1. The Fabric of Reality and its Continuum
In this article, I will use the terms continuum, physical continuum, dimensional continuum or even extensive continuum, to refer to the reciprocal order of things and bodies ingrained in the material substrate in which they exist and move.[1] This continuum is the invisible substrate we should think of as the arena (or background) of our lives: that which keeps reality together and ordered.
Image 1: The Fabric of Reality is the invisible continuum that keeps reality together and ordered; without it, reality would be like living in a surrealist painting (above: The Disintegration of the Persistence of Memory, Salvador Dali, 1954).
The order of things emerging through the continuum can be interpreted according to: (i) topology (order of position or situation between things or bodies, expressed by terms such as ‘above’, ‘below’, ‘inside’, ‘outside’, ‘beyond’, ‘next to’, ‘near’, ‘far’, etc.); (ii) metrics (order of position or situation expressed by distances reducible to abstract dimensional units); (iii) temporality (order of succession between things or bodies, expressed through their reciprocal presentation and duration: one before or after another, or simultaneous to it).[2]
It is a continuum properly because of the seamless continuity that exists not only between place (or what many call ‘space’) and time but also between place (or space), time, and matter. The material aspect is thus included in this sea of continuity. Crucially, this continuity also relates the object to the subject, which is another reason to call it a continuum. Ultimately, out of the continuum relations between entities are objectified and granted stability—temporal, local, and physical/material stability. Therefore, when a thing or physical entity emerges through the continuum, we should focus on the primordial unity that exists between matter, place, and time.
The inclusion of material properties as an integral part of the physical continuum—thus refuting the canonical division between matter and place (or space)—is a relatively recent finding; or rather, a re-finding, if we consider the long history of the continuum and the ways it has been conceptualized across epochs. In our own epoch, from a physical perspective, the continuum has taken the shape and name of the physical field. Matter is no longer considered a localized entity but a field of localization participating in the extended existence of the continuum itself. We will later see the implications of this vision for traditional concepts of space, place, and matter.
Conversely, spacetime is the clearest example of a dimensional continuum. It is dimensional in that it expresses a four-dimensional continuum—three basic spatial dimensions (width, height, length) and one temporal dimension. The fact that time is treated as an extension should already alert us to the intrinsic connection between time, space, and matter: in different times, and by different authors, extension has been taken as the defining character of space, place, time, or even matter. Yet in the conventional conception of spacetime, matter is severed from the continuum; its inclusion (after general relativity) remains contested and open to interpretation.
Looking back to the origins of this debate, we find that the fundamental state of reality was expressed through various terms: chaos, apeiron, pneuma apeiron, kenon, chōra, topos, anaphés phusis, spatium, locus, absolute space, ether, spacetime, etc. Each highlights a different intelligible aspect of the continuum—spatial, placial, material, or even immaterial.
The main question I want to raise is this: given that the continuum underlying the order of things and bodies is a real and undeniable datum (the world we inhabit is indisputably an ordered system), are all these different modes of expressing the continuum equally true, real, and effective?
That I am in this room, now, is true and real. It is a fact: the physical reality of this room, with its elements, ‘kicks me back’ whenever I am present here; and the same holds for anyone else who enters at any time.[3] Without appealing to the Cartesian “I,” there is no doubt that while I write these notes, I am here, now, in this place I call room. Yet I must ask: is it equally real, true, and effective if I say I am in physical space, in the same way I can say I am in this place—the room, properly—now?
By ‘true, real, and effective,’ I mean a correlation between the term (the symbolic entity of letters) used to describe the continuum—space, spacetime, place, etc.—and the continuum itself, the basic component of reality, the arena or background of our lives. Concepts are ‘true, real, and effective’ when they correlate with the ongoing reality of events occurring in a certain place and time, beyond any reasonable doubt. Conversely, if concepts fail to correlate, they are less effective—or not effective at all—in accounting for reality. This is the case for imaginary or abstract terms. For instance, the term ‘unicorn’ does not effectively represent any real animal ‘out there.’ It refers to an imaginary entity that does not correlate with the ongoing reality of facts; there is no unicorn that ‘kicks me back.’ The same holds for Gotham City, fantastic abstractions, or utopias. In such cases, terms fail to capture the correlation between subject and physical world; they may even impede the progress of knowledge, as arguably happened with the concept of space—as I will soon argue.
