Atoms as modes of universal oscillation

Disclaimer: The following essay will most assuredly be the most difficult to comprehend in this entire blog series. I will be placing the kind of demands on your faculty of imagination to which you have probably never been exposed. In the immortal words of Douglas Adams: Don't panic! In the future, I will spend as much time filling out the details of the methods that are here included, as well as arguing for why just these methods—as opposed to any others—are essential for the purpose of developing a "workable" theory of physical reality.

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The initial impulse of the "new" quantum theorists of the mid-1920's (as opposed to the "old" theorists from the early-1900's) was to describe elemental matter from within the context of spatial wave dynamics. The question of finding a way to understand the dynamical field-like structure of matter is what motivated the work of Louis de Broglie and Erwin Schrödinger in this period of time.

But due to the particularly "fuzzy" aspects of partial differential equations—which contain two or more independent variables, and are used in order to solve things like wave equations—there was destined to be a movement back towards the kind of "perfect solvability" that is obtained by the Newtonian point-location approach, which only utilizes the much simpler approach of ordinary differential equations—containing only one independent variable.

We can see from this historical progression that ease of simplistic mathematical formulation will tend to force philosophically intelligible explanation out of the confines of acceptable academic physical theory. The resulting ontological interpretations of atomic physics will then revolve around the question of the "reality" of things like probability functions and n-dimensional configuration space. However, the widespread (public) acceptance of any theory of physical reality ultimately requires that the theory be philosophically intelligible—that is, it must be directly conceivable by the imagination, rather than offering mere "predictions" of particular experimental situations.

The only reason not to consider the ontological significance of the sensible wave-fields of the de Broglie-Schrödinger variant of atomic theory is that it doesn't lend itself to simplistic algebraic formulation in the Newtonian tradition. It is from Newton that we have inherited the notion that the only "worthwhile" approach to physics involves tracking the trajectories of localizable particles through void space. From where I stand, however, the "failure" of the original post-Bohr-model atomic theorists to think in this kind of naive way about the fundamental structure of matter is the precise reason to take them seriously.

So here is the situation that we now have to work with: atomic matter must somehow be understood as a dynamical, oscillatory three-dimensional field. (This is obviously a much trickier notion that simple, lifeless point-particles!) The first stumbling block here is that the notion of a "three-dimensional oscillation" is not visualizable in the sense of a vibrating [linear] guitar string or a [planar] drum pad. In both cases, we can imagine the free space that these entities have have at their disposal to oscillate into. But when it comes to the oscillation of space itself, the only way to visualize it is by imagining that each spatial position (which are to be understood as "infinitesimal spaces" rather than "point locations") generically consists of various potentials, which can each be represented with a color. We can then think of the positions of lowest and highest potentials as respectively existing at the bottom of a valley and the top of a hill.

Just like a vibrating guitar string cycles through configurations such that the midpoint is now at position of maximum displacement and now at a position of zero displacement, the same idea can be applied to oscillating space, such that its center varies between a 1) state of maximum potential and 2) a state of zero potential. Applying this scenario to the language of general relativity, we can affirm that case 1 consists of the highest spatial curvature (or tension) case 2 consists of zero curvature—signifying the "flat" space of special relativity.

Einstein's theory, of course, did not consider the possibility that spatial curvature is itself a "primordial" phenomenon, and consequently that it could be thought of as a fundamental mode (modulation) of universal space itself. Now this possibility is highly compelling because we can begin to see a resolution to the matter vs. space duality that has been giving philosophers headaches since time immemorial.

The next issue is a highly complex one, and the only name that I can think to give it is: the boundary problem. That is, the only way that an oscillation mode makes sense is if it occurs within a bounded space. (Just like a vibrating guitar string only makes sense if it is anchored between two bounding points.) If, however, atoms consist of spatial oscillations, each within their own arbitrarily small bounding spheres, then the question of the nature of the interaction between mutually exclusive spaces must be satisfactorily explained. It is this precise question that has given rise to the doctrine that ontologically distinguishes the categories of "matter" and "radiation." (In many ways, this is just the same problem as the matter vs. space duality, but only dressed in slightly different clothes.)

