Section 31 (first articulated 1.28.2021)

Discrete Continuous- Quality Quantity

 (first thought June.9.2015)

Quantum Dialectic

(Vacuous — mindless, showing no thought)

The Progressive Development of the Idea

When we look at a particular object, we derive certain forms from it — its size, shape, color, and structure. Yet what ordinary understanding forgets is that the particular object is already a configuration of these forms — or rather, a state of being that captures the internal relations of these forms and externalizes them into the objects of sensation.

If we look only at the external relations of reality, the world appears irrational. Things seem chaotic, or even when order is perceived, such order seems purposeless. Why are some things ugly? Why do things die? Why are some people ignorant? Even if these phenomena have rational explanations, they still exhibit an element of unreason. As Marx observes, “Reason has always existed, but not always in a reasonable form.”¹

The presence of unreason in the world reveals a fundamental contradiction constituting the nature of reason itself. Externality is the efficient cause: that through which the internal relations of being produce form, and by which these forms become visible to consciousness. Hegel calls this appearance “illusory reflection,” where consciousness confronts its own categories as external phenomena.² External relations thus portray to consciousness the structure of its own thought, and this portrayal manifests through aesthetic value.

The Idea and Its Externalization

The idea is not a static substance but a process — a movement toward externalization. Returning to the particular object: the forms we derive from it are more fundamental than the object itself, for they constitute its principles. Carl Jung calls these archetypes, while Plato calls them forms.³ Both recognized the universality of these principles but could not fully explain the nature of the world in which these archetypes reside.⁴

When the idea takes on a form, that form becomes an ideology. The word derives from the Greek idea (form, concept) and logos (study or discourse). Thus, ideology means the study or systematization of ideas. When an idea transforms into an ideology, consciousness organizes and diversifies it into multiple expressions, each a particular manifestation of the same principle. Ideology, therefore, is consciousness studying its own ideas.

An ideology can develop in two directions: it can harden into dogma — accepting its principle as incontrovertibly true — or it can evolve into science, in which consciousness begins to prove its idea. The proof of an idea is dialectical: an internal dialogue through which thought attains self-consciousness, or the affirmation of its own affirming.

From Classical to Quantum: Ontology as Foundation

Every scientific discourse is predicated upon the discoveries that quantum mechanics now reveals. The quantum principle demands a deeper understanding than its conventional use in modern physics allows. Quantum mechanics is called the fundamental science precisely because its discoveries concern the most elementary facts of nature — though it is the most recent to emerge.

All physical disciplines, from atomic and molecular physics to chemistry and electromagnetism, can be derived from quantum mechanics. Yet even the human and social sciences — in so far as they concern Being — must be understood as ultimately quantum in nature.

What, then, is the true understanding of quantum mechanics? How does science account for the quantum as the rational process of Being? The answer begins when we recognize “quantum” as ontology — as a metaphysical structure of reality. Quantum mechanics, by its nature, is metaphysical because it addresses the relation between the physical and the non-physical. Modern science has not yet achieved the ontology necessary to comprehend the atom as the unity of both.

Internal and External Relations in Scientific Ontology

Every atom operates through internal relations. An internal relation is a relation that is constitutive of the being of what it relates — the parts do not exist independently of their relation.⁵ An external relation, by contrast, connects entities that retain their independence from one another; this is the foundation of atomism.

In atomism, the atom is conceived as an externally related, self-contained unit — a discrete particle existing apart from the field of relations. The classical view (Democritus, Newton) treats atoms as ultimate substances whose interactions are mechanical.⁶ This is ontology as external relation.

Quantum theory, however, reveals that atoms are not self-contained. They exist through internal relations — the wavefunctions, superpositions, and entanglements that constitute their being. The “quantum leap” characterizes this process of internal self-relation. At the quantum level, the atom is infinite in relation to itself, while at the general (macroscopic) level, it manifests finitude through determinate relations.

This finitude is not a limit but a determinate necessity. The particular relation — the finite manifestation — is the determining process, not merely the result. Process precedes result, yet the result is necessitated by process. This paradox is concrete in the quantum state: the atom is necessitated by internal relations, but those relations exist only through the atom. The atom is the necessity of internal relations — and through those relations, the atom is externalized as their universality.

Thus, the atom is both finite and unbounded. This is the universality of the quantum in the atom: the atom is everywhere in itself. Every material object is a spectrum of sublation — a process of self-overcoming that induces quantum behavior. This mediation occurs across scales, from microscopic particles to macroscopic forms. Every object acts as a wave-particle dualism — but where does this dualism find unity? What is the golden mean produced by this spectrum?

Being, Nothing, and Reason

The quantum constitution of the atom as internal relation presupposes Being. Matter, as science holds, can be altered but never created or destroyed — a metaphysical axiom grounded in Hegel’s dialectic of Being and Nothing. In the Science of Logic, Hegel explains that the beginning of all philosophy is paradoxical because pure Being is indistinguishable from pure Nothing; their unity gives rise to Becoming.⁷ This incomprehensibility of the beginning is the very foundation of quantum ontology.

The paradox of Being and Nothing has persisted since the Pre-Socratics. Anaxagoras first asserted that Nous (Mind or Reason) orders all things, a claim later developed by Socrates as the ethical dimension of reason.⁸ Aristotle’s Physics deepened this inquiry, revealing a tension between motion, potentiality, and actuality — a tension that anticipates the indeterminacy of the quantum.

For Aristotle, the universe is rational because it is virtuous — harmony is its virtue, and virtue is the rational ordering of relations.⁹ Virtue (aretē) is the right configuration of relations that facilitates reason. Thus, the basic claim of reason is virtue, and virtue follows a systematic process toward truth. This same claim underlies quantum physics implicitly: quantum as Notion is a truth about reality deduced from the general level and expressed in rational form.

The general level of nature involves continuity — substance as enduring and extended. The quantum form expresses that same substance as rational and self-relating. These two are not opposites but complements: each sustains the other through their difference.

Dialectical Unity and the Quantum Notion

The unity of continuity (the general) and rationality (the quantum) produces the conceptual negation of the quantum notion — not as opposition, but as sublation (Aufhebung). This negation bears the positive predicate of development: contradiction as resolution, the process as necessity. This is the dialectical nature of the quantum.

Aristotle began this implicit knowledge of the quantum when he identified virtue with reason. The term quantum is therefore not merely a scientific measure but a semantic revelation of reality as dialectical truth.

The beginning of the quantum cannot be separated from its advanced form. Continuity in substance at the general level necessarily assumes the quantum form — the former is advanced as the latter. This continuity explains phenomena such as consciousness in the organic unity of mind and body.

Reason thus constitutes the dual unity of the mental and physical. The universal form of the quantum is projected into the general level of being. Modern physics interprets this unity as a contradiction: that the laws of general relativity and quantum mechanics are inconsistent. But the contradiction is only negative at the abstract level; in concrete reality, it is positive. Concrete reality is positive because it includes the negative contradiction as its own moment.

Hegel distinguishes between positive and negative reason: positive reason characterizes the existence of quality in being, while negative reason describes the absence of quality in non-being.¹⁰ This dual process of internal relation constitutes substance at the general level. The atom assumes its quantum form through internal relations prior to its external relations. The external relations we perceive in the general level are therefore projections of internal relations — the visible necessity of invisible process.

Footnotes

1. Karl Marx, Letters to Arnold Ruge (1843).
2. G.W.F. Hegel, Science of Logic, Book I: Doctrine of Being, “Reflection and Illusory Being.”
3. C.G. Jung, Archetypes and the Collective Unconscious (1959).
4. Plato, Republic and Timaeus.
5. John McTaggart, The Nature of Existence, Vol. I (1921), defines internal relation as constitutive of the being of its relata.
6. Democritus, Fragments; Isaac Newton, Principia Mathematica (1687).
7. Hegel, Science of Logic, “Being, Nothing, and Becoming.”
8. Anaxagoras, Fragments; Hegel, Lectures on the History of Philosophy, Vol. I.
9. Aristotle, Nicomachean Ethics, II.6; Physics, II.1.
10. Hegel, Phenomenology of Spirit, “Reason,” §§230–240.

