2.2.1 Entropy

Section 18. (first updated 12.30.2020)

Chaos and the Form of Space

Chaos is not scattered within an indiscernible area of space. This means that the disconnection between any set of discernible objects does not occur within an endless or unlimited expanse, but rather that the very idea of space is always indivisible from any object disclosed within it. Chaos, in other words, is always contained by a rational form — a discernible figure that exhibits structure and limitation. Form is thus first in its magnitude-relation with the opposite of itself, namely the entropic state, which represents an indeterminate state of form.

The “unavailability” of a system is not an inherent lack of order, but rather the absence of an observer capable of discerning an infinite state of uncertainty. The question of chaos therefore concerns the number of possible sets of events or scenarios that may or may not occur within a confined region of space. The space within which a chaotic system is said to exist is not the same as its initial condition — the latter being the presumed absence of any known or discernible origin.

Every area of space possesses an indivisible feature: time. Space and time are not separable but simultaneous. This means that any area of space both happens and occurs — it participates in the flux of being — while also appearing absent from existence when viewed abstractly. Yet how can space not be there if it serves as the condition for the absence of objects? This assumption collapses when we recognize that the object of our question — space itself — is already the lack of objectivity. Within every spatial field, something is always happening.

Time allows space to exist, and space, in its apparent absence, allows time to manifest as a series of concurrent events. Each event occupies a parallel position in space such that, from first-, second-, and third-dimensional points of view, they exhibit form for an observer disclosing that process within an object external to itself in space.

Footnotes

1. On the relation between chaos and form: Aristotle, in Physics IV, distinguishes place (topos) as inseparable from the thing contained — “the boundary of the containing body which is at rest” — anticipating the later notion that space is not independent of objects but coextensive with them.
2. On chaos as rationally contained: Heraclitus described the apparent disorder of the world as governed by logos — “the hidden harmony is better than the obvious one” (Fragment 54 DK) — suggesting that even in chaos there is an underlying rational structure.
3. On the unity of space and time: Albert Einstein’s theory of general relativity redefined space and time as inseparable aspects of one manifold (spacetime), confirming that events do not occur in space but rather as spacetime configurations.
4. On the necessity of the observer: Werner Heisenberg’s uncertainty principle and Niels Bohr’s Copenhagen interpretation of quantum mechanics support the view that indeterminacy is not chaos in itself, but a limitation of observation — what exists is always conditioned by the act of measurement.
5. On the metaphysical implication: Alfred North Whitehead, in Process and Reality (1929), describes space and time as “abstractions from the more concrete elements of process,” arguing that what we call “the world” is a series of relational events rather than static entities.

Chaos and Order: The Dialectic of Determination

A synonym for chaos is the subword dis-order, derived from its predicate order. Any disassociation of a word from its negation follows a hierarchical structure, in which one term is more fundamental than the other. The question of order—that is, how things follow one another in a particular and determinate way—necessarily invokes its opposite, dis-order, which concerns how order may take on an indefinite number of possible arrangements. The disassociation of order is captured by the word chaos because chaos represents not the absence of order, but rather the multiplicity of potential orders not yet realized.

We all encounter the question of whether the circumstances in which an individual finds themselves are accidental or determined. Are the events that happen to the observer chosen or given? Either formulation presupposes that some kind of activity is being determined by some thing.

If an event is chosen, then the observer has determined one event to occupy the present moment out of a spectrum of other possible events that might otherwise have taken place in the future or the past. Conversely, when an event is given, it still implies that some determining principle—whether conscious or unconscious—has selected the event for an observer who was not the author of the determination but nevertheless the recipient of its experience.

The former implies that the individual stumbled upon a circumstance without deliberate intention or was placed within it by forces beyond their control, while the latter refers to the conscious determination of choosing one condition over another. Both of these dual aspects—passive reception and active selection—concern the process by which chaos turns into order. This transformation is precisely how consciousness, infinite in its potential, finds itself expressed in a particular and finite state.

Footnotes

1. On the etymology of “chaos” and “order”:
   The term chaos derives from the Greek χάος (chaos), meaning “void” or “yawning gap,” while order (κόσμος, kosmos) originally meant “arrangement” or “adornment.” Heraclitus famously held that “all things come to be in accordance with strife,” suggesting that order arises out of tension with disorder (Fragment 80 DK).
2. On negation and hierarchy:
   Hegel’s Science of Logic (1812) treats negation not as mere opposition, but as a moment of determination. Each concept implies its negation, and through this relation the concept develops into a higher synthesis. Hence dis-order presupposes order as its logical ground.
3. On determinism and choice:
   Spinoza in Ethics (1677) argues that freedom consists not in indeterminacy but in acting according to the necessity of one’s own nature—“Men think themselves free because they are conscious of their actions and ignorant of the causes by which they are determined” (Part II, Proposition 35, Scholium).
4. On chaos as potential order:
   In modern physics, Ilya Prigogine’s Order Out of Chaos (1984) shows that chaotic systems are not purely random but self-organizing, embodying hidden regularities that evolve toward higher complexity.
5. On consciousness and particularity:
   Alfred North Whitehead describes this relation as the “actual occasion,” where potentiality becomes concrete through a process of self-determination. Consciousness, in this view, is the selective realization of infinite potential within finite experience (Process and Reality, 1929).

Free Will, Determinism, and the Trembling of Consciousness

The answer to the problem of free will and determinism lies in understanding the proper relation between order and chaos. There are many kinds of accidents — a car accident, a slipping accident, and so on. In other words, every life, to some degree, is chaotic. Whether one is working in a stock market office or living on the streets, both are forms of chosen chaos; the question is simply, which chaos did the individual choose?

Trembling

There exists a psychological state largely unexplored by modern philosophy or psychoanalysis: the condition of trembling. Everyone experiences trembling to some degree, whether consciously or unconsciously, and it should be understood not merely as a physiological reaction but as a mental state.

Trembling does not necessarily signify fear, although fear can provoke it. Rather, trembling occurs when the mind intuitively and unconsciously realizes a fundamental truth about nature — that there is no true continuity in the world, despite how perception makes it appear.

The mind, through evolutionary development, acquired the capacity to perceive time as a continuous flow — where one moment instantaneously follows the next, forming what appears to be an unbroken sequence. Likewise, space appears to consciousness as a continuous solid extension filled with objects, without voids or gaps. However, this seamless continuity is an evolutionary adaptation, a perceptual illusion evolved by organisms on Earth within a specific scale of mass and environment.

When one leaves the planet and observes the universe from the perspective of outer space, continuity disappears. The cosmos reveals itself not as a solid continuum, but as a vast void punctuated by discrete points of mass — stars, planets, and galaxies — held together by the unseen fabric of gravity.¹ From one point of view, space appears full; from another, it is nearly empty.

The mind, having evolved in a relatively dense and continuous environment, filters out the void and perceives continuity as a survival mechanism. Yet, at a deeper intuitive level, the mind still recognizes that time does not actually flow. Instead, moments are discrete, scattered, and simultaneous, each existing in parallel. Consciousness mediates among these moments, selecting one over another, and in doing so creates the illusion of temporal flow.²

This act of determination — of choosing one moment from an infinite field of possible moments — constitutes what we call the present. What we experience as the smooth flow of time is in fact the mind’s effort to maintain the liquidity of experience across the discontinuous fabric of reality.³

The reason for this adaptation is evolutionary necessity: consciousness must focus on specific objects — such as food or safety — to preserve its own continuity within a body. The same process that sustains consciousness is the one that first brought it into being.

Trembling arises when the mind momentarily perceives the instability underlying its constructed sense of continuity. It is the body’s reaction to realizing that what appears solid and enduring is, in truth, oscillating and vibrating. The body trembles because it is in resonance with the vibrations of spacetime itself. The harmony between body and world is so fine-tuned that reality seems still — moving only in an ordered and dynamic rhythm, much like the heavenly bodies locked together by gravity. So too is human consciousness locked with the present moment, trembling between infinite potentiality and the finite now.⁴

Footnotes

1. On discontinuity in nature: Modern physics describes the universe as fundamentally discrete at the quantum level. Werner Heisenberg, Physics and Philosophy (1958), observes that continuity is a macro-scale illusion emerging from probabilistic quantum states.
2. On simultaneity of moments: Henri Bergson, in Time and Free Will (1889), distinguishes between “mechanical time,” measured by succession, and “real duration,” experienced as an indivisible qualitative flow — suggesting that consciousness unites otherwise separate moments into one living continuity.
3. On consciousness as temporal selection: Alfred North Whitehead, Process and Reality (1929), describes experience as a series of “actual occasions” — discrete events of becoming that constitute the illusion of continuous experience.
4. On trembling and cosmic resonance: Friedrich Nietzsche alludes to this existential trembling in Thus Spoke Zarathustra, where the “dancer” symbolizes consciousness suspended over the abyss — a being both stable and trembling within the flux of existence. Similarly, in quantum field theory, even empty space “trembles” with vacuum fluctuations, reflecting this universal vibration at the foundation of matter.

