1.49 The “edge” Universe Theory

Section 49 (first updated 02.17.2021)

On Black Holes, Infinity, and the Center of the Universe

The claim that a black hole is the “centre of the universe” requires careful clarification.

Modern science remains implicitly bound to an ancient assumption: that the universe possesses a shape, and that possessing a shape necessarily implies finitude. The notion that the universe is finite appears to contradict the idea that the universe is infinite only because infinity itself is commonly misunderstood. Infinity is often taken to mean that which extends endlessly into unbounded space. While this is one behavior of the infinite, it does not exhaust its meaning. Infinity does not merely describe extension without limit; it describes a mode of organization and relation.

If we examine the empirical phenomena known as black holes, what emerges is not evidence for a finite universe, but rather an approximation that the observable universe possesses form as infinity. To say that the universe has form is not to impose finitude upon substance. Substance, properly understood, is itself infinite, and infinity must be understood through substance rather than opposed to it.¹

The term black hole itself obscures the nature of the phenomenon. Linguistically, it presents the black hole as a discrete object among other objects in space, something locatable and isolable. Yet this terminology fails to explain what kind of “object” a black hole is. It indicates that something can be differentiated and sensed, but it falls short of explaining the unique ontological role the phenomenon plays—particularly since black holes confound ordinary sensory and spatial intuitions.²

The concept of a black hole overlaps significantly with what physics calls dark matter. Dark matter has never been directly observed but is inferred through its gravitational effects on ordinary matter such as photons and baryonic particles. In this sense, black holes and dark matter are not fundamentally different substances, but different modes of appearance of the same underlying reality. Dark matter is the abstract inference of the same principle that appears concretely in black holes. Black holes, unlike dark matter, are perceptible only through their interaction with luminous matter, especially stars.³

Black holes consume energy from stars, forming external accretion disks heated by friction—among the brightest observable phenomena in the universe. These “dark” entities are not ordinary objects with fixed qualities but rather fundamental processes: they exhibit power without being reducible to static attributes. Aristotle already conceived of such realities under the notion of energeia—pure activity rather than passive substance.⁴

This conception is not foreign to human thought. Arithmetic, for example, is the study of pure operations: numbers are not objects but symbols for relations and activities. Quantity excludes particular objects while retaining relational structure. A quantity is never merely a group nor merely an individual; it is always the relation between the two. Thus quantity itself denotes a unity of many—a single measure of multiplicity.

A black hole is one of the clearest natural examples of a pure relation, which is precisely why it confuses the senses. It is not a spatial object in the ordinary sense, because it is not fundamentally determined by position. Nor is it external to other objects in the way planets are external to stars. A black hole does not orbit a star; it emerges from a star. It is a moment in time in the life of an object. Whether as a supermassive black hole at the center of a galaxy or as an infinitesimal collapse point within a star, it is always relational and temporal.⁵

What we observe as “isolated” black holes are abstractions—snapshots of a process at a particular moment relative to a star’s lifecycle. Whether consuming matter, stabilizing, or (in speculative models) emitting matter as a white hole, the black hole represents the terminal phase of stellar existence. It is the transition of a star from a particle-dominated state into a wavelength-dominated one. This transition is necessary for the star’s duration in time to be gathered into a singular limit.

The familiar image of a black hole consuming a star via an accretion disk is not merely an interaction between two bodies; it is the same process by which a star’s life reaches its temporal limit. In the final moments of stellar collapse, all events constituting the star’s life are compressed—either experienced as infinite acceleration or as an instantaneous flash, analogous to a wavelength collapsing into a point.⁶

The principle—that the end of a duration is simultaneously its beginning—is fundamental to the notion of simultaneity in quantum mechanics. Simultaneity is not merely two events occurring at the same time but the deeper claim that the completion of a process is also its origin. This is what defines an inverse relation. An inverse relation does not merely mean two opposite determinations, but that from one standpoint the other is defined precisely as its “other.” When one determination completes itself, it inverts into the other.

Every duration presupposes an action and a consequence. Yet from the inverse standpoint, the consequence is itself an action. For example, whenever there is a killer, there is someone killed. From the killer’s perspective, the consequence is the killing. From the victim’s standpoint, the event is an action whose consequence is the existence of a killer. This inversion explains how an end can also be a beginning.

In lived experience, we abstract one side of this relation. We experience ourselves as acting and perceive consequences indirectly, or we experience consequences directly and perceive causes externally. But at an absolute point in time—what quantum theory describes as a quantum event—cause and effect arise simultaneously as a single packet of energy.⁷

This insight grounds a transcendental ethics: every action is absolute because its effects are inseparable from it. Effects are not secondary; they are the recorded value of the action itself. While classical physics models cause and effect as instantaneous (e.g., striking a cup and it falling), over extended durations the relation becomes nonlocal in time. In a purely temporal domain, the content of reaction is not bound to immediate spatial causality.

The senses register only one side of the equation at a given moment. But at the absolute level—time itself understood as pure activity—action and effect are simultaneous. This is where quantum mechanics intersects with metaphysics: in the quantum, cause and effect are not sequential but co-present.

Footnotes

1. Aristotle, Metaphysics, Book Λ; Spinoza, Ethics, Part I – Substance as infinite and self-causing.
2. Hawking, S., A Brief History of Time – On the limits of spatial intuition regarding black holes.
3. Peebles, P. J. E., Principles of Physical Cosmology – Dark matter as inferred gravitational structure.
4. Aristotle, Physics and Metaphysics – Energeia as pure actuality.
5. Penrose, R., The Road to Reality – Black holes as spacetime limits rather than ordinary objects.
6. Wheeler, J. A., “Geometrodynamics” – Collapse as spacetime boundary condition.
7. Whitehead, A. N., Process and Reality – Actual occasions and the simultaneity of cause and effect.

Black Hole as Nothing

The black hole should not be understood as a “thing” among things, but as a limit-condition of being, a point at which determinate qualities collapse into pure relational activity. Calling it “nothing” does not mean non-existence; rather, it signifies the absence of determinate, sensible qualities while retaining maximal causal efficacy. In Aristotelian terms, the black hole is not a substance with properties but an energeia—pure activity without form. It exerts gravitational influence, organizes surrounding matter, and structures spacetime itself, yet it does so without presenting itself as an object available to direct perception. This is why the senses fail before it: the black hole is not visible in itself, only inferable through its effects.

This “nothingness” is therefore not privative but structural. The black hole is nothing in the same way that zero is nothing in arithmetic: zero is not the absence of number but the positional condition that allows number to appear at all. Likewise, the black hole functions as a zero-point of spacetime relations. It is the place where extension, duration, and differentiation cease to be meaningful, yet precisely because of this, it anchors the measurable universe. The black hole is not empty space but the collapse of space into pure relation, where spatial distinctions lose their meaning while causal power intensifies.

From this perspective, the black hole is not external to the objects it affects. It is a moment in the life of matter, particularly stellar matter. A black hole does not encounter a star as one object encounters another; it is the star’s own internal limit made manifest. What appears observationally as a black hole “consuming” a star is, ontologically, the star completing its temporal process. The black hole is the star’s duration gathered into a single point, where time no longer unfolds sequentially but becomes simultaneous. Thus, the black hole is nothing other than time collapsing into itself, the end of duration that is also its beginning.

In this sense, the black hole exemplifies the principle you articulate throughout your work: the end of a process is simultaneously its origin. The black hole is the negative moment of matter—not negation as destruction, but negation as concentration. It is matter stripped of all qualitative appearance, retaining only the power to relate. This is why it is best described as “nothing”: it is not something among things, but that through which things are gathered, terminated, and re-originated.

Infinity Thesis

Infinity, as it appears in cosmology, is commonly misunderstood as endless spatial extension—an unbounded expanse that simply goes on forever. This conception mistakes infinity for a quantitative exaggeration rather than a qualitative principle. True infinity is not “more space” or “more time,” but the self-relation of substance, the capacity of reality to contain its limits within itself. A universe can possess form and still be infinite, provided that its form is not imposed from outside but generated internally through its own relations.

Black holes reveal this internal form of infinity. If infinity were merely endless extension, black holes would appear as finite anomalies—exceptions to an otherwise uniform space. But if infinity is understood as self-enclosure, then black holes are not exceptions but expressions of infinity’s structure. They demonstrate that the universe does not expand infinitely outward only, but also folds infinitely inward. Infinity is not linear but topological: it curves back upon itself. The black hole is where this curvature becomes explicit.

From this standpoint, the claim that a black hole is the “center of the universe” must be reformulated. It is not a geometric center located somewhere in space. Rather, it is a structural center, meaning that it represents the principle by which the universe gathers itself into unity. Just as the number 1 is present in every number without occupying a particular position in the series, the black hole represents the presence of infinity within every region of spacetime. Every finite structure presupposes a limit; the black hole is the universal form of limit as such.

Infinity, then, is not opposed to finitude. Finite things exist precisely because infinity limits itself. A lifetime, a star, a galaxy—all are finite articulations of an infinite process. The black hole marks the point at which a finite articulation exhausts itself and returns to the infinite field from which it arose. This is why black holes are temporally central rather than spatially central: they are the recall of the finite into the infinite, the place where duration is sublated into simultaneity.

In this way, black holes and infinity are not separate problems but the same problem viewed from different angles. Infinity is the universal capacity for self-relation; the black hole is that capacity appearing at the limit of matter. The universe is infinite not because it has no boundary, but because its boundary is internal to itself. The black hole is the name we give to that internal boundary when it becomes empirically visible.

Judgment After Death

All religions maintain, in one form or another, the claim that the moment of death constitutes a final judgment upon one’s actions during life. This judgment, however, is not properly understood as being imposed by an external, transcendent force identified as God. Rather, God—properly speaking—is the universal side of the individual.[^1] The universal assumes an indifferent position with respect to the particular determinations adopted by the individual throughout life. This indifference does not signify neutrality or incapacity, but rather the capacity to contain opposing determinations simultaneously. It is precisely this simultaneous containment that allows the particular—namely, the individual—to experience the relative distinction between cause and effect, and thereby to recognize actions as morally differentiated.

This distinction between cause and effect is the foundation of ethical valuation. Ethical judgment arises from relations of difference: when one determination appears as cause, the other appears as effect, and vice versa.[^2] During life, the individual experiences these relations asymmetrically—primarily as causes of action, and only indirectly as recipients of their consequences. At the end of a lifetime, however, this asymmetry dissolves. The entire duration of lived events becomes inverted, such that the individual now experiences as effects what were previously experienced as actions. What the individual once did is now done to them.

Judgment consists precisely in this reversal. The one who killed experiences the position of the killed; the one who harmed experiences harm; the one who nurtured experiences being nurtured.[^3] This is not retribution imposed from outside, but the internal completion of ethical relations. The consequences of action are not externally added to the agent; they are implicit in the action itself, unfolding necessarily across time. Transcendental morality is grounded in this principle: actions are absolute because their effects are inseparably entangled with them and must be experienced in full at some point in time.[^4]

For the senses, actions appear divided into causes and effects. When acting, one experiences agency and initiation; when acted upon, one experiences consequence and reception. This division, however, is perspectival rather than absolute. In reality, cause and effect are inseparable moments of a single process. What differs is only the standpoint from which the process is experienced.[^5]

This ethical structure is mirrored in nature. During the final moments of a star’s life, the totality of its prior processes collapses and reoccurs in an inverted and compressed manner within an instantaneous duration. The star’s entire history is gathered into a single terminal event. This phenomenon—where the end of a duration coincides with its total recollection—is not unique to stellar processes but is a universal principle of life itself.[^6] In death, whether of a star or a conscious being, duration is no longer sequential but simultaneous. The end becomes the beginning, and the whole of life is encountered at once from the standpoint of its consequences.

Footnotes

[^1]: This conception aligns with Hegel’s understanding of God as the universal that realizes itself through the particular, rather than as an external lawgiver. See Science of Logic, Book II, “The Doctrine of the Concept.”

[^2]: Aristotle’s ethics presuppose this relational structure, where moral evaluation depends on the relation between action (praxis) and its end (telos). See Nicomachean Ethics, Book I.

[^3]: Variants of this idea appear in multiple religious traditions, including the Buddhist doctrine of karma and the Christian notion that one is judged “according to one’s works” (Revelation 20:12), though here interpreted non-theologically.

[^4]: Kant’s concept of transcendental morality anticipates this structure, though Kant restricts its realization to the noumenal realm. See Critique of Practical Reason, Part I.

[^5]: This view parallels Spinoza’s doctrine that cause and effect are modes of the same substance, differing only in conceptual relation. See Ethics, Part I.

[^6]: Whitehead describes a similar principle in terms of “concrescence,” where the many become one in a final satisfaction. See Process and Reality, Part III.

Aristotle: Why the Circle Always Falls into a Line

The claim that “the circle always falls into a line” is not a literal geometrical error but a philosophical insight Aristotle develops across his Physics, Metaphysics, and logical works. At its core, the idea expresses Aristotle’s rejection of the notion that perfect circularity can exist as a self-sufficient actuality in the physical or logical world. While the circle is the symbol of perfection, completeness, and self-return, Aristotle insists that what exists in actuality must be determinate, bounded, and ordered according to principles that ultimately resolve into linear succession.[^1]

In Aristotle’s physics, motion and time are inseparable. Time is defined as the “number of motion with respect to before and after,” which already implies a linear ordering.[^2] Although circular motion appears to return upon itself, it can only be experienced, measured, and understood through a sequence of moments—earlier and later. Thus, even the most perfect circular motion “falls” into a line insofar as it must be articulated through linear temporality to be intelligible. The circle may symbolize eternity, but eternity cannot be perceived or enacted except through temporal succession.

This insight also appears in Aristotle’s critique of infinite regress and actual infinity. A circle suggests endless return without beginning or end, but Aristotle denies that such an infinite structure can exist as a completed actuality.[^3] Any attempt to actualize circularity collapses into a sequence of determinate steps. The infinite, for Aristotle, exists only potentially, never as a finished whole. Therefore, a circle—if taken as an actually infinite structure—must be decomposed into finite segments, which are linear. The circle thus resolves into a line because actuality demands limitation.

Logically, the same principle applies. A circular definition—one that defines a thing in terms of itself—is invalid in Aristotelian logic because it fails to provide explanatory priority.[^4] Explanation requires movement from prior to posterior, from premise to conclusion. Even if the object under consideration is reflexive or self-related, its explanation cannot be circular without becoming vacuous. Hence, reasoning that attempts to remain purely circular must be unfolded into a linear argument. The circle of meaning must be translated into a line of inference.

In Aristotle’s metaphysics, substance (ousia) is what exists primarily, and substance is always determinate.[^5] Circularity represents unity without differentiation, but determination requires distinction—form separated from matter, potentiality from actuality. The act of distinguishing already introduces linearity. Thus, the circle, as pure unity, cannot persist without differentiation, and differentiation introduces direction, order, and sequence. What begins as a circle becomes a line because existence itself is articulated through difference.

This is why Aristotle privileges linear causality—efficient cause leading to effect—even while acknowledging final causes that appear circular (the end explaining the beginning). Although the end (telos) gives meaning to the process, the process itself unfolds linearly.[^6] The acorn becomes the oak, but it does not become it instantaneously or circularly; it proceeds through ordered stages. The circle of purpose collapses into the line of development.

Thus, to say that “the circle always falls into a line” is to say that perfect self-identity cannot exist as pure actuality. Whether in motion, time, logic, or being, circularity must be translated into succession to become real. The circle belongs to thought as an ideal; the line belongs to existence as process. Aristotle’s insight is not a denial of unity, but a recognition that unity must be mediated by difference in order to exist.

Footnotes

[^1]: Aristotle, Metaphysics, Book Δ, where actuality (energeia) is defined as determinate being, as opposed to indeterminate potentiality.