Quanta and the Unity of the One and the Many

The word quanta refers to an amount that cannot be further divided numerically, yet nevertheless still constitutes an amount. The amount is necessarily and universally true: the One is always constituted by the Many, and the Many is composed of the One.

Religion introduces this relation as one between different forms of truth. It posits that the One does not share the same mode of being as the Many. Contemporary religions presuppose this distinction as the initial truth defining the relationship between God and humankind: God, the One, is believed to exist in a manner distinct from human beings, the Many. However, religion often interprets this difference as opposition, such that God’s existence becomes inconsistent with human existence.

Hegel refers to this alienation as the aspect of the “estranged soul.”¹ This inversion of religion arises when the One and the Many are conceived as dualistically opposed. In most religious ideologies, God is the One who stands independently from the Many creations — an external being in relation to an internal, finite world. Yet this gives rise to a negative contradiction in logic.

If the Many is constituted by the One, are they not essentially the same? The Many and the One have no meaning outside of their relation to each other. Amount always involves number, and this is mathematically true in the quantum state of reality. The quantum, then, expresses this fundamental unity: discreteness (the Many) is the very mode in which continuity (the One) appears.

Quanta as the First Principle of Nature

This principle forms the foundation of the laws of nature — a fact first illuminated by Max Planck.² The quanta refers to the quantity portraying a process: it is the measure of discrete energy transfer. This process is one of internal relations, which necessarily presuppose external relations. External relations — attraction and repulsion, gravitation and inertia — arise from the internal coherence of matter.

The universe cannot sustain infinite repulsion in matter. Planck revealed this paradox in his early studies of blackbody radiation and atomic energy.³ In classical physics, the electron orbiting the atomic nucleus was understood as a charged particle accelerating in a circular path. Acceleration implies a changing electric field, and thus, by Maxwell’s laws, the emission of radiation. But if the electron continually radiates energy, it should spiral inward and collapse into the nucleus — meaning atoms should not exist.⁴

To resolve this contradiction, Planck proposed that energy is transferred not continuously but in discrete packets, which he called quanta. This solved the problem of infinite energy loss by introducing discontinuity into the process of radiation. Energy, being quantized, could only be emitted or absorbed in specific amounts. Thus, the loss of energy at one discrete level does not imply the loss of energy across all levels.

Niels Bohr expanded upon Planck’s hypothesis, suggesting that electrons occupy fixed, quantized orbits around the nucleus — “allowed states” in which they do not radiate energy.⁵ Empirical evidence confirmed that physical structures obey these logical, discrete relations. Hence, the atom itself expresses a rational structure: a unity of continuity (wave) and discreteness (particle).

The Atom as Logical Form

Our image of the atom — an electron revolving around a nucleus — is not literal but conceptual. It represents the motion of form. The particle’s position on the orbit merely demonstrates the discrete form of the wavelength in motion. In nature, however, there is no separation between the discreteness and the wavelength; both are one process.

An electron does not exist at a single point in its orbit. Rather, it has a wave nature and exists simultaneously at all possible positions within the allowed orbit. What we perceive as a particle at a fixed location is merely an abstraction — a single moment extracted from the continuum of wavelength. This abstraction, when isolated from the whole, appears as a discrete unit — the quantum.

Physicists speak of “allowed orbits” and “allowed transitions” — these produce photons with specific frequencies, forming the characteristic spectral lines of each element. The Bohr atom, therefore, is a representation of these quantized states of motion.

Louis de Broglie’s hypothesis extended this view, proposing that all matter exhibits wave-like behavior.⁶ Although the notion of electron waves challenged centuries of belief in solid, localized particles, experiments with electron diffraction confirmed it. When electron beams were passed through narrow slits, they produced interference patterns — unmistakable evidence that electrons possess both wave and particle properties.

Thus, the bare form of the atom — the simple schematic of nucleus and orbit — does not capture the full contextual complexity of atomic reality. Contemporary quantum physics reveals that the atom’s form concerns the forms of conception itself. This is not to assert subjective idealism, for the conception is not externally imposed upon the atom; rather, the form of the atom is the form of conception itself.

Motion as the First Instance of Becoming

An object moving in a circle at constant speed is nevertheless accelerating, because the direction of its velocity vector continually changes. The first instance of motion — and therefore of Becoming — is this dynamic relation between continuity and change. The same principle governs the atom and the cosmos: the quantization of energy expresses the dialectic between unity and multiplicity, stasis and motion, the One and the Many.

Footnotes

1. G.W.F. Hegel, Phenomenology of Spirit, trans. A.V. Miller (Oxford: Clarendon Press, 1977), §§206–208 — discussion of the “alienated soul” in religious consciousness.
2. Max Planck, “On the Law of Distribution of Energy in the Normal Spectrum,” Annalen der Physik 4 (1901).
3. Ibid.; see also Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, 1982), ch. 3.
4. “Planck noticed a fatal flaw in our physics…” — University of Oregon, Cosmology Lecture 8: Quantum Theory, accessed November 2025, http://abyss.uoregon.edu/~js/cosmo/lectures/lec08.html.
5. Niels Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine 26 (1913): 1–25.
6. Louis de Broglie, Recherches sur la théorie des quanta (1924); confirmed experimentally by C.J. Davisson and L.H. Germer, Physical Review 30, no. 6 (1927): 705–740.

Discrete and Extensive Magnitudes in Quantum Ontology

Quantum as Limit and Plurality

Quantum has its limit in amount. Amount is defined by plurality: the One is constituted by the Many, and the Many by the One. The limit, in conjunction with amount, composes discrete magnitude. In discrete magnitude, the quantum is a plurality that has no being apart from its limit, nor is the limit something external to it. Limit and plurality mutually constitute one another.

The discrete nature of quantum possesses extensive magnitude. This means that within any discrete unit there exists a plurality of distinct determinations — the amount of one thing is outside the amount of another. Thus extensive magnitude is the continuity of discrete limits: it is the structure whereby discrete units coexist by externally bounding one another.

Continuity and Intensive Magnitude

However, the continuous nature of quanta also has the inverse form: intensive magnitude. Intensive magnitude is amount inside amount: a relation of inwardness. Since continuity is the unity of extensive magnitudes — the state in which the amount of one thing stands outside another — the sum total of all these amounts forms a general discrete amount. Intensive magnitude, by contrast, expresses that the amount of one thing is the same as the amount of another.

Thus continuity is the limit of the discrete, just as discreteness is the limit of continuity. The limit itself is the efficient movement whereby the discrete becomes continuous and the continuous becomes discrete. Continuity stands as the “beyond” of one discrete unit, just as that discrete unit is the boundary of continuity.

Finitude and Infinity in Quantum Determination

In quantum ontology, finitude and infinity — the “spurious infinite” mistakenly opposed to the finite — each contain within themselves the moment of the other. The limit that infinity reaches is itself finitude. But this finite limit becomes, in turn, the limit of the infinite as a beyond; and this beyond is again finite. Thus the limit of the finite is the infinite, and the limit of the infinite is the finite.

Beyond the finite is continuous quantum.
Beyond the infinite is discrete quantum.

Quantum as Limit Generally

Quantity in general is defined by the concept of quantum, which simply means limit — not this particular limit here or that one there, but limit as such. Quantum consists of two fundamental magnitudes:

1. Continuity,
2. Discreteness.

Initially, the difference between these determinations has no immediate importance, for both articulate the way limit is expressed.

Discreteness defines the nature of the particular. To be particular is to possess discrete quantity. Discreteness is extensive magnitude: the amount that is externally bounded. Continuity, by contrast, is always the step beyond the limit — the limit of the limit — and is therefore intensive magnitude: amount internally determined.

Extensive and Intensive Relations as Structure of Quantity

The extensive and intensive magnitudes explain the internal structure of quantity. Extensive magnitude — amount outside — equally implies the presence of amount inside that outside.

