—Revised 04-11-2019

Mere Concept vs Idea

Nature and its elements, its parts, are not concepts. Nature is Idea, the objective concept, the realized and embodied concept. All that is to be discussed from here is not what we think or believe of Nature, but what Nature itself must be in its intelligible articulation as what it is. We grasp only the concept of Nature in our minds, but Nature itself is this concept as a real independent object. That we comprehend the atoms, the crystals, and the birds of the sky through our conceptual cognition does not falsify the real individual existents of these kinds, nor does their individual existence falsify our concepts. The individuals are these concepts in their very being, their existence itself is through the Idea, the self-determining, the self-articulating power of objective Nature itself.

From Idea to Nature

Nature, Hegel tells us, is the Idea outside itself—it is self-externality. The shift from Logic to Nature is formally intelligible as 1) in the determinacy of Logic as complete an other which is opposite to it is equally to be determined in its otherness and not as subordinate to the categories of Logic even if it is built atop them, and 2) the Idea freely releases itself as it succumbs to its own process, i.e. the active being of Logic carries it forth into a new and opposite domain just as the being of Being shifted it into its opposite, Nothing.

Hegel notes that in the Absolute Idea we find the Idea itself succumbing to incompleteness in that it reveals itself to be merely the logical Idea, the self-enclosed subjective concept of objective reality, but not yet objective reality itself. This is what determines the entire sphere of logic as logic. In that the Absolute Idea carries out its process and determines itself as this one-sided incompleteness the dialectic naturally shifts towards its opposition in the objective domain we call Nature. The shift, as with all other shifts, is at first a mere upward shift which is not a new movement, but merely the recollected recognition of the movement all along. In the Absolute Idea we have the subjective and objective Idea, the concept and its objectivity, united—this is at once Nature, the first realized concept.

This transition is not a transition, it is simply the immediacy of the Idea. It is also, however, not a mechanically determined necessity. The Absolute Idea is complete and self-determining in its logical domain and as such insofar as a new determination comes about it only does so by the positing of the Idea itself. It is, then, a free self-determination, or as Hegel says, a self-release into Nature. This mysterious and mystical wording is purposive, there is much implicit in it which is also explicit given the Logic’s long journey. What Nature is is nothing essentially new from the standpoint of logic, all subsequent determinations will onward and always be repetitions of the concepts already developed in the logical determination, however, they are new in that these are specific and objective instantiations of logical relations and movements which will have their own beginnings and unique developments which will not be repetitions of the Logic’s concepts as they exist in mere logic. While logic is Idea in self-internal abstraction, Nature will be Idea in self-external abstraction.

The Powerlessness of Nature: Thinghood

A hallmark of Nature is how, because it is self-externality, its logical organization is dominated by externality and otherness; everything in it is incapable of fully containing its determinations. Nature is, simply, that which itself is not Idea as logic (self-contained thought), yet it is Idea. Nature is not explicitly and purely rational in that it is a domain which is open to spuriously infinite contingency, and thus itself not fully intelligible or explainable in-itself. All that is naturally existent finds itself under the power of another to some extent, and so Nature is powerless in attaining an absolute self-determination.

Nature in its most concrete form shall be understood as the system of the living organism once it is fully developed. In the living being the entirety of the system of Nature is sublated as one Idea—all of physics and chemistry come together under one containing unity where every process of nature has its place, the process of organic life.

Nature as such is dominated as a thing is dominated, it falls short of embodying proper subjectivity and self-determination. While with Logic we find that the components of concepts do not oppose their totalities, with Nature we find that the parts may come into opposition to the whole just as much as we may find the whole in opposition to another whole. All Natural being is material and for this same reason it is incapable of absolute self-determination even at its peak determination in the living being, for the organism as such can and must fail at full self-determination through the external relation to its environment both external and internal. The organism may fall to disease, the species to mutation or selective pressure, the individual being may succumb to the contingencies of natural accidents beyond its power.



Eternal Nature

Nature itself is not spatially nor temporally created, but endless and eternal. It begins and ends at all spaces and times, but it just as much does not. There is no first space nor first time, nowhere and at no time did Nature begin and as such it will never end. As such, an infinity of worlds existed prior, exist now, and will exist afterward. An infinity of scales of material being exist from the infinitesimally small to the infinitely large without limit—there is no final atom in any space or dimension, no final minimum or maximum measure. We are neither the first nor last species of intelligence, and unless we are foolishly hubristic we should not imagine that we are the highest any more than we imagine that we are the lowest. While Big Bangs may happen, they evince nothing of a beginning of the Universe let alone of Nature.

The Hegelian philosophy of Nature is at once seen as a contradiction. It is the greatest hubris, for it dares to proclaim to know the radical Other of pure Reason. It is, however, also the greatest humbleness, it demands that we not project our biases and arbitrary presuppositions and concepts onto Nature, to let its concept be just as Nature freely is. To conceive Nature according to what it has shown of itself, nothing more may be said. Make no final judgment of what we have not seen, build no castles in the sky and die on no illusory hills, but seek to see Nature in the intelligible light that faintly shines through the opaqueness of matter. Though Hegel himself does not always abide by this humbleness, his method itself demands it. What we have learned of Nature in the time since Hegel demand not only that this work be re-worked and updated, but that in this reworking we make no repetition of this hubristic mistake of making final judgments on what has shown itself again and again to so far be no mere trivial incompleteness of knowledge, but an immense ignorance on the part of humanity in its understanding of Nature and its secrets hidden in plain sight by the sheer complexity of its being.

What follows are my own expository explanations as I comprehend them for myself unless noted otherwise, but there are also comments on related topics and phenomena I find of interest and relevance. Hegel was fearless in his day to tread through every sphere and piece of science to show the intelligible reality of concepts, and so I endeavor the same. I am no expert in anything, but nonetheless I shall attempt to follow a line of conceptual reasoning in order to make my judgments. It is up to the reader to ascertain if my comments are of any worth to them.

CONTENTS of Interest

Mathematics And Nature (comment)

Spatial Dimensions

On Points And Black Holes (comment)

Time

On Time Dilation (comment)

Temporal Dimensions

Place, Motion, Matter

Space



The primary or immediate determination of nature is the abstract universality of its self-externality, its unmediated indifference, i.e. space. It is on account of its being self-externality, that space constitutes collaterality of a completely ideal nature; as this extrinsicality is still completely abstract, space is simply continuous, and is devoid of any determinate difference. —Philosophy of Nature §254, Allen & Unwin trns.