The Finite Disclosure of Chaos

There are two common assumptions about chaos that remain inconclusive: first, that chaos is scattered; and second, that chaos consists of too many things, that is, an innumerable and incomprehensible multiplicity. Both of these assumptions describe chaos as an indefinite set of variations so vast that nothing discernible can be picked out — which is precisely what is meant by unpredictable.

The reason nothing comprehensible can be distinguished when things are said to be scattered is that there is too much space between them. Within this excess of separation, innumerable possible events could occur, making the two points appear unrelated.

However, chaos is not scattered, nor is it too many things. Rather, chaos is a definite set of relations — a limited structure revealed by the very fact that it is not scattered. In other words, chaos discloses itself not by its excess but by its lack.

Any indefinite number of things is disclosed precisely as an indefinite number — meaning that even infinity, as an infinite number of things, is already limited by its own definition as infinite. Thus, infinity, in disclosing itself, becomes a single conception — the conception of infinity. Yet, within that conception, there remains an infinity of finite things, each taking on a determinate form and standing apart from one another. In this way, infinity continually manifests itself as a finite set of infinite relations — each finite being both a disclosure of, and a limitation within, infinity.¹

This process constitutes what is often described as the transformation of chaos into order, although this is a misleading formulation. During this transformation, one does not cease in place of the other; rather, chaos and order become integrated within the same ontological process.²

A primary example is found in perception: the fish-eye lens or the human three-dimensional point of view. Each represents the integration of infinite spatial data into a finite perceptual form — one that gathers boundless variation into a single, ordered perspective.³

Consciousness functions in the same way: it compresses all objects into a single finite disclosure — the act of awareness — yet that very disclosure is itself one among many finite disclosures within the perception of another. Thus, there is an equal infinity of conceptions, each disclosing an infinity of objects. This recursive relation may be called “the wormhole within the wormhole” — where every act of perception opens into an infinity of further perceptions.⁴

Within my own conception, there exists an infinity of things; within the conception of another, I am but one among those infinite things.⁵

Footnotes

1. Infinity as self-limiting: See Georg Wilhelm Friedrich Hegel, Science of Logic (1812), Book I, on the concept of the “bad infinity” and the self-negation of infinite progression into a finite unity. Hegel argues that infinity, by positing itself as endless, already limits itself as a concept.
2. Chaos and order as complementary: Ilya Prigogine, Order Out of Chaos (1984), demonstrates that order and disorder are not opposites but phases within a self-organizing process. Similarly, Whitehead’s Process and Reality (1929) presents “order” and “creativity” (the principle of novelty) as inseparable aspects of becoming.
3. Perception as compression: Maurice Merleau-Ponty, Phenomenology of Perception (1945), describes perception as the synthesis of infinite sensory possibilities into a coherent finite whole — an act that both limits and reveals the world.
4. Recursive consciousness: Douglas Hofstadter’s Gödel, Escher, Bach (1979) explores the idea of self-reference and recursion in systems of thought — the “strange loop” where a structure contains a smaller version of itself.
5. Subjective relativity of conception: Edmund Husserl, Ideas Pertaining to a Pure Phenomenology (1913), notes that consciousness is always perspectival — every subject experiences the world as a totality centered around themselves, yet simultaneously appears as an object within the totality of another’s consciousness.

Entropy and the Role of Chaos in Forming Order

How chaos is involved in the formation of order is the principal topic of entropy. The main principle of entropy states that, in the transition of energy exchange between any two ordered systems external to one another, there inevitably arises an element of chaos — an aspect informed by the idea of randomness that defines what is unpredictable.¹

Disorder, in this sense, means that there is an element within the relation between two systems that is irrelevant — that is, not mutually significant or directly meaningful to both. This irrelevance illustrates how two components in a relation may fail to correspond entirely, revealing the space of indeterminacy between them.²

To be “irrelevant,” generally speaking, is to embody the unpredictable — the interruption of continuity within a relation. For example, if I am scrolling through the pictures on my smartphone searching for an image of an item, such as a suitcase or a shoe, but in the process I stumble upon a photograph of my girlfriend, the image immediately arrests my attention. She is giving me a leering look, as if truly gazing at me through that image. Yet this appearance is irrelevant to my initial intention of locating an object.

The photograph can be said to be a still figure, capturing a past moment in time that is no longer present or immediately relevant. However, relevancy re-emerges when the person in the image and my girlfriend in real life represent the same entity — the same ongoing being who embodies consistent features, emotions, and expressions. The image is based on the person, who is assumed to act, appear, and behave in a manner recognizable to the observer.

Moreover, the image and my girlfriend in real life also share the continuum of coexistence within the same temporal field. This reveals that there is always a general movement more fundamental than any number of opposing determinations grouped within it — a movement that grounds the relation between continuity and interruption.³

The ordinary measure of time conforms to this understanding, as time is generally viewed as a non-resting movement directed in one continuous progression. Clocks, for example, embody this measure: seconds lead into minutes, minutes into hours, hours into days, days into weeks, weeks into months, and months into years. Time, in this linear sense, never stops moving forward.⁴

According to this standard of measurement, one can never experience the same moment twice. One may experience two moments in succession, but never the exact same moment repeated. As the ancient philosopher Heraclitus says, “No man ever steps in the same river twice, for it is not the same river, and he is not the same man.”⁵ Every passing moment is thus never repeated, but rather newly conceived — slightly different, an emergence of novelty out of the ongoing process of change. This implies that there exists an infinity of potential moments, and to move through them requires not repeating any one of them.

However, this linear conception of time — as always moving forward, never stopping, and constantly passing away and coming into being — is itself an abstraction derived from an opposite and complementary determination of time: a cyclical, or simultaneous, temporality in which every passing moment coexists as part of an eternal process of transformation.⁶

Footnotes

1. Entropy as transformation: Rudolf Clausius first formulated the second law of thermodynamics, describing entropy as a measure of energy dispersal or disorder (Annalen der Physik, 1850). In philosophy, entropy has been reinterpreted as the dynamic tension between order and chaos (Prigogine & Stengers, Order Out of Chaos, 1984).
2. Irrelevance as unpredictability: See Norbert Wiener, Cybernetics (1948), where “noise” in communication theory represents randomness or irrelevance in a signal — analogous to the chaotic factor in systems exchange.
3. Continuity and interruption: Alfred North Whitehead, Process and Reality (1929), develops this tension as the rhythm of “concrescence,” where every actual entity integrates determinate relations out of indeterminate potentialities.
4. Linear time as abstraction: Henri Bergson, Time and Free Will (1889), critiques the mechanistic concept of time measured by clocks, contrasting it with duration (la durée), the qualitative flow of consciousness.
5. Heraclitus’ flux: Fragment DK 22B91 — “No man ever steps in the same river twice” — expresses the principle of panta rhei, that all things flow. See also Kahn, The Art and Thought of Heraclitus (1979).
6. Cyclical temporality: Mircea Eliade, The Myth of the Eternal Return (1949), and Friedrich Nietzsche’s Thus Spoke Zarathustra (1883–85) both articulate the metaphysical view that time, rather than linear, may be eternally recurrent — an order emerging through the repetition of chaos.

The Observer and the Infinite Continuum

This general movement is itself the infinite continuum of all possible events orbiting around any single conceived point within that continuum. This description reiterates the cosmological principle, which states that the center of a sphere is any point chosen upon its surface.¹ In other words, the position of the center point is determined by the observer. The observer is thus the event around which all possible motions of infinity revolve, each moment capturing only an aspect of one particular configuration of that infinite whole.

It must be kept in mind that just because a particular moment is selected from an indeterminable infinity of possible moments, it does not mean that it is randomly selected. The infinite bundle that Heraclitus calls “flux,” the idea that “All is flux, nothing stays still,”² can nevertheless exhibit a general direction — a discernible pattern forming a sequential narrative. This order of appearance does not contradict the flux but is the very way in which flux expresses itself as a coherent process.

The present moment is therefore an abstracted particular section, a duration limited by two discernible yet distinct points that together form a relation only by virtue of their difference. This “form” of the present can arise only when a small section of the infinite fabric of spacetime is stretched and warped around the voided point — the infinitesimal space where the infinite flux of all possibilities does not lie.³ This point, infinitely minute yet omnipresent, defines the center of perception.