Anticipating the answer: contrary to appearances and longstanding presuppositions, I maintain that space is not an effective term to describe the physical continuum, at least if this is intended as an objective datum of reality. Space is an imaginary concept, a shadow cast on reality by our imagination; it is not fully effective in addressing the continuum as a concrete fact of nature. At worst, it can be deceptive if mistaken for reality itself. By contrast, a term that I regard as ‘true, real, and effective’ for expressing the continuum is place. It too is a shadow (language has intrinsic epistemological limits), but a shadow cast on reality by the actual entity—the physical continuum—that holds reality together and ordered.
Of course, in this play of mirrors between language and reality, even expressions such as physical continuum or dimensional continuum are shadows. Yet they are actual shadows, cast by the real entity we designate by those expressions, unlike mere products of imagination severed from physical reality. They are not fantasies, illusions, or hallucinations, but signs of something that truly grounds our being in the world.[4]
Image 2: Allegory of the Cave. What is real? Plato asked. By the same token, we want to answer the following questions: Is space real? Is place real? (above: engraving attributed to Jan Pieterszoon Saenredam, 1604).
Place and the continuum really exist. By contrast, like others, I argue space exists only within the domain of our imagination; it is an abstract construct, a figment of thought, and therefore not a proper term to define the actual, physical continuum in which everything exists and unfolds.
Yet we must be careful: language allows us to invent any term at any moment and claim that it represents something ‘out there’. That is a basic function of language. My concern, however, is with the historical primacy of certain concepts—in this case, the primacy of place over space in accounting for the properties of the continuum in the physical world—and with the effectiveness or appropriateness of particular terms to convey an adequate meaning in relation to what they signify. My interest in questions of space and place intensified when I realized that ‘space’ was not an adequate term (ironically, a limited term) for addressing the physical state of reality, despite the dominance it had acquired since Newton.
Thus, two interrelated questions arise: first, the nature of space and place from a historical perspective, as philosophical and scientific terms; and second, the linguistic perspective, which includes etymological and philological considerations. I am convinced that without engaging with both dimensions no philosophical, scientific or even architectural, social, or artistic inquiry into space and place can reach convincing results.
This inquiry into the continuum—both its ontological and linguistic dimensions—lies at the intersection of epistemology and metaphysics. Though unusual terrain for architects, it is one I believe they must increasingly confront. For the fundamental concepts through which this domain can be explored—space, place, matter, void, motion, and time—are not only primary to philosophy and science but also indispensable to architectural practice. And it was, in fact, my own practice as an architect—working intuitively with space, place, matter, and time—that led me back to a more fundamental inquiry into their meaning. I realized that the traditional definitions carried unresolved ‘grey areas’ which must be clarified if architects are to become more aware of the basic theoretical tools of their profession.
Returning to a phrase I used earlier—‘I am in this room, now’—we can distinguish three elements:
(i) ‘I am’, the proposition of the subject as a concrete, material entity existing in relation to others;
(ii) ‘in this room’, the container and incubator of events, things, and bodies (but then, what is the appropriate name for this continuum—place or space? and what difference does the choice make?);
(iii) ‘now’, the temporal dimension or duration that guarantees the ordered existence of the physical entities involved.
At the very least, if ‘I am’ represents an actual material entity (my body-mind, present), and ‘now’ represents the temporal duration of entities in the scene (the processes by which they emerge and persist), then ‘in this room’ represents a portion of the continuum that offers a concrete, seemingly stable field of existence for these entities within a given temporal interval. From here, the step is short to conceive that the room itself—both as geographical where (a local expanse) and as physical what (walls, floor, ceiling)—participates in the continuum as a unity, a unicum.
To sharpen this epistemological question—how the continuum can be represented without falling into conceptual traps—I will turn, once again, to a historical excursus. This will condense, in the form of a personal narrative, the arguments developed in my three preceding articles on the philosophical and scientific history of space, place, and matter.
Before that, however, I will pause to reflect more closely on the preliminary terms introduced in the title of this section: the fabric of reality and the continuum.
Image 3a: The Fabric of Reality is the physical continuum that keeps entities together and related according to their order of position and succession.
By the expression ‘the fabric of reality’ I refer to how reality is made—its fundamental essence, its most basic level—as it can be understood from a human perspective at the beginning of the new millennium. The expression, and some of the theoretical intuitions behind it, resonate with the work of two physicists: David Deutsch and Brian Greene.
In 1997, the British physicist David Deutsch published The Fabric of Reality: The Science of Parallel Universes and Its Implications, in which the fundamental state of reality is interpreted in light of the recent discoveries of quantum mechanics. I largely agree with the systemic approach of this book, which argues that reality cannot be reduced to a single ultimate principle—specifically, to an ultimate physical principle—but is rather the emergent result of a complex system of interacting principles. Deutsch calls them the ‘four strands’: physical, computational, epistemological, and biological/evolutionary principles, which mutually operate to determine the meaning and appearance of reality at large. This view parallels what I argue in my own work: following the philosopher and novelist Robert M. Pirsig, I also maintain that physical reality is composed of four interacting strands or principles, which I name physicochemical, biological, social, and symbolic (see the article On the Structure of Reality).