Space begins—in what is a common pattern to recognize in Hegel’s works— as a negative concept in relation to itself, the reflexive otherness as such. Space is the immediate form of self-externality which requires no other but itself. Now, what would it be for space to be outside itself? Collaterality, a term not too unfamiliar, denotes the ‘sidedness’ or extension of space, yet in mere space as such we do not actually have anything in any relation of space, nothing that can even be determined as being here nor there beside anything—this is why Hegel says that this collaterality is completely ideal and abstract, i.e. space as such is not yet actually these relations. Space as such, i.e. what it means to be spatial at all, is simply self-externality in abstract, with no determinateness—no definition—of spatial relations except the basic determinacy of externality.

Externality of what? The Idea. External to what? To itself, but there is no specific spatial configuration which space as such is in its immediacy. There is no direction, there is no dimension, there is nothing which space as such is external to and can be defined through in a spatial manner. Thus, we are unable to speak of the most intuitively easy ways to think of space, for in doing so we will have presupposed exactly what we wish to explain. So, we begin with the determination of the externality of space as simply this self-externality.

On The Existence of Space As Such

To ask whether space by itself is real, or whether it is only a property of things, is to ask one of the most well-worn of all metaphysical questions. If one says that it is something inherently substantial, then it must resemble a box, which, even if there is nothing in it, is still something subsisting within itself. Space is absolutely yielding and utterly devoid of opposition however; and if something is real, it is necessary that it should be incompatible with something else. One cannot point to a part of space which is space for itself, for space is always filled, and no part of it is separated from that which fills it.

Space is not a thing, a substance, which is opposed to another thing such as matter (energy). How do we know this? Because matter is spatial and not something else opposed to space. It isn’t matter and space, matter is always already spatial. To think that matter and space are different independent substances would leave us stuck in a Cartesian dualism where we have no explanation for why and how such substances relate. But what of empty space? That which we call empty space has shown itself to not be empty in content: quantum foam, the Cassimir effect, and gravity waves all protest and proclaim the materiality of empty space.

Further, space as such is not real in this substantial sense; it does not exist in relation to matter. To say that space does not exist is to say that it poses no opposition to matter, for that which is real existent substance resists in its incompatibility to another substance impinging on it. The truth of grasping ‘nothing there’ is that something has not presented resistance just like a veil of fog that seems to be solid yet ‘is not there’ when we finally contact it and simply walk through. To state more clearly: space does not exist in relation to matter for matter finds no resistance from space itself. Even in standard theories we may twist space, curl dimensions and enfold them as to be invisible to our three dimensional eyes, and yet matter moves along and through these dimensions unperturbed as matter. From the material perspective space always is simply spatial, simply my space and no distortion is perceived immanently.

The concept of an absolute space like what Newtonians posited is a priori inconceivable and existentially impossible, space cannot be the aether and absolute reference point of motion, the pure idea of spatiality as such is itself without reference and cannot be referenced in its abstraction. On the other hand, if one thinks like (Hegel’s) Leibniz that space is something external to things themselves—is only the external relation of things—and thus is made other to them as itself nothing real, then one is just as wrong. Leibniz grounds spatial relationships in thing themselves, the monads, and would say their spatial relationships still inhere in them even if we abstract the realm of space away from them, but this is a contradiction for such inner determinations of relation would presuppose space. Hegel gives a quick remark: if space were emptied of these noumena, Leibniz’s logic leads us to claim that their spatial relationships remain despite there being no space. These relationships of externality, however, are already presupposing the very idea of space, and thus to speak of the separation and externality of monads to each other is to presuppose spatiality.

For Hegel there is nothing noumenal outside of space which is indifferent to its external determination as spatial; rather, space is the externality of those noumenal things themselves. Space is externality itself, not an externality. All that is external is itself in a spatial relationship.

Space As Such Cannot Be Constituted By Anything

String theories remain a hopeful attempt at resolving the conundrum of unifying General Relativity with Quantum Mechanics, however, one must ponder the fruitfulness these attempts may hope to have concerning the answer to fundamental questions of Nature. For one, what justifies the initial determinations of such entities, and second, how are we to make sense of claims of generating space and time from such entities when clearly these entities and their actions already presuppose spatial and temporal being?

Loop quantum gravity (not a string theory) and related endeavors, for example, seem to speak about what “makes” space and time. There is no shortage of issues, however, with such conceptions when we wish to speak of these metaphysical categories. In LQG we find that space is determined as being constituted by the lower element of these quantum loops in linked networks, but again, how can this explain space when these loops already exist as spatial determinations? One may claim that these mathematical relations are what explain the extension of space, but this is nonsense. We wish to know the why and intelligibility of extended spatiality itself, not of an already determinate given spatiality. No equation, no function, admits to spatial or temporal interpretation without already being presupposed as spatial. String theories in general cannot explain space; at best they explain further determinations of space after it is already given, yet this itself is already suspect in that the strings have already been given dimensional determination beyond mere space, they have likewise been given the determinations of motion without explanation.

Bent Space or Bent Things?

Hegel’s notion of space as such has implications for the notion of the “bending of space” which is common in standard theories of physics today. The problem with such notions, particularly the more “speculative” ones like space warping technology (wormholes, etc.) is that they treat space as if it were itself a material object we can abstract from and manipulate. The analogy often given is of an object traveling along a sheet a paper: bend the paper and the object can get from A to B much faster. However, this is a misleading analogy. When we bend a lower dimensional object we are not bending a dimension as such, which is what the analogy is supposed to convey. The idea is that if the paper was a dimension, whatever way it is bent or distorted is from within it of no consequence to its own operation. Bend the 2d world and the citizens in it would for themselves experience nothing different other than your anomalous interactions coming in and out of it. The only 3D material representation we can really make of this concept is with something like a fish tank: we can shape the spatial configuration of matter in many ways, however, this is not the shaping of a dimension and the fish within can tell the space is now differently configured even if they can still move within it relatively unobstructed.

Never in history have we bent any space as such, we’ve only bent material objects in spatial relations, nor do we have any idea how such bending could materially be done. Besides the wild claims made in pop-science outlets, we have never witnessed space itself compress or expand, theories of dark energy and cosmic expansion included (it is an interpretation based on presuppositions on the nature of galactic redshift), and even the current experiments attempting to see such in new versions of the Alcubierre drive can not legitimately claim they have changed space as such in a dimensional sense, for only that which is spatial bends, compresses, or expands. Only matter is seen to do such not just empirically, but logically only it can be comprehended in this manner. We bend things through the dimensions, but it does not make sense to think we have bent the dimensions themselves unless we treat the dimensions no longer as what they are, but as things of matter themselves.

Why Mathematics Is So Capable of Describing Nature

There are always nuggets of wisdom in Hegel, but sometimes those nuggets are said with such simplicity and answer such deep questions that it truly boggles the mind. To anyone that has even an inkling of the link between mathematics and Nature as a whole, meaning that this relation is not uniquely restricted to physics equations, nothing should be more astounding and baffling than the question of why this link is so. From how the Fibonacci sequence and the golden ratio are so ubiquitous in nature, to why the Riemann Zeta function about the relationship of prime numbers can describe some of our most mundane comings and goings, the capacity of math to describe our world is baffling. Were the reality of mathematics and its power limited to merely functioning at empirical description it would still be amazing, but what is certainly beyond baffling is that what seems to be pure mathematical relationships themselves hold in our world such that they may predict things.