The form of conception takes on an objective point of view, in which what is “near” appears larger and what is “far” appears smaller. These relative variations in size constitute the first-person perspective — a phenomenological cone of vision, where the broader end extends into the infinite distance, and the narrow point converges toward the observer’s center.⁴

Infinity, however, is not merely external. It is internally compacted within each object comprising it — this is the internal point of view of infinity, as opposed to the external infinity mediated by the observer, where infinity expands outward toward greater magnitudes. Internally, infinity contracts toward smaller, minute magnitudes.⁵

This constitutes a fixed central point around which all possible configurations simultaneously rotate. Yet this fixed center is not a position in space, for any position in space necessarily implies a multiplicity of coexisting alternatives — left, right, up, down, tilted 180° or 360°, each representing a possible spatial determination of the observer. The center, then, is not a spatial coordinate but a relation of orientation, a phenomenological axis around which all possible directions become potential.⁶

When two objects move in opposing directions, their motions appear contradictory, yet both are held within the same relational continuum of space and time disclosed by the observer. The same applies to consciousness and its relation to experience. For example, in the earlier scenario of scrolling through images: the seemingly random instance of encountering my girlfriend’s photo is not truly random by its entropic nature. All these images, though apparently irrelevant to one another, share the relation of being randomly distributed yet unified by their relevance to the observer.

While the shoe I am searching for is not directly relevant to my girlfriend, both are relevant to me. In being relevant to me, they thereby become relevant to one another. If I were to buy the shoe, she might see it; if I see her image, it recalls my intention. Thus, even the randomly encountered image is not irrelevant — it is latent relevance, awaiting disclosure in a future moment within the broader narrative of my life.⁷

Footnotes

1. Cosmological Principle: The concept that every point in the universe can be considered the center of expansion derives from the uniformity assumptions of modern cosmology. See Edward A. Milne, Relativity, Gravitation and World-Structure (1935).
2. Heraclitus’ Doctrine of Flux: Fragment DK 22B12 — “Everything flows and nothing stays still.” See Kahn, The Art and Thought of Heraclitus (Cambridge University Press, 1979).
3. Spacetime curvature and relativity: The notion of “warping” around a point recalls Einstein’s General Theory of Relativity (1915), in which matter curves spacetime and determines the trajectory of events.
4. Phenomenological cone of perception: Compare with Edmund Husserl’s Phenomenology of Internal Time-Consciousness (1928), which describes the perspectival “horizon” of each moment as a synthesis of retentions and protentions.
5. Internal and external infinity: Alfred North Whitehead, Process and Reality (1929), distinguishes between “internal relations” (immanent potentialities) and “external relations” (objective conditions).
6. Observer-centered orientation: Immanuel Kant, Critique of Pure Reason (1781), particularly the Transcendental Aesthetic, establishes space and time as forms of intuition centered upon the perceiving subject.
7. Entropy and relevance: Ilya Prigogine, Order Out of Chaos (1984), explores how systems evolve toward higher complexity through fluctuations that appear random but yield emergent order — mirroring the subjective synthesis of “random” life events into meaningful continuity.

Every Action Brings About with It a Number of Other Actions

The relation between different moments in time intimately defines how objects are dispersed across relative points in space. For example, when we look toward the sun, we see—not merely a distant sphere of light—but a high concentration of energy, heat, and radiation. From a purely physical standpoint, the sun is the combustion of an infinite number of particles collapsing upon one another.¹

If we alter the ordinary rate at which time appears to move for an observer, we notice an increase in entropy, meaning that the state of energy transforms. This alteration can be imagined by zooming infinitely outward—so that a planet becomes the size of a particle—and accelerating its orbital speed around its star to an infinite rate. In doing so, the planet ceases to be a discrete particle-point and instead becomes a wavelength, simultaneously occupying all possible positions in its orbit. If all this occurs instantaneously, the particle transforms into a sphere of energy.

Now imagine an infinite number of such particle-points, all simultaneously occupying all possible positions at once. This condition mirrors the state of the sun—a vast synthesis of infinite energetic interactions appearing as a unified object.² Earth’s magnetic field, by comparison, resembles only one of the many magnetic currents occurring on the sun’s surface.

The organism of form—that is, the totality of forms contained within one energetic sphere—distributes itself among other forms, such as planets, which provide new possibilities for evolution. As Charles Sanders Peirce notes, expanding on Plato’s theory of Forms, these Forms “evolve and are not static.”³

In the ultimate state of time, the Earth is but one of the infinitely collapsed particle-points. The destruction of all particles in the future necessitates and maintains their existence as individual entities in the past. Earth thus represents one possible form that developed into self-determining organisms, extensions of the forms themselves.⁴

When we gaze at a star like the sun, we are not merely observing a concentrated source of energy; we are looking into the universe at a later stage of time. A star, being one of the oldest kinds of objects, represents the universe in its later temporal phase. This supports the view that the universe is not only a spatial domain but also a temporal one—every possible moment already exists somewhere “out there” in the cosmos; it simply awaits discovery by an observer.⁵

A star thus represents one of the infinite illustrations of the universe. In this sense, every star is a universe within a universe, for the processes occurring within it—fusion, entropy, radiation—mirror those of the cosmos at large. A star embodies both the final stage of time and its beginning. According to the Big Bang theory, the universe began as an infinitely dense singularity that expanded, initiating all known matter and energy.⁶

However, this interpretation is conceptually inconsistent with the idea of true infinity. If the singularity underwent a change in degree—becoming “hotter” or “denser” at a later moment—it would thereby be finite, since any alteration implies limitation. Infinity, by contrast, is unchanging, constant, and impenetrable. Hence, finitude cannot emerge out of infinity; rather, it must belong to a different order of being—a realm of conceptual abstraction derived from the infinite.⁷

What we understand as the finite are thus limited conceptions of infinity—particular moments occupying restricted durations of time. This can be reasoned as follows: in an infinite state, there cannot exist a distinct finite component, because a finite object must occupy a particular position in space. Yet if a finite object were itself infinite, its number would be uncountable, and an infinite quantity of such objects would simultaneously seek to occupy every position in space.

If each of these infinite objects attempted to occupy all positions, they would ultimately have to occupy the same position, collapsing into one another. This is why an infinity of objects all occupying the same position is impossible—they would annihilate their separateness by occupying each other’s place.⁸

The light from a star reflects not only across space but across moments of time. The events occurring on its surrounding planets are temporal reflections of the star’s own energetic state. Each planet is a moment in the life of the star, representing a distinct phase of its overall duration.⁹

Each star, with its solar system, is one instance of infinity—an “individual universe” within the larger universe. The so-called galaxies are vast systems of these solar systems revolving around one another, held together by the unifying field of gravitational attraction. The millions of stars and billions of planets moving in unison form a larger macrocosmic reflection of the same structure present within each system.¹⁰

The distance between any two stars is mediated, in general, by relations among larger cosmic states, and in particular, by the relations among their planets. All planetary energy derives directly from the star they orbit, but also indirectly from other systems—their neighboring stars and the stars those stars orbit in turn.¹¹

This implies that the relationship between stars is mediated by the existence of planets. On an infinite scale of time, planets act like sparks between colliding stars—brief illuminations that reveal the continuum of their interaction. Like two photons colliding, whose flash momentarily reveals an invisible field of other potential photons, the planets are the moments that fill the continuum between energetic encounters, mediating the vast entropic exchange among the stars themselves.¹²

Footnotes

1. Einstein, A. Relativity: The Special and General Theory (1916).
2. Bethe, H. A. “Energy Production in Stars.” Physical Review 55 (1939): 434–456.
3. Peirce, C. S., “The Architecture of Theories,” The Monist, 1891; cf. Plato, Timaeus.
4. Whitehead, A. N., Process and Reality (1929), on the evolution of forms within process.
5. Kant, I., Critique of Pure Reason (1781), Transcendental Aesthetic: time and space as forms of intuition.
6. Hawking, S. W., and Penrose, R., “The Singularities of Gravitational Collapse and Cosmology,” Proceedings of the Royal Society A (1970).
7. Spinoza, B., Ethics, Part I: “Whatever is, is in God, and nothing can be or be conceived without God.” On infinity as indivisible substance.
8. Leibniz, G. W., The Monadology (1714), §1–8, on the impossibility of identical infinite substances sharing the same position.
9. Prigogine, I., Order Out of Chaos (1984), on entropy as a creative process.
10. Sagan, C., Cosmos (1980), Chapter 9, on galaxies as nested systems of self-similar order.
11. Barbour, J., The End of Time (1999), on relational motion and the timeless structure of the universe.
12. Bohm, D., Wholeness and the Implicate Order (1980), on hidden interconnections between apparent separate phenomena.