For example:

• If one atom occupies space, then space is the extensive magnitude of the atom.
• Conversely, the atom is the intensive magnitude of the space.

Both intensive and extensive magnitudes articulate discrete and continuous quanta simultaneously. Quanta are both discrete and continuous: discrete as bounded, continuous as surpassing their own bounds.

Quantum as Self-Relating Limit

Quantum, as limit in general, is:

A. The self-relating discrete unit of continuity.
B. This discrete unit is enclosing: it is bounded on all sides.
C. Being bounded, it is other-excluding; this individual unit of discrete continuity is called a quanta.

But this exclusion is the very continuity of the limit being another limit. The “limit of the limit” means that quanta — matter — is always in motion.

This is reflected in mathematics: each number is a quanta, a discrete unit distinguishable from other numbers, yet each number presupposes an entire continuous series. Quanta alter into further quanta; the fact that this alteration proceeds infinitely lies in quantum’s inherent self-limiting nature. Every quanta limits itself by becoming another. Quantum is limit because it is inherently self-contradictory.

This self-limiting nature is the duplicating mechanism of determination: one determination becomes another, and the potential for further duplication becomes the ought-to-be of the next determination.

Magnitude

A proper understanding of magnitude treats quantity as a determinate quality — a measure within a specific movement, not a measure abstracted from movement or from the essential relations of that movement.

Hegel writes:

“In mathematics magnitude is usually defined as what can be increased or decreased. This definition is faulty, since it still contains what is to be defined; but it does imply that magnitude is posited as alterable and indifferent, so that, notwithstanding a change of this determination, the thing in question… would not cease to be what it is.”¹

Qualities such as color demonstrate how magnitude can alter quality. A decrease in the depth of red yields pink. But the mere notions of increase and decrease do not explain this qualitative transition, because mathematics assumes the quality remains unchanged while its magnitude varies.

Hegel continues:

“The Absolute as pure quantity is an indifferent determination: distinctions in it are only quantitative. Pure space, time, etc., may be taken as examples of quantity, insofar as reality is grasped as an indifferent filling of space or time.”²

And further:

“When magnitude is said to be capable of increase or decrease, this means that magnitude is alterable as such. But quality is alterable too; the distinction appears in the fact that, whatever direction magnitude changes, the thing remains what it is.”³

Thus what remains through quantitative alteration is the conception, and the conception is pure quantity — the universal that persists through determinate change.

The Observer and the Limits of Quantitative Exactness

Hegel warns that it is misguided to treat only mathematically calculable objects as possessing “exact” cognition:

“There would indeed be something badly amiss if we had to renounce exact cognition of freedom, law, ethical life, and God, simply because they cannot be expressed in mathematical formulae.”⁴

Measurement alone cannot grasp the unmeasurable structure of conception — including the observer, consciousness, and internal relations.

Organic and Inorganic Magnitudes

Hegel also notes:

“Quantity plays a more important role in inorganic nature than in organic nature.”⁵

In inorganic nature, a large region of space is occupied by relatively few distinct qualities — hence it is more purely quantitative.

In organic nature, a smaller region of space contains far more distinct qualities — hence it is more qualitative. Organic matter contains more activity within a smaller spatial magnitude.

Footnotes

1. G.W.F. Hegel, Science of Logic, trans. George di Giovanni (Cambridge University Press, 2010), 99.
2. Ibid., 101–102.
3. Ibid., 103–104.
4. Ibid., Addition to §98.
5. Ibid., Additional Remarks on Quantity in Organic and Inorganic Nature.

101 — Quantum: “How Much”

1. Quantum and Limitation

Quantum deals with how quantity is limited—the quality of quantity that determines limits, distinguishing quantity into distinct qualities, regardless of the quality itself but rather the act of distinguishing qualities.

“Quantity, posited essentially with the excluding determinacy that it contains, is quantum or limited quantity.”¹

2. Quanta and Determinate Magnitude

“Quantum is the way that quantity is there, whereas pure quantity corresponds to being, and degree (which will come next) corresponds to being-for-itself. … Whereas distinction is initially present in pure quantity only implicitly (as the distinction between continuity and discreteness), in quantum, on the other hand, distinction is posited.”²

This means that quantum always appears as a distinguished or limited quantity. Because of this, quantum breaks up into an indeterminate multitude of quanta or determinate magnitudes. Each determinate magnitude, distinct from the others, forms a unit, yet considered by itself, it is also a many. In this way, quantum is determined as number.

3. Meaning of Quantum

The plural term quanta refers to an indivisible discrete unit of process. Quantum is literally a point of relation where two variables are in contradiction. It is the relation that takes on an energy state. Quanta is literally a unit of process. Process is the generation of possibility—bringing out, or making explicit, a form.

Quantum refers to matter that is infinite in supply.

The term “quantum leap” refers to the abrupt movement from one discrete energy level to another, with no smooth transition—there is no “in-between.” The quantization or “jumpiness” of action, as depicted in quantum physics, differs sharply from classical physics, which represents motion as smooth, continuous change.

Matter develops in the quantum realm more abruptly. Quantum is the smallest indivisible unit of quantity that produces discrete energy levels. This means that energy levels are invariably generated in the quantum realm.

But what gives rise to such abrupt energy levels? These abrupt levels are the product of reasoning: whenever a contradiction is reached, it manifests as a quanta. Thinking is at the same time acting, and so the act of thinking is an exertion of energy—in other words, it takes energy to think.

Matter being infinitely produced is the infinite working of reason. There is no difference between logic and matter; each logical notion simultaneously takes on a material form.

4. The Observer and Internal Relation

This is why, at the quantum realm, the “observer” is synonymous with the object. There is no external means of observing the object; the observation of the object means, at the same time, the existence of it.

In external relations, the observer is externally engaged with the object—objects bear a relative nature to one another, in which differences assume relative positions of locomotion, subsistence, form, etc. External relations are only true after internal relations. Internal relations define indivisible quantity: one proposition only exists relative to another.

5. Packet of Energy — The Matrix

The observer is a physical substance inherent in any phenomenon.

Quantum mechanics goes further than classical mechanics not merely in describing how the physical world operates but in revealing what forms of existence disclose the mechanics of nature.

In classical mechanics, nature exhibits behaviours operating independently of the observer. The observer is restrained methodologically because the phenomenon is said to operate on its own without intervention.

Quantum mechanics revolutionized the notion of the observer by making the nature of the phenomenon itself capable of being changed by an aspect from its own conception. A new scope of existence disclosed the ordinary mechanics of nature.

In classical mechanics the observer is in nature; in quantum mechanics, the nature the observer is in is itself disclosed by a further form—known as dark matter—which shares the nature of the observer as having the capacity to conceive without being conceivable. We discern evidence of dark energy only indirectly through gravitational effects but never as an object in itself.

Dark matter being unknowable is not a lack of explanation but rather a reaffirmation of possible explanation as potential energy, which marks the broader notion of change itself.

6. Potentiality and Change

In quantum mechanics, what discloses the laws of nature is its potential for change. Change is not merely an aspect of time governing transitions but also a physical form that maintains the structure of an object.

For example, when an apple is metabolized, its physical structure changes from a fruit to a vitamin source for the blood, which then changes into muscle tissue, etc. These forms of change pre-exist in the apple as potential energy.

The transition between different forms—apple, vitamin, muscle—occurs through organs that disclose these forms. The relationship between drastically different moments constitutes their quantum entanglement: how seemingly unrelated events follow from one another.

Entanglement concerns how unrelated objects across the universe can have a relationship at a distance, just as it concerns how differing magnitudes of dimension relate—how can a bacteria be in a man?

(Shape-shifting example omitted but implied)

7. The Matrix as Boundary

In nature, each number is a possible event, a detail disclosed within the present of the object. The idea of an underlying matrix behind things hints at the infinite variability of concrete things.

Numbers describe the discreteness between objects while maintaining general physical continuity. A quantity is simply a distinguished quality.

Velocity, for example, is the intensity of motion—its rate of positional change. It is a vector because it distinguishes direction. In the infinite scale of uncertainty, each number is every other number while simultaneously being a particular number.