Most do not grasp the significance of a deep distinction. That mathematics has effective functional use in describing Nature is actually rather unsurprising given the operational and pragmatic origins of mathematics. If such mundane effectiveness as a physics equation is what we mean by the surprising effectiveness of mathematics, then we can only be surprised because we are ignorant of how it can be effective in that much is already designed to be such by conception, but we are also ignorant of how most mathematics actually has no effective use. No, what is surprising is not that we can craft an equation that fits the bill to anything. What is surprising is that an equation about mathematical objects in relation to themselves has effectiveness at all. That the relation of primes to primes appears in Nature at all is boggling to an infinitely greater degree than that we found a practical use for complex numbers after a clever interpretation which was not immanent to their origin.

Now, what is Hegel’s answer to this question of the effectiveness of math in Nature?

Space is, in general, pure quantity, no longer in its merely logical determination, but as an immediate and external being.

How does Hegel get to make such a claim? Well, despite it seeming a mere dogmatic claim Hegel is simply using what he has already developed in the Science of Logic. The explanation of what quantity is cannot be expounded here, but from what he says here and what we can gleam if we look over the beginnings of the logic of quantity, Hegel isn’t just making an off-handed remark here without logical nor empirical basis. Quantity involves a logic of indifferent difference and otherness… very much like what space is showing. While before Hegel Kant attempted to ground mathematics in space through geometry, Hegel has already established the reality of the elements of mathematics in pure logic itself, and when space is developed he immediately recognizes the element of mathematics—quantity—immanent to its very concept structure. Space is mathematized explicitly in its concretization as geometry, but this geometry is not the limit of mathematics’s embodiment in nature. Nature is so receptive to mathematical treatment because its most basic form of space is embodied mathematics itself. This does not mean all mathematics as such must be embodied in Nature, but it gives reason to why mathematics appears in Nature to the extent that it does at all.

Sacred Geometry

Jumping to things not yet developed, but which will be mostly at hand at the end of this chapter in the Philosophy of Nature (PhoN), the reality of what may be called ‘speculative’ mathematics in nature is most ubiquitous for itself as what is most known by the term sacred geometry. It is something that all should find of deep interest. With ‘pure’ geometry (spatial mathematics) we may, as some have intuited in the past and present, find the origin of matter—Hegel will certainly give it a role, particularly to the simplest form of the circle/sphere; thus, geometric ordering (and movement) of space is essential to material being. As Hegel comments later, speculative mathematics seems possible even if extremely difficult to discover or develop, and he gives the Pythagorean theorem as proof. Being that the Pythagoreans were quite interested in sacred geometry, the right triangle being one such divine form, and Hegel’s use of geometry in explaining the arising of matter, we can infer that sacred geometry has some implicit important role in the Hegelian picture of Nature even if it concerns very basic determinations which in the grand picture have less importance.

Sacred geometry is unique in that it is founded on reflexivity of geometric shape through measured relations of these geometric shapes to themselves. Sacred geometry begins from various bases which may be posited or discovered through various means. In these posited geometries the fundamental relations are 1 and 1/2. The measure of 1 is of identity and unity, it is also at once the unity of the universal reflexive operation which produce the shape. By the law of one, or rather the one law, the shape is fully articulated through its closure on itself. The tetrahedron is the triangle enclosing itself in 3D, the cube is the square, etc. The measure of 1/2 is of reflexive opposition through the identity, an opposition of duality and difference. A determinate line is 1, yet reflexively opposed to another 1 we find their unity and difference at the half way that is their meeting in a totality. This relation arises not just in external opposition, but internal opposition where the 1 is itself divisible into many 1s, with 2 or what in the 1 appears as 1/2 being the primordial opposition. From reflexive relations we can derive the infinity of all other possible relations, i.e. eventually one can come to see any geometrical relation in sacred geometry by virtue of the mere endless repetition. Sacred Geometry itself comes to be generally defined by minimal articulations which manifest the absolutely necessary form which is irreducible.

Take for example Metatron’s Cube, which is derived from a circle encircling itself and then repeating this encirclement with the explicit limitation of the first encirclement’s quantity, and so 1-6-6 is the total of circles. Self-encirclement of the circle necessarily yields 6 circles around a circle. Why, however, only a second set of 6 circles? It seems that these are the minimal requirement for the central circle connection points necessary to derive 2d projections of all 5 Platonic solids. This is but one possible way to derive these shapes, the center point of the circle is not the necessary point from which we must connect lines of projection. The Platonic solids themselves have the structure of self-reflexion, i.e. each platonic solid is derived from an absolute angular reflexion which when repeated in regular fashion must yield a perfectly regular self-enclosed shape.

The circle is a most unique geometric determination, it has no equivalent in pure mathematics. For example, π is not a number, but an infinite relational operation impossible to ever fully determine with any finite determinations of lengths or numbers. There are various methods for determining π, and each is made to deal with the peculiarity of how to approach the curved line with the straight line. The circumference as a ratio to the determinate diameter is incalculable as a finite quantity, it exerts an infinitely spurious determination on its elements which none can fully manifest this determination as a complete finite determination. Another example, the straight line turned upon itself in order to form a circle must exert an infinite angular determination on its elements. No non-zero regular line and angle yields the circle, only an increasingly high polygonal shape which approximates but never achieves circularity.

Along with geometry, a second derivative form which pertains to a higher domain than mere geometry appears in the science of material frequency, cyclic and repeating patterns of change which in Nature as such are embodied in a direct or derivative form of material absolute-motion, the motion of matter about itself as an existent circularity. Cycles, though they do not appear as circles in space, nonetheless are the existence of a circle through time; they are thus not directly geometric, but are indirectly through their repeating periodicity plotted on a graph and appearing as a sinusoid. In material relations of sound we find a concrete material reality immanently related to sacred geometry (one can see this directly instantiated in cymatics), and it is actually surprising that there is relatively little mentioned in common pop science about ‘sacred’ frequencies considering that certain frequencies generate sacred geometric shapes when applied to a physical. With cymatics we see the immanent relation of sound to geometry in the self-mediated arrangement of material in relation to itself and a vibrating plate according to its frequency. While resonance is far more concrete than mere space and matter, it is made intelligible why it has mathematical nature when we keep in mind the mere concept of space.

On The Possibility of Philosophical Mathematics

Hegel notes, despite his usual disdain for mathematical formalism, that he believes a genuinely speculative and philosophically valid mathematics is necessarily possible.