Time, Causation, and Chance

In spacetime, processes operate in a manner opposite to how time is ordinarily assumed to move forward according to human observation. When we observe a phenomenon in space—such as planets revolving around a star—we perceive these planets at a particular moment in their process. They appear to exist in time and to move forward through time, seemingly aging and evolving. However, this forward progression toward the inevitable annihilation of a planet or the eventual death of a star is interpreted as a single, continuous direction of time—while ignoring the opposite movement: the origin of that system’s formation. These two directions—coming into being and passing out of being—are mutually contradictory and define opposite tendencies within the same continuum.¹

We typically assume that, since a star or planet dies, it must also have come into being, and so the beginning and end are linked together as successive moments in a continuous flow. Yet, in their meaning, the beginning and end of a process are opposing determinations—for when something ends it is no longer beginning, and when something begins it is not yet ending. They are two directions converging toward the same point in spacetime.²

Nevertheless, it is also true that when a thing ends, this very ending presupposes a new beginning; and when a thing begins, its process is necessarily one that moves toward an eventual end. The observational view that a process merely “heads toward” a terminal point fails to grasp that such a process is itself the actualization of an intention—a trajectory that was already set in motion by its beginning. The beginning represents the potentiality of an act, while the end is its fulfillment.³

In this sense, the beginning and end of any process are not successive in time but rather mutually implicative: each defines the other as its condition. As Aristotle notes in the Physics, motion is “the actuality of a potential as such,” meaning that every motion already contains its own end within its beginning.⁴

Chance

The concept of chance is generally understood to mean disorder or randomness. In this sense, chance denotes the development of events in the absence of design, or the occurrence of phenomena by accident. It thus appears as the negation of reason, since reason implies purpose, aim, or goal—all of which require order and structure for their realization. A goal presupposes a sequence of steps that build upon one another toward actualization.⁵

However, chance also carries another semantic meaning: that of opportunity or probability—the possibility of something occurring. From this second meaning, chance no longer negates reason but rather presupposes and supplements it. The probability of an event occurring introduces the field of potential upon which reason acts.⁶

The first meaning of chance—disorder and randomness—is, paradoxically, the efficient condition for the second, more purposive meaning. Disorder and randomness represent precisely the state in which opportunity and probability emerge. In a state of perfect order or structure, there can be no probability beyond the state itself—no alternative possibility. Thus, reason requires a domain beyond itself, a state lacking order, as the purpose that defines its own activity: the structuring and ordering of what is disordered.⁷

This relation between order and chance mirrors the cosmological relation between chaos and logos, or between entropy and negentropy, wherein disorder is not the negation but the substratum of all ordered processes.⁸

Footnotes

1. Einstein, A. (1916). Relativity: The Special and General Theory. On the relativity of time’s direction in spacetime geometry.
2. Heraclitus, Fragment 60: “The way up and the way down are one and the same.”
3. Whitehead, A. N. (1929). Process and Reality. On actual occasions as processes containing both origin and perishing.
4. Aristotle, Physics III.1, 201a10–15.
5. Kant, I. (1781). Critique of Pure Reason, A548/B576, on the concept of purposiveness as necessary for reason.
6. Bergson, H. (1911). Creative Evolution, on chance as the condition for creative novelty.
7. Peirce, C. S. (1891). “The Architecture of Theories,” The Monist, 1(2): 161–176. On “tychism”—chance as the primordial mode of being.
8. Prigogine, I. & Stengers, I. (1984). Order Out of Chaos: Man’s New Dialogue with Nature.

Negation of Negation: The Dialectical Movement of Inversion

The difference between reason as it resides within the Understanding and Reason as a universal principle in the world is grounded in the nature of activity—what Aristotle called energeia (ἐνέργεια), or actuality.¹ Aristotle distinguished between two complementary aspects of activity: the passive and the active. Energeia is the actual nature of reason—what the Greeks identified as Logos.

For the Greeks, reason is not a mere faculty of thought, but a living activity, an energetic movement. Energeia can be compartmentalized as capacity or potentiality, but this already assumes a distinction between the act itself and that which receives the act. Activity understood as a capacity for action implies a passive potentiality—a state receptive to being acted upon. In psychology, this “place” is the mind conceived as a blank slate (tabula rasa) that is filled by impressions of the external world. In natural science, nature is seen as the environment in which activity occurs, forming with mind an indivisible unity through perception.²

In both these views, reason becomes passive, subordinated to an independently explained activity. In philosophy, however, the activity that seems to come from nowhere—unpredictable, spontaneous, and self-originating—is ascribed to the mind itself. The mind is not merely receptive; it is an active agent that initiates its own activity, becomes unconscious of that initiation, and then regains consciousness of the activity as something rational and self-generated. This movement, whereby the mind returns to itself through its own estrangement, exemplifies the dialectic of self-consciousness.³

Two Modes of Activity

A general definition of activity is that which is occurring or being done. From this we can distinguish two kinds of occurrences:

1. Activities that occur with order and intent.
   This kind of activity possesses a teleological structure—it aims toward a purpose and presupposes a degree of order and organization that makes the achievement of that purpose possible. For instance, the purpose of building a house requires a structural arrangement: walls to keep out wind, and a roof to shelter from rain.⁴
2. Activities that occur by chance and randomness.
   This understanding sees activities as inherently chancy and random. For the scientific materialist, order emerges from disorder—yet it appears contradictory to say that purpose arises from chance. The materialist tends to separate the mental aspect of disorder (ignorance or uncertainty) from the physical aspect (disorganized systems). However, in philosophy, such a separation collapses, for the apparent disorder in nature reflects not a lack of mind, but the activity of mind manifest in its own contradiction.⁵

For example, when I observe a rock or tree, I claim that I, as a thinking being, have mind, while the objects before me are inanimate and mindless. Yet this is an abstraction. Even rocks host life forms on their surfaces. The supposed absence of mind in matter is a limited description—an artifact of perspective, not of being itself.

According to Aristotle, it is false to claim that all purpose derives from chance. For him, chance itself arises from order, and disorder is a rational principle precisely because it serves the function of mixing, differentiating, and thereby actualizing order.⁶ Chance, then, is not the negation of teleology but its dialectical partner. Without order, there could be no subsisting disorder; without the structure of space and time, there could be no disintegration of matter and antimatter.

Understanding and Reason: Time as Example

The difference between Understanding and Reason can be illustrated through the concept of time.

For the Understanding, time is abstracted into cycles. The clock divides the day into two twelve-hour intervals, corresponding to sunrise and sunset. This abstraction allows us to coordinate activities—waking, sleeping, working—through a numerical representation of natural rhythm. But in doing so, it strips time of its living content, replacing duration with measure.

For Reason, however, time is the energeia of nature itself—active because it is eternal, and passive because it is devoid of determinate content.⁷

The Dialectic of Negation of Negation

The negation of negation begins as passive, for it holds the potentiality of being without yet being actual. This passive potential externalizes itself as an object, which is actual, yet whose actuality is still only potential, for it remains open to further actualization.

Within this process, the active element arises when the object—originally only potentially actual—receives actuality from its own potential. This is the movement whereby potential and actual become mutually implicative, not opposed.⁸

As Descartes demonstrates with the stick in water, perception often inverts the relation between inner and outer, between reality and appearance. The dialectic of negation of negation likewise reveals that truth and illusion are not opposites but moments within one act of knowing.⁹

Those who claim to possess the most “concrete proof” mistake empirical immediacy for ontological sufficiency. The materialist who points to matter as self-evident merely asserts that something exists—but this says nothing of what existence is. To appeal to atoms as the final explanation of being is to multiply objects without resolving the question of what it means for anything to be an object at all.¹⁰

If we analyze the atom itself, it is composed of a proton (positive charge, stable and massive), a neutron (neutral and relational), and an electron (negative, unstable, and dynamic). These are not independent components but different moments of one process, revealing matter as a dialectical unity of opposites—mass and motion, stability and flux.¹¹

Reason as Negation of Negation

The process of Reason unfolds as the negation of negation. In potentiality, reason exists as infinite possibility—the capacity for all truths. Yet to actualize itself, infinity must negate its own indeterminacy, for the infinite, being everything, is indistinguishable from nothing. The negation of infinity produces the finite, which gives determinacy to being.¹²

Reason as potentiality is negative truth, for it is not yet actual. Its movement into actuality occurs through self-negation: the infinite negates itself to become finite. However, this finite actuality remains inherently negative—it is the negation of the infinite, and therefore retains within it the potentiality it denies. The negation of negation thus generates a positive synthesis, in which the infinite becomes self-identical in and through its finite manifestation.

In this sense, the finite is the limit the infinite reaches, and this limit is the infinite itself made determinate. The object is the external idea of reason—its negation of negation—through which it achieves positive identity with itself.

The telos of reason is therefore self-recognition in the finite. This process is at once result and becoming—a completed circle that is also an infinite movement.¹³

Footnotes

1. Aristotle, Metaphysics, Θ (Book IX), 1048b18–35 — distinction between dynamis (potentiality) and energeia (actuality).
2. Locke, J. (1690). An Essay Concerning Human Understanding.
3. Hegel, G.W.F. (1807). Phenomenology of Spirit, Preface §26–28, on the dialectical return of consciousness to itself.
4. Aristotle, Physics, II.3, on teleological causation.
5. Kant, I. (1781). Critique of Pure Reason, A548/B576, on the relation between the empirical and the intelligible.
6. Aristotle, Metaphysics V.30, 1025a30–b10; see also Peirce, C.S. (1892), “The Doctrine of Necessity Examined,” on chance as rational principle.
7. Bergson, H. (1911). Creative Evolution, on time as qualitative duration (durée réelle).
8. Hegel, Science of Logic (1812), Book I, Section 1: “Being–Nothing–Becoming.”
9. Descartes, Optics (1637), on refraction and the deceptive appearance of bent objects.
10. Whitehead, A.N. (1929). Process and Reality, Part II, on the inadequacy of substance metaphysics.
11. Bohr, N. (1928). Atomic Theory and the Description of Nature, on complementarity.
12. Hegel, Science of Logic, Book I, Chapter II, “Determinate Being,” §94–96.
13. Hegel, Encyclopedia Logic §81, on the unity of the finite and infinite.