This general uncertainty is warped by a particular element that produces a general static picture: 1 is 1, 2 is 2, 3 is 3, etc. This is how general uncertainty maintains distinct things.

The discrete measure between objects constitutes an unknown space where an infinite set of potential events could take place.

The matrix is this boundary—a quantum state.

8. Dialectic and the Quantum State

The matrix is the condition of an infinite dialogue. In this dimension, propositions in thought have substance. Unlike ordinary thought, where words refer to external objects, in the absolute dialectical state the proposition carries the actual being of its content.

This absolute state is the quantum state, the state of a quantized system.

Packet of Energy — Quantization

Potentiality comes in the form of a packet of energy in the mind.

A packet of energy—also called a quantum—is the smallest discrete unit in which energy, action, or change can occur.
It cannot be divided into smaller portions without ceasing to be what it is. Quantization is the principle that certain physical properties—such as energy, angular momentum, or charge—can only exist in discrete values, not in a continuous range.
Instead of flowing smoothly, these properties come in units, or quanta.

Quantization means:

• A property can only take certain allowed values,
• And nothing in between.

This is why an electron in an atom cannot orbit at just any energy level; it must occupy one of the discrete, quantized energy states

In classical physics, energy changes smoothly and continuously.
In quantum physics, energy changes in steps, not in a continuum. Each step is a packet.

Quantization is what prevents the electron from “spiraling” into the nucleus (the classical paradox).
Because energy comes in packets, an electron cannot lose energy continuously—it can only lose it in specific quanta.
Thus the atom remains stable. In other words, atoms maintain their energy during their moments of non-being rather than being, as the latter is the moment of energy consumption or exhaustion. When an atom enters a discrete measure, it alternates between being and non-being. During this alternation, the moments of nothing maintain the energy of the atom during the moments of being. In other terms, the moment of non-being is proportional to the duration of being.

This is a confusing notion because it is so counterintuitive and defies what we observe, or how we see energy and the common world in the classical mechanical sense. From mere perception, and even in basic motions, everything appears to be continuously happening and flowing in a continuous state. However, the energy maintaining this apparent continuity is itself discrete. This means that, deep down inside the matter of objects, there exists a non-being state where the energy of that object approaches zero.

From this state, energy is, ironically, such that whether there is no energy or infinite energy results in the same outcome: finite energy is only exhibited by the finite conceptions and formations of the object. However, as a particular and finite object becomes closer to non-being, or nothing, it becomes greater in potentiality. It lacks itself and becomes more capable of being anything other. The potential state of the object increases while, simultaneously, its real form decreases.

Energy approaching zero does not mean a lack of energy or less energy, but rather a return to infinite energy, as that is the place where energy rests. It returns, per se, or restarts to what it is, which is active force and determination. The best explanation of energy is that it continues to determine, and the best way to continue determining is to be able to restart a determination, or rather, to make another determination.

Déjà vu Phénomène

Phenomena like déjà vu or recollection introduce uncertainty into what is considered “real” or “possible.” One difficulty is foreseeing an event in a dream or daydream, which we take to be merely imaginary because it has not yet happened.

After an event occurs, however, it is difficult to imagine that it had not happened.

A dream may pick out aspects of an event that are more real than the event itself. The dream isolates underlying inclinations or feelings that do not occur physically.

Potentiality is concentrated, not dispersed. It does not occupy the present, and so cannot be located perceptually, but speculative thought considers potentialities as discrete concentrations of variables. If one variable does not occupy its place, the entire possibility becomes another possibility.

This form of potentiality is the packet of energy in quantum mechanics. A quanta is the measure of variables occupying a necessary relation.

9. Quantization, Probability, and the Observer

A quantized system provides a distribution of probability for the observable outcome of each measurement. Observable simply means measurable.

Different forms involved in transformation are discerned by assigning different observers to different frames of reference. Each change is accounted for by a specific observer disclosing a discrete reference frame. This is an automorphism, an isomorphism from an object to itself that preserves structure.

A mixture of quantum states is again a quantum state. States that cannot be written as mixtures are pure; all others are mixed.

A pure state is represented by a ray in Hilbert space. A unit vector may be chosen freely, though its phase factor remains important for superposition.

10. Dialectical Operations and Experience

In dialectic, a proposition of an idea is a probability of a thought process presupposing opposing determinations. These ideas hold their ground by manifesting the opposing element.

An idea presupposing theft manifests as an event where an individual becomes a thief. A life form is an organism because it undergoes transformations to exhibit specific functions. The individual is the function; the idea is the operation.

The moment-now is the clarity and concentration of one event, whereas convulsion is the set of moments that are not present.

Footnotes

1. G.W.F. Hegel, Science of Logic, Book II: Doctrine of Being, Quality–Quantity transition.
2. Ibid., Section on “Quantum.”

Pure Conception

This means that something true is objectively itself. In Hegelian terms, objectivity is an idea as object: it has within itself the means of its own self-creation[^1].

The conception is therefore objective by virtue of its ability to self-create or, rather, self-produce. It is pure when it approaches the non-being state of energy discussed in the context of quantization, where an atom preserves its energy during discrete measures, or moments of nothing. This alternating effect between being and non-being actually conserves its energy.

A conception is pure in the sense of being capable of this power or energy. The energy preserves itself by approaching zero, which is paradoxically also infinite energy, since energy can simply restart or become active again—like an electric current reinstated, or a battery recharged.

Additionally, we must consider the role of subjective nothing. The conception is subjective when it does not create or produce the current state of reality, but rather, through observation, represents it as an idea of what it assumes reality to be. This assumption about reality is based on, or made within, an already predisposed reality. However, there is a fundamental disassociation: the subjective can never fully represent the objective form. The subjective always loses the exact meaning of the objective. This limit in the subjective conception operates in exactly the same way as the discrete energy states of atoms. In other words, atoms are primarily an abstract conception of the mind, creating reality and becoming lost within it.

Discrete and Continuous

Discrete and continuous are forms of extensive and intensive magnitudes[^2]. The discrete form describes intensive magnitude because it is the distinctiveness of quality, separating it as a distinct and definite determination. Intensive magnitude, as a discrete form, is the internal relation of a determination with that of the negation of its inverse.

Continuous, by contrast, is extensive magnitude because it is the relation where inverse determinations take on the same form while remaining distinct. Extensive magnitude relates to the covering of area. Inorganic matter can be considered more quantitative than organic matter, reflecting the predominance of measurable, extensive relations.

Discrete and continuous are synthetical conceptions, meaning that they cannot exist on their own without the presupposition of the other. It is important to discern in what sense discreteness is fundamental to continuity and how continuity involves discreteness[^3].

Discreteness is often left out by the senses, a limitation that becomes apparent in the form of the conception.

The Limit of the Senses in the Form of Conception

The abstract powers of the mind, in conjunction with the sensible faculties, have evolved to provide the most stable and efficient conceptual form for the development of the organism operating in nature[^4]. The most efficient conception, however, is by no means a complete conception.

The sensible faculties lack a comprehensive perception of continuity because not all details forming the object are perceived within the reference frame in which it is contained. A medium of quality is picked out. For example, air is an element that is not seen but only felt. However, this does not mean that air lacks physical qualities that are discernible, because at the subatomic level, air particles have mass and shape, and some microorganisms rely solely on respiration[^5]. Realistically, air is a species of trillions of particles, and if perception attempted to pick out each particle, it would be too distracted to perceive anything else. This is why perception did not evolve to perceive elements like air in detail; otherwise, the perception of macroscopic objects would be muddled. In comparison to the microscopic world, our macroscopic perception of things provides only a vague continuity.

The sensible faculties also do not perceive the accurate discrete form of things. The faculties filter out the conception itself and focus only on the content of the conception, because the conception is disclosed by a formless void, which may not be necessary for perceiving the object. The void is not perceived as disclosing the object because the object is already disclosed by its conception. Therefore, when the conception changes from one object to another, the void disclosing the conception does not have to be accounted for as part of the transition[^6].