One could go further and work out the thought of a philosophical mathematics apprehended through notions, instead of the assumed determinations from which the method employed by the understanding derives ordinary mathematics. It is because mathematics is the science of the finite determinations of magnitude, which are supposed to remain firmly and consistently in their finitude, and may not go beyond these determinations, that it is essentially a science of the understanding; and since it is capable of realizing this science in a perfect manner, it has the advantage over other sciences of this kind, of not being contaminated by the admixture of heterogeneous notions or empirical application. It is always possible therefore that the Notion may establish a more exact awareness of the guiding principles of the operations of arithmetic (cf. § 102) and the theorems of geometry.

Hegel gives two examples of these conceptual proofs. The first of them is Pythagoras’s theorem,

Which presents the perfect determinateness of the triangle, in that in it, only the right angle is completely determined, its adjacent angle being equal to it. This theorem is therefore superior to all others as an illustration of the Idea. It presents a whole which has divided itself within itself, just as each shape in philosophy is divided within itself as Notion and reality. Here we have the same magnitude twice, first as the square of the hypotenuse, and then divided into the squares on the two cathetuses. [Emphasis added]

In Pythagoras’s theorem, A² + B² = C² only if the triangle is right angled. Given just this single determination about a triangle, the universal necessary form is determined as the relationship of the equation. Likewise, any of the two individual lines of the triangle determined as having a right angled determination will generate the entire determinate relation of any triangle. The existent individual determinateness of an actual triangle involves measured lengths, but this is a matter of contingent existence and the lengths of the lines are themselves inessential to the triangle as such, for the triangle is essentially only its relational number, not its relative lengths.—Because of this conceptual form of the right triangle, one could hold it as the ideal or True triangle of which all others are merely defective forms. . . make of this thought what you will.

The second is a proof of the circle where with the Pythagorean theorem we can derive the equation for the mathematical determination of a circle in Cartesian coordinates through (x²+y²=r²) as our determining equation.

There is a higher definition of the circle than that based on the equality of radii, in which difference is taken into account, so that the perfect determinateness of the circle is obtained. This occurs in analytical treatment, and contains nothing that is not found in Pythagoras’s theorem. The cathetuses are the sine and cosine, or abscissa and ordinate, and the hypotenuse is the radius. The relationship of these three constitutes the determinateness of the circle.

Further, he says this:

The truly philosophical science of mathematics considered as the doctrine of quantities, would be the science of measures; but this already assumes the real nature and the particularity of things, which is first present in concrete nature. Because of the external nature of quantity, this would certainly also be the most difficult of all sciences.

The science of measures would be the true science of mathematics for two reasons: 1) because it is the concrete concept of determinate mathematics as qualitative quantities, and thus 2) the form of mathematics which is truly capable of existing determinately and self-subsistent as objective, i.e. as natural mathematics. It would be the most difficult of all sciences for this simple reason: it is beholden to the empirical efforts of discovery. The measures of interest here are surely not a question of the arbitrary measures of a pound, a ton, or a liter, rather it is the true measures of nature, i.e. the necessary quantitative relations of qualities (geometric measures such as the right triangle, phi, pi, etc) or between qualities such as the mass and charge, gravity and electricity, more tangibly the relationship of universal scales, the relationship which determines the stable being of an atomic element, the determining relation of why the electron and proton have such a ratio, the fractal nature of forests, or something like a science of cymatics (material frequencies in relation to material structural arrangements).

Within the science of measure fall the concepts of the “constants of Nature” such as the speed of light, the rate of radioactive decay, the G-constant, etc. There is, however, significant empirical and rational reason to be wary of notions of such constants given our limitation to testing only a relative portion of the universe as well as having no knowledge of an intelligible reason for these constants, i.e. no logical derivation of any kind. Of all these constants, C is most suspect for being posited arbitrarily. It is quite important to discover true measures, for often we conceive ones that are merely an arbitrary unity of correlations, IQ is one such measure under endless scrutiny.

Spatial Dimensions

Space is implicitly the Notion in general, and as such has the differences of the Notion within itself: (a) in its indifference it has them immediately as the three dimensions, which are merely different, and quite devoid of determination. —§255

Here Hegel is simply offering his usual anticipatory claims, and thus his mention of the three directional dimensions as merely implicit concept (notion) can be forgiven. I don’t think one can simply attack him precisely because he acknowledges that while we may think we can jump to the three dimensions of everyday experience, we would know no difference in these dimensions at this point. The three dimensions are noted as height, length, and width with no particular meaning in themselves, and when it comes to mathematical treatment these are indeed indifferently reduced to the mere formal XYZ triad. In order to derive these three dimensions space itself must be developed into being capable of 3-dimensional determination, and this is what follows.

(b) Spatial difference is however essentially determinate and qualitative. As such it is (1) in the first instance the point, i.e. the negation of the immediate and undifferentiated self-externality of space itself. (2) The negation is however the negation of space, and is therefore itself spatial. In that this relation is essential to the point, the point is self-sublating and constitutes the line, which is the primary otherness or spatial being of the point. (3) The truth of otherness is however the negation of negation, and the line therefore passes over into the plane. Although one aspect of the plane is that it constitutes surface in general, in that it is a determinateness opposed to line and point, it also has the aspect of being the transcended negation of space, or the reinstatement of that spatial totality which now has the negative moment within it. It is therefore an enclosing surface, which divides off and separates a distinct part of space.—§256

Space, as self-external, is capable of being outside itself and is determinate as space first in the immediate negation of this very outsidedness. Space which is external to externality is the point. The point is ideal and subsumed by space as such, it is a moment of it and reflects space as an other to itself which itself too is point-like in relation to the point; thus, the point is outside a point and self-external as absolute point. The line is this existence of point outside a point . The line, itself spatial, is also outside itself, and the plane is the relation of line outside line.—In the Science of Logic the other is in truth the other of the other; thus, a negation of itself, i.e. negation of negation, and thus the very enclosing of itself as being-in-itself. This is why Hegel says the plane is the negation of negation, it is the first form of enclosing surface; it is also the return of space within itself.

[Comment:] It is a very curious thing that Hegel somehow did not seem to think it important to go beyond the plane into the volume. One would need nothing but to take up the obvious next negation, the self-externality of the plane as the volume. Three-dimensional geometry was already around, so this cannot be an oversight and must be deliberate. Perhaps the most likely reason is this: the plane can enclose itself perfectly fine, that is, a plane can be outside a plane by simply extending into another plane surface, e.g. a square within a square. With the attaining of the plane surface an immense amount can be developed not just with points and lines, but planes themselves. However, this seems flimsy, for the same can be said of the line which can contain an infinite many lines of shorter lengths within it. While this settles the basis of Euclidean geometry, the three dimensional volume seems to remain a logical possibility that should be explored. The zusatze in the section gives no indication as to why he does not consider it. This is nonetheless strange, for in the next chapter he will mention the sphere as the plane which moves about itself, yet this is not possible without the determination of volume. As a further curiosity, nothing in this conception of space demands that we cease at the four spatial dimensions (0-point,1-line,2-plane,3-volume)—nothing, except that our own experience requires (so far) nothing more.