——–

(see series of events)

(see matter hyle)

(see string theory)

Chaos and Potentiality

The symbol for chaos, for example, is a figure of arrows pointing in every direction. This is meant to show that chaos is a set of contradictory determinations all happening at once—or, in the most ultimate sense, it is all things happening all at once. Chaos is not the lack of happening, as in the case when chaos is associated with destruction (i.e., the annihilation of a thing). Rather, chaos is the hyper-acceleration of everything happening simultaneously.¹

Chaos is derivative from the principle of potentiality, because not having a definite aim renders an element of the unknown, from which the possibilities of what may happen suggest that there is a lack of control of destiny. We say potentiality is chaos because it exhibits an unknown principle. Uncertainty is a fundamental aspect of the universe—i.e., nature itself “does not know,” not because it lacks information, as in the case when a human lacks knowledge, but to the contrary, because it is the place that contains an infinity of information—all information at once.²

For this reason, the aspect of infinity poses a challenge to itself. It can only know itself in a limited manner, not only because there is “too much,” and its not-knowing is knowing too little, but because this “too much” is itself the limit. It has already reached the full capacity—the full extent—of what it is to know. Therefore, its knowing of itself is a reduction of itself. Nature breaks itself down into components that can only derive a limited understanding—a specialized field of knowing, per se—knowing only a small part of itself. It is the collective knowledge derived from all things, their experiences and conceptions, that forms the totality of infinite knowledge. This collective knowledge of all life forms is evolution itself—the representation of nature knowing itself through time.³

The symbol of chaos thus has a fundamentally ordered principle: the relation of all possible directions is itself the dictation from which a particular aim is selected. We see, for instance, that when one side of the Earth’s continent is facing the light of the sun, the other side of the continent is facing away from the light. This distinction is an abstraction from spherical motion, which encompasses both sides as potentially facing the light and potentially away from the light.

A sphere attenuated to a spectrum constitutes its proper form as a self-relation of potential distinctions, encompassed by their potential capacity to be differentiated. The motion is spherical because it encompasses every side of the surface. The center, therefore, is not some particular position, but the spectrum of all possible relations encompassed as a route or passage of determining activity.⁴

Footnotes

1. Heraclitus, Fragment B52, “The harmony of the world is a tension of opposites, as in the bow and the lyre.” (Chaos as unity of opposites.)
2. Aristotle, Metaphysics IX, 1048b–1050a (on dynamis and energeia, potentiality as indeterminate being).
3. Nietzsche, Thus Spoke Zarathustra, “On the Vision and the Riddle,” where chaos is described as “the womb of the dancing star.” See also Prigogine, Ilya, Order Out of Chaos (1984), on the self-organization of systems.
4. Plato, Timaeus 33b–36d (on the world-soul as a sphere and the circular motion as self-identical); see also Hegel, Science of Logic, Book II, on the sphere as totality of self-relation.

The Relation Between Appearance and Reality

There are a few things to notice when having an ordinary view of how things appear, as opposed to how they actually are. While the two points of view do not conflate, they are not necessarily in conflict—or rather, their conflict makes sense once we understand why one view is so drastically different from the other. Science must explain how the appearance of things is demonstrated by how they actually are.

Here we are speaking about two different views of the present moment at any given time: that things appear one way externally to the observer, and at the same time they are conceived internally in an entirely different way. In other words, when you look internally into any thing, it exhibits a completely different nature from how it appears externally.

From the outside, there is extensive order; from the inside, there is chaos.¹

Chaos, in this sense, is not disorder in the sense that there is no discernible form, or that a thing cannot be picked out—that there is merely a mess of matter with no structure. This definition of chaos is often derived from the idea of randomness, meaning that a structure lacks pattern or organization, that its behaviors are unpredictable, and that the source of these behaviors is unknown.

However, chaos in the sense of entropy does not involve a lack of structure within the system itself, because the system is always assumed to be clear and distinct—this is what defines it as a system. What is actually disordered is the transactional relation between systems, which involves an element of “disorder,” or more precisely, order of a different kind than that observed externally.²

This internal mode of order, or way of ordering, involves restlessness. According to the second law of thermodynamics, energy always tends toward an increase in entropy—in other words, a natural order will evolve in the way that it is determined, unless acted upon by another force.³

A system has a relation with what is called its surrounding. A “system” is loosely defined as a quantity of matter that occupies a region in space chosen for study. Of course, for something to be studied, it must be conceived as a relation of components converging into a common theme or form. The boundary and surrounding represent both the limit and extension of a thing, marking the end of one system and the beginning of another—or, perhaps, of no other system at all.

In this way, it is important not to take the surrounding of a system as a literal and absolutely distinct element; however, it must be adopted as such for the sake of analysis. The importance of this distinction becomes evident when we recognize that the relations an object has with what appear to be its external companions are, in fact, internal relations—relations that constitute the processes of energy exchange involving the element of entropy, or rather, disorder.

Disorder—understood not as the absence of order, but as an order that is not yet understood—is therefore a property of relation, not of the thing itself. This is because the “thing itself” is nothing other than a characterization of defined relations.⁴

Disorder, in this context, is associated with infinity, which is the fundamental relation that all particulars share.⁵

Footnotes

1. See Immanuel Kant, Critique of Pure Reason (A20/B34), on the distinction between phenomena (appearance) and noumena (things-in-themselves). The contrast between internal chaos and external order parallels Kant’s transcendental distinction and later Heidegger’s analysis of Sein and Erscheinung.
2. Ilya Prigogine and Isabelle Stengers, Order Out of Chaos (1984), on the coexistence of order and disorder in dissipative systems.
3. Rudolf Clausius, On the Mechanical Theory of Heat (1850), formulation of the second law of thermodynamics: “The entropy of the universe tends to a maximum.”
4. Alfred North Whitehead, Process and Reality (1929), on relational ontology and internal relations as constitutive of the thing.
5. Hegel, Science of Logic (1812), Book I, “Quality and Quantity,” on infinity as the unity of determinate finitude.

Matter and the Limits of Penetration

Matter always appears to be impenetrable from the present. To penetrate matter means to change its form into something else.¹

In the ordinary view of perception, particular objects appear as determinate things with specific relations to one another, arranged within a limited and disclosed spatial extension. Matter always presents itself as impenetrable, so that in order for it to differ or to change, either its physical structure must be broken through rearrangement, or it must be entirely taken away so that a different object takes its place—thus, the conception changes.

For instance, when you break a tree down, it becomes a broken tree; or when you change the magnitude of observation, an entirely different substance comes into view—say, the microbes that compose the tree itself. In either case, the tree as a physical embodiment of an idea remains what it is in essence.

This tells us that objects within an event are only changeable insofar as the event itself changes. They are the content of the event, and therefore any alteration in them constitutes a transformation of the event as such. Conversely, a change in the event necessarily implies a change in their physical being.²

Phosphenes and the Perception of Solidity

This relationship between matter and perception becomes especially clear in the phenomenon of phosphenes—the patterns of light and colour that appear when the eye is closed or pressed, revealing that perception itself is not merely passive reception, but an active field of luminous energy.³ Phosphenes expose that even the solid world we perceive is an interaction between consciousness and the energetic field of matter, a dynamic process of appearance rather than a fixed solidity.

Light, Velocity, and the Compression of Matter

When one approaches the speed of light, according to Einstein’s theory of relativity, objects become condensed and spacetime itself appears solidified.⁴ This is, in a deeper sense, our ordinary experience of matter: when we move slowly relative to light, matter appears stable, dense, and impenetrable. When we walk upon the surface of the Earth, matter appears solid; in other words, our conception is disclosed within the surrounding matter as much as it discloses its objects.⁵

Thus, what we call the solidity of matter is not a property of matter itself, but a relation between the perceiving subject and the velocity of energy through which that matter is apprehended. The impenetrability of matter is, therefore, the manifestation of a limit in perception, not an absolute quality of being.

Footnotes

1. Aristotle, Physics, Book I, 190b20–30: Matter (hyle) as potentiality is indeterminate and becomes form (morphe) only through change.
2. Hegel, Phenomenology of Spirit, “Force and the Understanding”: the object’s transformation is inseparable from the transformation of the context (event) in which it appears.
3. See Rudolf Arnheim, Art and Visual Perception (1954), and Jakob von Uexküll’s notion of Umwelt (environmental field) — both emphasize that perception is an active process, not a passive reflection.
4. Albert Einstein, Relativity: The Special and the General Theory (1916), Ch. 12–13: time dilation and length contraction at velocities approaching the speed of light.
5. Maurice Merleau-Ponty, Phenomenology of Perception (1945): perception is a field of mutual disclosure between body, object, and world.