[^2]: Aristotle, Physics, Book IV, 219b1–2: “Time is the number of motion in respect of before and after.”

[^3]: Aristotle, Physics, Book III, where he denies the existence of an actual infinite and allows only potential infinity.

[^4]: Aristotle, Posterior Analytics, Book I, on the impossibility of circular demonstration (diallelus).

[^5]: Aristotle, Metaphysics, Book Ζ, on substance as primary being and the necessity of form.

[^6]: Aristotle, Physics, Book II, on the four causes and the role of final causation in natural processes.

The Schwarzschild Radius and the Black Hole as Lack of Structure

The Schwarzschild radius defines the threshold at which a mass becomes a black hole. It is not a physical surface in the ordinary sense, but a limit beyond which the known laws of classical mechanics and spacetime geometry cease to function as expected.[^1] This radius does not describe a structure within space; rather, it marks the collapse of spatial structure itself. What we call a black hole is therefore not best understood as an object among objects, but as a limit-condition—a region where extension, location, and ordinary causal relations lose their classical meaning.

In classical mechanics, mass, size, and gravitational influence are proportional: larger and more massive objects exert stronger gravitational forces, while smaller objects exert weaker ones. A black hole appears to violate this principle. It can be infinitesimal in spatial extent, yet possess an extreme gravitational pull, far exceeding that of vastly larger objects. Conversely, we observe supermassive black holes whose masses exceed billions of suns, yet whose defining feature is not size but the same limiting radius relative to their mass. This contradiction—maximal gravitational influence combined with minimal spatial extension—cannot be explained purely in spatial terms.

The paradox dissolves when the black hole is understood not as a spatial object but as a temporal and durational phenomenon. The Schwarzschild radius marks the point at which mass becomes infinitely extended inwardly rather than outwardly. The black hole does not occupy space the way ordinary matter does; instead, it represents a collapse of duration into an infinitesimal limit. In this sense, a black hole is not “small” in the usual way—it is infinitely deep rather than infinitely wide. Its mass is not distributed across space but condensed into a temporal singularity.

This is why black holes appear to oppose all ordinary intuitions about mass and gravity. Gravity is no longer a force emanating outward from a body but a manifestation of spacetime curvature that has reached an absolute limit.[^2] The black hole is thus best described as a lack of structure rather than a structure: a region where spatial relations fail, where extension becomes meaningless, and where duration folds back upon itself.

Micro–Black Holes and the Infinitesimal Vertex

Empirical astrophysics maintains that only stars with very large masses can become black holes. This is correct within the limits of current observation.[^3] Our Sun, for example, is not massive enough to collapse into a black hole; instead, it will eventually exhaust its nuclear fuel and end its life as a white dwarf. However, this empirical claim does not exhaust the metaphysical implications of black hole physics.

From a relational perspective, an infinitesimal point, when perceived relative to a vastly larger system, appears as a force rather than an object. Gravity itself operates this way: it is not directly observable as a substance, but only through its effects. In this sense, the black hole reveals something implicit in all matter—namely, that every object contains within it a limiting point where its relations to space and time converge. While not every object becomes an astrophysical black hole, the principle of inward collapse is latent in all mass as a tendency toward limit.

Thus, what we observe as isolated black holes in space are extreme manifestations of a more general structure of reality. They are vertices—points at which extension terminates and relation becomes absolute. The black hole is therefore not merely an endpoint in stellar evolution, but a conceptual boundary that exposes the limits of spatial explanation itself.

Defining the Schwarzschild Radius

The Schwarzschild radius is defined as the radius at which the escape velocity from a mass equals the speed of light. It is given by the formula:

[r_s = \frac{2GM}{c^2}]

where ( G ) is the gravitational constant, ( M ) is the mass of the object, and ( c ) is the speed of light.[^4] Importantly, this radius does not depend on the composition or structure of the object, only on its mass. This reinforces the idea that the black hole is not defined by what it is, but by what it does: it sets a limit beyond which information, causality, and spatial order cannot return.

The Black Hole as Vertex

A black hole is a vertex in the strongest sense of the term. It is the point at which spatial magnitude collapses into temporal intensity, where duration becomes instantaneous and the distinction between beginning and end dissolves. In this way, the black hole embodies the same principle found throughout nature and logic: the limit at which quantity gives way to quality, and structure gives way to pure relation.

Seen this way, the black hole does not contradict nature—it reveals its deepest logic.

Footnotes

[^1]: Karl Schwarzschild, On the Gravitational Field of a Mass Point According to Einstein’s Theory, 1916.

[^2]: Albert Einstein, The Foundation of the General Theory of Relativity, 1916.

[^3]: Stephen Hawking, A Brief History of Time, Bantam, 1988.

[^4]: Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, 2004.

The Schwarzschild Radius and the Paradox of Structure

The Schwarzschild radius defines a black hole not as a structure, but rather as a limit where structure breaks down. In other words, there is a paradox in how black holes are perceived within the universe: they appear as objects that oppose the assumptions of classical mechanics. In classical physics, an object’s mass, size, and weight determine its gravitational effects proportionally—larger and more massive objects exert stronger gravitational pull, while smaller and less massive objects exert weaker effects. A black hole, however, seems to violate this rule.

A black hole can be infinitesimal in spatial extent, meaning it can be the smallest conceivable object, while at the same time exerting the greatest gravitational pull. Conversely, we also observe supermassive black holes that exceed any known structure in the universe in terms of mass, yet are still defined by the same principle: collapse within a Schwarzschild radius. These contrasting extremes of magnitude challenge our ordinary conception of mass as it relates to gravity. A black hole can possess greater gravitational influence than objects that appear far larger and more massive, while itself appearing comparatively smaller in spatial size.

This paradox cannot be explained purely in terms of space, or by treating the black hole as a spatial object among other spatial objects. Instead, it becomes intelligible when understood as an element of time and duration. A black hole is not extended outward in space like ordinary matter; rather, it is infinitely extended inward, collapsed within the surface defined by its Schwarzschild radius. What appears as “smallness” in space is, in fact, an infinite concentration of duration and curvature.

The Schwarzschild radius therefore does not describe a material boundary, but a reference frame limit beyond which spatial relations lose their meaning. Within this limit, mass is no longer distributed across space but condensed into a temporal singularity. The black hole is thus not a structure in the usual sense, but a lack of structure—a point at which spatial extension, classical causality, and proportional magnitude cease to apply. Gravity here is no longer a force emitted by an object, but the manifestation of spacetime itself reaching an absolute limit.

Footnotes

[^1]: Karl Schwarzschild, “On the Gravitational Field of a Mass Point According to Einstein’s Theory,” Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 1916. Schwarzschild introduced the radius at which spacetime curvature becomes singular.

[^2]: Albert Einstein, The Meaning of Relativity, Princeton University Press, 1922. Einstein emphasizes that gravity is not a force but the curvature of spacetime.

[^3]: Stephen Hawking and Roger Penrose, The Nature of Space and Time, Princeton University Press, 1996. Their singularity theorems demonstrate that black holes represent limits where classical spacetime descriptions fail.

[^4]: Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, 2004. Carroll explains that the Schwarzschild radius is not a physical surface but a causal boundary.

[^5]: Aristotle, Physics, Book IV. Aristotle’s distinction between magnitude and limit anticipates the idea that extremes of size can coincide with conceptual boundaries rather than extended substances.

Black Hole as Limit, Tunnel, and Transition

The limit of this “structure” cannot truly be called a structure at all, because what is encountered at the Schwarzschild radius is not matter but the fabric of nature itself—spacetime. For this reason, a black hole is more accurately described, metaphorically, as a tunnel: an infinitely extended deformation of spacetime rather than a bounded object. It is not merely a region from which light cannot escape, but a limit that surpasses both perceptual visibility and conceptual representation.

In this sense, the black hole extends beyond the domain of objects that emit or reflect light and enters a regime where spatial and temporal distinctions collapse. What crosses this limit does not simply disappear; rather, it undergoes a transition from a material state into a theoretical or abstract state, where the ordinary categories of objecthood, location, and duration no longer apply. The black hole thus marks a transformation in the mode of being of an object, not merely its spatial concealment.

To speak of a black hole as a tunnel is not to claim the literal existence of traversable wormholes, but to indicate a directionality without spatial extension—an inward infinity where spacetime folds back upon itself. What is infinite here is not size in space, but depth in curvature. This is why the black hole resists classical description: it is not a thing within spacetime but a limit-condition of spacetime itself, where matter is no longer externally related but absorbed into pure relation.

At this boundary, physical description gives way to abstraction. The black hole is therefore not only an astrophysical phenomenon but also a philosophical one: it is the point at which material determination becomes indistinguishable from theoretical determination, where the object ceases to be an empirical entity and becomes a problem of form, limit, and negation.

Footnotes

[^1]: Albert Einstein, The Meaning of Relativity, Princeton University Press, 1922. Einstein emphasizes that spacetime is not a container for objects but the structural condition of physical reality.

[^2]: Karl Schwarzschild, “On the Gravitational Field of a Mass Point According to Einstein’s Theory,” 1916. The Schwarzschild solution describes a limit of spacetime curvature rather than a material boundary.

[^3]: Stephen Hawking, A Brief History of Time, Bantam Books, 1988. Hawking explains that beyond the event horizon, classical concepts of space and time cease to function.

[^4]: Roger Penrose, The Road to Reality, Jonathan Cape, 2004. Penrose discusses singularities as regions where physical description must become abstract.

[^5]: G.W.F. Hegel, Science of Logic, trans. A.V. Miller, 1969. Hegel’s notion of limit (Grenze) describes a transition where determinate being passes into its negation.

[^6]: Aristotle, Metaphysics, Book IX. Aristotle distinguishes between potentiality and actuality in transitions where form ceases to be materially instantiated.

In what Sense Is the Black Hole the “Edge” of the Universe?

When we speak of a black hole as the “edge” of the universe, this claim requires clarification. The “edge” is not meant as a spatial boundary beyond which nothing exists, but rather as the point furthest removed from consciousness, where determination, representation, and conceptual grasp break down. In this sense, the center corresponds to consciousness or the point of conception, while everything between the center and the edge constitutes the content of that conception. The edge, then, marks the limit at which content can no longer be formed or unified.

The term edge is commonly defined as the outside limit of an object, area, or surface—a place or part farthest away from the center. In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.[^1] A vertex (plural: vertices) is a point where two or more curves, lines, or edges meet. In a polygon, an edge is a line segment on the boundary and is often called a side.^2

In a polyhedron, or more generally a polytope, an edge is a line segment where two faces meet.[^3] A segment joining two vertices while passing through the interior or exterior of the figure is not an edge but a diagonal. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron that are not connected by an edge. The word diagonal derives from the ancient Greek διαγώνιος (diagonios), meaning “from angle to angle,” emphasizing traversal across a form rather than along its boundary.[^4]

The contrast between edge and diagonal is important: the diagonal cuts across the interior, while the edge defines the limit. Analogously, consciousness moves diagonally through experience, synthesizing relations internally, whereas the black hole—as edge—marks the boundary beyond which such synthesis is no longer possible.

The Relation Between the Edge and the Center

In geometry, the center (from the Greek κέντρον) of an object is the “middle” point of a circle or sphere, equidistant from every point on the circumference or surface.[^5] It is the middle not merely because it is spatially between points, but because it is the point that encompasses all points on the edge by being equally related to them. The center is thus defined by its relation to the edge: it is what holds the totality together.

In a line segment, the center is the midpoint between two ends. In a circle, the center is the point equidistant from all points on the circumference. In a sphere, it is equidistant from all points on the surface. More abstractly, if geometry is understood as the study of isometry groups, then a center is a fixed point under all transformations that map the object onto itself.[^6] The center is what remains invariant while the edge changes position.

The center of a circle is characterized by the point. In geometry, a point is a location represented by a dot, having no size—no length, width, or depth. Euclid defined a point as “that which has no part.”[^7] The point thus represents a pure potential location rather than an extended magnitude. As such, it functions axiomatically: it is accepted as self-evident and foundational. An axiom is a proposition taken to be true without proof, precisely because it underlies the possibility of proof.

The center, understood as a point, is therefore a potential value: it is not extended, but it makes extension possible. Likewise, consciousness functions as a center—it is not one object among others, but the point from which objects are disclosed.

Multiple Centers and Relational Unity

Geometry further shows that an object may have multiple meaningful centers, depending on the relations under consideration. In the case of a triangle, several special points are defined as triangle centers:

• the circumcenter, the center of the circle passing through all three vertices;
• the centroid (or center of mass), the point at which the triangle would balance if it had uniform density;
• the incenter, the center of the circle tangent to all three sides;
• the orthocenter, the intersection point of the triangle’s three altitudes; and
• the nine-point center, the center of the circle passing through nine significant points of the triangle.[^8]

These multiple centers show that “center” is not a single absolute location, but a function of relation. Analogously, the universe may have no single spatial center, yet still possess a conceptual center—consciousness—and a conceptual edge—where relational structure collapses. In this sense, the black hole can be understood as the edge of the universe, not because it lies at a spatial extremity, but because it marks the limit at which form, relation, and intelligibility dissolve into pure indeterminacy.

Footnotes

[^1]: Euclid, Elements, Book I.

[^3]: H.S.M. Coxeter, Regular Polytopes, Dover Publications, 1973.

[^4]: Euclid, Elements, Book VI; see also Strabo, Geographica.

[^5]: Aristotle, Physics, Book IV.

[^6]: Felix Klein, Erlangen Program, 1872.

[^7]: Euclid, Elements, Book I, Definition 1.

[^8]: Roger A. Johnson, Advanced Euclidean Geometry, Dover Publications, 2007.

In What Sense Is the Line Segment on the Boundary of the Center?

The edge always presupposes the center. This raises a deeper question: what is the edge of the center itself? A point is its own center, but does it have an edge? If so, the edge of the point is not something external to it, but the relation in which the point encounters itself as other. The edge of the center is therefore the place where the center-point ends by relating to itself.

The edge of the center is where the point connects sides. A side, understood as an extended line of a shape, is not merely the joining of vertices; it is the boundary where the point distinguishes itself from itself. Euclid described a line as a “breadthless length” that “lies equally with respect to the points on itself.”[^1] The line is thus nothing other than the distinction of the point from itself. Since the point has no quantity, the line emerges as the reference of the point to itself. The line is, quite literally, a reference point extended.

By definition, a diagonal presupposes that two vertices are not on the same edge. Yet, in a deeper sense, every line is diagonal, because the vertices it connects are not identical points. This is why the abstraction of a straight line is often depicted with arrows: arrows signify motion, and motion always carries the potential for curvature. That an edge connects to a vertex follows from the fact that the line “lies equally with respect to the points on itself.” In other words, the point, in moving away from itself, forms the connection that is the line.

The Horizon Example: Line as Self-Relation of the Point

Consider the calculation of the distance to the horizon. The importance of this example is not the numerical derivation of that distance, but the way it illustrates how a center point constitutes the internal relation of two external factors.

When I look toward the horizon, the point at which my vision ends is constituted by the same center as the point from which my vision begins. The height at which I stand and the distance to the horizon are externally related, yet they are internally unified by the radius of the Earth. The radius is present both in the height and in the distance; it is the internal relation that makes their external relation possible.

The radius is the center of the Earth insofar as the Earth is a sphere. The center of a sphere is defined as the point equidistant from all points on the surface.[^2] Equidistant means that the same distance is maintained at every point. What is often misunderstood is that equidistance is thought to be an effect derived from two opposing points. In truth, the “equal” is the center. It must already exist prior to the comparison. There must already be a sameness—an identity—that makes difference measurable.