The best (?) way to avoid descending into a state of hopeless confusion is to simply assert that the atomic modes of spatial oscillation are strictly universal in nature. That is, there are to be no arbitrary boundaries that cause a distinction between intra- and inter-atomic space. (My ultimate intention is to prove that it is only in this manner that the action-at-a-distance question can be philosophically settled—assuming, that is, that one finds the modern point-particle approach to be problematic.) It is from within this context of the pure mutual inclusivity of the modes of oscillation of universal space that the whole of my theory of physical reality is to be understood.

(As an aside, we have come to the crux of the philosophical distinction between "particle" and "wave." Waves are things that do not directly affect one another, in the sense of the kind of action-reaction "billiard-ball style" mechanisms of the Newtonian paradigm. That is, arbitrary numbers of waves are able to share the very same space while each constituent wave keeps its particular structure. The shared space, however, can be said to consist of a singular, composite wave; the structure of which is found by the "superaddition" of the displacements/potentials of the coincident elements of the individual waves into a resulting displacement of the composite wave. It is in this way that the universe can sensibly be said to consist of the pure mutual inclusivity of all of the elements of matter. In opposition, particles are just things that cannot possibly occupy the same space at the same time—they are naively considered to be "perfectly hard." The way that academic physicists explain this situation, however, is not to give a phenomenological account of this "perfect hardness," but rather to eliminate the very possibility of mutual inclusivity by way of denying the existence of the "internality" of elemental matter.)

But now, if all material elements (modes of oscillation) share the same universal space, and if an oscillation only makes sense as a function of a bounded system, then in what way can we think of these atoms/modes as existing within a physical system of constant relative motion? That is, if we think of all modes of oscillation as being a function of the same universal boundary, then simple logic tells us that the centers of oscillation of every possible atomic mode will coincide at the exact same location. Within this scenario, the only possible relational difference between each atom will consist of mere rotation, with no possibility of translation.

The solution to this problem lies in the use of a purely logical fourth spatial dimension, which will allow us to think of universal space as existing in the form of a so-called hypersphere. This is to say that the notion of the universe existing as a three-dimensional interior space that is bounded by a sphere only raises the problem of the discontinuity of space (due to the fact that space abruptly stops), as well as begs the question of the interior vs. exterior duality, if only from a different perspective as before (due to wondering about the nature of the "emptiness" that exists on the other side of the boundary). The only way to think of the universe truly as a uni-verse is to understand how it may be "self-cohesive," such as when we imaginatively fashion a circle (or sphere) from out of a straight line segment (or flat, circular disc).

The way that we can imagine a single mode of oscillation, then, is to think of the three-dimensional corollary of forming a vibrating guitar string (or drumpad) into a vibrating circular (or spherical) shape. In the [unimaginable] three-dimensional case, the entire spherical boundary will be made to connect into a single point at the polar opposite end of the universe, in relation to the maximally displacing structural center-point. In the language of wave mechanics, the points of a constant null displacement (such as the boundary points) are known as "nodes," and the points of maximal displacement are known as "antinodes."

The use of this "atomic wrapping procedure" will allow us to locate the various connection points of the different atoms at any arbitrary location on the universal hypersphere, therefore allowing for the kind of relative translatory motion that had been previously denied to us. Furthermore, given that each of these connection-points is nothing other than a compressed version of the nodal boundary that was used in order to establish the oscillatory behavior of each atomic mode, and given further that 1) the compression factor of the various positions within atomic space is a function of the inverse of the square of the distance from the connection point (this is the same essential issue faced by map projections), and 2) the nodal connection-point is, by definition, always a point of maximum stability (that is, lowest potential), then the result is that we have found a purely geometric description of the various attractive forces that are described in terms of potential difference—i.e. the effects of the gravitational and electrical fields.

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I have certainly tried to pack quite a bit of mind-bending information into a relatively small amount of space. I am not aware of anyone else who has attempted such a treatment in order to combine the most salient features of wave mechanics with those of Riemannian (n-dimensional manifold) geometry. The former topic is that which occupies the branch of physics that utilizes the Schrödinger equation—also known as quantum theory. And the latter is that which concerns the branch of physics that takes the Einstein field equations as its point of departure—which is better known as general relativity.