Each conception of a different thing is separated by a discontinuity of not being the other. The discontinuity between events is part of the change of the conception from one thing to another. The change between things is mediated by the disclosure of the conception within nothing. When perceiving one object, the reason we do not see another is that the sensible faculties filter out the form of the conception itself, so the void does not appear as part of the directly perceived object. This ensures a single reference frame, allowing the transition of the conception between objects to appear continuous.

Moreover, this mechanism has an evolutionary function: for survival, continuity of perception is crucial. If a discontinuity occurred in the perception of an event—such as a lion running toward an observer—a gap could result in missing critical details that determine life or death. The form of the conception is filtered out from the object of perception, leaving only the object itself perceptible, with the conception merely presupposed in the abstract. Yet the form of the conception is as much a part of the object as the object is a part of the conception.

The senses purposely limit the total qualitative makeup of reality to a specific resolution, not capturing all possible details in every possible form. This limitation of continuity simultaneously limits discreteness. Limiting both magnitudes is necessary for an efficient framework within which a finite life form can operate, bounded by certain circumstances. However, this narrow framework of continuity and discreteness is not comprehensive, nor is it an entirely accurate depiction of a fundamental state of reality independent of the organism’s needs[^7].

Discreteness is left out to provide a sense of continuity, and continuity is reduced to provide a sense of discreteness. The interplay between these two limits is necessary for a coherent conceptual framework.

Footnotes

[^1]: Hegel, Science of Logic, on the idea of self-determining objects and the concept of objectivity as self-creating.

[^2]: Extensive magnitude refers to measurable, additive properties (like length, mass), whereas intensive magnitude refers to qualities like temperature or potential, which are distinct in themselves.

[^3]: Hegel emphasizes that discrete and continuous are co-dependent; one presupposes the other in the formation of conceptual reality.

[^4]: This refers to the Hegelian notion that cognition evolved for stability and survival, shaping the way we perceive both discrete and continuous aspects of nature.

[^5]: Microorganisms such as bacteria and protozoa respire and interact with air particles at a microscopic level, illustrating hidden qualities not perceived by the senses.

[^6]: Hegel’s concept of nothing underlies the transition between determinations; perception only registers the object, not the void or transition.

[^7]: The human perceptual framework is efficient but limited, providing a pragmatic but incomplete picture of reality.

Being-for-Self, Discreteness, and the Quantum Analogy

The most familiar example of being-for-itself is the “I.” We know ourselves to be beings that are there—first, as distinct from other such beings and related to them; but secondly, we know that this entire expanse of being-there is, so to speak, gathered into the simple form of self-relation. When we say “I,” we express an infinite self-relation that is at the same time negative: it affirms itself only by excluding what it is not.¹ To say “I,” to posit a self-identity, is simultaneously to exclude all things not identified as “I.”

This same structure appears in the way conception (Begriff or Vorstellung, depending on level) organizes experience. When we perceive an object, the discreteness implicit in the conception of the event is left out of the perceptible frame. The senses focus on the object as conceived, leaving out the void or nothingness within which the form of the conception is disclosed. What is omitted in perception is precisely the mediating negativity that makes the object distinct from every other object. Perception seems to deliver a smooth, continuous field; yet this continuity is an illusion produced by leaving out the innumerable discrete transitions that occur whenever the conception shifts its focus.

We fail to notice this because the change from one conceived object to another appears as a lucid transition within a single, stable conception. But this appearance presupposes what it seeks to explain: namely, how objects are conceived as distinct. The difference between objects cannot simply be taken as given; it is the product of the negative self-relation through which a conception sets itself off against what it is not.²

Quantum Analogy: Discreteness of Conception

(Quantum addition, edited for coherence)
At the quantum level, physical changes do not necessarily occur as continuous flows but often as discrete transitions. This offers a helpful analogy—not an identity—for clarifying the discreteness implicit in conception. For every quantum event, the system occupies a definite state only upon measurement; each such state may be thought of as a distinct frame of disclosure.³

Likewise, in the realm of thought, every change in the conception of an object functions as the emergence of a new determination. The object appears only within a void—a moment of abstraction that differentiates it from the newly formed conception that follows. The discreteness of the object is thus the discreteness of its conception, which discloses it within nothing so as to demarcate it from the next disclosure.

In this analogy, each conception would be its own “event,” rather than one continuous stream. Our experience of continuity—such as when turning the head and smoothly transitioning from one object to another—rests on an underlying sequence of discrete conceptual determinations that are not given as discrete in perception. Perception presents objects as externally connected, but the order of thought is internally mediated and not bound to sensory chronology.

The Order of Thought vs. Sensation

In thought, events need not unfold in the same temporal order as in sensation. The future of an event can be conceived before the beginning. For example, one may first imagine the end—falling in love—and only afterward conceive the steps leading up to it. Thought determines the end and then draws out the means.⁴ Sensation, by contrast, proceeds from means toward end.

As Alan Watts remarks, the mind is like a camera whose lens can turn back upon itself: thought can internalize its own process, circling through conceptions and negating each one to form the next. This is closer to the actual discreteness of conception, where each determination is maintained as a distinct disclosure of content. Ideas do not appear as objects externally placed beside one another; each one internally becomes the next.

Misapprehension of Relativism

A common misunderstanding arises from the claim that conception determines the object. It is argued that if there are many conceptions, and no standard outside them, then no shared reality is possible. But in Hegel, the object is not merely “made up” by conception; instead, the object is the self-developing totality of its conceptual determinations. Relativism falsely presupposes multiple unrelated conceptions. Hegelian logic shows that conceptions are not private or arbitrary; they are shapes of the universal Concept, which determines itself through negation and reconciliation.⁵

Footnotes

1. Hegel, Science of Logic, “Being-for-Self” (Quality). The “I” as infinite negative self-relation: “The I is this pure self-identical negativity.”
2. Ibid., “Being-for-One,” “Repulsion,” and “Attraction.” Distinction arises from negativity, not from spatial separation.
3. Analogy only. In the Doctrine of Being, the transition from continuity to discreteness appears in Quantity, especially “Number” and “Discrete and Continuous Magnitude” (§§ Science of Logic, Quantity). Your timestamp “5:23:00” likely corresponds to a lecture segment discussing this.
4. Hegel, Encyclopedia Logic, §204: the Concept determines the end and mediates itself through the means.
5. Hegel, Science of Logic, “The Concept” (Begriff). The universal-particular-individual structure avoids both naïve realism and relativism.

Atomism and Rationalist Metaphysics: Two Opposed Conceptions of the First Principle

The atomistic attitude approaches the ontology of Being in a manner that is, in a certain sense, the inverse of rationalist or objective-idealist metaphysics. The fundamental difference lies in which principle is regarded as primary.

Rationalism—especially objective idealism—maintains that thought, or Reason, is the first and essential principle of the world. By making this abstract principle primary, rationalism reduces material substance to a derivative status. In the strict logical sense, such an abstract principle is “nothing,” not in the sense of nonexistence, but because its Being is equal to its Nothing—each passes into the other; when one is posited, the other is already contained within it. Being and Nothing exist, but they are ultimately one. The first principle of objective idealism may therefore be described as Nothing, which is at the same time a Being, or more precisely, the truth of both: Becoming.¹

Thus idealism does not claim that Being emerges out of an empty void; instead, it asserts the deeper identity of Being and Nothing—not merely as a conceptual equation, which is difficult for ordinary consciousness, but as a unity of substance, a unity experienced in the presence of the quality itself. This abstract process presents itself as “nothing,” or as inconceivable, yet it is still graspable indirectly through all the faculties of mind, and becomes intelligible when reflected upon as a self-mediating movement.