Thus, the equidistant point is not the result of the height and the distance; it is their cause. It is the same point found in both. It is the relation itself. This point is often abstracted as a “third” point, but in reality it is the first point of the relation. To put this symbolically:
1 + 2 = 3, and 3 − 2 = 1.
If 3 is the result, then 1 is the cause—and 1 is found in both 2 and 3.

The equidistant point is therefore the thought of the entire relation: the unity that constitutes difference. The line originates from this point into another point and, because of this origin, remains equidistant in all its distributions.

From Finite Center to Infinite Center

In the case of the Earth, the center is a finite point with measurable density; we can identify the core as the center. But what happens if we apply the same form of relation to an infinite center, such as the center of a black hole? How does such a center constitute the height and distance of the event horizon, or more generally, the structure of the universe?

This question is not about numerical calculation but about physical form: how does an infinite point maintain finite relations? The answer lies in rethinking mass, density, and volume.

Black holes are described as the “heaviest” objects in the universe, but this is not because they possess more mass in the ordinary sense. Rather, their defining feature is density. Density is mass per unit volume.[^3] A black hole is “heavy” not because it adds new mass, but because it represents an extreme compression—or accumulation—of mass into volume.

Mass refers to the total amount of matter in an object, typically measured in kilograms. Volume refers to the amount of space an object occupies. Density expresses how much mass is contained within a given volume. Black holes are characterized by density because they contain mass rather than merely possess it. They are not objects with mass among other objects, but volumes in which mass is gathered to its limit.

This distinction only seems paradoxical if quality and quantity are treated as static categories. In fact, they are relational and inverse. Quantity is a quality of extension; quality is a measure of relation. Volume, in relation to mass, functions qualitatively.

Black holes form in two principal ways:

1. By compressing a fixed amount of matter until it reaches a critical density, as in the collapse of massive stars into black holes following a supernova.
2. By adding matter until a critical threshold is reached, as when neutron stars merge.

In both cases, it is the volume–density relation that determines the black hole, not mass alone.

Schwarzschild Radius as Relational Center

To understand this tipping point, two concepts are required: the Schwarzschild radius and the mass of a spherical object. The Schwarzschild radius—named after Karl Schwarzschild—defines the distance from a center below which nothing, not even light, can escape.[^4] The greater the mass involved, the larger the Schwarzschild radius.

The Schwarzschild radius is not merely a boundary; it is the center-point of the total volume of relation. It is the same relational point manifested across differing masses. If the universe has a center in this sense, it is not a spatial location but a relational center—a point that holds together finite distances through infinite inward extension.

Footnotes

[^1]: Euclid, Elements, Book I, Definition 2.

[^2]: Aristotle, Physics, Book IV; Euclid, Elements, Book III.

[^3]: Isaac Newton, Principia Mathematica, Book I; modern definition standard in physics.

[^4]: Karl Schwarzschild, “On the Gravitational Field of a Mass Point According to Einstein’s Theory,” 1916.

What Is the Center of the Diameter of the Sphere?

The center of the diameter of a sphere is neither its area nor its circumference. A diameter is a line segment passing through the center and joining two points on the surface. Its center is a point, not a surface or boundary. The area of a sphere refers to its surface—the total extension of its outer boundary—whereas the circumference properly belongs to a circle, not a sphere, and denotes the enclosing boundary of a two-dimensional figure.[^1] Thus, the center of the diameter is not an area, nor a circumference, but the point of equidistance that makes both intelligible.

Area and circumference differ not merely quantitatively but categorically. Circumference is a limit—a boundary that encloses—whereas area is an extension—a surface that fills. In the case of a sphere, the surface area expresses the totality of the boundary, while the center expresses the principle by which all boundary points are equally related. The center is therefore not part of the surface, yet without it the surface would have no determinate form.

Density, Volume, and the Black Hole as Self-Identity

To say that a black hole is infinitely dense is not merely to attribute to it an extreme physical property, but to say that it is the form of density itself. Infinite density implies not an accumulation of mass in the ordinary sense, but a structure in which mass, extension, and differentiation collapse into unity. In this sense, the black hole may be said to have no mass of its own, yet to contain all mass relationally. It is self-identical activity—that which remains what it is through all change.

This self-identity is what may be called nothing, not as a negation of being, but as pure capacity. Volume, in its most abstract sense, is not “stuff,” but the capacity to hold. Capacity itself must be uniform, self-equal, and internally consistent in order to exhibit quantity at all. Thus, infinite density corresponds to infinite capacity: a volume that is not extended outward, but inwardly infinite.

The Problem of the Sphere’s Center and Consciousness

A unique problem arises when we say that the center of the sphere is its defining principle. Unlike the center of a line, the center of a sphere is not determined by position among parts. It has no spatial markers. Its defining characteristic is that it has no parts at all. For this reason, it has often been likened to consciousness itself: an ultimate observer that is nowhere in particular and yet present to all things.

However, this analogy immediately raises a difficulty: what exactly is consciousness, such that it can function as the center of a sphere? If consciousness were merely one object among others, it could not occupy this role. The initial answer is that consciousness is not an object, but pure activity. Activity, by its nature, possesses form—not as shape, but as structure. Whatever the activity is, its form is its essence.

The center, described as a point with no properties and no determinate location, mirrors this peculiarity of consciousness. Consciousness is not a thing with attributes in the way objects are. It is rather that by virtue of which attributes appear at all.

Impartiality and the Unobserved Observer

If we take one aspect of consciousness—what it becomes, its formed activity—we still fail to account for what remains impartial, that is, not limited to any particular form. Yet this impartiality is precisely what characterizes consciousness most fundamentally.

Consider the statement: the universe, from the point of view of the black hole, is like looking inside a sphere. This formulation is meant to deny the ultimate reality of an “outside.” Whatever is conceived as external is always internalized within experience. Locally, there may be surroundings; universally, there is only the identity of conception and object.

We can distinguish between the object of consciousness—the Milky Way, for example—and consciousness itself, which has no features. The latter is difficult to grasp because we habitually identify the observer with some particular object: myself, my brain, my body. But this only postpones the question. When I say “I am the observer,” I am simultaneously an object of observation for someone else.

If person A observes person B, and person B observes person A, both become objects to one another. What, then, is the observer that is not itself observed, yet is presupposed by all observation? Let us call this observer Q. If the interior and exterior of the sphere correspond to observed content, then Q—the unobserved observer—is the center. But this center is nothing in itself, and precisely for that reason it is everything: the whole sphere.

The Unconscious as a Dimensional Center (Jung)

Carl Jung provides a concrete analogue of this structure in his conception of the unconscious. Jung argues that the unconscious is not merely an unexplored region of the psyche, but a dimension of reality, analogous to space and time.[^2] It is not possessed individually, like a brain in a skull, but is universal in scope.

This is where Jung decisively diverges from Freud. Freud reduced the unconscious to a functional component of the individual psyche (the id). Jung instead understood the unconscious—particularly the collective unconscious—as a shared field in which ideas exist independently of any single thinker.

Objects are located in space and time, but space and time are not located in objects. Similarly, individual thoughts occur in minds, but ideas themselves are not confined to individual minds. When an individual thinks an idea, this act is not the creation of the idea, but an observation of it within the unconscious.

Thus, two individuals may observe the same idea simultaneously because the idea exists at the shared base of their consciousness. One might visualize this as two cones touching at their bases: the apexes represent individual observers, while the shared base represents the idea as it exists in the unconscious. The center, once again, is nowhere in particular—yet it is the condition for all particularity.

Footnotes

[^1]: Euclid, Elements, Book I & Book III.

[^2]: C. G. Jung, The Archetypes and the Collective Unconscious, Collected Works, Vol. 9, Part 1.

Convergence of Observer Perspectives

Imagine two cones placed base to base, their wide ends touching. The larger side of each cone corresponds to the shared perceptual “volume” of two distinct observers, representing the bulk of what is mutually experienced or conceived. Moving away from this shared base toward the apex of either cone is to move toward the smallest, most particular, and divergent points of observation, points farthest from the mutual conception of reality. This structure provides a dynamic model for how two observers, though distinct, converge on a generalized reality: their shared perception forms a “thicker” base, while their differences, representing alternative possibilities or interpretations, extend outward toward the apexes. In other words, the areas furthest from the shared base represent the space of alternative possibilities, where the conception of each observer diverges from the general, shared conception of reality.

This model allows us to visualize how individual consciousnesses relate to collective experience. The convergence at the base is not a literal merging of observers but an abstraction representing common understanding, the points of intersection where subjective observations cohere into general knowledge. The apexes, by contrast, reveal the boundaries of individual perception and interpretation. In this sense, the geometry of the cones serves as a metaphor for the relation between the particular and the general, echoing Aristotelian logic: what is shared among observers is general, and what is divergent is particular.

The Fundamental Point of Consciousness

Beneath this model lies a more fundamental perspective: the base of the cones itself is derived from the same single, unifying point. This point can be conceived as the origin of consciousness, the source from which individual perspectives emerge. In this sense, the shared base of the two cones is only distinguished in speculation; in reality, both cones form parts of a single sphere of consciousness. The apparent duality is a matter of perception, not ontology. The point from which the cone bases originate represents the pure, undifferentiated center of experience, an abstract unity underlying all particular observations.

This conception aligns with Peirce’s philosophical insights regarding the law of mind and the structure of perception. According to Peirce, ideas are not merely located in the minds of individual observers but exist relationally in a semiotic field, where signs and interpretations converge in a structured space.[^1] The apexes of the cones correspond to individual signs or interpretations, whereas the shared base corresponds to the semiotic “common ground” in which communication and mutual comprehension occur.

Hyperbola and the Structure of Observation

The dynamics of these cones and their convergence can be further formalized through hyperbolic geometry, as suggested by Peirce. A hyperbola consists of two branches diverging from a center, with the property that the difference in distances from any point on the curve to the foci is constant.[^2] In the cone analogy, the foci represent the individual observers, and the hyperbola illustrates how differences in perspective are constrained by a common underlying relation. As observers move away from the shared base (the center), their perceptions diverge along predictable trajectories, forming a structure analogous to the hyperbola.

In the inverse hyperbola, this relation is mirrored: the apexes of the cones can be interpreted as points where alternative possibilities converge inversely to the shared base, producing a kind of reflected or latent relational structure. This allows us to visualize both the divergence and convergence of consciousness: the hyperbola encodes the logical and perceptual constraints that make individual perspectives intelligible relative to the shared “center” of understanding. In other words, the apparent multiplicity of observations is unified by an underlying geometric law, much as the sphere unites the cones’ bases into a single totality.

Thus, the two-cone model and its hyperbolic formalization provide a way to conceptualize the relation between individual perception and collective reality, the particular and the general, and the observable and latent possibilities of consciousness. The duality of apex and base is ultimately grounded in a single, unifying point, which is the fundamental center of consciousness. This approach integrates geometry, logic, and semiotics, illustrating how the multiplicity of observations can arise from a single, undivided source, in a manner that aligns with Peirce’s philosophy and the mathematics of hyperbolic relations.

Footnotes

[^1]: Charles Sanders Peirce, Collected Papers of Charles Sanders Peirce, Vol. 2, Elements of Logic, Harvard University Press, 1932–1958.

[^2]: Peirce’s treatment of curves and relations can be seen as a semiotic and logical analogy to hyperbolic geometry; see Peirce, New Elements of Mathematics, Vol. 4, 1906.

Step 1: Two Cones Base-to-Base

      /\
     /  \
    /    \
   /      \
  /        \
 /          \
/            \
\            /
 \          /
  \        /
   \      /
    \    /
     \  /
      \/

• Two cones share their wide base at the center.
• The tip of each cone represents the individual observer’s “perspective” extending away from the shared conception.

Step 2: Points of Observation

      A
     /\
    /  \
   /    \
  /      \
 /        \
/______\ <-- shared base (general conception)
\          /
 \        /
  \      /
   \    /
    \  /
     \/
      B

• A and B are the tips of the cones—two distinct observers.
• The base represents the convergent general reality formed when two perspectives meet.
• Moving away from the base toward the tips shows alternative possibilities—points of divergence from the shared conception.

Step 3: Overlaying Hyperbola

      A
     /\
    /  \
   /    \
  /      \
 /        \
/----*---\  <-- shared base (intersection of perspectives)
\          /
 \        /
  \      /
   \    /
    \  /
     \/
      B

• The hyperbola can be visualized as a curve passing near the tips (A and B), showing how each observer’s perception diverges but is related mathematically.
• In Peirce’s concept, the hyperbola reflects inverse relations: as one tip moves away from the base, the other tip’s corresponding point shifts inversely, maintaining the relational balance.

Step 4: Conceptual Notes

• Shared base: general reality, where independent observations converge.
• Tips of cones: individual observers, alternative possibilities, subjective perspectives.
• Hyperbola: models the inverse relation between observers’ perspectives—distance of one tip inversely affects the other.
• Sphere analogy: All of this is “contained” in the same sphere of consciousness; distinctions are conceptual, not separate in reality.

The Schwarzschild radius—sometimes historically called the gravitational radius—is the radius of a sphere such that, if all the mass of an object were compressed within that sphere, the escape velocity from the surface would equal the speed of light.[^1] Importantly, the Schwarzschild radius is not a line extending from the center of the sphere to its edge, as the term “radius” might suggest in ordinary geometry. Rather, it should be understood as the spherical boundary itself: the limit within which the mass is contained. It is the circumference as a whole, the totality of the “center point” of a sphere, in that it defines the sphere’s form and encapsulates all mass within it.[^2] In this sense, the Schwarzschild radius is the geometric manifestation of potentiality, defining the limits of gravitational influence and forming the structure of the sphere itself.

A sphere may be thought of as composed of an infinite number of circles. Each circle has a radius, which is half its diameter, and a circumference, which is approximately three times the diameter. The area of a circle can also be interpreted geometrically as the accumulation of circles, given the relation (A = \pi r^2) or equivalently (A = \text{circumference} \times \text{radius}). Extending this concept into three dimensions, a sphere represents pure potentiality, or capability, as it contains every possible point within its boundary, yet does not privilege any one point over another.[^3]

When considering the black hole as the center of a galaxy, its role is best understood in relation to the conception of the system around it. The black hole forms the effective circumference of gravitational and energetic influence around itself. Thought—or universal conception—functions similarly: it is distinguished from particulars while remaining fundamentally the same point. The black hole occupies the central point because it is equidistant from all points on its effective surface of influence, analogous to how a thought identifies a reference point, such as the center of the Earth. The radius of the Earth, for example, functions as a center only because it is a reference point of thought: it allows for relational measurement of height, distance, and position relative to that point.[^4]

In geometry, the point and the line are mutually defining: a point may extend to form a line, while a line itself is a connection of the point with itself. This means the line is not separate from the point but is the relational manifestation of the point’s potentiality. In the case of a black hole, this conceptual framework helps explain how the central point (the black hole) organizes the system around it. The galaxy we observe is not the black hole itself but rather the conception of the galaxy formed by the black hole, with the highest concentrations of energy at the center and the lowest densities distributed toward the edges of its effective circumference.[^5]

Since a black hole possesses no inherent dimensional features, any object or feature with dimensionality in relation to it exhibits its potential dimensions relative to the black hole’s center. From this single point, all potential dimensional features can be abstracted and analyzed. This aligns with concepts in string theory, where elementary particles are understood as vibrating one-dimensional objects called strings. Here, dimension is defined as the minimum number of coordinates necessary to specify any point within a system, highlighting that dimensionality is relative to a reference frame rather than intrinsic to the black hole itself.[^6]

Finally, the concepts of curvature and rotation are essential to understanding how a black hole organizes space-time. The Schwarzschild radius is not merely a boundary but also a locus of curvature in the fabric of space-time: space bends infinitely toward the center, creating what is observed as gravitational pull. Rotation, as in the case of Kerr black holes, further modifies this curvature, introducing frame-dragging effects where space-time itself is twisted in the direction of rotation. Curvature and rotation thus provide the geometric and dynamic framework by which the black hole influences the surrounding galaxy, shaping the energy distribution from center to edge while preserving the singularity as the infinitely dense point at the core.[^7]

[^1]: Schwarzschild, K. (1916). On the gravitational field of a sphere of incompressible fluid according to Einstein’s theory. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften.