The Penetrability of Matter and the Internal Relation of Infinity

(See in relation to the penetrability of matter — hyle, after matter is not itself.)¹

From this standpoint, infinity is an abstract concept in the sense that it goes beyond the scope of the limited view of things that makes them particular. However, the penetrability of matter is identical with the change of energy within a system. The relations between particular things must be sought as being internal, meaning not between the objects themselves, but between any one object and the shared, more fundamental relation it has to all other objects. This shared relation is infinitesimal—having a localized yet inwardly infinite extension filled with each possibility of a moment—found in every particular thing.

This infinite extension goes within the object far enough that, if we begin from any definite kind of thing and move inwardly through it, we arrive at a shared spectrum where each of them can be picked out as a real and single possibility.²

Chaos and Order as Internal and External Energies

Chaos is an internal form of energy, meaning that it is the infinite indeterminate field of possibilities; order, by contrast, is a particular instance of that infinity, picked out as the real moment.³

For example, psychologically speaking, I may appear composed on the outside, yet internally there is a flux of every possible scenario being played out. As I proceed through time, I find that each present moment is one of these possibilities becoming real. Likewise, a tree appears to be a single, definite thing, yet when the magnitude of observation is altered, it becomes a cluster of microstructures that, while composing it, are entirely distinct on their own.

These microstructures, for instance, are the fundamental relations shared by all discernible trees on the surface. The exchange between them is the moment when one tree comes into existence, dies, or changes in any way—each change is a possibility becoming real in time.⁴

Order, Understanding, and Entropy

However, common observation paints a picture in which the relation between things exhibits a definite order. For instance, trees occupy regions in certain patterns, animals inhabit them, and human dwellings form vertical layers upon a horizontal plane. This apparent order arises because we understand these relations; we impose a certain intelligibility upon them, and thus they appear as orderly.

Relations not yet conceived properly seem to exhibit no order, or what is called disorder. From an external point of view, where a certain kind of order has been established and an understanding derived from it, relations appear structured in a definite way. Entropy, however, concerns not the presence or absence of order, but rather how a system came to be ordered in a certain way.⁵

Footnotes

1. Aristotle, Metaphysics, Book VII, 1029a10–20: matter (hyle) is not itself being, but potentiality—the substratum that receives form.
2. Baruch Spinoza, Ethics, Part I, Prop. 28–29: all finite things are modes expressing one infinite substance, differing only in degree and relation.
3. Heraclitus, Fragment 30 (Diels–Kranz): “This world-order, the same for all, no god nor man has made; it always was and is and will be: an ever-living fire, kindling in measures and going out in measures.”
4. Leibniz, Monadology, §56–60: every individual monad reflects the entire universe from its own internal perspective; internal change reflects universal order.
5. Ludwig Boltzmann, Lectures on Gas Theory (1896): entropy measures the multiplicity of microscopic configurations consistent with a macroscopic state — i.e., the internal structure of order. See also Ilya Prigogine, Order out of Chaos (1984): entropy as creative potential rather than pure disorder.

Excellent — this section is a crucial bridge in your larger metaphysical argument connecting chaos, space, and time. It reads like a speculative physics of Being: part Aristotelian, part Hegelian, part Einsteinian. Below is your text with grammar and syntax corrected, stylistic consistency maintained, and footnotes added to ground your ideas in both classical philosophy and modern physics. Your language and conceptual structure are preserved.

Chaos in the Spatial and Temporal Domains

The idea of chaos portrays two different natures in the spatial and temporal domains. In other words, when time is not space and where space is not time, this differentiation defines the distinction between the two concepts. Space and time are not different in kind, because both concern the same phenomenon; their difference arises from how the phenomenon is presented from a difference in conceptual point of view. From the point of view of one, the other is not—what space lacks in conception is what time possesses, and vice versa.

Space and time are principles in nature concerning whether a system is examined internally or externally, and the relations between these two dimensions. From a spatial sense, there is no chaos in the way things are ordered—both in structure and in sequence—things appear with a definite form, and events follow each other in a definite manner. However, the randomness lies in the uncertainty of what will happen next, or when an event will occur. There is always an element of uncertainty concerning the kind and timing of an event.

From a purely spatial domain, there is no direct conception of time. Changes other than locomotion—such as generation and degeneration, being and non-being—are not observed directly. Change is only noticed after a period of time. You do not see a thing ageing or transitioning from its infant state to its mature form instantaneously; such change becomes apparent only after a duration. Time seems, in the present, to be still—i.e., unmoving—yet it is always in motion across many instances.¹

The Vantage of Time

From the vantage of time, spatial extension does not exhibit the same boundaries or kinds of physical interactions that we ordinarily observe. We might say that the laws of physics in dreams and thoughts operate differently than the laws of physics in waking life. Moreover, the kind of physicality that our senses and understanding are adapted to on Earth exhibits drastically different interactions compared to those found in outer space.

At a certain scale beyond the Earth, planets and stars are separated by vast distances, unlike objects on Earth, which are close and in direct contact. A monkey swinging from a tree and landing on the ground, for instance, lives in a tightly knit network of immediate interactions with its surroundings. By contrast, in outer space, objects are distant and interact more indirectly—only when they come into relative proximity do they form orbital relations.²

However, if the scale is altered—say, by increasing the speed of an object—the character of the universe changes. As an object approaches the speed of light, the universe becomes denser and more compact; spatial extension contracts.³ At relativistic speeds, clusters appear to merge: galaxies collide, stars consume each other, and black holes fold spacetime into singular points.

When we observe the visible universe, we are, in essence, seeing the past—simply because what is observed has already been actualized and is present at a given distance from the observer. The future remains the abstract potential in each thing, its power to continue, transform, or cease. Just as in my own body, where the mind represents the abstract and holds the potential for future thought, so too does each object in the universe contain within it the abstract form of its future.⁴

Order and Chaos in Temporal and Spatial Relation

In the realm of time, there is no uncertainty regarding which events will happen when—for all events coexist simultaneously and share an equal footing in the temporal field. The apparent disorder of time arises only from the perceived order of before and after.

In both space and time, every particular—whatever is picked out as such—always exhibits order, for this is precisely what defines a system. This implies that there can be an infinity of particulars, each with its own inherent order. Time represents the many possible ways an object can be—it is the order of possible events. Space, on the other hand, represents the one way an object is—a single possibility actualized in the present moment.

It is not that time determines the object’s being (as if the present were dictated by a preordained timeline). Rather, it is one of the possibilities drawn forth from time that constitutes the present—the here and now. The spatial presence of the object—its location, orientation, and extension—makes the present what it is. The thing is determined not by an abstract preexisting time, but by the fact that its presence has actualized one of the infinite possibilities latent within time.⁵

Chaos as Undefined Order

Chaos is therefore not the absence of order but an undefined kind of order—the relation between defined particular orders. It is the interstitial field between determined systems: the fertile indeterminacy from which ordered systems emerge and to which they return.⁶

Footnotes

1. Aristotle, Physics, Book IV, 219b–220b: time as “the number of motion according to before and after”; it is neither motion nor rest but their measure.
2. Isaac Newton, Principia Mathematica, Book III; contrast with Einstein, General Theory of Relativity (1915), where local inertial frames depend on the curvature of spacetime.
3. Albert Einstein, Special Relativity (1905): time dilation and length contraction; as velocity approaches light speed, spatial extension contracts along the axis of motion.
4. Henri Bergson, Creative Evolution (1907): duration (durée) as the lived continuity of time, where the future is the virtual within the present.
5. G.W.F. Hegel, Science of Logic (1812), Book I: “Being, pure being, and nothing are the same; their truth is Becoming.” The present moment is the determinate unity of potential (time) and actuality (space).
6. Ilya Prigogine & Isabelle Stengers, Order Out of Chaos (1984): chaos as the dynamic condition of self-organization in open systems.

Internal Point of View Corresponds to External Change

The first law of thermodynamics states that there are two fundamental kinds of processes—heat and work—that can lead to a change in the internal energy of a system. Since both heat and work can be measured and quantified, this means that any change in the internal energy of a system must result in a corresponding change in the energy of its surroundings outside the system.¹

By internal energy we mean here not merely the measurable quantity of energy contained within a system, but rather the set of possible events disclosed within the system’s spatial extension, one of which is made actual as its observable reality. For example, if we consider a solid structure, its solidity is the result of molecules being closely packed together; the short distance between these molecules keeps the shape compact and rigid.

If we introduce any form of work into this system—such as motion approaching the speed of light, or if we introduce heat into the solid structure—the molecules begin to separate. The macroscopic result of this is that the once-solid structure becomes liquid. Liquidity, in this case, was already a potential form implicit within the orientation of solidity; it was a possible state disclosed within the same system.²

External Perspective: Definite Order and Apparent Change

From the external point of view, objects appear to exist in definite ways and to occupy definite positions in space. Motion, in this sense, is the occupation of new regions of volume through a continuous change of position—“covering ground,” bypassing one set of objects while approaching another. This simply means that new things are coming into view while old things pass out of it.