Atomism likewise insists on a first principle, but it disagrees entirely about the nature of that principle. For atomism, Nothing is not first; rather, Being is. In this respect atomism resembles idealism: both insist that the first principle is not a mere proposition but a substance, something whose existence is necessary. But whereas idealism begins with the unity of Being and Nothing, atomism begins with Being as immediate, as matter. Matter is taken to be directly perceptible, observable, and self-identical—something that persists absolutely. To account for change, atomism posits Nothing only as the relations or empty intervals between these units of being—the atoms—which exist eternally.²

The atomist position has an intuitive plausibility: at the foundation of all corruptible or mutable things, there seems to be a material force or substratum that does not come into being and does not cease to be. This eternal substrate appears to have the same certainty of existence as the objects we perceive; thus Being seems more primordial than Nothing.³

Yet the deficiency of atomism, which appears more “realistic” than idealism at first glance, lies in the fact that its fundamental claim remains an assumption. It assumes that at the core of all things matter continues to exist with the same certainty, indestructible and permanent. It assumes that Being is always present in Nothing, and that the void is merely the external spacing between absolutely self-sufficient units. Atomism thereby presupposes precisely what it needs to prove: that immediate Being, in the form of discrete atoms, is the ultimate truth of things. Hegel criticizes this as a form of uncritical metaphysics—a fixation of the understanding upon a one-sided determination of Being.⁴

Footnotes

1. Hegel, Science of Logic, “Being–Nothing–Becoming”: Being and Nothing are both immediate, both indeterminate, and both pass into one another. Their truth is Becoming.
2. Ibid., Addition on Atomism (around SL, Quality → Being-for-Self): atomism posits the One and the void; the void is repulsion represented as nothingness between atoms.
3. Ibid., critique of atomism’s claim that the atom is the indestructible substrate of all things.
4. Ibid., the critique of the understanding’s fixation on abstract, unmediated determinations (e.g., pure Being, the One, the atom), which remain undeduced assumptions.

Hegel on Atomism, Discrete and Continuous Magnitude, and the Logic of Quantity

Hegel characterizes atomistic philosophy as the standpoint at which the Absolute is determined as One and as many Ones. Atomism treats the repulsion contained in the concept of the One as the fundamental force, while the union of atoms is attributed not to attraction but to chance, that is, to something without thought.¹ Because the One is taken as fixed, its coming-together with other Ones is necessarily conceived as something external. The void, added as the second principle of atomism, is nothing but repulsion represented as the nothingness that lies between atoms. Modern atomistic physics, though having abandoned indivisible atoms in favor of molecules or small parts, still retains this presupposition and thereby comes closer to sensible representation while abandoning determination by thought. And since modern physics adds a force of attraction alongside repulsion, the antithesis is indeed made complete—though this “discovery” has produced more pride than insight.²

Because atomism remains popular among natural scientists who reject metaphysics, Hegel emphasizes that one does not escape metaphysics by embracing atomism. The atom is itself a thought-determination, and the interpretation of matter as made up of atoms is a metaphysical interpretation.³ Newton warned physics to avoid metaphysics, but—Hegel adds—Newton did not obey his own warning. Only animals would be “true” physicists by this standard, for they do not think; humans, as thinking beings, are born metaphysicians. The only question is whether we employ the right kind of metaphysics—that is, whether we grasp nature through the concrete logical Idea, or cling instead to one-sided thought-determinations of the understanding. It is this one-sidedness that condemns atomism.⁴

The ancient atomists, like many modern thinkers, regarded everything as a many, and took the relation among the many to be accidental—atoms floating about in the void. But the relation of the many to one another is not merely accidental. It is Kant’s achievement to have conceived matter not as the sum of atoms, but as the unity of repulsion and attraction. This correction is essential: attraction is the other moment of being-for-itself, just as necessary to matter as repulsion. Kant’s “dynamic construction of matter,” however, remains defective because the two forces are simply postulated, not deduced from the concept.⁵

Continuous and Discrete Magnitude

Hegel writes that in its immediate relation to itself—in the self-equivalence posited by attraction—quantity is continuous magnitude; but in its other determination, that of the One, it is discrete magnitude. Yet each moment contains the other: continuous quantity is continuous only as the continuity of many Ones, and discrete quantity is discrete only as the unity in which the many are identical.⁶

Neither determination can exist independently. The difference between continuous and discrete magnitude is only that the same whole is posited first under one determination and then under the other. From this, Hegel derives the classical antinomy of infinite divisibility: if space or time is treated solely as continuous, it is divisible ad infinitum; but if treated solely as discrete, it consists of indivisible Ones. Each claim is one-sided.⁷

As the proximate result of being-for-itself, quantity contains within itself as ideal moments both attraction and repulsion; therefore, it is both continuous and discrete. Whenever we treat them as two species, this is merely the result of abstractive reflection. Thus we say that the space which a form occupies is continuous magnitude, while the hundred people in that space form a discrete magnitude. But space is also discrete—since we speak of points and subdivide lengths into feet and inches—and a discrete magnitude such as one hundred people is also continuous, grounded in the species “humanity” that unites them.⁸

Extensive and Intensive Magnitude (Degree)

Hegel further distinguishes extensive and intensive magnitude. The limit of a quantum is identical with the quantum itself. As multiple within itself, the quantum is extensive magnitude; as simple determinacy, it is intensive magnitude or degree.⁹

The difference between continuous/discrete magnitude and extensive/intensive magnitude is that the former concerns quantity as such, whereas the latter concerns the limit of quantity. As before, the two are inseparable; whatever has extensive magnitude has intensive magnitude, and vice versa.¹⁰

Zeno, Number, and Spurious Infinity

Hegel approvingly cites Zeno’s remark that to say something once is the same as to say it forever.¹¹ This corresponds to the quantitative infinite progression—the bad infinite that never transcends the finite but endlessly repeats the “ought.” Spinoza rightly called this the infinitum imaginationis.¹² To reach the true infinite, one must renounce this endless progression and grasp the infinite as the self-returning unity that contains the finite within itself.

Pythagoras is said to have philosophized with numbers, regarding number as the basic determination of things. To ordinary consciousness this seems absurd. But philosophy’s task is precisely to trace things back to determinate thoughts. Still, the attempt to map determinate numbers onto determinate thoughts—e.g., 1 as immediacy, 2 as mediation, 3 as unity—is arbitrary. The further we proceed, the more arbitrariness appears: 4 can be the unity of 1 and 3, or twice 2; 9 can be the square of 3, or the sum of 8 and 1, 7 and 2, etc. Secret societies may assign deep meaning to numbers, but such symbolism is merely a harmless game or a sign of defective thinking. What matters is not that we can think about something, but that we actually think, and the genuine element of thought lies not in symbols but in thinking itself.¹³

Ratio and the Infinite of Quantum (Logic of Mathematics)

As being-for-itself, quantum is self-external; this self-externality constitutes its quality. In this externality quantum is self-related. Posited thus, quantum becomes quantitative relation (ratio): a determinacy that is both an immediate quantum (the exponent) and a mediation—namely, the relation of one quantum to another. The terms of a ratio do not count according to their independent value; their value arises only within the relation itself.¹⁴

The infinite implicit in quantum is therefore not an external beyond but the value of self-determination, the unity of being-for-itself and externality. This is the logical basis of the mathematical concept of ratio and proportion.

Footnotes

1. Hegel, Science of Logic, “Being-for-Self”: the One and its repulsion.
2. Ibid.: critique of modern physics and the pride taken in positing forces.
3. Ibid., addition on atomism as metaphysics.
4. Ibid.: the right versus wrong metaphysics; animal vs. human cognition.
5. Kant, Metaphysical Foundations of Natural Science; Hegel’s commentary in Science of Logic, addition on matter as unity of repulsion and attraction.
6. Hegel, Science of Logic, “Quantity,” “Continuous and Discrete Magnitude.”
7. Ibid.: the antinomy of infinite divisibility.
8. Ibid.: each magnitude contains both determinations.
9. Hegel, Science of Logic, “Degree (Intensive and Extensive Magnitude).”
10. Ibid.
11. Ibid., reference to Aristotle’s report of Zeno.
12. Spinoza, Ethics, scholium to I.15; Hegel repeatedly cites this.
13. Hegel, Science of Logic, addition discussing Pythagorean number symbolism (p. 167).
14. Hegel, Science of Logic, “Quantum” → “Quantitative Relation (Ratio).”