It is of interest to note that Hegel immediately warns against the idea that the higher concepts of space are constructed through the lower elements, e.g. the notion that the line is made out of points, or that the plane is made out of lines. Such a notion is seemingly intuitive, but in truth it is the opposite of experience and reason. The point, being infinitely small, can never constitute any higher ontological structure. An infinity of points, lines, and planes do not and cannot possibly constitute a higher order themselves. The zero-dimensional does not build up to the one-dimensional, let alone the two-dimensional. The line can only exist as line within the plane, the point within the line, etc. This is based on nothing but two simple considerations: 1) the very intelligible meaning of space, and 2) the very structural necessities of existence and determinacy, that is, the very necessities for the very possibility of definition in material and conceptual sense.

[Comment:] On the notion of higher dimensions: it is completely logically possible and an open real possibility. The reason to limit the exposition to merely three spatial dimensions is simply the limit of our own experience and need. Mathematics is quite capable of grasping these other spatial dimensions in description though our intuitions are completely incapable of such experiential comprehension without a lower representation, and we can find nothing of the higher dimensions so far other than some confirmations in our regular experience of three dimensions. Now, some may think the logical possibility of further spatial dimensions remains empirically possible unless we come to know of another spatial factor which may give complete explanation for a limited quantity of X dimensions, but the rebuttal is simply that there is no current need to posit such out of any rational or empirical experience. The notion that a determination could be made about the number of real spatial dimensions through something merely posited by our arbitrary beginnings such as in string theory or the older Kaluza-Klein 5D theory is misguided at best despite how interesting it is.

Further, the idea of ‘enfolded’ dimensions which are not readily apparent in our normal experiential world, yet present in it, is one of the ways of trying to explain why we do not see these higher dimensional manifestations as spatial, i.e. most of what seems to point to higher dimensions are seemingly non-local force effects, but is this necessary? Does it not appear conveniently contrived as an ad hoc explanation as to why some hypergeometric results may correspond to empirical reality? The problem with a purely geometrical-mathematical consideration of dimensions is that because of our limited experience we are unable to determine what geometries and what dimensions are actually in play in our world. Unless we can get significantly determinate points of evidence in our dimensions of the existence of higher-dimensional phenomena beyond mere mathematical fine-adjusting to fit phenomena into theory so that it becomes evidence, then we are at a loss with these higher dimensions and their relation to us. Some believe that quantum phenomena like entanglement may point to the reality of a 4th or more spatial dimensions, however this is not conclusive.

Aside On Points



There is something interesting to note in that the point as such is in-itself as indeterminate as space, in the common conception the latter infinitely extended beyond itself and the former infinitely non-extended within itself. In Hegel’s concept of the point, the extent of extension is not what is in operative issue, for the point is the concept of space external to space as an other, a space which is not outside itself. When space is no longer considered outside itself but instead outside of another it appears as the point. If we consider space in total as our object we do not know how to conceive it other than as a point in relation to us who consider ourselves in abstraction outside it, after all, what does space look like in spacelessness? If abstracted in absolute form space is indistinguishable from the point as absolute.

We see this logical identity in speculative physics, where some theorize that the singularities of supposed zero-dimensional black holes may, despite their contradiction, harbor the space of entire universes within them (something Hegel himself alludes to in saying the point is the being-for-self of space within itself, i.e. it is the form of its infinite determination, of space seen from the non-spatial consideration we call time). This is to be expected, for the rational consideration of the point leads us right back to the consideration of unbounded space when its idealization is left behind. What we find in the spatial point as such is necessarily a continuation of space in its entirety.

As a secant on the very notion of black holes, Hegel has something interesting to say which may pertain to them without ever having encountered the notion in his day. Hegel comments: “If anything were no longer external to itself, but only to others it would be a point; but as no here is the last, there can be no such thing.” The point is an ideal possibility of space, yet if one ever existed it would just as immediately not exist by its very being, for what it is in-itself is just this self-externality as space; thus, what falls into the point has merely fallen right back into space unperturbed. The point is an ideal entity which differentiates space indifferently—its being there is an interruption that itself cannot interrupt the continuity of space, for it is merely the being of self-externality itself and thus simply the continuation of space. A black hole only appears zero dimensional and infinitely dense to us, but cannot be such in itself, for there is no minimal metric to space as such, and to posit such (which standard physics in some theories does) is nothing based in a necessary reality as much as the requirements of our arbitrary assumptions of what is fundamental.

Real space can ideally be divided in any measure we wish with no rational limit to this division, and thus no matter how stubborn we are in positing points in it, if these points designate real things we can conceive their eventual division as extended spatial objects. We put a dot on a graph and call it a point, yet no matter how fine that dot is we know it is in fact not a point. Physics treats its objects often as ideal point particles, even planets are treated as such for calculative efficiency, but though a planet may seem a point on a solar scale we need only zoom into it and see the truth.

Supposing that such a phenomenon as an endless collapse of matter under gravity is even possible—and there are empirical as well as rational considerations that should make us question such a possibility even without Hegel regardless of what mathematical positing and its correlated evidence says—we could only rightly conceive this object as an increasingly dense, yet never actually infinitely dense object. If black holes were actual points this would lead to interesting consequences, particularly the consequence that the reality of everything material is in fact truly non-spatial and non-temporal since their spatiality is absolutely negateable without destroying the presence of their natural effects, e.g. gravity. But if things were not ‘in’ space… where would they be and how could they relate spatially at all? The problem of Hegel’s interpretation of Leibniz above returns. Anything crushed into the zero dimensional would be nothing but the presence of a space outside of space. Where has the matter gone? Into another space which for us appears as a point, a non-spatial space for us, but which is nonetheless a space which is extended in itself in its extended relation to us.

Whatever the true nature of the large scale astronomical phenomena we identify as effects of black holes is, the reality of these objects cannot be comprehended as zero-dimensional masses regardless of the mathematical formulas that we are told assure us of their existence. The original impetus to believe in black holes was in a peculiar situation with the Schwartzchild solution which posited an object that collapsed beyond its Schwartzchild radius. Such an object could only be conceived as originating under immense material pressures as of yet truly unknown to this very day, and secondly the infinite collapse is posited on the simple basis that we know of nothing which would counteract this collapse. The name black hole comes from the fact that anything collapsed beyond its Schwartzchild radius would have a gravitic pull so strong not even light speed could provide an escape velocity. That objects with unparalleled immense gravitic effect exist is without question, we have known this with certainty since the observations of Sagittarius A. That these objects are black holes proper, solid objects collapsed beyond their Schwartzchild radius, is still in question and many anomalies should caution anyone from becoming an instant believer in the singularity hypothesis.