What we now possess (if only theoretically) is an immanently imaginable geometric atomic form whose intrinsically dynamic character allows for the basis of an understanding of universal physical reality that includes time within its very structure rather than using time merely as an external agent for the purpose of "forcing" insensible "matter-points" to move between static locations within a void spatial background. And this notion of temporal inclusion is perhaps the most important piece of the puzzle, in that it allows for a robust theoretical context—without resorting to ad hoc teleological arguments—upon which to understand the "naturalness" of the bio-chemical dynamics that underlie the evolutionary processes of the organic/life sciences.

Atoms v. Particles

Important Note: In the following essay, I will be referring to things called "atoms." My only intention is to think of this word solely in the philosophically pure context of a spatially-extended, yet ontologically simple material body, rather than in the derivative context of the contemporary natural sciences—i.e. consisting of so-called sub-atomic particles. The atom is to be considered in contradistinction to the notion of the zero-dimensional "particle" of theoretical physics. Both of these entities are "indivisible," but in vastly different ways. While an atom may be conceptually subdivided for the simple reason that spatial extension itself is built upon the notion of the possibility of unlimited divisibility, each of the conceptual subdivisions are reciprocally dependent upon every other for its existence. In other words, there cannot possibly be separate existences of the subdivisions of an atom; an atom is ontologically indivisible. On the other hand, a particle is indivisible solely because it cannot even be conceptually subdivided—it is by definition unextended, and therefore "partless" in every sense of the term; a particle is logically indivisible, and not, strictly speaking, ontologically indivisible for the simple reason that it is not ontologically anything.

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In the common vernacular, all of matter (and energy) consists of "tiny particles." In the more rigorous context that is academic theoretical physics, however, a particle is a thing that occupies one and only one location at any given time; and a location ,furthermore, is just a zero-dimensional construct that represents the solution to a particular algebraic equation.

In the sensible world, a thing must at least occupy a finite volume of three-dimensional space in order for it to be considered to have any size at all, whether this size be considered small, large, or somewhere in the middle. Anything less than the occupation of three full dimensions banishes a thing into a state of nothingness.

Opposed to the mathematically localized particle, the concept of the atom relies upon the philosophically sensible idea of three-dimensional (i.e. "spatial") occupation. Such a thing as an atom, however, does not correspond very well (if at all) with rigorous algebraic calculability. That is, there is no easy way to cause a unified region of space to result from a mathematical equation.

It was for this reason that Newton "simplified" the concept of the space-filling material body, so that it would correlate exactly with his algebraic technique (i.e. "calculus"), by way of saying that a body can be located at its center of mass. But of course this simplification is nothing but a case of mathematical convenience that seeks to evade the much more daunting—and potentially embarrassing (and possibly career-threatening)—question of how, precisely, a material body is fundamentally structured.

Newton was thus able to abstain from taking an official position concerning the ontological "fundamentals" of physical reality. By asserting that a cosmic body could be mathematically "located," and that this kind of locatability through time lies at the heart of the scientific project, the implication is that the only important question about the theoretical fundamental elements of the material world—i.e. "atoms"—consists of their mere locations within universal space.

Perhaps the most notable attempt to come to grips with the way in which matter ultimately "looks" is in Plato's dialog, Timeaus. No matter how believable the final result, the fact remains that Plato at least tried to give a sensible explanation as to the ultimate forms of physical reality. Because of the inherent subjectivity of the Platonic project—being that it involves rational ideas rather than immediate experiences—the particularly empirically minded contemporary Westerner has seen fit to relegate all such enterprises into the dustbin of pointless metaphysics.

But we must not allow the apparent difficulty of the task at hand to cause us to forget about its profound significance! Instead, we must redouble our efforts to see if any progress can possibly be made...

First of all, let us reconsider the question of scale in terms of its theoretical significance. In the previous blog entry, I upheld that all of the fundamental entities are to be treated as existing on the "universal scale." This seems to be perfect nonsense—until we realize that the only reason that we consider something to be "microscopic" concerns the empirical fact that our senses only consist of a finite amount of resolving power. If, therefore, our eyes had the magnifying power of the world's most technologically advanced microscopes, then the line that divides the worlds of the small and large would exist at a vastly different place than it currently does.

The wise interlocutor, however, might very well object that it is not truly a question of the subjective visual appearance of a thing that determines its scale, but rather the way that it relates to an objective standard of measure, such as a meter stick. But of course, in what way is it meaningful for a thing to have a certain scalar relationship with another thing without our first being able to [subjectively] sense each individual thing, as it is?