[^2]: Misner, C., Thorne, K., & Wheeler, J. (1973). Gravitation. Freeman.

[^3]: Euclid. Elements. Book III. Geometry of circles and spheres.

[^4]: Kant, I. (1781). Critique of Pure Reason. Concept of space and reference points.

[^5]: Penrose, R. (1965). Gravitational collapse and space-time singularities. Physical Review Letters.

[^6]: Greene, B. (1999). The Elegant Universe. String theory and dimensionality.

[^7]: Kerr, R. (1963). Gravitational field of a spinning mass. Physical Review Letters.

Modern Misunderstanding of the Black Hole

A common modern description defines a black hole as a region of space where gravity is so strong that not even light can escape. This gravitational intensity is said to arise because matter has been compressed into an extremely small volume.[^1] According to contemporary astrophysics, black holes form through several mechanisms: primordial black holes may have formed in the early universe; stellar black holes form when the core of a massive star collapses inward, often accompanied by a supernova; and supermassive black holes are believed to have formed alongside the galaxies they inhabit.[^2]

Because no light can escape a black hole, it cannot be observed directly. Instead, its presence is inferred from its gravitational effects on nearby stars, gas, and radiation. Astronomers detect unusual stellar orbits, high-energy emissions from accretion disks, and relativistic jets to identify black holes. On this basis, it has been concluded that nearly every large galaxy contains a supermassive black hole at its center, including the Milky Way, whose central black hole is known as Sagittarius A.[^3]

Black holes are currently classified according to inferred mass: primordial, stellar, and supermassive. Stellar black holes may contain up to tens of solar masses, while supermassive black holes can exceed millions or billions of solar masses. This classification, however, rests on an important assumption—namely, that the size or mass attributed to a black hole is intrinsic to the black hole itself.[^4] It is precisely this assumption that requires philosophical clarification.

The Mistake of Treating the Black Hole as a Measurable Object

The common error lies in treating the black hole as a spatial object among other objects, whose size can be determined independently of its relational context. In practice, the “size” of a black hole is not measured directly but is inferred from the dynamics of the surrounding galaxy—stellar velocities, orbital distributions, and gravitational lensing effects. In other words, the size of the black hole is derived from the proportional size and behavior of the galaxy, not the other way around.[^5]

This means that what is often called the “size” of a black hole is actually a function of the galaxy’s structure, rather than an intrinsic property of the singularity itself. The event horizon—the Schwarzschild radius—marks a boundary of observational relevance, not a physical surface in the ordinary sense. To equate this boundary with the black hole as an object is to confuse a limit of relation with a thing possessing extension.[^6]

The Black Hole as Center

The black hole’s role as the center of a galaxy should be understood in the geometric sense of a center: not as a measurable piece of matter, but as a point of reference that organizes relations. In geometry, the center of a circle is not defined by its size or substance but by its being equidistant from all points on the circumference. The center is a potential value, not an extended object.

Likewise, the black hole functions as the potential center of the galaxy, not as a spatial structure comparable to stars or planets. The galaxy is not arranged around the black hole as though it were a large object; rather, the galaxy manifests the center as its organizing principle. In this sense, the galaxy is the concrete realization of the black hole’s centrality. The galaxy is the axiom; the center is the point presupposed by that axiom.[^7]

One Center, Many Galaxies

Although it is commonly said that there are many black holes—one for each galaxy—this multiplicity is misleading. All galaxies share the same structural principle: a central singularity that functions as the point of maximal density and minimal extension. The apparent plurality of black holes arises only because the galaxies themselves are distinct relational systems.

What all galaxies share is not merely the fact that they have black holes, but that their centers function identically. The black hole, understood properly, is not a collection of distinct objects but a single principle instantiated relationally across galactic systems. There are many galaxies, but only one center, repeated as a structural necessity rather than as a numerical multiplicity.[^8]

Universe as Uni-Verse: The Center as Consciousness

The word universe derives from uni- (one) and versus (turned or oriented), suggesting not many independent realities but many orientations of a single principle. Galaxies are “verses” or units of this orientation. Each galaxy has a center, but this center is not different in kind across galaxies; it is the same formal center expressed through different configurations of matter and scale.

At its most abstract level, this center corresponds to consciousness itself—not consciousness as a psychological faculty, but as the point of pure reference that conceives without itself being conceived. When consciousness turns upon itself, it becomes an object among objects; when it does not, it remains the invisible center organizing all appearances. In this sense, the black hole symbolizes the point at which conception reaches its limit: the place where all relations converge, yet nothing appears.[^9]

Footnotes

[^1]: NASA, Black Holes, nasa.gov

[^2]: Hawking, S. (1988). A Brief History of Time.

[^3]: Genzel et al. (2010). “The Galactic Center massive black hole.” Reviews of Modern Physics.

[^4]: Carroll, S. (2019). Spacetime and Geometry.

[^5]: Penrose, R. (1965). “Gravitational Collapse and Space-Time Singularities.”

[^6]: Schwarzschild, K. (1916). Original solution to Einstein’s field equations.

[^7]: Euclid, Elements, Book III; Aristotle, Metaphysics.

[^8]: Hegel, Science of Logic, Doctrine of Essence.

[^9]: Kant, Critique of Pure Reason; Jung, Collected Works, Vol. 8.

Black Holes, Limits, and the True Location of Infinity

Black holes may be understood as the cosmic analogue of the limits of human inquiry. The central dilemma in investigation is that when consciousness relentlessly pursues its own limit, it does not arrive at a new object but instead encounters a nullity. The limit is never something that can be reached and grasped as a determinate content; it is always already beyond what can be conceived. Thus, the pursuit of the limit ends not in discovery but in the confrontation with nothingness. In this sense, the limit and what lies “beyond” the limit are not two different things. For conception, they collapse into the same point: the blackness where determination fails.[^1]

If black holes are therefore understood as the limits of consciousness at the most macroscopic scale, the question of infinity must be reformulated. Infinity cannot be conceived as something that exists endlessly “out there” in external space, extending forever beyond the observable universe. Such an understanding merely converts infinity into a quantitative excess, which in turn becomes another limitation for conception. An infinity conceived as endless extension is still measured by distance, duration, and comparison—and thus remains finite in form.[^2]

When consciousness reaches its limit in this outward direction, it encounters nothing further—not because there is “more nothing” beyond it, but because distinctions such as more and less no longer apply. Beyond the limit of conception, difference itself collapses. There is no further outside to nothingness, since the notion of an outside already presupposes a measure. At this point, infinity reveals itself not as endless magnitude, but as the end of measure itself.[^3]

However, if we reverse the direction of inquiry and turn inward, infinity takes on an entirely different meaning. Instead of being conceived as infinitely extended outward space, infinity appears as the infinitesimal—an inwardly infinite depth or duration. In this inward sense, infinity is not a matter of scale but of intensity. What appears externally as macroscopic darkness—the black hole as the ultimate limit—corresponds internally to an inexhaustible richness of microscopic and temporal determinations.[^4]

Thus, the outer darkness of the universe and the inner infinity of consciousness are not opposites but inversions of the same principle. The black hole marks the point at which outward extension collapses into nothingness, while inward reflection reveals that this nothingness is not empty but qualitatively infinite. Infinity, then, does not lie beyond the universe in endless space, but within the structure of duration, relation, and consciousness itself.[^5]

Footnotes

[^1]: Kant, Critique of Pure Reason, on the limits of reason and the noumenon.

[^2]: Aristotle, Physics, Book III, on the distinction between potential and actual infinity.

[^3]: Hegel, Science of Logic, Doctrine of Quantity and Measure, on the collapse of quantitative distinction at the limit.

[^4]: Leibniz, Monadology, on the infinitesimal and internal infinity of substance.

[^5]: Whitehead, Process and Reality, on the intensive nature of reality and duration.

Black Holes and Void

Supermassive black holes are often described as necessary for galaxies to form in the first place, insofar as they provide the gravitational influence that organizes matter and stabilizes galactic structures during their early stages.[^1] From an empirical standpoint, this appears as a plurality of black holes—one at the center of each galaxy. Yet this multiplicity is, on one level, an abstraction arising from the observable effects of light and matter warping around regions of extreme gravitational curvature. What is emphasized observationally is not the black hole “itself,” but the deformation of spacetime produced by the surrounding galaxy, which renders the void perceptible as though it were a distinct object.

At the same time, the particular composition and motion of each galaxy seems to confer upon the black hole a kind of physical individuality, as if it were a three-dimensional entity around which the galaxy revolves. However, this individuality is derivative rather than intrinsic. The void itself has no identity of its own; being nothing, it cannot possess determinate qualities. Instead, it adopts the identity of the galaxy whose structure outlines it, while remaining, in essence, void. The black hole thus appears as something precisely because it is nothing, functioning as a relational center rather than a substance.[^2]

This paradox becomes especially evident in the phenomenon of gravitational lensing. Gravitational lensing occurs when light from distant galaxies is deflected by regions of intense gravitational curvature, producing arcs, rings, or spherical distortions in the visual field.[^3] What is striking is that light does not pass through the void as though it were a transparent medium; instead, the void manifests itself precisely through the deflection of light around it. The result is the appearance of an orb-like distortion, a 360-degree reflection of surrounding galaxies. What is known about this distorted region is not what it is, but rather that it is empty of any determinate being, and for that very reason capable of reflecting the totality of what surrounds it.

The void thus has a dynamic character: it remains void while simultaneously conforming to the outline of a particular galaxy. In this way, the effect of the galaxy upon the void renders the void the apparent center of mass around which the galaxy revolves. Yet insofar as light is neither emitted nor absorbed by the void, it remains entirely empty. We are therefore confronted with a dual structure: on the one hand, a void that is whole and unaffected in itself; on the other, the same void as it appears shaped by the galaxy’s structure. This produces a “sphere within a sphere,” where both spheres are void, yet distinguished by the identity imposed by the galaxy.[^4]

This leads to a deeper difficulty concerning the nature of distinction operative in nature itself. The distinctions produced by the understanding appear to correspond to real natural complexities, yet they do not divide reality into static categories. The understanding recognizes, on the one hand, the variability of galaxies—their diverse forms, sizes, and motions—and, on the other hand, the invariability of abstract principles such as gravitation or symmetry. However, variability and invariability are not opposed as fixed domains; rather, they represent different regions of a continuous spectrum.

Where variability ends and invariability begins is not a boundary but a passage. This passage characterizes the continuity of universal motion itself.[^5] The black hole, in this sense, functions as the hyperbolic limit of the galaxy. When we observe a black hole, we perceive it only hyperbolically—that is, as an asymptotic object approached by matter and light but never directly encountered. Likewise, when one occupies a particular position on the surface of a sphere, the surface appears locally as a hyperbola: a partial curvature mistaken for an absolute form.

When two circles merge, they become one. This provides a conceptual model for understanding how black holes form larger black holes. What truly merges is not a collection of discrete substances, but the event horizons themselves. Each black hole’s event horizon is not composed of different material; it is the same underlying void, differently outlined by surrounding energy and matter. When two black holes merge, the energies and spacetime curvatures around them coalesce, yielding a single, larger horizon.[^6]

Thus, what appears as many black holes is, at a deeper level, one and the same void, articulated through different galactic configurations. The merging of black holes does not create a new substance, but rather reorganizes the energetic and gravitational relations that disclose the void as a determinate center.

Footnotes

[^1]: Kormendy, J. & Ho, L. C., “Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies,” Annual Review of Astronomy and Astrophysics, 2013.

[^2]: Heidegger, What Is Metaphysics?, on nothingness as disclosed through relational being.

[^3]: Einstein, A., “Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field,” Science, 1936; see also observational summaries at the CFHTLenS project.

[^4]: Hegel, Science of Logic, Doctrine of Essence, on identity as reflection through difference.

[^5]: Aristotle, Physics, Book III, on continuity and motion.

[^6]: Thorne, K., Black Holes and Time Warps, on black hole mergers and event horizons.

Formation of Supermassive Black Holes

The origin of supermassive black holes (SMBHs) remains an open and active field of research in astrophysics. There is broad agreement that once a black hole is established at the center of a galaxy, it can grow through the accretion of matter and through mergers with other black holes. What remains uncertain is the nature of the initial “seeds” from which supermassive black holes originate, as well as their initial masses.[^1]

One widely discussed hypothesis proposes that these seeds are stellar-mass black holes—on the order of tens or perhaps hundreds of solar masses—left behind by the collapse and explosion of massive stars. Over cosmic time, such black holes could grow by steadily accreting surrounding gas and dust. Another model suggests that, before the formation of the first stars, enormous gas clouds collapsed into so-called quasi-stars. In this scenario, the quasi-star becomes unstable due to processes such as electron–positron pair production in its core and collapses directly into a black hole, without undergoing a supernova explosion that would otherwise eject much of its mass.[^2]

A further hypothesis involves dense stellar clusters undergoing core collapse. Because such systems have negative heat capacity, energy loss causes the core to heat up, driving stellar velocities to relativistic speeds and potentially triggering black hole formation.[^3] Finally, some theories propose that primordial black holes may have formed directly in the earliest moments after the Big Bang due to extreme density fluctuations. While black holes formed from stellar collapse are well supported by observation, the other models remain largely theoretical.

A central difficulty in forming supermassive black holes lies in concentrating a sufficiently large amount of matter into a sufficiently small volume while maintaining very low angular momentum. In most astrophysical systems, angular momentum acts as a barrier to collapse, forcing infalling matter to form accretion disks rather than plunging directly inward. Transporting angular momentum outward is therefore a key limiting factor in black hole growth and a foundational problem in accretion disk theory.[^4]

Gas accretion is both the most efficient and the most observable growth mechanism for black holes. Periods of rapid accretion manifest as active galactic nuclei (AGN) or quasars. Observational data show that quasars were far more common in the early universe, indicating that supermassive black holes formed and grew rapidly within the first billion years after the Big Bang.[^5] The existence of quasars with billions of solar masses at such early times strongly constrains formation models.

Observations also suggest a gap in the mass distribution of black holes. Stellar-mass black holes typically range up to a few tens of solar masses, while the smallest confirmed supermassive black holes are on the order of 10⁵ solar masses. The apparent scarcity of intermediate-mass black holes may indicate distinct formation channels, though candidates such as ultraluminous X-ray sources have been proposed.[^6]

There is also a theoretical upper limit to black hole growth. So-called ultramassive black holes—with masses exceeding ten billion solar masses—appear to encounter a growth ceiling around fifty billion solar masses. Beyond this scale, accretion becomes inefficient, and the surrounding disk may fragment into stars rather than feeding the black hole further.[^7]

The Black Hole as the “Inside Edge” of the Universe

The black hole is often misconceived as the outer edge of the universe, as though galaxies were centers and black holes their surrounding shells. This is an abstraction produced by observational perspective. In reality, the black hole is not the outer boundary of the galaxy, but its inner limit. It functions as an “inside edge” rather than an external perimeter.

When we empirically observe a black hole, we are not seeing the boundary of the universe in the ordinary spatial sense. Rather, we are looking inward—toward what functions as a universal center. Our own observational position, by contrast, occupies the outer circumference of that structure. This inversion of perspective has profound consequences for how time, causality, and cosmological direction are understood.