Space as such does not exist, and we can safely extend this non-existence to point singularities, one dimensional lines, and two dimensional planes as such—all of them exist for us as independent only ideally. While perhaps it is possible that due to spatial dimensional relations we may find that a totality of space may indeed be treated as point, line, plane, or volume from a higher geometrical perspective in a manner that a space can be bent without causing any internal disturbance to it, we currently have no empirical access to any evidence of this sort as far as we are aware, and even worse, we have no rational basis to believe this is possible.

On The Continuity of Space

Space is therefore punctiformity without points, or complete continuity. If one fixes a point, space is both interrupted and simply uninterrupted. The point has significance only in so far as it is spatial, and so external both to itself and to others. . . . This is the complete externality of space. This other of the point is itself just as external to itself however, and consequently both are undifferentiated and unseparated; space is still at unity with itself as its otherness beyond its limit; and it is this unity in extrinsicality which constitutes continuity.

The distinctions of space, because they are spatial, ultimately only are a continuation of space despite their seeming discrete break with it. A point is only a point in its spatial separation to other points, and space is only space in its self-externality. Space as such is unbroken through all of nature, for its own breaks merely affirm its continuity and all that is spatial is in relation to space as simply itself and thus offering no resistance. Space is continuous precisely in its very discontinuity: in being outside of itself it merely is within itself again.

Time

The negativity which relates itself to space as point and develops its determinations within it as line and plane, is however also a being-for-self within the sphere of self-externality; it posits its determinations within space, but at the same time, in conformity with the sphere of self-externality, and is therefore apparently indifferent to the immobile collaterality of space. Thus posited for itself, this negativity is time.

—§257

With space developed to its current determination, now determinate within itself, the totality of space as this determined whole reaches the point of negation of itself. Space is self-external to itself in its dimensions only to return into continuity with itself, and the differences of space just as immediately collapse into the indifference of space as mere continuations of it. The very externality of space is external to it as the negative power through which it develops itself into point, line, and plane. The externality of space by which it is truly external to itself in its totality is time—it is the spatial point logically developed for itself, for the point is the self-externality of self-externality. Space as a totality of dimensions is itself inert and time is the what unites the immobile totalities of space as separate within it.

[Comment:] Time may be the self-externality of space as such, but it is not immediately clear why time should have the concept of Becoming and thus be the power of change. In §258 the movement seems to be this: Time as pure negativity abstracted from space is purely abstract and thus has the structure of pure Being in the Science of Logic, but it is the necessity of abstract Being to immediately be Nothing and thus engage the movement of Becoming. There is, however, a much simpler reason for it, and it is simply in the already stated fact that time, as the negative unity of space, is the process which determines this very spatial outsidedness, an outsidedness which itself is the other of space, a non-spatial externality (thus the reference to the logical form of the point which is the non-spatial within space; time, however, is the true point as that which is the negation of space as such). Time as a whole is determined by space as a whole ceasing to be and coming to be.

With time space truly manages self-externality as a totality. The whole of space manages to be outside itself as temporal moments.

[Edit:] The first line of this section, “The negativity that relates itself to space as point…” admittedly caused me confusion because of the phrasing of “the negativity”, which I interpreted as referring already to time, and thus making the determinations of space to be because of time. This did confuse me, for if this were so then Hegel’s presentation of the order wasn’t right. I had seen this section before in a different translation from a prior version of the Encyclopaedia, and there it was clear that time was the totality of space outside it itself, but such is the way of translations and additions. Reading Richard D. Winfield’s book on the philosophy of nature, however, made me look through the sections again and reconsider the first interpretation as the more intelligible one, though admittedly the idea that time is the cause of the dimensionality of space is interesting.

[Comment:] The idea that time is something other than the negating spatiality of things themselves comes from the assumptions of an ultimate atomic existence at the foundation of Nature, an ontological level which is itself absolute and unchanging. Through time and space these bodies interact externally but never penetrate into each other for they have no internal structure to be penetrated into, nor do they have any any power of self-negation to give them the reality of change. Whether it is a spatial atom, or a logical atom (energy), the ultimate being of the world changes only in appearance but never has its essential being touched neither by space nor time.

On The Reality of Infinite Quantities

In the introduction Hegel mentions the question of the infinity of space and time as well as their division. If the infinity is qualitative boundlessness, then both space and time are truly infinite when taken in their universal form of the concept as such, but if the infinity is a quantitative infinity of finite spaces or moments the infinity is only ideally possible, but not real. This claim is based on the very concepts of infinity and finitude developed in the Logic; that which is finite is always preceded and succeeded by another finite indefinitely without a final absolute starting or end point possible. Finitude itself is always caught in the middle of itself no matter what, and thus all finite things are always beginning and ending without ever having an absolute point of beginning or ending. On this account, the speculations of so-called cosmologists concerning the origins of the universe are not only poor because they lack philosophical rigor, but because they answer questions that are badly posed.

Time As A Container

But everything does not appear and pass in time; time itself is this becoming, arising, and passing away, it is the abstraction which has being, the Cronos which engenders all and destroys that to which it gives birth. . . . Time does not resemble a container in which everything is as it were borne away and swallowed up in the flow of a stream. Time is merely this abstraction of destroying. Things are in time because they are finite; they do not pass away because they are in time, but are themselves that which is temporal.

Time, like space, is not a container, and thus things do not move in or through it. This a priori denies the possibility of one of our most popular modern tropes: time travel and its speculative physics cousin, relativistic time dilation. Because the very fact of spatial finitude and change through self-negation is time, time itself has no rate of change and cannot slow or accelerate its movement. The time of things is simply the finite life process of things, and spatial things appear timeless only relatively by outlasting other things they are compared to. The empirical fact that clock rates increase and decrease with movement and position in a gravitational field is telling of only that: the rate of clocks, objects which only ‘tell’ anything based on arbitrary cycles of motion comparisons.

But what of the observed prolonging of the half-life of short-lived particles at relativistic speeds, does this not show the notion is right? Certainly, the relative time of these entities is being prolonged through what many should concede as currently mysterious factors, for even if one accepts the space-time relation in relativity it is in no way an explained relation, but time itself is not being changed nor traveled through. One could much more simply explain the phenomenon by simply changing the theoretical presuppositions of the nature of space and time, e.g. if space is always filled with matter we must expect resistance as one moves in relation to it. This would make the phenomenon of clock acceleration or retardation as simply the same phenomenon of spinning a propeller out in space, in air, and in water. As the medium becomes denser the ease of motion becomes more strained. This would also explain the nature of radiation as a consequence of spatial pressures capable of maintaining atomic objects together. This is, however, merely conceptual speculation.