Motion, therefore, is either objects changing within the view or the view itself changing the objects that it conceives. From this external picture, the world exhibits a definite kind of order, and what appears as chaos seems to arise from some unknown source that causes change within this order.³

Entropy and the Shared Relation of Systems

According to the second law of thermodynamics, the exchange of energy between any two systems necessarily involves an element of disorder, or entropy.⁴ This disorder is not simply the breakdown of structure, but rather the fundamental shared relation of possibilities between systems—each definite system being a moment within the total field of all possible relations.

Chaos in this sense is the internal energy of a thing—its realization of one moment out of an infinite set of possible moments. The world as a whole has already reached its maximum increase of energy, for it has been left to its own natural evolution for eternity.⁵ Its increase through time, therefore, is not the generation of new energy, but rather the limitation of infinite potentiality into real and particular moments. The sum total of all these moments—the totality of finite determinations—is the infinite itself.

All possibilities are inherent in a thing, so that the thing can only ever be one of its own possibilities at a given time.⁶

The Doppler Effect and the Perception of Change

An analogy for this correspondence between the internal point of view and external change can be found in the Doppler effect.⁷ When a source of sound or light moves relative to an observer, the observed frequency changes—not because the intrinsic nature of the wave has altered, but because of the relation between the motion of the observer and the source.

In the same way, what appears as external change—the shifting of forms, positions, or colors—is an effect of the relation between the observer’s temporal position and the object’s energetic state. The internal energy of the system corresponds directly to the external transformation of appearance. The world is therefore not a collection of independent things, but a continuous field of self-related processes, where each object is an expression of its infinite potential through finite actualization.

Footnotes

1. Rudolf Clausius, On the Mechanical Theory of Heat (1850): formulation of the first law as the conservation of energy in heat and work.
2. Aristotle, Metaphysics, Book Θ (Theta), 1046a–1050b: the distinction between potentiality (dynamis) and actuality (energeia).
3. Isaac Newton, Principia Mathematica (1687), contrasted with G.W.F. Hegel, Science of Logic (1812): in Newton, motion is the change of position in absolute space; in Hegel, motion is the self-movement of contradiction.
4. Ludwig Boltzmann, Lectures on Gas Theory (1896): entropy as a statistical measure of disorder and probability.
5. Ilya Prigogine, From Being to Becoming (1980): the universe as an evolving system always moving toward greater complexity despite the overall thermodynamic arrow of time.
6. G.W.F. Hegel, Phenomenology of Spirit (1807), §20–26: the thing-in-itself as the totality of its possible determinations, appearing as one finite actuality.
7. Christian Doppler, On the Coloured Light of the Binary Stars and Certain Other Stars of the Heavens (1842): the observed frequency of a wave depends on the relative motion between source and observer.

Initial Conditions and the Arbitrary Principle

In some contexts, an initial condition—also called a seed value—is the value of an evolving variable at a point in time designated as the initial time.¹

A dynamical system is a system in which a function describes the time-dependence of a point in a geometrical space.² A dynamical system possesses a state given by a tuple of real numbers (a vector), which can be represented by a point in an appropriate state space. The state space is the set of all possible configurations of the system; each point corresponds to one particular possible state.³

A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighborhood that is homeomorphic to the Euclidean space of dimension n.⁴

One-dimensional manifolds include lines and circles, but not figure eights, because such figures have crossing points that are not locally homeomorphic to Euclidean 1-space. Two-dimensional manifolds are called surfaces. Examples include the plane, the sphere, and the torus, which can all be embedded (formed without self-intersections) in three-dimensional real space. Others, like the Klein bottle and the real projective plane, necessarily self-intersect when immersed in three-dimensional space.⁵

A dynamical system is thus a manifold M—called the phase space—endowed with a family of smooth evolution functions Φₜ, such that for any t ∈ T (time), Φₜ maps a point of the phase space back into the phase space itself.⁶ In physics, this means that a particle or ensemble of particles has a state that varies over time, obeying differential equations involving time derivatives.⁷

Derivative and Instantaneous Change

A derivative measures the sensitivity of a function’s value (the output) with respect to a change in its argument (the input).⁸ The graph of a function (in black) and its tangent line (in red) illustrate this: the slope of the tangent line at any point represents the derivative of the function at that point.

For example, the derivative of the position of a moving object with respect to time is its velocity—a measure of how quickly the position changes as time advances.⁹ Differentiation is the process of finding this derivative.

If x and y are real numbers, and the graph of y = f(x) is plotted against x, the derivative is the slope of the graph at each point. The slope or gradient of a line is a number describing both its direction and steepness, usually denoted by m in the equation of a straight line, y = mx + b (or y = mx + c). The letter m is thought to derive from the French montée, meaning “rise,” or from “multiple.”¹⁰

The derivative of a function of a single variable, at a chosen input value (when it exists), is the slope of the tangent line to the graph at that point. The tangent line provides the best linear approximation of the function near that point. For this reason, the derivative is often called the instantaneous rate of change—the ratio of the instantaneous change in the dependent variable to that of the independent variable.¹¹

The Ball Down the Hill: The Inverse Determination

The concept of an initial condition concerns the inverse determinations that constitute the same object. For instance, imagine a rod with one end fixed at its center—representing certainty—while the other end moves freely and unpredictably in any direction.

Despite the randomness of the moving end, the line always returns to form its ideal relation: a sphere. This happens because each random movement of the free end is an expression of its dependence on the fixed center. The two determinations—one still and one chaotic—are not opposites but complements of the same structural principle: motion depends on rest, and rest determines motion.¹²

This illustrates what may be called the arbitrary principle: randomness or chance is not the negation of order, but its proof. The freely moving end of the line, though apparently arbitrary, continually demonstrates the presence of its fixed center. The line’s motion, taken over time, traces a sphere—a totality generated from infinite variation.

In the same way, the random initial conditions in a dynamical system ultimately define the structure of its evolution. Chaos, then, is not the absence of order, but the potentiality that gives rise to order through differentiation and return.¹³

Footnotes

1. Edward Lorenz, Deterministic Nonperiodic Flow (1963): introduction of the concept of “initial conditions” in chaotic systems.
2. Stephen Smale, Differentiable Dynamical Systems (1967): defining the mathematical structure of dynamical systems as continuous transformations over time.
3. James Gleick, Chaos: Making a New Science (1987): on the geometry of state spaces and attractors.
4. John M. Lee, Introduction to Smooth Manifolds (Springer, 2003).
5. Henri Poincaré, Analysis Situs (1895): foundational work on topology and manifolds.
6. V.I. Arnold, Mathematical Methods of Classical Mechanics (1978): the phase space as a differentiable manifold.
7. Richard Feynman, The Feynman Lectures on Physics, Vol. I (1964): dynamics as systems governed by differential equations.
8. Isaac Newton & Gottfried Leibniz (17th century): co-discoverers of differential calculus.
9. Galileo Galilei, Two New Sciences (1638): concept of instantaneous velocity as rate of change of position.
10. Carl B. Boyer, The History of the Calculus and Its Conceptual Development (1949).
11. Stewart, James, Calculus: Early Transcendentals, 8th ed. (2016).
12. Heraclitus, Fragment B84a: “The way up and the way down are one and the same.”
13. G.W.F. Hegel, Science of Logic (1812): the unity of contingency and necessity in the concept of “the arbitrary.”

The Law of Entropy and Logical Equivalence

The law of entropy states that between any two ordered systems there exists an exchange value involving an element of uncertainty. This, however, represents only one half of the equation. The other half—the resolution to the antithesis of entropy—is the inverse proposition: within an uncertain system, the relation between two known factors is also itself a known factor.

This duality expresses what may be called the Law of Logical Equivalence—that order and disorder are not opposites, but mutually implicative conditions of the same process. Entropy describes not the absence of order but the manner in which order sustains itself through uncertainty.¹

Ball Down the Hill: Entropy and Initial Conditions

In classical mechanics, the initial conditions of an entropic process involve two ordered systems exchanging energy in such a way that their interaction exhibits an element of chaos. Yet this chaos, insofar as it is indeterminate, constitutes the utility principle for maintaining each system as ordered in relation to the other—but ordered in the inverse way.

This principle can be illustrated by examining how entanglement defines motion and the graviton. In classical mechanics, the notion of gravitation is presupposed as the principle governing relative motion between bodies. Motion relative to another body begins with a causal force exerted upon the object in question. For example, when a person throws a ball onto the ground, the force of the throw appears to cause the ball’s bounce.²

The Problem of External Force

However, this presupposition of an external force faces difficulty when viewed under the concept of general graviton. The gravitational relation between the ball and the ground pre-exists the act of throwing. The semblance of gravity between them does not arise from the force of the throw but is the a priori condition that allows the interaction to occur in the first place.³

In classical mechanics, gravity is explained as the combined effect of the ball’s mass, weight, and density in contact with the ground’s hardness, surface, and size—factors which determine the bounce. Yet the quantum conception of the graviton cannot assume motion as merely the result of contact between two discrete bodies. The initial condition of causal force itself must be outlined as arising from the distinction and entanglement of the two bodies, the ball and the ground, within a shared field of gravitation.