If one conceives the universe as observed from the inside outward—placing the black hole at the circumference—then observation is oriented toward the past, toward the conditions that produced the present configuration. Conversely, if one conceives the black hole as the area and the luminous universe as the circumference surrounding it, then observation is oriented toward the future: toward the empty potentiality beyond matter, marked by the event horizon and the speed of light as the limit of physical determination.

This dual orientation mirrors the structure of mind and body. The mind functions as a center, while the body forms a circumference around it. The black hole, analogously, has two dimensions: as a center it is void; as a circumference (the event horizon) it discloses structure. The circumference reveals form, while the centre remains empty.

Expansion and the Direction of Time

An instructive metaphor is that of a balloon. If the air inside the balloon represents the black hole, then the universe is not expanding outward into emptiness; rather, consciousness is emerging inward toward the void. World evolution, on this view, is not dispersion but convergence: an attainment toward singularity.

The universe is not moving away from itself but returning to its origin—pure nothingness—after having exhausted every possible configuration of something. What appears as expansion is, from this perspective, an internalization rather than an outward movement.

Empirically, it is estimated that ordinary (baryonic) matter constitutes roughly 4–5% of the universe’s total energy content.[^8] This suggests that what we observe is only a thin surface of a much deeper structure. Expansion appears outward only because we observe from a relatively fixed position within the system. If two objects move away from a stationary observer at equal rates, they appear to recede from each other, even though the motion is relative to the observer’s frame.

In this sense, cosmic expansion can be understood as the center moving away from the circumference—not spatially, but structurally. The black hole, as the central void, holds together the fabric of spacetime itself, not as a material anchor, but as the limit-condition that gives form to extension, duration, and motion.[^9]

Footnotes

[^1]: Kormendy, J. & Ho, L. C., “Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies,” Annual Review of Astronomy and Astrophysics, 2013.

[^2]: Begelman, M. C., Volonteri, M., & Rees, M. J., “Formation of Supermassive Black Holes by Direct Collapse in Pre-galactic Halos,” Monthly Notices of the Royal Astronomical Society, 2006.

[^3]: Binney, J. & Tremaine, S., Galactic Dynamics, Princeton University Press.

[^4]: Frank, J., King, A., & Raine, D., Accretion Power in Astrophysics, Cambridge University Press.

[^5]: Fan, X. et al., “A Survey of z > 6 Quasars,” Astronomical Journal, 2006.

[^6]: Farrell, S. A. et al., “An Intermediate-Mass Black Hole of Mass ~500 Solar Masses,” Nature, 2009.

[^7]: King, A., “Black Holes, Galaxy Formation, and the MBH–σ Relation,” Astrophysical Journal Letters, 2003.

[^8]: Planck Collaboration, “Planck 2018 Results,” Astronomy & Astrophysics, 2020.

[^9]: Wheeler, J. A., A Journey into Gravity and Spacetime, on spacetime structure and horizons.

The Mexican Hat Potential

The Mexican hat potential—also known as the wine-bottle potential—is a way of describing a system whose most symmetric state is not its most stable one. In its simplest physical formulation, the potential has a circular ridge with a peak at the center and a lower-energy ring surrounding it. The center of the “hat” represents a state of perfect symmetry, where all directions are equivalent, while the circular trough represents a set of equally stable but distinguished states. The system does not settle at the center because that point, although maximally symmetric, is dynamically unstable. Instead, it “falls” outward into one of the infinitely many equivalent minima on the ring.[^1]

This structure is crucial because it demonstrates that symmetry alone does not determine actuality. The center of the Mexican hat is not empty in the sense of lacking content; rather, it is too full, too undifferentiated. It contains all possible determinations at once, which makes it incapable of sustaining any particular one. Stability therefore requires the breaking of symmetry. The moment the system selects one point on the ring, a direction is chosen, a distinction is introduced, and form appears. What emerges is not a loss of symmetry in the absolute sense, but a transition from implicit universality to explicit particularity.

This directly mirrors the philosophical distinction between pure potentiality and realized determination. The peak of the Mexican hat corresponds to pure potential—analogous to the point, the void, or the black hole as nothing. It is perfectly self-identical and therefore contains no internal difference. The ring, by contrast, corresponds to the emergence of structure: each point on the ring is distinct from the others, yet all are equivalent in value. In this sense, the Mexican hat does not describe the creation of something from nothing, but rather the necessity that something arise from nothing if stability is to exist at all.

In modern physics, this model is most famously associated with spontaneous symmetry breaking, particularly in quantum field theory and the Higgs mechanism. Before symmetry breaking, the Higgs field exists in a symmetric state with no preferred orientation. Once symmetry breaks, the field acquires a nonzero value, and particles interacting with it acquire mass.[^2] What is essential here is that the laws themselves remain symmetric, even though the realized state does not. The symmetry is preserved at the level of principle but broken at the level of manifestation.

Within your cosmological framework, the Mexican hat potential provides a precise way of understanding how the black hole as center relates to the structured universe as circumference. The center—pure symmetry, pure nothing, pure potential—is not where actuality resides. Actuality exists at a finite distance from the center, just as the stable state of the Mexican hat lies not at the peak but along the ring. The event horizon can be interpreted as this ring: the surface where pure potential resolves into determinate structure without ceasing to be grounded in the center. The black hole, like the central peak, is not a thing among things but the condition that makes differentiated things possible.

The circular nature of the Mexican hat is also significant. Because the minima form a continuous ring, there is no single privileged outcome. Any point on the ring is as valid as any other. This explains why many galaxies, many particles, or many observers can arise from the same underlying principle without fragmenting it. Each realization is a particular expression of a universal ground, not a division of it. In this way, multiplicity does not contradict unity; it expresses it.

Philosophically, the Mexican hat potential formalizes the idea that difference is not imposed from outside, but arises internally from the instability of absolute identity. A perfectly symmetric state cannot persist as actuality because it lacks relational tension. The fall from the center into the ring is therefore not accidental but necessary. It is the same necessity by which a point extends into a line, a line curves into a surface, and a surface encloses a volume. Form arises because pure identity cannot remain merely itself.

Finally, the Mexican hat potential resolves the apparent paradox of infinity and limit. The center is infinite in potential but finite in realization; the ring is finite in distance but infinite in possibility. Infinity, therefore, is not located at the edge of extension but at the center of potential. What appears as outward structure is the inward unfolding of nothing into form. In this sense, the Mexican hat is not merely a model in particle physics—it is a geometric logic of becoming itself.

Footnotes

[^1]: Goldstone, J., Salam, A., & Weinberg, S., “Broken Symmetries,” Physical Review, 1962.

[^2]: Higgs, P. W., “Broken Symmetries and the Masses of Gauge Bosons,” Physical Review Letters, 1964.

I. The Mexican Hat Potential and Peirce’s Law of Mind

Peirce’s Law of Mind states, in its most general form, that ideas tend to spread continuously and to affect one another, and that the universe itself is best understood not as a collection of inert substances but as a continuum of habits in formation.[^1] Reality, for Peirce, is not grounded in static being but in process, tendency, and continuity (what he calls synechism). The Mexican hat potential gives this law a precise structural analogue.

At the peak of the Mexican hat, the system is perfectly symmetric. No direction is privileged, no distinction has yet emerged. This corresponds to what Peirce calls Firstness: pure possibility, quality, immediacy, feeling without relation. Firstness is not nothing, but it is indeterminate. It is exactly this indeterminacy that makes it unstable. A state of pure Firstness cannot persist as actuality because it lacks habit, resistance, or determination.

The fall from the peak into the circular trough corresponds to the emergence of Secondness—the category of reaction, resistance, brute fact. When the system “chooses” a point on the ring, it encounters limitation: this direction rather than that one. The symmetry is broken not by an external force but by the internal necessity of determination. This is precisely Peirce’s view that actuality arises through encounters and constraints, not by arbitrary imposition.

However, the most important alignment occurs at the level of Thirdness. The ring of minima in the Mexican hat is continuous: every point is equally valid, and transitions between them are smooth. This continuity is the hallmark of Thirdness—law, mediation, habit. Once the system settles into a minimum, it does not merely remain there as a static fact; it establishes a pattern, a lawful regularity that can propagate. In Peirce’s cosmology, laws themselves evolve: habits form from chance (tychism), stabilize through repetition, and become increasingly regular.[^2]

Thus, the Mexican hat potential models Peirce’s cosmology exactly:

• Firstness → the symmetric peak (pure potential)
• Secondness → the fall, the resistance, the selection of a minimum
• Thirdness → the stable ring as law-like continuity

Importantly, the peak does not disappear once the system settles into the ring. It remains as the condition of all possible determinations. Likewise, in Peirce, pure possibility is never abolished; it is continuously present as the ground from which new habits may emerge. The universe, for Peirce, is therefore not a finished structure but an ongoing symmetry-breaking process, exactly what the Mexican hat describes.

II. The Mexican Hat Potential and Hegel’s Logic

Where Peirce emphasizes continuity and habit, Hegel emphasizes self-differentiation through contradiction. Yet the Mexican hat potential aligns just as naturally with Hegel’s Science of Logic, particularly with the transition from Being → Nothing → Becoming and later Essence → Appearance → Actuality.

At the center of the Mexican hat we again find a point of pure symmetry. This corresponds to pure Being, which Hegel famously shows to be indistinguishable from pure Nothing.[^3] Because pure Being has no determination, no content, no difference, it collapses immediately into Nothing. This is not annihilation but indeterminacy. The central peak of the Mexican hat is exactly such a state: maximologically defined, yet dynamically empty.

The instability of the peak corresponds to Becoming, the movement that arises because Being and Nothing cannot remain abstractly identical. Becoming is not an external motion but an internal necessity. Likewise, the system must “roll down” from the peak—not because something pushes it, but because pure symmetry is self-negating. Determination is required for actuality.

The circular trough corresponds to what Hegel calls determinate being (Dasein) and later Essence appearing as existence. Each point on the ring is a determinate state, but no single point exhausts the totality. The unity of the system is preserved not by remaining at the center, but by expressing itself through differentiated yet equivalent determinations. This is a concrete universal: the universal exists only in and through its particulars.

Crucially, the Mexican hat avoids a common misunderstanding of Hegel. The center is not the “true” state while the ring is a degradation. On the contrary, actuality exists only in the differentiated ring. The center is true only as ground, not as realized being. This mirrors Hegel’s insistence that truth is not abstract unity but unity-in-difference.

In later Hegelian terms, the Mexican hat also models the logic of Ground and Appearance. The center is the ground that cannot appear directly; it would annihilate appearance if it did. Appearance therefore necessarily occurs at a distance from the ground—at the ring. The ground is present in every appearance, but never as an object among objects. This is structurally identical to your treatment of the black hole as center: it is not one thing in the universe, but the condition by which the universe appears at all.

III. Convergence: Why Peirce and Hegel Meet in the Mexican Hat

Although Peirce and Hegel differ in style and emphasis, the Mexican hat potential shows their deep agreement. Both reject static substance ontology. Both insist that indeterminacy is productive, not deficient. Both understand actuality as the result of a necessary transition from unity to difference.

Peirce frames this transition probabilistically and habitually; Hegel frames it dialectically and logically. The Mexican hat is neutral between them. It shows, in one structure, how:

• Absolute symmetry (pure possibility / pure being) is unstable
• Determination arises necessarily, not contingently
• Multiplicity does not destroy unity but realizes it
• The ground remains present precisely by not appearing directly

In this sense, the Mexican hat potential is not merely a physical model borrowed by philosophy. It is a geometric expression of speculative logic itself—the same logic that Peirce describes as the growth of mind and Hegel describes as the self-movement of the Concept.

Footnotes

[^1]: C. S. Peirce, Collected Papers, vol. 6, §102–163 (“The Law of Mind”).

[^2]: C. S. Peirce, “The Doctrine of Necessity Examined,” 1892.

[^3]: G. W. F. Hegel, Science of Logic, Book I, “Being,” especially the opening chapter.

The Singularity, Expansion, and the Present as Center

This line of reasoning suggests that the expansion of the universe is not governed by matter dispersing outward into empty space, but rather by a singular principle that functions as the center of spacetime itself. The difficulty with the standard illustration is that it implicitly treats the gravitational mass of the singularity as the causal determinant of spacetime curvature, as though the singularity were simply an object exerting brute force. Yet the singularity is defined precisely as the point at which such causal descriptions fail.

In contemporary physics, a singularity is described as a region—often modeled as a one-dimensional point—where density and curvature become infinite and where the known laws of physics break down.[^1] This immediately implies that the singularity cannot be understood merely in terms of gravitational mass acting within spacetime, because spacetime itself ceases to have determinate structure at that point. The singularity is not in spacetime in the ordinary sense; it is the limit at which spacetime becomes indeterminate.

This is further complicated by the empirical fact that the average density of a supermassive black hole (SMBH), defined as its mass divided by the volume enclosed within its Schwarzschild radius, can be lower than the density of water.[^2] The Schwarzschild radius scales linearly with mass, while volume scales with the cube of the radius; as a result, larger black holes can have lower average densities. This undermines the intuitive idea that black holes are “dense” in the everyday sense. Their gravitational dominance is not a simple function of local density.

What, then, determines the singularity as the center?

The Singularity as Perfect Absorption and Containment

A decisive clue lies in the fact that a black hole is a perfect absorber: it absorbs all incoming radiation and reflects nothing. In this sense, it functions as a perfect blackbody.[^3] Nothing escapes it; nothing is external to it from the standpoint of causal interaction. The singularity, therefore, is not simply a massive object among others but the point at which everything else is contained.

But what kind of “point” can contain everything without itself being extended? This is precisely the paradox that points beyond physics toward the structure of mind.

The singularity corresponds, not metaphorically but structurally, to the present moment of consciousness. The present is the point at which the entire past is retained (as memory, trace, or condition) and the entire future is implied (as possibility, intention, or potential). Everything that exists exists relative to the present, yet the present itself has no duration. It is infinitesimal, yet it bears the totality.

In this sense, the singularity has “the strongest gravitational pull” not because it possesses the greatest local density, but because it represents the total mass of everything relative to any particular thing. This explains why a black hole can appear infinitesimal and yet outweigh its host galaxy: the mass attributed to it is a relational measure, not a spatial one. (Strictly speaking, the black hole’s mass equals the mass–energy of what collapsed into it; the philosophical point concerns relational centrality, not additive mass.)

Expansion, Observation, and the Role of the Observer

Modern cosmology describes the universe as expanding, with galaxies receding from one another. But recession is always measured relative to an observer. To say that two galaxies are moving away from one another presupposes a frame in which the space between them is being apprehended.

If I observe two galaxies separating, I must already be conceiving the expanding space in which that separation is measured. This implies that the observer is not merely stationary within an expanding universe, but is functionally receding from the galaxies as well. The appearance that galaxies are moving away may equivalently be described as the observer’s frame expanding relative to them.

In this sense, the expansion of the universe is not simply a movement of objects outward, but a deepening of the frame of reference itself. Expansion is internalization: the universe does not move away from us; rather, we move inward toward the principle that contains it.

Numbers, Change, and the Abstraction of Activity

This brings us to the question of number. What is a number, really?

Numbers are symbolic abstractions that mark transformations within the activity of thought and experience. They function to stabilize relations—to render change countable by isolating moments within a continuous process. What we call an “amount” is already a totalization, but every number is itself a total: a particular relation abstracted from other relations.

This raises the classical problem: are numbers qualities or quantities?

They are both. Quantity cannot exist without quality, because to be a quantity at all is already to have the quality of measurability. Conversely, pure quality without any quantitative determination is indistinguishable from indeterminacy. Hegel resolves this by showing that quantity is quality sublated: quantity is quality rendered indifferent to its own determinations.[^4]

Quantity is result; quality is process. Quantity is the stabilized outcome of an activity, while quality is the activity that produces and sustains that outcome. Numbers are qualitative insofar as they represent relations of activity, and quantitative insofar as they fix those relations into discrete values.