Infinity, Magnitude, Curvature, and Discreteness

1. Infinity as a Single Determination

Infinity is itself one determination. It may be approached in two opposite, but equally valid, ways:

1. Extensively (A): by collecting all things into a single all-inclusive whole;
2. Intensively (B): by beginning from a single thing and discovering within it an inexhaustible multiplicity.

These correspond to Hegel’s distinction between extensive and intensive magnitude.¹

In extensive magnitude, one may “zoom out” indefinitely: as the observer recedes from an object, the object becomes progressively larger relative to the frame of reference, until the collection of all things appears as one unified magnitude. Inversely, in intensive magnitude, by “zooming in,” one uncovers an infinity of details and determinations within a single individual.

The observer thus occupies the middle between the extensive and the intensive. At the limit of both magnitudes—the point of infinity—size becomes indiscernible: the largest thing, insofar as it approaches the infinite, cannot be determined as large; the smallest thing, approaching infinite divisibility, cannot be determined as small. Their similarity increases as both approach the same limit.

A simple analogy is a bell curve: the two points closest to the apex differ least, whereas points farther from the top diverge most widely in magnitude.

2. Curvature as the Form of Opposing Determinations

In quantum physics (used here analogically), every determination brings with it a set of inverse determinations: if energy increases in one place, the corresponding remainder decreases. The vertical extensive relation presupposes an intensive, horizontal difference; and when the vertical is rotated, the horizontal becomes its inverse relation.

The totality of these mutually presupposed opposites is structurally expressed by the circle. The circle does not depend on the concrete content of any determination; it represents the form that contains their reciprocal relations.

This is why curvature appears in all objects. A straight line is not the fundamental form; rather, it is abstracted from the circle, just as a tangent is abstracted from a curved surface.²

A table, which appears straight from a distance (extensive magnitude), reveals under magnification an irregular landscape of curves and ridges (intensive magnitude). Straightness, then, is the extensive disclosure of what is intensively curved.

The diameter of a circle symbolizes infinite extension: a straight line that extends without bound in both directions. The circumference discloses this infinite extension by enclosing it as a finite totality. The circumference is the line pointing to the infinite extension that it binds; the radius marks the particular determinations that arise from the unity of infinite potentialities.

The radius thus represents how any finite determination presupposes an infinite field of opposite determinations. The void at the center is the negation of a given determination—its empty place for its potential inverse.

3. Discreteness, Nothing, and the Logic of Determination (Quantum Analogy)

When a particular determination emerges, it brings with it the void of its inverse determination. The void is not content but pure form, the place where the content may be reversed. Thus every determination appears as the possibility of becoming an other, and both share the same null background.

In the quantum analogy, events are discrete because each determination is disclosed upon the background of nothingness, which outlines it as distinct.³ Nothing serves as the form by which something is recognizable. Were the “void” anything other than nothing, the distinction between two determinate beings would vanish.

Yet nothing, insofar as it outlines the thing, is also the other of the thing—equal to itself, undifferentiated, and universal. A thing maintains itself only by continually distinguishing itself from nothing; in so doing it must constantly differentiate itself internally. The result is that the thing is self-related continuity, yet also discrete from itself through constant self-negation.⁴

Thus:

• Continuity arises because the thing must remain itself against nothing.
• Discreteness arises because it must continually become other to avoid lapsing into nothing.

This double movement mirrors Hegel’s treatment of continuous and discrete magnitude, where each contains the other.⁵

4. Extension, Matter, and the Scale of Discreteness

Extension has long been associated with matter—Spinoza explicitly identifies extension as one of matter’s fundamental attributes.⁶ But the phenomenon of extension varies across scales.

In the solar system, the continuity between bodies is minimal: vast voids separate planets; their motions appear discrete. But at smaller scales—within a planet—the continuity of matter increases: air, oceans, organisms, soils all form interpenetrating, continuous manifolds. Zoom in further and the microscopic world again displays extensive voids and discrete bodies, each forming their own continuous systems.

Thus the perceived continuity or discreteness of phenomena depends on the relation of magnitude between observer and object. Discreteness at one scale becomes continuity at another.

The “void” between discrete bodies is filled by their contradictory relation: their differences synthesize into an environment, a field in which they extend into one another. This is the unifying third that reconciles their discreteness and continuity.

5. Natural Motion and the Conception of Center

The “naturalness” of motion is determined by the conception guiding the relation between directions. Upward motion is unnatural relative to a downward-directed center; downward is natural relative to a lower center. But the center is not merely perceptual—standing in front of us—but also ideal: a purpose, end, or abstract destination.

In cities, “downtown” functions as an objective center; going toward it is “down,” going away is “up.” This practical center is determined by a conception, and time itself appears faster or slower depending on the density of relations occurring in a given space. Where interactions are numerous, time feels “fast”; where they are scarce, time feels “slow.”⁷

By analogy, in the solar system fewer interactions occur, so the temporal field is “slower” compared to the densely interacting environment of Earth.

Footnotes

1. Hegel, Science of Logic, “Quantity,” especially Continuous and Discrete Magnitude and Extensive and Intensive Magnitude.
2. Ibid., discussion of curvature and the circle in relation to magnitude; see also Hegel’s remarks in the Encyclopedia Logic §259 Addition.
3. Hegel, Science of Logic, “Being-for-Self”: the One, repulsion, and the void.
4. Ibid., the self-negation of determinate being and the transition to being-for-self.
5. Hegel, “Continuous and Discrete Magnitude.”
6. Spinoza, Ethics, Part I, Definitions & Axioms: extension as an attribute of substance.
7. Cf. Hegel, Philosophy of Nature, §§257–260: time as the “negative unity” of space, dependent on the relational activity within spatial configurations.

integrate these sections into a single coherent philosophical chapter,

expand the quantum analogy using Hegel’s logic of the One and Many,

add diagrams for the circle/line/radius argument,

The Fourth Dimension

1. Empirical Science and the Primacy of Three Dimensions

Empirical science deals primarily with three-dimensional objects because the third dimension uniquely provides stability, spatial certainty, and physical persistence for bodies in motion. In everyday and scientific practice, the dimensions are often treated as independent geometric parameters—length, width, and height—without initially considering time. This implies that space is primary, while time appears as a subordinate or external measure of motion.

This assumption arises because spatial magnitudes—length, width, height, depth, breadth—are conceived as incorruptible in the sense that their quantitative structure is not inherently altered by the change of objects that possess them. A meter remains a meter regardless of what occupies it. Yet the qualities of objects that instantiate magnitudes are corruptible, and even magnitudes vary. The key is understanding in what sense quantitative properties are “incorruptible.”

Impenetrability and Incorruptibility

Impenetrability means that two bodies cannot occupy the same place at the same time—a notion central to classical physics.¹ This property gives matter a form of substratum or stability, allowing measurement without requiring immediate reference to time. Time is not excluded but is treated as a derivative quantitative aspect of spatial relations (e.g., velocity = distance/time).

In this sense, time as a dimension is still subject to the principle of impenetrability because the temporal continuity of an object—its persistence—is a kind of corporeality of duration. Something endures in time because it resists dissolution into nothingness.

2. Incorporeality, and the Problem of Decay

All major religions address the distinction between corporeality and incorporeality because matter, being penetrable and divisible, is inherently subject to decay. This intuitive recognition of transience leads to doctrines of incorporeal or immortal principles—e.g., soul, spirit, Logos, or pure form.²

3. Impenetrability, Indivisibility, and Substratum

Impenetrability as Substratum

Impenetrability is the necessary condition for anything to subsist amid uncertainty, multiplicity, and change. Penetrability is the capacity to be altered; impenetrability is the enduring ground that confronts or receives change. This explains the connection between impenetrability and indestructibility.

Indivisibility as Indestructibility

Indivisibility means that something cannot be divided into equal parts because its being consists of an internal relation such that, when one element is excluded, another necessarily remains.³ Indivisible relational being cannot be annihilated without remainder; its identity persists through transformation.

