much more pragmatic and this-worldly, such that economic factors will inevitably begin to dictate the concepts that are eventually accepted as being "true."
In conclusion, then, it can be reasonably said that the entire "material point" paradigm is the result of empirically minded researchers who simply want to "get on with business" rather than waste time quibbling over the finer points of an ontology of physical reality that can satisfy the higher aspects of the human imagination. It is my goal to spend as much time as necessary for the development of a theory that once again pays heed to the Platonic commandment that there be a rigorous mathematical description of the way in which matter ultimately occupies space.
That is, the fact that there is no possible way to empirically investigate the necessarily space-filling geometries of electrons does not give us sufficient reason to uphold a positive doctrine of the zero-dimensionality of such entities. The philosophical problem with this doctrine is that the difference between a small, three-dimensional form and a point is wrongly taken to be one of mere scalar reduction. But the difference is truly one of negation: not once, but three times! That is, in order to logically move from sensible, space filling reality into the realm of the pure mathematical location, we must in turn eliminate the third, second, and first dimensions from the object under consideration.
Because of these obvious difficulties, physicists will evade the issue by simply referring to fundamental objects with the descriptive qualification: "point-like." It is in this way that they are allowed to be agnostic when it comes to the question of material forms. But this refusal to commit to an answer of such an obviously significant question only serves to shine a light on the particularly un-theoretical (anti-theoretical?) postures of the people that labor under the title of "theoretical physicist."
Whenever it is assumed that "Observations prove theories," then there will never be cause to take a stand on an issue that is so far divorced from the world of visual sensibility.
But apart from this merely negative reason to uphold the non-dimensionality of fundamental material entities, there exists a far more compelling positive reason. For, when it comes to the notion of mathematical solvability, there are no things more "precise" than the simplistic algebraic equations whose results come in the form of point locations. That is, if a thing truly occupies one and only one location at any given time, then it can be rightly said that there is a perfect theoretical correlation between this "easy" kind of mathematics and the real world (even if said correlation can never be truly realized with real world measuring devices).
But if a thing truly occupies three-dimensional space, then the nature of the connection between the existing body of theoretical literature and the actual physical universe suddenly becomes much more problematic. Given, however, that the origin of the current "point based" paradigm can be traced back at least to the time of Descartes (and possibly much further back than that), there will obviously be quite a lot of institutional resistance to any implication that such a fundamental premise must be reconsidered.
But all is not lost. The geometers of the world have at least been able to reclaim the first dimension, in the name of "string theory." The philosophical problem with this new theory is that it is still based upon the same scalar prejudice that makes an ontological distinction between the worlds of the small and the large.
In the realm of pure geometric forms, however, there is no such distinction. That is, there is only one circle and there is only one square. To be a structure whose radius is everywhere equal or that consists of four equal sides and four right angles is to be a singular conception. While it is true that we can easily perform a mental synthesis of the distinct notions of geometric form and relational comparison, the fact is that the former is a priori necessary for any possible experience while the latter comes to us only through our everyday experiences with real world objects.
Whenever we speak about differences in scale, we are truly referring to the problem of the resolving power of our sensory apparatus, which question belongs purely within the realm of engineering feasibility. Keeping this in mind, it becomes necessary that any legitimate universal physical theory deal only with those concepts that are necessary for the possibility of experience rather than being merely derived from experience.
In my theory, the fundamental objects are forms that are defined everywhere within universal space. That is, there is only one scale, and that is the universal scale. In this way, the notion of "empty space" is also abandoned. But while this general notion might garner popular appeal with certain individuals who are always searching for underlying unity (i.e. "holism") in their concepts of physical reality, there is an immanent danger that the crucial benefits of the atomic doctrine will likewise be abandoned.
The crux of the problem is that the everyday notion of the mutual exclusivity of "solid things" does not necessarily deserve a place within the confines of foundational theoretical physics. The phenomenon of [im]penetrability, however, should be explained by our theory rather than reflexively assumed to be self-evidently necessary. In other words, in what way does it make sense to affirm that a circle is or is not penetrable? I would assert that neither of these affirmations make any sense at all.
We must always be consciously aware, therefore, of the vast difference between 1) a theoretical derivation of physical reality that deals only with pure mathematical forms and 2) a method (algebra) for the efficient arrangement of various experimental results. In the case of the former, we are speaking of the act of searching for truth, for no reason other than the satisfaction of the philosophical impulse. In the latter case, however, we start to get into issues that are much more pragmatic and this-worldly, such that economic factors will inevitably begin to dictate the concepts that are eventually accepted as being "true."
In conclusion, then, it can be reasonably said that the entire "material point" paradigm is the result of empirically minded researchers who simply want to "get on with business" rather than waste time quibbling over the finer points of an ontology of physical reality that can satisfy the higher aspects of the human imagination. It is my goal to spend as much time as necessary for the development of a theory that once again pays heed to the Platonic commandment that there be a rigorous mathematical description of the way in which matter ultimately occupies space.
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