The point I am trying to make here is very subtle, and a thorough understanding of it will go a long way toward helping us to find our way into the heart of my ultimate thesis. When it comes to our experience with everyday objects, we think of them as having definite (discrete), impenetrable bounding surfaces. But the empirically determined location of a given surface necessarily depends upon the sensitivity (i.e. the resolving power) of a particular sensory device. It is crucial to understand here that the sensitivities of our manufactured measuring instruments consist of just as much potential subjective error as do the instruments—such as eyes and ears—that are innate to the human body.

If only, therefore, it were technologically feasible to construct a device with an arbitrarily high resolving power, then there is no reason to assume that the effectively detectable surface of a given object would not exist at an arbitrarily greater distance (from the object's center) than what we had originally (and so crudely) surmised. Given this same line of reasoning, it makes sense that a measuring device of "perfect" resolving power would be able to register a surface distance that is as large as the entire universe.

But there is a hidden difficulty in gaining a full appreciation of the point that I am trying to make, and that involves the way in which we think about the problem of light (the signal of the thing) versus matter (the thing itself). The commonly accepted "solution" is to treat both of these entities as "particles," with the result being that they are both equally relevant to the locatability (exact solvability) of the standard algebraic treatments of modern physics. The acceptance of this scenario, however, leads us right back to the problem of the zero-dimensionality—and therefore the implied non-existence—of the entirety of physical reality.

The only reason why we require the concept of "light" (or any other force carrying mechanism) is so that we may understand how [localized] matter particles may be able able to affect one another.

Now that we understand 1) that the notion of the localization of matter is purely a function of a desire to "reduce" reality in a way so that it fits into the context of "easy" mathematical calculability, and 2) that the empirically determined sizes of objects is fully contingent upon the arbitrary sensitivity of the measuring device in question, then there is no longer any theoretical justification for the bifurcation of physical reality into the domains of matter and matter's indicator.

To continue down this line of reasoning, it is necessary to affirm the senselessness of a doctrine (such as is given to us by the scientific establishment) of pure mutual exclusivity—for, this doctrine is only possible if "all there is" comes in the form of zero-dimensional point-locations; thereby negating the physical sensibility of reality itself. Furthermore, given the philosophical untenability of a doctrine that includes arbitrary mixtures of mutual exclusivity and mutual inclusivity, the only alternative is to simply accept a doctrine of pure mutual inclusivity. And by "mutual inclusivity," I just mean that a material body actually fills three-dimensional space and that a device would therefore be able to sense this body directly if only it shared this same volume of space. The reason why a mixture of the two would be arbitrary (as previously asserted) is that the effective sensitivity of any possible device that exists to sense a material body is solely a [contingent] empirical fact.

We have, therefore, arrived at the unavoidable conclusion that the only philosophically tenable sense for the term "material body" is that it is some kind of a universally space-filling geometric form. (The descriptor "geometric" is wholly unnecessary here, because anything that occupies space in any manner whatsoever is necessarily geometric. The purpose for its use is to emphasize the fact that we need to recast our understanding of what it means to be "truly" mathematical within the context of the possible ways in which matter occupies space, as opposed to the standard modern treatment that understands mathematics primarily from within the realm of solvable point-location algebraics.)

After all of this, we have—in a purely philosophical way—come into an understanding why it is that the term "atom," in the sense of a universally extensive geometric form, serves as a much more robust template for the fundamental entities of physical reality than does the term "particle," which signifies nothing other than the ontologically (as opposed to logically) irrelevant solutions to the algebraic equations whose only purpose is the rather mundane task of detailing the trajectories of arbitrary material bodies (whether cosmic/complex or atomic/simple) as a function of time.

What is the point?

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.

Wiping the slate clean

The general problem with modern theoretical physics is that it implicitly begins from a philosophical posture that ultimately sows the seeds of its own destruction. The assumption that is everywhere taken for granted in the current age is simply stated as such: Observations prove theories. On its face, the preceding statement is perfectly reasonable. But when we investigate the matter more closely, irresolvable problems begin to manifest.

The alternative assumption that I would make is this: Theories simplify observations. Given that no two observations are ever perfectly alike, the purpose for any theory is to discover the commonalities between them. And the more general (or universal) that a theory is, the more observational diversity exists that must be taken into account.