When we count “one dog,” we are not counting the infinite micro-changes occurring within the animal. We are abstracting a stable form from an uncountable activity. The dog is countable because it is the totality of its activities; it is uncountable because it is the activity of those activities. Change itself is practically infinite.

Sensation, Stability, and the Origin of Mathematical Structure

Mathematics succeeds in quantifying activity because perception presents the world as relatively stable. Sensation organizes the world into enduring objects so that the body can interact efficiently with its environment. This is not a neutral presentation; it is an evolutionary achievement.

Earth’s long evolutionary history has produced an environment stable enough for complex organisms—and rationality—to arise.[^5] Sensation tells the mind that knowledge is “out there,” in objects, but it does not tell the mind where to begin. The mind therefore turns back upon itself and projects its logical structures onto the world.

Logic and mathematics are not arbitrary constructions; they are balanced systems that begin with the infinite in order to avoid fragmentation. Consciousness dissects the infinite into finites without reducing the infinite to a finite. This is possible only because infinity is reiterated endlessly within finite determinations.

Zero, the Circle, and the Priority of Form

Arithmetic presupposes infinity in the form of zero. Zero is not merely a number; it is a placeholder, a positional necessity. Philosophically, it corresponds to the “ought,” the demand for determination without content. Zero is the first digit because it marks the position presupposed by all others.

Geometrically, this corresponds to the circle—the most elementary universal form. The circle has no privileged beginning or end. Likewise, zero has no magnitude but structures all magnitudes.

The value of π, defined as the ratio of a circle’s circumference to its diameter, reveals a deeper inversion. We ordinarily think of the circumference as form and the diameter as content. But the logic of the black hole suggests the inverse: the diameter—pure activity, pure relation, nothing—is the form, while the circumference—extended being—is the content.

Thus, content is divided by form. Being is articulated by nothing. The universe is structured not by what appears, but by what does not.

The singularity is not merely the gravitational center of galaxies; it is the structural center of intelligibility. It is present as absence, active as nothing, and universal precisely because it is not one thing among others. The expansion of the universe, the structure of number, and the operation of consciousness all converge on this same principle: the infinite is not “out there forever,” but inwardly present as the condition of every finite determination.

Footnotes

[^1]: S. Hawking & G. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press, 1973.

[^2]: See: “Supermassive Black Hole,” average density discussion, standard astrophysical sources.

[^3]: J. Bekenstein, “Black Holes and Entropy,” Physical Review D, 1973.

[^4]: G. W. F. Hegel, Science of Logic, Book I, “Quantity.”

[^5]: C. S. Peirce, “The Law of Mind,” Collected Papers, vol. 6.

Form and Content: Mutual Generation Rather Than Priority

The question of how form generates content, and how content in turn maintains form, cannot be resolved by assigning absolute priority to either side. Form without content is empty abstraction; content without form is indeterminate excess. Their relation is not linear but reciprocal. Each exists only insofar as it is expressed through the other.

Consider the circle. Without the diameter, there can be no circumference, because there would be no determinate distance through which curvature could be articulated. The diameter establishes the relation of distance—the possibility of extension from a center. At the same time, without the circumference there would be no length in the geometric sense, because length arises only when distance is articulated as a path or boundary. Distance alone is abstract; length is distance realized through form. Thus, neither diameter nor circumference is ontologically prior. Each is the condition of the other.

This immediately dissolves the idea that form is a static container and content a passive filling. Form generates content by establishing relations; content maintains form by continuously realizing those relations. The circle exists not as a fixed object but as an ongoing coherence between radial distance and circumferential extension.

π (pi) as the Mediator of Form and Content

π (pi) is fundamental precisely because it expresses this irreducible reciprocity. Defined as the ratio of a circle’s circumference to its diameter, π is not a measurement of either alone, but the invariant relation between straightness and curvature.[^1] The diameter represents linear extension—straight, directional, differentiating. The circumference represents curvature—returning, enclosing, integrating. π is the constant that binds these opposites into a single intelligible unity.

This is why π appears universally wherever rotational symmetry, oscillation, or periodicity arises. It is not that π is “hidden everywhere” as a mystical constant, but that any process involving the translation of linear motion into cyclical motion—or vice versa—necessarily instantiates the same relational structure. Waves exemplify this directly. In light and sound, wavelength relates linear distance to periodic repetition; frequency relates temporal succession to spatial form. The mathematics of these relations inevitably involves π because they involve rotation, phase, and recurrence.[^2]

Thus, π characterizes measurements such as length over distance, arc over chord, period over frequency. It governs not merely static shapes but sequences of change. A circle is not just a completed boundary; it is the continuous process of turning through all possible directions while maintaining constant distance from a center. π expresses the law of that turning.

π (pi) and Internal Relations

What makes π philosophically significant is that it captures not relations between objects, but the relations that constitute objects internally. A circle is not an aggregate of points; it is a rule of generation. Likewise, physical entities are not collections of independent properties but coherent patterns of internal relations. The identity of an object is determined by the way its parts relate, not merely by their presence.

In this sense, π can be understood as an abstraction of relational totality—not because it literally enumerates all relations in the universe, but because it expresses the form of relationality itself: the conversion of linear difference into cyclical unity. Wherever a system maintains identity through change—whether in orbital motion, wave propagation, or even biological rhythms—the same formal structure recurs.

This aligns with the insight, found in both classical philosophy and modern science, that laws describe invariants of relation rather than substances.[^3] π is not a substance, nor a cause, but a structural constant: it describes how form sustains itself through content, and how content returns to form without collapsing into indifference.

Form, Content, and Becoming

The deeper implication is that form and content are phases of a single process of becoming. Form generates content by differentiating possibilities; content maintains form by realizing those possibilities in determinate ways. The circle is therefore not a static ideal but a dynamic equilibrium. Its “perfection” lies not in immobility, but in the fact that every point on the circumference is equally related to the center—a balance of difference and sameness.

π captures this balance numerically, but its significance is ontological. It expresses how unity persists through multiplicity, how identity survives continuous variation. In this way, π belongs not merely to geometry, but to the logic of nature itself: the logic by which the many become one without ceasing to be many.

Footnotes

[^1]: Euclid, Elements, Book I–III; see also modern treatments of ratio and proportion in geometry.

[^2]: J. D. Jackson, Classical Electrodynamics, sections on wave equations and harmonic motion.

[^3]: G. W. F. Hegel, Science of Logic, Doctrine of Essence; C. S. Peirce, “The Law of Mind,” Collected Papers, vol. 6.

Why Does π (pi) Begin with 3?

The decimal expansion of π begins as 3.14… only after the integers 0, 1, 2, and 3 are already presupposed. This is not accidental in a merely numerical sense, but conceptually revealing. π does not arise within counting; it arises at the limit where counting gives way to relation. The integers 0, 1, 2, and 3 mark the logical preconditions for a ratio to appear at all.

π is defined as the ratio of a circle’s circumference to its diameter. A ratio is not a quantity but a relation between quantities. Therefore, π cannot meaningfully appear before the minimum structure of relational difference is in place. This structure emerges only once the logical movement from unity to multiplicity and back to unity has occurred.

0, 1, 2, 3: The Logical Genesis of Number

The sequence 0, 1, 2, 3 is not merely arithmetical; it encodes a logic of being.

0 represents nothingness, not as absence, but as pure indeterminacy. Philosophically, nothing is infinite—not because it contains everything, but because nothing limits it. In this sense, 0 is not “less than” something; it is the condition for anything to appear at all.[^1]

1 is determinate being. It is finitude—the emergence of something from indeterminacy. Yet this finitude still bears the trace of nothingness, because to be one is already to be bounded.

2 is becoming. It is the relation between being and nothing, the tension between unity and difference. Two is not merely “one more than one,” but the first appearance of multiplicity—the beginning of distinction.[^2]

3 is mediation. It is the unity of unity and difference. Three expresses the fact that difference itself is relational, not absolute. The relation (2) is itself unified (1), and this unity of unity-and-difference is 3. This is why 3 is the minimum number required for structure, form, and system.[^3]

Only at this point—once mediation exists—can a ratio like π appear. π begins with 3 because it presupposes mediation: straightness (diameter), curvature (circumference), and the relation that unites them.

The Operative Function of 0 in Mathematics

In mathematical operations, 0 functions as the positional condition for all numbers. Any operation presupposes empty places before and after a value. We usually omit these zeros for convenience, but logically they are always present.

Thus, the equation
1 + 2 = 3
is implicitly
0 + 1 + 0 + 2 = 0 + 3

The inclusion of 0 is not optional: it establishes ordinal position. Without it, numbers would have magnitude but no place in a sequence. Cardinality presupposes ordinality.[^4]

Fibonacci Sequence and the Logic of Quality and Quantity

The Fibonacci sequence—0, 1, 1, 2, 3, 5, 8, 13…—begins with 0 and 1 because any quantity must emerge from a qualitative condition. Mathematically, 1 + 0 = 1. Logically, a quality—even the quality of nothing—is still something that can be counted as one instance.

The first “1” marks the presence of a determinate value. The second “1” expresses the fact that this value persists even when nothing is added. Quantity thus emerges from quality, and quality remains implicit in quantity.[^5]

2 arises when the quality (0 as nothing) and its determination (1 as something) are held together in relation. Quantity measures the sequence of action in thought; quality is the process underlying that sequence.

From Mathematics to Physics: The Schwarzschild Radius

This logical necessity manifests physically in the Schwarzschild radius. Every physical object contains internal voids—spaces where mass is not present. If an object collapses into a small enough region, its gravitational density increases until the escape velocity equals the speed of light. At that point, the object becomes a black hole.

The Schwarzschild radius is thus not merely a physical parameter; it is a geometric synthesis between arithmetic order (0 as position) and circular relation (π as ratio). The radius of a black hole is itself a sphere such that being is enclosed within nothingness.[^6]

Singularity, Nothing, and Inversion

The term singularity signifies two things:

1. An infinitesimally small point or region.
2. Absolute isolation—nothing else is present.

The singularity does not specify a particular form of being; it specifies the presence of peculiarity within nothingness. Empirically, this appears absurd: when an object collapses into a singularity, it seems to cease being anything at all.

Yet the implication is more subtle. It is not that the object becomes a singularity; rather, the black hole reveals the singularity already implicit within the object. Every being contains nothing as its internal limit. When being collapses into this limit, it transitions into nothing—and nothing, being infinite in potential, can give rise to new determinations.

This is why black holes are associated with extreme energy phenomena. It is not that being arises from nothing, but that being and nothing are internally related aspects of one process.[^7]

Inversion Geometry and Becoming

In inversion geometry, transformation occurs by mapping interior to exterior and vice versa. Philosophically, this mirrors the relation between being and nothing:

• Being internally contains nothing.
• Nothing externally contains being.

This inversion does not negate either term; it reveals their identity through opposition. Becoming is precisely this inversion—this continuous transformation of form into content and content into form.

π belongs to this logic because it encodes the relation between straightness and curvature, finitude and infinity, diameter and circumference. It begins with 3 because only mediation makes such a relation possible.

π does not begin with 3 because of mystical numerology. It begins with 3 because relation presupposes mediation, and mediation presupposes the logical structure encoded by 0, 1, 2, and 3. Mathematics, physics, and ontology converge here: the same logic that governs number governs form, motion, and becoming.

Footnotes

[^1]: G. W. F. Hegel, Science of Logic, Book I, “Being.”

[^2]: Ibid., Doctrine of Becoming.

[^3]: C. S. Peirce, “The Law of Mind,” Collected Papers, vol. 6.

[^4]: Frege, The Foundations of Arithmetic.

[^5]: Devlin, The Language of Mathematics.

[^6]: K. Schwarzschild, “On the Gravitational Field of a Mass Point,” 1916.

[^7]: Hawking & Ellis, The Large Scale Structure of Space-Time.

Gravitational Lensing

The black hole may be understood as the plane of matter such that matter takes form around it.

It is important not to conflate dark matter with the concept of space. Space is an externalized nature, just like time. It is defined relationally: space is always the outside of something, and therefore, by logical necessity, the place beyond an object. Dark matter, by contrast, is characterized not by extension but by its apparent absence of determinate properties. In this sense, dark matter is not “empty space,” but rather no-thing—yet not a mere negation. It exhibits an internal coherence without spatial distinction, without “here” or “there.” In this way, it is something precisely insofar as it is the thing that is no-thing.

From our standpoint, nothing appears as no-thing and is therefore unimaginable. Yet in itself, this very capacity of nothing—its ability to remain indeterminate—is what allows it to generate the world: light in darkness and darkness in light. This helps explain why black holes are so difficult to visualize. When we attempt to form an image of a black hole, we find that it resists ordinary representation. Observational images from telescopes such as Hubble or the Event Horizon Telescope do not show an object in the usual sense, but rather an obscuration or distortion of light against the background of space.

This distortion is explained by gravitational lensing. According to general relativity, massive objects curve space-time, causing light to follow curved paths. For example, stars positioned behind the Sun appear slightly displaced from their actual locations because the Sun’s gravitational field bends the light traveling from them to us. Black holes distort light far more extremely. Light does not enter and exit a black hole in the ordinary way; instead, near the black hole it can orbit along unstable paths, forming what appears as a luminous spherical region surrounding a dark void.

Black holes are especially perplexing to modern physics because beyond the event horizon the familiar laws governing matter and space-time no longer apply in their standard form. The event horizon marks a boundary beyond which information cannot escape to an external observer. Outside this boundary lies the photon sphere, where light can orbit due to intense curvature. Beyond it, classical descriptions of space and time break down, and quantum considerations become unavoidable.

If a photon enters the extreme gravitational field near a black hole, its behavior can no longer be described purely as that of a localized particle. Quantum mechanics allows the photon to be treated as a wave, meaning it is no longer confined to a single point but is distributed across a region. In this sense, the photon becomes “everywhere at once” relative to classical localization. This does not mean that the photon literally occupies two places as two objects, but that its state is spatially extended. This extension is what gives rise to wave–particle duality: a wave is a single entity that contains internal differences while remaining one and the same.

Time, too, behaves differently near a black hole. In classical mechanics, the law of non-contradiction applies both spatially and temporally: something is either here or there, now or then, but not both. However, in relativistic and quantum contexts, temporal ordering becomes observer-dependent. Near a black hole, time dilation becomes so extreme that, from the perspective of a distant observer, infalling matter appears to freeze at the event horizon. Each moment of motion appears isolated, as though the process were decomposed into static frames. This does not imply that objects literally duplicate themselves, but that temporal succession loses its ordinary coherence.

If we combine the suspension of classical spatial localization with the suspension of ordinary temporal succession, we arrive at a peculiar structure in which the distinction between quality and quantity begins to dissolve. Conceptually, we can describe this structure as follows:
(A) a black hole as a nucleus characterized by indeterminacy;
(B) an extended field of light or radiation forming a spherical region around it; and
(C) motion within this region such that each phase of activity can be treated as a determinate configuration.

From this perspective, the universe itself can be analogized to an atom—not in the sense of being the smallest unit, but in the sense of being a fundamental structure that repeats across scales. The atom is not a fragment extracted from the universe; rather, the universe is atomic in form. While empirical investigation proceeds by analyzing ever-smaller scales, this does not imply that the atom is absolutely minimal. Instead, the more fundamental a structure becomes, the less it can be specified by fixed quantitative measures.

The atom, understood in this way, does not possess a determinate size. Because it is fundamental, it potentially contains all magnitudes. As we probe deeper into matter—whether by accelerating particles toward the speed of light or by magnifying spatial scales—the result converges: we encounter the same foundational limits of nature. What appears as “smaller” is not merely reduced in size but is closer to the underlying principles from which size itself emerges.