To explain the phenomenon of time cannot be left to a mere set of mathematical formulas which have been arbitrarily concocted in a mixture of a priori assumptions and empirical fudge factors to fit a theoretical framework, but what is certain is that the explanation cannot involve claims about a rate of time as such nor about moving within it at a certain rate. What changes in time-dilation is the decay/movement rate of things, changes which appear in spatial determination. The life of beings may be prolonged with interventions of medicine, yet we do not mistake this to be a meddling with time as such. Likewise, the movement of objects may be increased and slowed down merely by changes in mediums of movements and conditions of movement, yet this is hardly considered a change of time as such. Why clocks and short lived atoms should be privileged as telling us about time itself is merely based on assumptions which are, when investigated, unwarranted.

The Dimensions of Time

Time, as the negative unity of self-externality, is also purely abstract and of an ideal nature. It is the being which, in that it is, is not, and in that it is not, is. It is intuited becoming; admittedly, its differences are therefore determined as being simply momentary; in that they immediately sublate themselves in their externality however, they are self-external.

—§258

Time, as another form of self-externality, is outside itself just as space is, but its self-externality is determined as space and not within itself, for time itself is purely the self-negation of space—it is the negative unity of space, that is, the negation of space by space. Taken apart from space and as the other of space, time is merely abstract negativity. Time itself at first is abstract and as continuously indifferent as space in that in its self-negation it only returns identically to itself endlessly as a now, which resultant as a totality of mere space is indifferent to the last now. Time as such, like space as such, does not exist independently.

If time is external to itself, however, we may still speak of its dimensions insofar as the spaces separated as external to each other by time are indeed time’s determination. The past, present, and future are to be used in naming these determinations, but here they only have a partial identity with our normal understanding of these dimensions.

The present, future, and past, the dimensions of time, constitute the becoming of externality as such, and its dissolution into the differences of being as passing over into nothing, and of nothing as passing over into being. The immediate disappearance of these differences into individuality is the present as now, which, as it excludes individuality and is at the same time simply continuous in the other moments, is itself merely this disappearance of its being into nothing, and of nothing into its being.

The finite present is the now conceived as concrete being against the non-being of the abstract past and future; thus, it is the negation of the negation, the negative unity of past and future. Time is a ‘flow’ as Becoming, of ceasing and coming to be endlessly in one moment.

The present is Being, the future and past are Nothing. The present, however, is only the coming to be of the future and the ceasing to be of the past at the same moment, thus the ceasing of Being and the coming to be of Nothing; thus, its being is its disappearance. The present now is the individual moment concretized from its double negation of past and future, and this moment is a totality of space. In the now the differences of time—the past and future—come together into an individuality, however, this individuality is immediately denied by its abstract universality, for every now as such is indistinguishable from every other now. Further, this individual now is also negated by its own negativity as a totality of space and once again self-externalizes. The now remains continuous with itself in the past and future, for they are merely the now that has been and the now that is not yet, but it is precisely the concept of the now to be and not be. The now that is is at once the now that is not—it is only coming and ceasing to be, a Becoming. The future is Nothing passing into Being in the now, and the past is Being passing into Nothing in the now, and thus the now is being and nothing at one and the same moment. The now is the future of the space preceding it, and the past of the space succeeding it, and finally is itself this very succession as time.

The dimensions of time do not exist in nature as what we normally think of past and future, for in nature time is the now as the separately subsisting different total spaces, and for it the past is as much the future, merely a totality of space indifferent to any other—no mere moment of time has any special significance. The past, present, and future are only ideally for us as subjects as representations in memory (past), or fear/hope (future). In nature the past and future of time are reduced to the now as total spaces, i.e. the spaces outside each other, and thus space is negated time. The individualities of the present—the differentiated spaces—are, however, themselves indifferent and continuous with each other as self-externality. Space actualizes itself in time, yet time actualizes itself in space. Within each we find an immanent indifference in their moments, and between them we likewise find an indifference as each merely disappears into the other through relentless self-externality forcing them into a beyond which is only a return to the continuous same.

[Comment:] It is quite interesting that Hegel here makes the present the result of the negative unity of past and future. This goes counter to the common assumption which privileges present now of conscious experience is the existence of time and that it is from the now that the past flows and the future is posited. This notion of time may perhaps be termed psychological time, and this is clearly not the time Hegel is considering. Thus, Hegel is not a presentist when it comes to time despite the claims of some like Heidegger. Another pernicious assumption is that the determination of the present is exclusively a result of the past, and thus we have so-called determinists who seek the reason for the present by digging empirically or theoretically into the material of the past. This obsession with the past as the only explanation is based on assumptions which not only deny the reality of purposes, of future telos which just as much enter the determination of the present, but also are ignorant of the present and deny the otherwise obvious reality that when things are determined, and thus their causes and effects realized, it is always in one single moment of the present.

On A ‘Science of Time’

There is no science of time corresponding to geometry, the science of space. Temporal differences do not have this indifference of self-externality which constitutes the immediate determinability of space, and unlike this determinability, do not therefore give rise to figurations. Time first becomes capable of such figurations when the understanding paralyzes it and reduces its negativity to a unit. This dead unity, which is thought’s highest externality, gives rise to external combinations; these are the figures of arithmetic, which may be applied by the understanding to equality and inequality, identity and difference.

Time itself is not like space in that time does not exist outside itself as time which is sublated back into pure time; thus, it has no collaterality for itself like space does. Time realizes it’s self-externality only as space, but itself does not and cannot embody mathematical quantities like space. Time only enters mathematical form when it is abstracted as a unit, but this is already sublated time in a form which goes beyond time as such; thus, to chase after such theories is foolish.

On Eternity

Absolute timelessness is eternity, which is devoid of natural time, and is therefore to be distinguished from duration. In its Notion, time itself is eternal however, for its Notion is neither the present nor any other time, but time as such. Its Notion is, like all Notion, eternal, and thus also constitutes the absolute present. Eternity will not be, nor has it been, it is. Duration is therefore to be distinguished from eternity, in that it is merely a relative sublation of time; eternity is however infinite, that is to say, not relative, but intro-reflected duration.