Change as an Impenetrable Object

Matter is impenetrable not simply as a solid but as continuity itself—the fact that change is conserved. In physical science, change (energy, momentum, angular momentum) cannot be created or destroyed, only transformed.⁴ Thus change-itself functions as the ultimate “impenetrable” object, and this stabilized continuity is what we call space.

4. The Dimensions

(a) The First Dimension: Pure Duration

The first dimension is commonly represented as length—a straight line. Metaphysically it corresponds to duration, pure change abstracted from any determinate form. A one-dimensional object has only length, no other discernible quality.

(b) The Second Dimension: Form

The second dimension introduces width, thickness, and figure. Duration becomes discernible as form: a shape that can be measured and distinguished from others.

(c) The Third Dimension: Form in Motion

The third dimension synthesizes the first two:

• duration (1D) becomes
• form (2D)
• which now persists while in motion (3D).

Two objects moving at the same speed will maintain relative positions unless their speeds are altered; motion is the change of position over time.

Angular Momentum as the Essence of the Third Dimension

Angular momentum—the rotational analogue of linear momentum—is central to the stability of three-dimensional objects.⁵

A sphere is the simplest 3D object because it is the synthesis of:

• continuous duration (1D)
• fixed form (2D)
  whose contradiction resolves in a rotational self-relation.
  The sphere embodies the motion of a thing that changes while remaining self-identical—like a person walking while swinging their arms.

Angular momentum conserves identity through continuous transformation.

5. The Fourth Dimension

The fourth dimension is the potential of duration that has externalized itself into form, becoming the determinative object toward which matter is moving. It is the ideal end or telos of spatial-temporal becoming.⁶

The 4D dimension is not simply “time,” nor merely a geometric extension, but the projection of a becoming-form beyond itself, the dimension of purpose, directionality, or development—the trajectory toward which a 3D form tends.

This reflects the idea that matter is always in a state of becoming something other than itself, and the “fourth dimension” names the structure of that becoming.

6. Space and Time: Inversion Inside and Outside Earth

On Earth, space is extensive:

• we traverse it physically, moving from point A to B.
  Time, by contrast, is intensive:
• it manifests as internal changes within things—aging, memory, growth, decay.

But outside Earth, this relation inverts.

Space Outside Earth Is Intensive

In outer space:

• there is no directional extension (no up/down/left/right)
• spatial relations between bodies are determined by their internal gravitational boundaries
• planets and stars are spherical intensive unities that contain vast internal depth

Space is not traversed in the terrestrial sense; it is experienced through the internal spatiality of astronomical bodies.

Time Outside Earth Is Extensive

The relation between planets and stars is primarily temporal, not spatial.
To go from one star to another is to traverse their temporal durations:

• their life cycles
• their stages (main-sequence, red giant, white dwarf, etc.)
• their evolving gravitational fields

Thus cosmic motion is essentially temporal extension: a star’s identity is given by where it is in its life-time, not by its position in space.

This yields:

Realm	Space	Time
Earth	Extensive	Intensive
Cosmos	Intensive	Extensive

This inversion reflects the different ways continuity and discreteness manifest in the micro- and macro-cosmic scales.

Footnotes

1. Newton, Principia Mathematica, Book II: definitions of impenetrability and solidity.
2. Plato, Phaedo and Timaeus; Aristotle, De Anima; Christian, Islamic, and Buddhist metaphysics on incorporeality.
3. Hegel, Science of Logic, “Being-for-Self” and “The One and the Many”: indivisibility through relationality.
4. Noether’s theorem and conservation laws in physics.
5. Classical mechanics: angular momentum as conserved quantity unless acted on by external torque; see Euler, Lagrange.
6. Hegel, Philosophy of Nature, §§257–270: time as the “negative unity” of space and the emergence of higher-dimensional determinations.

Summery

Impenetrability is the invariable necessity for a substratum to subsist in any framework of uncertainty and change. The penetrability aspect of an object is its potential for changing; penetrating an object changes it. Impenetrability is the substratum that subsists, or is what is being met by the change. How impenetrability explains incorruptibility concerns what it means for indivisibility to be indestructible. Indivisibility is indestructible because there is the factor of an element which cannot do away from another, and this is indestructible because the object is not reducible to a single variable, the exclusion of which denotes a nullity, but is a relation whereby when one factor is excluded the other is presupposed to take place. This is why indivisibility is defined as something unable to be divided into equal parts: because in a relation, the moment one component is gone, there is always a residue or a remainder of another part.

The fact of matter being impenetrable is simply the fact about the object’s subsistence, that the physical impenetrability of an object is its quality of continuing a duration, or that the duration itself is a continuity, and there is no other type of being than that. When an object is penetrable it changes into something else by becoming another object, but the change itself endures the transition and qualifies as an impenetrable object. Change itself is the scientific object of physical impenetrability: it cannot be created or destroyed, only altered, and therefore in this way stabilized as space.

The first dimension is commonly defined by length, e.g., the x-axis. For example, a straight line is a good description of a one-dimensional object which exists only in terms of length and has no other discernible qualities. In other words, the first dimension is the abstraction or duration of pure change itself as an object.

In the second dimension the change itself becomes discernible as a form, a figure: the measurement of length, width, thickness, etc.

In the third dimension we have a synthesis between the first two, where we have a form that is in motion. In three dimensions we have a figure that is able to move while maintaining form.

The way this works is: two objects moving at the same speed but one is at a further position than the other will always be ahead unless the other changes its speed expediently. Speed is the change of position.

The third dimension is distinguished by the fact of angular momentum. The stability of the first dimension being a duration, and the second dimension being the duration itself as an indivisible form—there is always a remaining component—means that in the third dimension the mediation of these two takes on a distinct form, an angular momentum. The angular momentum is the motion of going round and round in circles: a dog chasing its tail, a snake eating itself, forming a stable form, a sphere. A sphere is a simple three-dimensional object because it is the synthesis of the first and second dimension.

As a duration is continuous in that it is happening, and as a happening it is indivisible because it cannot be otherwise—red is red unless it is green, which means green is green unless it is grey, etc.; white cannot be at the same time as black because it becomes something else, grey—the first and second dimensions contradict each other. In order for a duration to be continuing, it presupposes a constant change in form, and therefore a form becomes indiscernible as a figure; while in the second dimension, in order for a form to be fixed as a discernible figure, the duration must have halted on some level at a particular determination.

The third dimension resolves how a duration can still be eluding while maintaining a homogeneous form, because every time a duration moves in time it takes on a sequence of spatial extensions; but when the spatial extension stretches towards a definite direction it can easily shift its form in another manner while maintaining the angular structure of the past. In the third dimension the nature of the movement being maintains a static form while changing; e.g., just because a man is swinging his hands back and forth while walking does not lose his identity as the man walking.

In physics, angular momentum is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a system remains constant unless acted on by an external torque. It is the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity.

The fourth dimension is the potential of a duration that became a form outside of it as its determining object. It is the idea that the matter is moving towards.

If we look at the distinction between how space and time relate on Earth as opposed to outside of Earth, we can see an inverted ratio of extensive and intensive magnitude. On Earth, space is extensive—or rather, there is extension of space: you can walk on the ground to get to point B from point A. Time, on the other hand, is intensive; it is disclosed within things as their subtle change. The future, for instance, is not external nor is the past; they rather happen at one point and either exist as a memory in the thing or as part of its being.

If we leave Earth and venture out into space, what we find is the opposite relation: space is intensive and time extensive. Outside of Earth, objects in space are spheres disclosing within them an infinite spatial extension; you can go within, within, within a planet into a microscopic scale. While outside in space there is no extension of space, there is no direction—up, down, left, right. The relation between objects in space, like planets and stars, is not spatial but rather their relation is time. To get from one planet to another is identifiable with the life duration of that planet itself: it determines for that planet its stage of life, and also its physical condition—whether it is an ultra-hot big massive star, or a white dwarf, or a brown dwarf at the end of its life, or whether it has exploded or not.