Footnotes

1. General Relativity and Gravitational Lensing
   Albert Einstein, Relativity: The Special and the General Theory; see also Einstein’s 1915 field equations describing curvature of space-time by mass-energy.
2. Photon Sphere and Event Horizon
   The photon sphere exists at 1.5 times the Schwarzschild radius for a non-rotating black hole. See Kip Thorne, Black Holes and Time Warps.
3. Wave–Particle Duality
   Louis de Broglie’s hypothesis (1924) and later developments in quantum mechanics establish that particles exhibit both wave-like and particle-like behavior depending on measurement context.
4. Time Dilation Near Black Holes
   Extreme gravitational time dilation follows directly from general relativity. From an external frame, infalling matter asymptotically approaches the event horizon without crossing it.
5. Indeterminacy and Nothingness
   Compare with Hegel’s Science of Logic, where Being and Nothing are shown to be internally identical and resolved through Becoming.
6. Atom as Universal Form
   This echoes ancient atomism (Democritus) but also modern structural realism, where fundamental entities are defined relationally rather than as isolated substances.
7. Limits of Measurement
   The Planck length and Planck time mark limits where classical notions of space and time cease to apply, suggesting that “smaller” does not mean more determinate.

The problem with outer space is that it does not conform to our ordinary intuitions of time and space. Objects in the universe are separated by such vast distances that the time required for any signal, even light, to travel between them is often equal to—or greater than—the lifespan of the objects themselves. As a result, what we observe is never the universe as it is now, but always the universe as it was. This temporal delay means that the universe cannot be grasped as a completed or self-identical whole at any given moment. Instead, it appears as a continuously shifting field of relations, always in flux, never fully present to observation.

Because of this, the universe is not merely changing within time; rather, change is constitutive of what the universe is. There is no fixed snapshot of the cosmos that could be taken as its definitive state. Every observation already belongs to a different temporal layer than the event observed. The universe therefore resists comprehension as a static “thing in itself.” It is inherently dynamical, unfolding across durations that exceed the scale of human perception, memory, and even biological existence.

This difficulty becomes especially acute when we consider that nearly everything we know about the universe is mediated by light. When light from a distant object reaches us, it has traversed immense spans of space-time, often undergoing gravitational bending, redshift, or scattering along the way. In such cases, it becomes unclear whether what we perceive corresponds directly to the object itself or merely to a distorted trace of its past state. Gravitational lensing, for example, can cause a single object to appear in multiple locations at once, or to appear where it no longer exists. What we “see” may be less the object than the history of light interacting with the gravitational structure of the universe.

In this sense, the universe is fundamentally relational through light. Objects are not simply located in space; rather, they are disclosed to us through light as temporal processes. Light is not merely a medium that transmits information about objects—it is the very condition under which objects appear at all. Since light itself is finite in speed, every relation in the universe is temporally displaced. This means that simultaneity on a cosmic scale is impossible: there is no single “now” shared across the universe.

Consequently, cosmic reality is never fully present, either to consciousness or to measurement. The universe is an extended magnitude whose parts are bound together not by immediate coexistence but by delayed correspondence. What we call an “object” in space is therefore better understood as an event stretched across time, whose identity is inseparable from the path of light that reveals it. The cosmos is not a collection of stable things, but a living structure of ongoing disclosure—one in which appearance, change, and distance are inseparable from the very nature of being itself.

Just as space and time in our ordinary experience make sense in that, when you traverse land, it takes a discernible amount of time that does not affect the space itself, time appears measurable because it is constant and independent of space. In everyday experience, distance does not alter the structure of time, and time does not alter the structure of space.

In outer space, however, these principles are far more interrelated and dependent on one another. Distance, lifespan, and time period become inseparable: how far an object is from us corresponds directly to how long it has existed in the past, how long its light has traveled, and often to the duration of the object’s own life cycle. In this sense, spatial distance becomes a temporal measure, and time itself is no longer independent of space but is shaped by it.

The Progressive Development of the Atom

When we zoom into the substratum of matter, we encounter what appear to be increasingly fundamental components. At first glance, these components often seem scattered, discrete, and unrelated to one another. Contemporary materialism tends to interpret this appearance at face value: that reality at its most basic level consists of isolated units whose relations are contingent rather than necessary. However, before accepting this conclusion, we must ask whether this apparent disconnection belongs to the objects themselves or instead reflects a limitation in our mode of comprehension.

As we investigate matter more deeply, we do indeed find progressively more fundamental structures—molecules, atoms, subatomic particles, and quantum fields. Although these elements may appear ontologically independent, they nevertheless presuppose one another both physically and conceptually. Wherever we find a terrestrial body, it is composed of combinations of elements such as hydrogen, helium, oxygen, and carbon. Even at the most basic physical level, these constituents do not exist in isolation but only in determinate relations that allow higher-order structures to emerge.¹

Yet physical science often resists attributing any ontological sequence or hierarchy of necessity to these constituents. While elements are said to require one another in the formation of compounds, they are not treated as requiring one another in a developmental or logical order. No element is said to be more fundamental than another in the sense of being a necessary presupposition for its being. This stance is logically consistent with a broader fallacy: the assumption that because our findings present themselves as a collection of discrete objects, reality itself lacks an intrinsic structure of necessity.²

When we observe atomic or subatomic structures, we typically refrain from inferring that these structures are fundamental in a developmental sense. Instead, we treat them as merely smaller parts uncovered by passing through layers of macroscopic matter to reach microscopic processes. However, this interpretation overlooks a crucial fact: the very possibility of discovering one level through another indicates an internal relation between them. Intuition—and indeed the logic of nature itself—suggests that if one level of reality is found within another, then their relation cannot be merely accidental.³

This implies that the constituents of matter must bear necessary relations grounded in a fundamental process of development. In other words, there must be a developmental logic governing how these components evolve and relate, rather than a mere aggregation of unrelated parts. Even if our current scientific models fail to capture this sequence accurately, the existence of such a sequence is philosophically unavoidable. To deny it would be to deny the intelligibility of nature as a coherent whole.⁴

From this perspective, the atom cannot be understood merely as a static object or as a convenient abstraction used to explain material composition. Instead, the atom must be conceived as an evolutionary organism—a dynamic unity whose internal differentiations unfold according to lawful necessity. Its components are not simply assembled; they are moments of a process. The atom, therefore, is not reducible to its parts, but neither is it independent of them. It is a living structure in the philosophical sense: a self-organizing unity that develops through internal relations rather than external aggregation.⁵

Seen in this way, matter itself is not dead or inert, but inherently active. What appears to us as scattered components are, in fact, differentiated expressions of a single underlying process. The atom is thus not the smallest unit of reality, but a nodal point where the universal logic of development becomes materially visible. To understand the atom as an organism is to recognize that reality at its most fundamental level is structured not by randomness, but by an immanent, self-developing order.⁶

Footnotes

1. Standard chemistry already presupposes relationality: elements exist meaningfully only within bonding structures and energetic constraints, not as isolated substances.
2. This parallels Hegel’s critique of the understanding (Verstand), which fixes distinctions and treats them as absolute rather than moments of a whole (Science of Logic).
3. Aristotle already argued that form cannot be separated from matter without abstraction; what exists in something exists through it (Physics, Metaphysics).
4. Kant’s principle of systematic unity also presupposes that nature must be intelligible as a connected whole, not a mere collection (Critique of Pure Reason, Appendix to the Transcendental Dialectic).
5. Hegel’s notion of the organism describes a unity whose parts exist only through their relation to the whole (Philosophy of Nature).
6. This view aligns with Peirce’s Law of Mind, where continuity and habit govern even physical reality, as well as modern process metaphysics.

The Development of the Atom: From Hydrogen Onward

If we seek the beginning of atomic development, we must start with hydrogen. Hydrogen is the most abundant element in the universe, not merely by accident, but because it is the simplest possible atom: one proton and one electron. In this sense, hydrogen requires nothing prior to itself in order to exist. It is the first determination of matter out of abstraction. Every element that follows presupposes hydrogen, while hydrogen presupposes only itself. It is therefore not merely the first element empirically, but the first element logically.¹

The question of what comes before hydrogen cannot be answered in the same register. Prior to hydrogen there is no atom, no determinate element, no discrete object. What precedes hydrogen is an indeterminate physical condition—often referred to in contemporary physics as quantum fields, primordial energy, or dark matter—none of which yet possess atomic identity. This “before” is not a temporal predecessor in the ordinary sense, but an abstract condition of possibility. As discussed in the prior section, this corresponds to the notion of infinity: not a thing among things, but the unbounded field from which determinate being emerges.²

Hydrogen → Helium: The First Determination of Relation

Hydrogen does not remain isolated. Under sufficient pressure and temperature—such as those found in the cores of stars—hydrogen atoms undergo nuclear fusion. In this process, hydrogen atoms combine to form helium. Helium is therefore not merely another element added to hydrogen, but hydrogen transformed. Helium expresses the first stable relation between multiple hydrogen units, where unity is preserved but enriched.³

Philosophically, this marks the transition from simple being to relational being. Hydrogen is immediacy; helium is mediated unity. Helium contains hydrogen within itself, but no longer as isolated units. The atom has now developed internal complexity, while still remaining light, stable, and abundant. This transition exemplifies how nature does not leap arbitrarily from one form to another, but unfolds its determinations through necessity.

Helium → Lithium: The Emergence of Difference

The transition from helium to lithium marks a significant qualitative shift. Lithium cannot be formed through simple hydrogen fusion alone; it requires more complex stellar processes, including supernovae or cosmic ray interactions. Lithium is rarer precisely because it represents a further determination—one that nature reaches only under exceptional conditions.⁴

Here we see the emergence of difference within unity. Lithium introduces greater instability and reactivity, signaling the beginning of chemical diversity. While helium remains largely inert, lithium is active. It is the first step toward chemistry as such, where atoms no longer merely exist, but interact in structured ways. The atom is no longer just a physical unit but a bearer of potential relations.

The Sequential Development of Elements

From lithium onward, elements progressively develop through stellar nucleosynthesis: beryllium, boron, carbon, oxygen, nitrogen, and so on. Each new element incorporates the previous ones while introducing new structural possibilities. Carbon, for example, becomes foundational for organic chemistry not because it appears arbitrarily, but because its atomic structure allows for stable, diverse bonding. Oxygen enables combustion and respiration; nitrogen stabilizes biological systems.⁵

This sequence is not accidental. Each element represents a necessary moment in the unfolding of material complexity. The universe does not merely accumulate elements; it organizes itself through them. Each atomic form is a layer in the articulation of nature, from simplicity to complexity, from abstraction to concreteness.

Atoms as Layers of the Universe

The atoms that compose particular objects are not merely the materials of those objects; they are the materials of the universe itself. When we look microscopically into what things are made of, we are not just analyzing local constituents—we are witnessing the general structure of reality. The microcosm reveals the macrocosm.⁶

Thus, atomic layers are not only components of matter but expressions of cosmic order. The universe is stratified through atomic development, and every object participates in this stratification. To study atoms is therefore not merely to study parts, but to study the universe in its most fundamental modes of self-expression.

The progression from hydrogen to increasingly complex elements is not merely a physical process but a passage of nature itself. It is nature opening itself into determinate forms, each one preserving what came before while surpassing it. Matter develops not by chance aggregation, but by internal necessity. The atom, in this sense, is not a static building block but a moment in an ongoing cosmic evolution.

Nature passes through the atom in order to become visible to itself.

Footnotes

1. Hydrogen’s primacy is recognized both empirically (Big Bang nucleosynthesis) and conceptually as the simplest atomic structure.
2. This aligns with modern cosmology’s account of the early universe as a hot, dense, undifferentiated field, as well as with philosophical notions of the infinite as indeterminate being.
3. Stellar fusion processes are well established in astrophysics; philosophically, this corresponds to unity-in-difference.
4. Lithium’s scarcity is a known problem in cosmology (“the lithium problem”), emphasizing its transitional nature.
5. Heavier elements are formed in stars and supernovae, a process known as stellar nucleosynthesis.
6. This mirrors the classical philosophical principle that the structure of the whole is reflected in the structure of its parts (e.g., macrocosm–microcosm).

Oxygen, the Organic Atom, and the Cell

Oxygen occupies a unique position in the development of matter because it stands at the threshold where chemistry becomes biology. It is not itself alive, yet without oxygen, complex life as we know it cannot exist. Oxygen enables stable energy transfer, metabolic reactions, and the formation of water, which is the medium of life. In this sense, oxygen may be called the organic atom: not because it is a cell, but because it makes the cellular world possible. It is the atomic condition for organized vitality.

The cell, however, is not merely a larger or more complex atom. A cell is an environment. It is a bounded space within which countless processes occur simultaneously, coordinated but not centrally controlled in the way organs are in an organism. The cell maintains internal conditions—temperature, pH, chemical gradients, electrical potentials—that allow microscopic processes to persist. In this way, the cell resembles a world more than a thing. It is not simply an organism acting in an environment; it is an environment that hosts life.

Within the cell exist numerous subsystems—organelles such as mitochondria, ribosomes, and the nucleus—that function semi-autonomously. Some of these components, especially mitochondria, retain their own genetic material, leading to the widely accepted theory that they originated as independent microorganisms that entered into symbiosis with early cells. This means that a cell is not a single living unit in a simple sense, but a cooperative assembly of once-independent life forms. Life, even at its most basic level, is already plural and relational.

As we examine the cell more closely, we encounter entities that blur the distinction between organism and mechanism. Viruses, for example, exist at the boundary of life: they possess genetic material and can evolve, yet they cannot reproduce independently and require a host cell to activate their functions. Proteins, enzymes, and molecular machines operate with extraordinary specificity and responsiveness, yet they are composed of atoms and follow physical laws without intention. At this scale, it becomes increasingly difficult to say where life begins and non-life ends.

This ambiguity deepens as we approach the quantum domain. Subatomic processes—such as electron tunneling, quantum coherence, and probabilistic behavior—play roles in biological systems, particularly in photosynthesis and enzymatic reactions. At this level, components are indistinguishable in the classical sense: they are neither clearly alive nor clearly lifeless. They are processes rather than things, events rather than objects. Life here is not a property but an activity, emerging from relations rather than residing in substances.

Thus, the cell should not be understood primarily as an organism analogous to a multicellular being, but as a structured field of interactions. It is a dynamic environment that sustains, regulates, and integrates countless micro-processes. Just as a galaxy hosts stars, and a star hosts nuclear reactions, the cell hosts biochemical and quantum processes. Each level encloses another, and each level redefines what counts as an individual.

From this perspective, the development from atom to cell is not a jump from non-life to life, but a continuous deepening of organization. Oxygen enables complex chemistry; complex chemistry enables cellular environments; cellular environments enable life. At no point does a clear boundary appear. Instead, there is a gradual transition from indeterminate activity to determinate organization. The cell is therefore best understood not as the smallest unit of life, but as the first stable world in which life can appear.

In this way, the atom, the cell, and the organism are not separate categories but moments in a single unfolding process. Each stage preserves the previous one while transforming it. Matter becomes environment; environment becomes life; life becomes consciousness. And at the deepest levels, the distinction between what is alive and what is lifeless dissolves into the activity that produces both.

Black Holes, the Limit of Matter, and the Shape of the Universe

Whatever a black hole ultimately is, it marks a limit of matter. The obscurity a black hole presents in relation to light differs fundamentally from that of any other object, because it is not merely dark but limitative. A black hole does not simply fail to emit light; it absorbs light absolutely, thereby functioning as a boundary beyond which ordinary physical description breaks down. If the black hole is infinite in this sense—not spatially infinite, but infinite as a limit—then its effects on matter cannot be accidental or local. They must be foundational.