I claim to have developed something that I call The Universal Theory of Physical Reality. In this way, it is necessary that every possible observational commonality be simplified within an immanently conceivable system of thought. When most people think of theoretical physics, they think mainly of complicated mathematical expressions. It is for this reason that the average person thinks that the subject matter of theoretical physics is inherently beyond their comprehension. But this kind of thought is not truly warranted.

The major problem here is that while mathematics is necessary for the development of any legitimate theory of the physical universe, it is not true that the essence of mathematics lies within the confines of obtuse symbolic formulation.

In reality, we should rather think of mathematics as just that which is manifestly true, through its own intuitive power. In other words, the particular forms of mathematical statements are simply arbitrary constructs that are meant to refer to notions that are patently obvious. No matter how fancily we dress it up with symbolic artifice, the fact that one and one equals two is just something that the mind itself must already understand in order for any kind of experience to be possible.

It will do a great service for us to thoroughly flesh out the distinction between algebra and geometry. By doing this, we will be able to understand the nature of the relationship between these disciplines, and we will further be able to understand why it is that modern theoretical physics currently finds itself in such a sorry state of affairs.

Geometry is the study of the possible forms of an arbitrarily (n-) dimensional continuous space. That is, a geometric form is a structure that is necessarily "self cohesive." Examples of such structures are lines, planes, and volumes. For the sake of convenience, however, we will simply refer to each of these respectively as 1-, 2-, and 3- dimensional spaces.

The entire significance of algebra, however, concerns the notion of a compact and rigorous notation to aid in the communication of geometrical ideas. In other words, without an underlying geometric "reality," the entire discipline of algebra loses all meaning.

Algebra grew up as "analytical geometry," but it has now seemed to mature into an independent and self-subsisting entity. Set theory, for instance, would seem to consist of ideas that are separate from but equal to any advances in topology. But the fact remains that the concept of the set only makes sense as a set of things and that a thing only makes sense when it is built upon the idea of the spatial form.

The notion that particular sets abstract away the forms of things, leaving only qualitative characteristics (e.g. mass, charge, or color), does not change the fact that a thing—whatever the nature of its "secondary" attributes—must necessarily occupy space in such and such a way.

But this fact is all but lost on modern physical theorists. The notion that any possible thing must necessarily have a geometric form simply smacks too much of idealism, according to today's professional empiricists (a.k.a. "scientists"). When considering Platonic atomism, the contemporary scientific mind finds occasion for a good chuckle. The only problem, however, is that instead of honestly dealing with the question of the ultimate form[s] of matter, mainstream physics simply ignores it altogether.

The reason for this ignorance is that there is truly nothing empirical about the concept of the geometric form. A circle, for instance, is nothing other than a self-bounded, smooth, one-dimensional space. The sensible things that we refer to as being circular rely upon "real" objects that necessarily occupy three-dimensional space. The experience of visualizing circularity simply sparks within our own minds the notion of a perfect geometric entity whose radius is everywhere equal.

So, if a theory of physical reality depends crucially upon the a priori force of the mathematical discipline that is known as geometry, then any axiomatic appeal to observational proof will necessarily cause such a theory to be impossible. As such, my job here is not so much to convince the reader of the significance of the positive aspects of my theory, but rather to develop an argument that is sufficiently critical of the philosophical mindset that reflexively accepts the notion that "Observations prove theories."

I hope that you will do me the honor of allowing me to begin with an empty philosophical canvas so that my theory of physical reality does not become confused with the various emprical speculations (or hypotheses) that unfortunately are passed off as theories. In point of fact, my theory would perhaps be better described as a mathematical theorem, keeping in mind that by the term "mathematical," I am always ultimately referring to possible forms of n-dimensional space.

As such, it is easy to understand why there might be a dearth of algebraic formalism within the exposition of the theory. In other words, my goal is to give the reader an intuitive sense of the most basic of physical phenomena, such as gravity, electricity, magnetism, and the propagation of light. My attempt is to show how such phenomena can sensibly exist side-by-side within a comprehensive geometrical framework that ultimately reduces to a singular kind of spatial form and a singular dynamic law.

My intention is to create for you a kind of impressionistic image rather than a full-blown working blueprint of every possible empirical situation. (I couldn't even begin to wrap my head around the complexities of, say, DNA replication or the output of so-called high energy particle colliders!)