In 2004, the American physicist Brian Greene, a well-known string theorist and scientific popularizer, published The Fabric of the Cosmos: Space, Time, and the Texture of Reality, a broad scientific narrative centered on the physics of the twentieth century and on the concepts by which the fundamental state of reality—space, time, spacetime, physical fields, strings, branes, and so on—can be described.
Some of the concepts and terms I use in my own texts draw inspiration from these two authors. However, the basic idea of a fabric (or texture) of reality—understood as a fundamental constitutive element of reality, that which lies beneath and sustains appearances—is something I had already been using intuitively in my architectural work, long before reading their books. In particular, I employed the term texture in an architectural context to refer to the intricate structure that underlies and enables the emergence of phenomenological space, conceived as a basic element of architecture. This use emerged during a series of theoretical studies that I eventually grouped under the title Archi-textures. The term itself, with some distinctions, I began to adopt after reading Henri Lefebvre’s The Production of Space.[5]
Image 3b: The Fabric of Reality as ‘Archi-texture‘ – the grounding territory for architectural forms. Meta-project for the Vaxjo Tennis Hall, Alessandro Calvi Rollino Architetto.
Figuratively, the expression fabric of reality emphasizes the critical interweaving of the fundamental concepts with which philosophers and scientists, across different epochs, have sought to interpret the ground of reality—concepts such as matter (or more precisely, substance, from the Latin sub-stare, ‘that which stands under’… appearances), place, space, and time. I regard this fundamental fabric as a constitutive and connective medium, a kind of invisible glue that binds things and bodies together and orders them. The very terms we use to characterize the basic nature of things—matter, place, space, and time above all—are themselves integral parts of this continuum, an almost inextricable continuum that also relates objects and subjects as they emerge on larger scales. This means that the continuum, by holding together names and things, simultaneously secures the possibility of human knowledge.
To investigate the continuum through our rational faculties requires a high degree of abstraction: something of the authenticity of physical reality is inevitably lost, but communicability is gained. In sum, we might say that the fabric of reality is the invisible glue that holds things together, connects them, and enables them to emerge with the apparent continuity and stability we experience. Without such a fabric to sustain the actualization of processes and the apparent continuity of events, reality would resemble a surrealist painting (see Image 1, above) : without actualization, there would be no certainty in the arrangement of elements, no certainty in the forces acting upon them, and no certainty regarding the duration of events. The future could precede the past.
The image of a unifying structure of reality—the fabric of reality—understood as the ultimate place from which physical/material, local, and temporal properties simultaneously emerge, is, I believe, a productive and effective image for describing the fundamental structure of reality. Indeed, no material entity exists in isolation: every entity emerges within and through the continuum, in relation with others. From the outset, each physical entity—what we call matter—appears as a condensate of (i) material substance (an existent with non-zero intensity or extension), (ii) localization, and (iii) temporality or duration. These three aspects appear together. Thus, we can understand matter—or physical matter—as that which simultaneously encompasses physical substance (the product of intensive or extensive forces within the continuum), localization, and duration: it is the pure physical presence of an entity in the world.
Image 4: Physical Matter understood as the place of actualized processes after which material/dimensional, situational and temporal properties emerge from the continuum.
Image 5: The Fabric of Reality can be interpreted as a physical continuum, i.e., as that which guarantees the seeming continuity and stability of relations of order and succession between the entities that emerge from and exist within the fabric.
Dimensionality, understood as physical extension, is intrinsic to matter. This is also what Descartes meant by res extensa in Part II, Principle IV of his Principles of Philosophy, where he states: ‘the nature of matter, or of body considered in general, does not consist in the fact that it is hard, heavy, colored, or affects the senses in any other way; but only in the fact that it is a thing possessing extension in length, breadth, and depth.’ [6]
Looking more closely, we can say that matter and dimension (understood as physical extension) are unified and concretized by an intrinsic force—a tension acting within the continuum. When this tension acts inward, we speak of intension (intensio, from intendere, ‘to stretch toward, to direct inward’), producing compression or density within the continuum—we can speak about intensive continuum, properly (Image 6, below). This results in higher mass and/or energy—a material entity.
Image 6: Physical Matter understood as the actualization or concretization of intensive forces acting in the continuum.