Black holes thus appear to reveal what might metaphorically be called the “edge” of the universe: not an exterior rim in space, but a boundary-condition of physical reality itself. This notion is difficult to grasp because the shape of the universe differs radically from the shapes of ordinary objects. The universe is not one object among others; it is the universal form within which all objects appear. Its circumference is therefore not like the outer surface of a visible body, nor like the frame of a painting. It is not an exterior that can be seen from outside, but a limit encountered from within.

One way to approach this problem is through the concept of the speed of light. At ordinary speeds, moving toward an object makes it appear larger in one’s field of view. Distance shrinks as one approaches. However, if one were hypothetically to travel at the speed of light while facing an object—say, a star—the object would not appear larger. Instead, paradoxically, it would appear to recede. This is because, at light speed, one’s field of view would expand so drastically that light from increasingly distant regions of the universe would reach the observer simultaneously. The apparent recession of the object is not due to its motion, but due to the expansion of the observer’s horizon of perception.¹

Traveling at the speed of light would therefore generate a field of view so vast that it would, in principle, encompass all visible matter in the universe. This leads to a profound cosmological question: where is the center of the universe? Modern cosmology answers that the center is everywhere. This is articulated by the cosmological principle, which holds that the universe is homogeneous and isotropic on large scales—meaning that from any location, the universe appears broadly the same, with galaxies receding uniformly in all directions.² There is no privileged spatial center.

From this perspective, modern science should not be too quick to dismiss Aristotle’s so-called geocentric model. It is not entirely clear that Aristotle intended the Earth to be the fixed physical center of the universe in the modern spatial sense. Rather, his model describes the Earth as the reference point around which the heavens appear ordered. The celestial spheres rotate around the Earth not necessarily because Earth is the absolute center of space, but because it is the center of experience and observation.³

Aristotle further proposed that the heavenly bodies are composed of an incorruptible substance he called aether (αἰθήρ). This substance was distinct from the four terrestrial elements and was characterized by eternal circular motion. Interpreted philosophically, aether can be understood not as a material substance in the modern sense, but as a principle of continuity and duration—what later thinkers would associate with time itself.⁴ Aether, in this sense, is not a thing but the condition under which motion persists without decay.

Interestingly, the term ether reappears in modern chemistry with a very different, yet symbolically suggestive meaning. In organic chemistry, ethers are a class of compounds characterized by an oxygen atom bonded to two carbon-containing groups (alkyl or aryl groups), expressed generally as R–O–R′.⁵ These compounds are structurally defined not by a central substance, but by a relation—a linkage that connects otherwise distinct molecular groups.

Ethers play a crucial role in organic and biochemical systems. They appear in carbohydrates, lignin, and various biological molecules, functioning as stable connectors that enable complex structures to persist. A familiar example is diethyl ether (CH₃–CH₂–O–CH₂–CH₃), once widely used as an anesthetic.⁶ The ether group does not dominate the molecule by mass, yet it determines the molecule’s functional identity. It is structurally minimal but relationally decisive.

To clarify the terminology: an alkyl group is derived from an alkane by the removal of one hydrogen atom, forming a substituent with the general formula CₙH₂ₙ₊₁.⁷ An aryl group, by contrast, is derived from an aromatic ring such as benzene and includes groups like phenyl (C₆H₅) or naphthyl (C₁₀H₇).⁸ In chemical notation, placeholders such as R (for alkyl) and Ar (for aryl) are used to indicate generality rather than specificity.

The philosophical resonance here is striking. Just as Aristotle’s aether functioned as the incorruptible medium of celestial motion, the ether group in chemistry functions as a connective medium within organic structures. In both cases, ether is not a substance that appears prominently, but a relation that enables structure and continuity. This suggests a deeper continuity between ancient metaphysical intuition and modern scientific description: what is most fundamental is not always what is most visible, but what binds, relates, and sustains.

From this vantage point, black holes, cosmology, aether, and organic ether all converge on a single idea: the limit is not mere absence, but generative structure. The boundary of matter, whether conceived as a singularity, a cosmological horizon, or a relational bond, is not simply where things end—it is where form itself becomes possible.

Footnotes

1. Einstein, A., Relativity: The Special and the General Theory — implications of light-speed reference frames.
2. Peebles, P. J. E., Principles of Physical Cosmology — cosmological principle.
3. Aristotle, On the Heavens, Book II.
4. Aristotle, Physics, Book IV; later interpretations link aether with eternal time.
5. McMurry, J., Organic Chemistry, ether functional groups.
6. Ibid.; historical use of diethyl ether in medicine.
7. IUPAC nomenclature for alkyl groups.
8. Carey & Sundberg, Advanced Organic Chemistry, aryl groups and aromaticity.

Time as a Biochemical Feature of Life and the Cosmological Center

Time, as it is ordinarily experienced, is not merely a physical parameter but a biochemical feature of life. Duration, sequence, anticipation, and memory arise from living systems that metabolize energy, maintain internal order, and respond to change. Outside of such systems, time does not “flow” in the same phenomenological sense; it is instead a structural relation used to describe physical processes. This distinction becomes crucial when we attempt to understand cosmology, where the universe as a whole does not occupy time in the way organisms do, but rather defines the conditions under which time can be measured.¹

Aristotle describes the heavens as composed of crystalline spheres rotating around the Earth at different, uniform speeds, producing the regular motions of celestial bodies.² While this model is empirically outdated, it represents an early formulation of what is now called the cosmological principle. Aristotle’s insight was not primarily about astronomical mechanics, but about form: the universe, taken as a whole, must be finite, ordered, and spherical, because the sphere is the only shape that is complete, self-contained, and without privileged direction.

The modern cosmological principle states that the universe is homogeneous and isotropic on large scales: it looks broadly the same from every location and in every direction.³ Subjectively, this means that the observer is always at the center of the observable universe. Objectively, it means that the universe has no unique center in space. The “center” is not a place but a relation. Wherever an object intersects with perception, that intersection functions as the center of the observer’s frame of reference. When attention shifts, the center shifts with it.

A simple phenomenological example illustrates this: choose any object in your visual field and focus intently on it. That object becomes the center of your perceptual frame, while surrounding objects recede into peripheral blur. The center is not fixed in space; it is generated by the act of relation between observer and observed. In this sense, the expansion of the universe is always centered on the observer, not because the observer is cosmically privileged, but because centerhood itself is relational.⁴

Black Holes, Negative Curvature, and Spherical Form

Black holes appear to “hold the universe together” through what is described in general relativity as spacetime curvature. While the phrase “negative curvature” must be used carefully in technical contexts, the essential idea is that black holes produce extreme distortions in the geometry of spacetime.⁵ Aristotle’s claim that the universe is fundamentally spherical gains new significance here: the spherical form is not imposed from outside but emerges from the way light, mass, and spacetime relate under extreme conditions.

This can be clarified through inversion geometry. Inversion is a geometric transformation in which points inside a circle are mapped to points outside it, and vice versa, relative to a fixed radius. Under inversion, straight lines become circles, and circles can become lines. A standard reflection can be understood as a limiting case of inversion in which the radius of the inversion circle becomes infinitely large.⁶

In spherical projection, a plane can be mapped onto the surface of a sphere such that the plane and the sphere are topologically equivalent. This means that what appears flat locally can be globally curved. Light bending around a black hole can be understood analogously: light does not simply “curve” around an object in space, but rather follows the shortest paths (geodesics) in a curved spacetime manifold. The distortion of light near a black hole is therefore not accidental but structural.

The Black Hole as Internal Edge and Diameter

What lies beyond a black hole is not another region of space, but pure potential—what could be, rather than what already is. In this sense, the universe is as large as the mind can conceive, because beyond the limits of conception lies no determinate object, only possibility.

This requires a reversal of ordinary geometric intuition. We are accustomed to thinking that objects have diameters and that circumferences surround them from the outside. But in the case of the universe, the black hole must be understood as the diameter, not the circumference. It is an internal edge, not an external boundary. Objects—the galaxies, stars, and structures of matter—form the circumference around this internal limit.

A common counterargument arises here: empirical science observes many black holes of different sizes. If the universe has one circumference, how can there be many black holes? This difficulty arises from empirical abstraction. The apparent size of a black hole depends on its distance from the observer and on the distribution of background light it obscures. A more distant black hole may appear larger because it blocks the light of more distant stars.⁷ Size, here, is relational, not intrinsic.

The deeper issue lies in how we visualize the universe. If we imagine it as a two-dimensional diagram, black holes appear as isolated masses scattered across space. But if the universe is understood as a three-dimensional—or higher-dimensional—curved manifold, then black holes are not separate objects but expressions of the same underlying curvature at different relational points. They are not many edges, but many manifestations of one limiting principle.

Event Horizons, Activity, and Inversion

If black holes were merely massive objects, one might expect light to reflect from them, as it does from a mirror. Instead, light forms an event horizon. The usual explanation is gravitational attraction, but this alone does not explain why nothing escapes. Attraction explains motion, not absolute capture.

The more fundamental explanation is that the black hole represents the limit of physical properties themselves. At the event horizon, physical quantities—space, time, mass, energy—lose their ordinary meanings. Matter approaching this limit is not merely pulled inward; it is reduced to its most basic state. The black hole is therefore not only a quantity (a measurable mass), but also a quality—an activity that produces form.

The universe is not contained by the black hole as an external shell. Rather, the universe is a reflection generated from an internal form. In inversion geometry, a moving circle can generate its own reflected image, and that reflection can appear to contain the original. The motion and the reflection are not two different things; they are the same activity viewed from different relational positions.

If two circles are nested and a line is drawn from the circumference of one to the circumference of the other, that line will follow a curved path determined by the geometry of the circles. Light wrapping around a black hole behaves analogously. The universe is not the container of the black hole; the universe is the circumference generated by the black hole as internal center. This is precisely what the event horizon reveals.

Organic Logic and the Photon

This logic is organic, not mechanical. The black hole is “nothing,” yet from this nothing arises structured being. This mirrors organic development, where form precedes material differentiation. Life does not begin with parts that later organize; it begins with an organizing principle that differentiates into parts.

A suggestive physical parallel is the photon. The photon has no antiparticle.⁸ Matter and antimatter annihilate each other through opposite charges, but the photon is its own identity. Positive combined with positive remains positive. This makes the photon an absolute principle of being within physics: pure relation without opposition. In this sense, the photon is closer to form than to substance, closer to activity than to thing.

The black hole and the photon thus mark two extremes of the same logic: one absorbs all distinction, the other propagates relation everywhere. Together they outline the structure of the universe as an organic whole—generated from an internal limit, structured by curvature, and disclosed through perception.

Footnotes

1. Bergson, Time and Free Will; Prigogine, Order Out of Chaos.
2. Aristotle, On the Heavens, Book II.
3. Peebles, Principles of Physical Cosmology.
4. Husserl, Ideas I, on intentionality and perception.
5. Einstein, The Meaning of Relativity.
6. Needham, Visual Complex Analysis; inversion geometry.
7. Carroll, Spacetime and Geometry.
8. Weinberg, The Quantum Theory of Fields.

The Earth as a Living Organism

The Earth can be understood, not merely as a mechanical system, but as a living organism—or more precisely, as an organic mind. At a certain stage of complexity, reason no longer merely represents the world abstractly but physically experiences its own thought. Mind externalizes itself into living form and then encounters itself again through that form. Thought is within the human being, yet the human being is also the activity of thought itself. In this sense, mind does not merely inhabit nature; it becomes nature and experiences itself through natural processes.¹

The quantum realm may be interpreted, philosophically, as the shared context between universal thought and its particular expressions. It is neither purely abstract nor fully concrete, but the domain in which form and content are not yet fully distinguished. Here, distinctions such as subject and object, thought and thing, are only potential. This liminal domain functions as the connective tissue between the universal activity of reason and the finite ideas through which it manifests.

Cities as Organic Extensions of Reason

If one examines aerial images of major cities, a recurring structural feature appears: a central core surrounded by radiating highways and ring roads. This is not accidental. It reflects an organic logic rather than a purely technical one. Plato, in Laws, argues that the ideal city should be structured around a central point, with concentric arrangements that mirror harmony, order, and proportionality.² The city, for Plato, is not an arbitrary aggregation of buildings but an embodied form of reason, modeled after the order of the soul and, ultimately, the cosmos.

In this sense, cities resemble living bodies. There is a center analogous to the heart or brain, arteries analogous to roads, and peripheral zones analogous to limbs. This resemblance is not metaphorical only; it is structural. Everything artificial is a sublation (Aufhebung) of the natural: it both negates nature and preserves it at a higher level.³ The next organism in the sequence of development will therefore not abolish the human but will sublate it—just as the human sublates animal life without eliminating it.

This is why cities often look like enlarged human bodies. They are reason externalized into space.

Sublation and the Relation of Universal and Particular

To clarify the logic of sublation, consider a comparison between the Amazon rainforest and the website Amazon.com. At first glance, the comparison may seem absurd, yet it reveals an important structural similarity. The rainforest contains a vast diversity of species; the website contains a vast diversity of products. Both are systems organized around universal categories instantiated in particular forms.

On Amazon.com, there exist many individual MacBook Pros with different specifications and prices, yet all belong to the same product kind: MacBook Pro. One may purchase one, two, or all available units, yet the kind remains available as long as the capacity to produce that kind exists. The universal, therefore, is not the sum of all particulars. It persists even in the absence of any given particular, so long as the potential for its realization remains.

This illustrates a fundamental philosophical point: the universal is more fundamental than the particular, not because it is an abstract generalization, but because it is the activity and potential that generates particulars.⁴ The universal is both the condition for the existence of particulars and the principle that unifies them, while the particular is the finite expression of that universal under specific conditions.

Artificial and Natural: Inversion of the Same Relation

The difference between the artificial and the natural lies not in substance but in the direction of abstraction. In social and economic systems, such as money, the process is inverted relative to nature. Making money involves extracting abstract, quantitative value from concrete objects. One sells a physical item and receives an abstract numerical equivalent. This is abstraction from the concrete.

In nature, the process runs in the opposite direction. Nature realizes the abstract into the concrete. Form becomes material; potential becomes actual. A tree is not assembled from parts according to an external plan; it unfolds according to an internal principle. Art occupies an intermediate position: it begins with the concrete object and derives from it an abstract form or feeling. Law performs a similar inversion by taking natural behavior and assigning to it moral and normative values.

Thus, the abstract and the concrete are indivisible, but their relation differs depending on the domain. Nature concretizes the abstract; society abstracts from the concrete; art mediates between the two.⁵

Ethics, Nature, and the Human Problem

A common critique arises at this point: we seem to project morality onto the world, even though the world itself appears morally indifferent. Nature, it is said, knows no good or evil—only processes. Yet human beings, who are themselves part of nature, are undeniably ethical beings. How can this be?

The resolution lies in recognizing that ethics is not imposed from outside nature, but emerges when nature reaches a certain level of self-relation. Ethics arises when an organism is not only alive but capable of reflecting on its own actions. The world as a whole is not ethical because it does not stand outside itself to judge itself. The human being, however, is nature that has become self-conscious.⁶

Ethics is therefore not a contradiction of nature but its internal development. Just as life emerges from chemistry without abolishing chemistry, ethics emerges from nature without abolishing natural law. Morality is nature reflecting on itself through the medium of rational beings.

Footnotes

1. Hegel, Phenomenology of Spirit, on spirit realizing itself in nature.
2. Plato, Laws, Book V; see also Timaeus on cosmic order.
3. Hegel, Science of Logic, Doctrine of Essence, on Aufhebung (sublation).
4. Aristotle, Metaphysics, on potentiality and actuality; Hegel, Logic, Universal–Particular–Individual.
5. Marx, Grundrisse, on abstraction in economic value; Aristotle, Physics, on form in nature.
6. Kant, Groundwork of the Metaphysics of Morals; Hegel, Philosophy of Right.

last updated 1.20.2026