Time itself is not temporal. Time does not begin, it is not finite, but is an infinite universal. Eternity is not before or after time, but transcends time and never comes to be nor ceases to be. Eternity is absolute present in that it is all moments of time in completed whole. There is a famous mystical phrase, “The present is eternal,” and it is quite easy to grasp. The present as such never comes or ceases to be, we are always present and all things occur presently. The infinite past happened in the present, and the infinite future will happen in the present; thus, the present has itself never come to be or ceased to be, nor has it changed. It is also a consequence of the logic of time that the present is its negation of negation, the completed concept of time unifying past and future in one. To end:

The present is only because the past is not: the being of the now has the determination of not-being, and the not-being of its being is the future; the present is this negative unity. The not-being replaced by now, is the past; the being of not-being contained in the present, is the future. If one considers time positively one can therefore say that only the present is, before and after is not, but the concrete present is the result of the past, and is pregnant with the future. The true present is therefore eternity.

Place, Motion, Matter

Space, in its actualization of self-externality, is only the pure negativity of itself and transforms into time. Time for itself is the self-sublation of its moments and thus self-negates, is external to itself in the immediate collaterality of the spaces differentiated by the now, but this externality of spaces to each other is only the concept of space once more; thus, time collapses into the externality of space in undifferentiatedness. Time has not merely collapsed back into abstract space, its development gives space its dimensions.

Place is this concrete point of space and time united as the here and now; it can also be said that place is the spatiality of time. This point, as the reality of space as its self-externality, is concretely determined as a totality of spatial dimensions, and as the reality of time it is a self-sublating now. The ‘point of duration’ (the now) is in unity and identical to the spatial point as one determination in the concept of place.

Initially, the place which is thus the posited identity of space and time is also the posited contradiction set up by the mutual exclusiveness of space and time. place is spatial and therefore indifferent singularity, and is this only as the spatial now, or time. As this place, it is therefore in a condition of immediate indifference to itself; it is external to itself, the negation of itself, and constitutes another place. This passing away and self-regeneration of space in time and time in space, in which time posits itself spatially as place, while this indifferent spatiality is likewise posited immediately in a temporal manner, constitutes motion. To an equal extent however, this becoming is itself the internal collapse of its contradiction, it is therefore the immediately identical and existent unity of place and motion, i.e. matter.

As a spatial determination, place is self-external and thus posits another place beyond itself through its own temporality; at the same moment, a place changes itself through its temporality. Motion is this process of passing away and regeneration of place—it is the higher temporality of place. “One place does not merely imply another, it sublates itself into becoming another.” As a higher form of time, motion engages a logic of Becoming as well and collapses into a higher form of space resultant from its differentiating process. Matter is this resultant unity of place and motion; it is moved place as self-negated motion. This development is of a deep ingenuity, for with it Hegel captures the origination of matter as a process of differentiation (motion) and as itself an unmoving enduring product of such differentiation. Self-negated motion is motion opposed to itself and thus come into its own paralysis. It also makes intelligible the composite being of matter as such by its very spatio-temporal being in which it is composed of various places.

[Comment:] Here we see an interesting appearance of the Being-Becoming-Existence logical development. Place is Being, motion is Becoming, and matter is the settled result of Becoming’s internal collapse/negation as Existence.

The Determination of Matter

What follows is something which is a bit of a difficult passage, part of the zuzatse. It is Hegel’s full conceptual articulation of the concept of matter. The basic thing to keep in mind here is the absolute form which is being considered here. When Hegel says place returns from motion we are talking not of difference places out side each other, but of place as such moving in relation to itself.

* * * *

Rectilinear motion is not motion in and for itself, but motion subordinated to another term, of which, in that it has become a predicate, or sublated, it is a moment.

Motion in a straight line can only be determined in relation to something which is moved in relation to.

The re-establishment of the duration of the point in opposition to its motion, is the re-establishment of the immobility of place. This re-established place is not immediate, but the return from alteration, and is the result and ground of motion.

Motion, like time, immediately returns to space as unmoving place as the enduring substance of movement. It is important that one remember this return is not immediate place, but moved place, for it has importance for the determinations of space. Here we are not dealing with places, but with place as such—absolute place.

In that it is dimension, and so opposed to the other moments, it is the centre.

This is a bit hard. Place, in that it is dimensional space as determinate, is center. Why? Because the first determination of dimensionality is the singular ideal point within space. Place which moves itself first moves into itself as this center.

This return as line is the circular line; it is the now, before, and after,joining itself with itself; it is the indifference of these dimensions, in which the before is just as much an after as the after is a before. This is the first necessary paralysis of these dimensions posited in space. Circular motion is the spatial or subsistent unity of the dimensions of time. The point tends towards a place which is its future, and vacates one which is the past; but that which it has behind it, is at the same time that at which it will arrive; and it has already been at the after towards which it tends. Its goal is the point which is its past.

The return of place to itself through motion, in the further determination of line is the line which returns in movement to itself, and thus is the circular line which moves in relation to itself in circular motion. This can be comprehended as the line which moves in relation to itself. The before, now, and after are the temporal moments of the line as the points determined in it. In the circle all points are the before, here, and after to every other point and to themselves. In the circle the moments of time are first paralyzed as a totality in space.

The truth of time is that its goal is the past and not the future.

This has meaning beyond the truth of Nature’s time. In the Phenomenology of Spirit’s Preface Hegel notes that purpose realizes itself in simply returning to itself, thus the actual natural finite existence of concepts is in a way the enduring return of things towards the essence which is their past.

The motion which relates itself to the centre is itself the plane, that is to say the motion which, in that it forms a synthetic whole, itself contains its moments or is its dissolution in the centre, as well as the radii of the circle, which relate it to the dissolution. This plane itself moves however, and so becomes its otherness, an entirety of space, i.e. the motion returns into itself, and the immobile centre becomes a universal point, in which the whole sinks into quiescence.

Moving place, determined as plane, fully relates itself to the center as the full determinate externality of the central point. The plane contains its moments (the point and line); it contains its ‘dissolution’ in the center, meaning, its temporality/motion or negation in this center. The radii of the circle, the line related to the center, is how the plane determinately relates to this center. This movement towards the center, if followed through by the plane, would dissolve it into abstract space and time. This plane is the moving plane, however, and as a totality of space it finally moves and thus is outside itself as self-externality of space. This total space returns to the form of the point and is for itself immobile, for place which moves in relation to itself is this: it is place moving against itself. Absolute motion is motion in opposition to itself, and necessarily is realized as a static immobility of matter.

It is in fact the essence of motion which has here sublated the now, the past, and the future, or the different dimensions which constitute its Notion. In the circle these dimensions are precisely one, and constitute the re-established Notion of duration, or of motion extinguishing itself within itself. This is posited mass, durability, that which has condensed itself through itself, and displays motion as its possibility.

Motion is the ground of space, time, place, and finally, itself. This is why it is the Notion (concept) as the self-differentiating and self-developing unity. The circle is the ‘absolute form’ of space and time, and circular motion as absolute motion of place is posited matter and explains its necessary durability as that which has abstracted itself from a nebulous abstract universal into a determinate concrete reality through its self-posited power of self-moving place.