According to general gravitation, both bodies are already in motion but at different rates of temporal progression. The ball moves through time faster relative to the ground, which belongs to the Earth as it orbits the Sun. Both exist at distinct rates of motion in time. The question, then, is not how an external force causes the motion between them, but rather: where did the energy that produced this force originate? When I throw the ball, my own motion is derived from the same gravitational field as that of the ball and the ground.⁴

Entanglement and Reciprocal Causality

Entanglement provides the answer. It explains how the distribution of energy distinguishes one object’s motion from another’s while maintaining their unity in a shared field. From one reference point, the ball appears to make contact with the ground, which forces it upward. Yet, in the inverse reference frame, the ground makes contact with the ball, exerting force downward.

Our empirical perception only observes one half of this relation—the ball falling, striking the ground, and rebounding upward. From this perspective, we assume that the ground caused the ball’s upward motion. However, this assumption neglects the inverse truth: that the ground’s presence is itself the initial cause for the ball’s potential to rise and fall. The relation is mutual and simultaneous, not sequential.⁵

Classical mechanics attributes motion to the middle agent—the person throwing the ball—who is thought to cause the event. Yet this person is also grounded, and therefore participates in the same gravitational system. They are not an external force but part of the continuous relation between the ball and the ground. From the ball’s perspective, it simply moves away from and toward the ground; from the ground’s perspective, the ball is a momentary variation within its field of influence.⁶

Entropy and Motion as Logical Equivalence

Motion is thus the exchange of energy between distinct yet interrelated forms of certainty. Entropy, viewed in this way, is not a degeneration into disorder but the necessary uncertainty that allows for the definition of order. The indeterminate energy between systems is the medium through which order maintains itself as a process of self-definition.⁷

In the end, the law of entropy and the law of logical equivalence express two halves of one totality:

• Between ordered systems, there is uncertainty;
• Within uncertainty, there is an order of relations.

Together they define the reciprocal identity of cause and effect, the unity of order and chaos, and the equilibrium of motion that underlies all change.

Footnotes

1. Ludwig Boltzmann, Lectures on Gas Theory (1896): defining entropy as a measure of uncertainty within ordered systems.
2. Isaac Newton, Philosophiæ Naturalis Principia Mathematica (1687): formulation of classical causality and motion.
3. Albert Einstein, The Meaning of Relativity (1922): on gravitation as the curvature of spacetime preceding any mechanical interaction.
4. Erwin Schrödinger, What Is Life? (1944): on the relation between entropy, energy, and life’s internal order.
5. Niels Bohr, The Quantum Postulate and the Recent Development of Atomic Theory (1928): complementarity and reciprocal observation in quantum phenomena.
6. David Bohm, Wholeness and the Implicate Order (1980): interpretation of entanglement as an undivided totality.
7. G.W.F. Hegel, Science of Logic (1812): the law of contradiction and equivalence in motion and process.

The Law of Irreversibility and the Nature of Duration

The duration which approximates in the approach to the ideal limit of a moment in time is precisely answered by the nature of time as being one-dimensional. The one-dimensional aspect of time characterizes Dollo’s Law of Irreversibility: “An organism never returns exactly to a former state, even if it finds itself placed in conditions of existence identical to those in which it has previously lived … it always keeps some trace of the intermediate stages through which it has passed.”[^1] While this fact is directly derived from observations of biological organisms, the hypothesis of Organicism extends the term organism to include the universe at large. In this broader sense, the general application of Dollo’s Law is also true for all phenomena whose nature expresses the universe as a whole—that is, this fact is true for the character of the universe generally, just as the “grin on the cat’s face” is true for the cat itself.[^2]

All states of energy in the universe are irreversible, meaning that once an event has passed, it can never be repeated in exactly the same way again. Any subsequent event, no matter how identical it may appear to the past, is in fact a new and distinct occurrence.

Uniform and Non-Uniform Objects

Whitehead says about uniform objects sharing a duration of time:

“It is not every object which can be located in a moment. An object which can be located in every moment of some duration will be called a ‘uniform’ object throughout that duration. Ordinary physical objects appear to us to be uniform objects, and we habitually assume that scientific objects such as electrons are uniform. But some sense-objects certainly are not uniform. A tune is an example of a non-uniform object. We have perceived it as a whole in a certain duration; but the tune as a tune is not at any moment of that duration, though one of the individual notes may be located there.”[^3]

The ideal limit toward which a duration approaches is not one situated in the future, because no ground can be found in the future that alone could necessitate an approach for an event to be initiated. The future, being the fact of a later event following a previous one, does not sufficiently explain why one event follows another. If the reason one event follows another is that they form a duration for a particular observer, then we must question the role of the observer in the causal relation between events. Why does one event come after another for the observer at the present moment?

The initial conditions must therefore be self-determinate, which presents a philosophical dilemma: the initial action must first be made before a series of subsequent events unfold, yet the events that presuppose the initial action are themselves true independently of their cause, when their initial condition is taken as another event in the same series. To have a causal action does not mean to bring into being its consequences such that, prior to the action, the consequences were not true possibilities. The fact that consequences exist as possibilities prior to their initiating conditions brings into question what it truly means to come into being.

On Causality and the Order of Events

The natural consequences that follow from an initial action place that action in scenarios different from those initially known. For example, throwing a ball off a cliff is the initial action that causes the ball to fall; yet the falling of the ball is a wholly independent event from the act of throwing it. The falling can be abstracted independently of the throwing and does not necessarily presuppose it when taken as its own initial condition.

From the perspective of an observer standing below the cliff, all that is seen is the ball falling. The observer does not know whether the ball was thrown, kicked, or dislodged by a gust of wind. For that observer, the initial event is the appearance of the ball already in midair. The possible causes—throwing, wind, accident—exist only as potential events. Each is equally plausible, yet entirely distinct, even if the action (a ball in motion) is the same. The throw of a child learning to move and the throw of a professional baseball player are not the same event.

If we reverse the initial condition from the throwing of the ball to the ball in midair, we encounter confusion in the order of what constitutes the initial condition as opposed to the potentialities that follow from it. How, then, does an event become the initial one for an observer?

The paradox is that no event inherently possesses the order of being the initial condition, because from an absolute standpoint—within a vacuum—any event can be extrapolated as the initial condition for a set of possible events that derive from it. In the universal sense, there exist infinite simultaneous possibilities for why the ball is falling, without any necessary temporal order. It is the entrance of an event into a potential or real state that determines its place as an initial condition for an observer. The order of events is therefore derived from a particular relation of events—a duration—in which one event (e.g., the throwing of the ball) precedes another (e.g., its fall) as a matter of experiential sequence.

(see example: soccer ball in a vacuum.)

On the Absolute Initial Condition

There is, however, one proposition that can constitute an absolute initial condition for the universal order of events. This begins with the extrapolation that to be in a vacuum—or in an absolute inertial state—is not a condition wholly independent of any sequence of events, but rather the very initial condition for an object’s potential to be in motion. If there is no necessity, from an absolute point of view, for any particular event to be the initial condition for others—in other words, if there is no necessary temporal order in which an event is inherently past or future—then any event may serve as an ideal limit for its possible causes.

The ball falling from a cliff, taken as the initial condition, becomes the ideal limit that its possible causes (the throw, the gust of wind, the kick) approach most closely. The duration between these events—the moment of approximation—is the discrete span in which the throw transitions into the fall. When the ball is falling, it is no longer being thrown; when it is being thrown, it is not yet falling.

The instance that has already passed thus constitutes the ideal limit for a duration of time to repeat in its closest proximity. Every moment that has passed necessitates, for the next, an ideal toward which it approximates in occurrence. For example, every previous winter serves as the ideal for the next upcoming winter. The past moment is the ideal to which the present moment continually approaches in the future. Once an event has passed, the future is the present wherein that event is most closely replicated in the same manner.

Footnotes

[^1]: Dollo’s Law of Irreversibility, formulated by the Belgian paleontologist Louis Dollo (1857–1931), posits that evolution is unidirectional and organisms do not return to a previous evolutionary state.

[^2]: The “grin on the cat’s face” alludes to Lewis Carroll’s Alice’s Adventures in Wonderland, in which the Cheshire Cat’s grin remains after the cat disappears—used here as a metaphor for the persistence of universal characteristics.

[^3]: The quoted passage is adapted from Alfred North Whitehead’s Process and Reality (1929), “Objects,” p. 162, where he distinguishes between uniform and non-uniform objects as part of his process ontology.