Conversely, when the forces act outward, we speak of extension (extensio, from extendere, ‘to stretch outward’), producing rarefaction. When extreme, such outward forces make matter so diffuse as to become imperceptible, often epitomized as space, an extensive continuum (Image 7, below).
Image 7: Physical Matter understood as the actualization or concretization of extensive forces acting in the continuum.
At one end of this spectrum of tensions lies the maximum rarefaction of the continuum, where matter dissolves into the continuum-as-background;[7] this state of matter or energy tends to zero. At the other end lies maximum density, where compression is so intense that nothing can escape its attraction. Between these extremes lie the usual forms of matter with which we are phenomenologically familiar. This explains why the extensive continuum is often equated (misplaced) with space: it is the portion of the spectrum where matter/energy appears absent—at least to human perception. Conversely, where intensive forces dominate, matter manifests palpably, hence its association with the intensive pole of the continuum (a material continuum).
Yet both states—extensive and intensive—share a fundamental trait: they are both dimensional, non-zero phenomena. Extension and intension are not opposites but two modalities of the same tensional continuum. That’s why the void is an abstract concept and reality can only be understood as a plenum, something which has a non-zero dimension – no matter how small it can be – even in the most remote places, where the intensive character of matter is maximally rarefied and is better described as extensive character, producing the illusion of space as a physical existent: extension and intension are just two different names for the same fundamental phenomenon concerning the tension in/of the continuum. For this reason, Descartes could say that space and matter are not ultimately distinct: both belong to the fundamental plenum of reality, understood as a non-zero tensional state.[8] Aristotle, too, affirmed this: for both him and Descartes, reality was not a void, but a plenum—full, continuous, and dimensional, even in the most rarefied regions we too easily mistake for empty space.
reality is a plenum
As you may have already noticed, this terminology produces a kind of inversion. When tension in regions of the continuum tends to a maximum and is directed outward (maximum ex-tension), we witness the minimum extension of the usual forms of physical matter—that is, its maximum rarefaction. Beyond this point, matter dissolves entirely into the continuum, and we can only speculate on what lies beyond. At this limit we enter metaphysical speculation in the literal sense of the word: meta ta physika means ‘after physics,’ that is, beyond the realm of the physical. Yet it is difficult to draw a clear boundary between the physical and the metaphysical. As Heidegger suggests, each contains the other: ‘it makes little sense to say that the Physics precedes the Metaphysics, because metaphysics is just as “physics” as physics is “metaphysics”’ (see note [21] in Being as Place: Introduction to Metaphysics – Part One).
What lies ‘after’ the physical—that is, ‘after’ that which is concrete and bounded (the very reason Aristotle defined the physical realm as topos, place)—is the unbounded, apeiron in Greek, and by semantic affinity the void, kenon, or even space. Indeed, from the extreme rarefaction of matter, its dissolution into an apparent nothingness, arises the very idea of space as pure extension: the ‘block of glass without glass’ that Julian Barbour attributes to Newton’s absolute space (see Image 11 below). Similarly, Epicurus described the anaphés phusis—intangible substance—conceived as pure dimensionality, i.e., the distance or interval between things (diastēma).
As I have argued elsewhere (see Back to the Origins of Space and Place), the Greek word spadion (or stadion) shows how space first entered philosophical debate as ‘distance’. Returning to the continuum that mediates between physics and metaphysics, we may also speculate on chaos, the primordial, indeterminate state out of which the ordered cosmos emerged. Here too the unbounded may be understood as an indistinct, formless mass—apeiron. For this reason, while Aristotle defined place (topos) as bounded, it is useful to contrast the bounded and sensible (the physical) with the unbounded and chaotic (yet still intelligible, otherwise we couldn’t even speak of it).
Put simply, we are questioning the difference between what has a limit (peras), the nature of place according to Aristotle, and what lacks a limit, such as Anaximander’s apeiron, the unbounded, the void, space, or chaos. Edward Casey reminds us in The Fate of Place that many ancient mythologies and cosmologies describe place as the first ordered state of existence after chaos. Cosmos itself—literally ‘order’—is a place of places emerging from chaos. Thus, there is both logical and psychological necessity to cling to matter as an ordered state in order to describe the fundamental physical reality.
At the extremity of the gradient—that which exists but tends toward zero (a nearly zero form of energy, as I have elsewhere suggested)—a ‘short circuit’ appears between matter and place, matter and space, or matter and void. The most appropriate concept to disclose this short circuit, I believe, is place. It is place that allows matter to appear in the physical world as an ordered state, simultaneously sensible and intelligible: a material datum or fact.
In the extended meaning I propose here, place transcends dimensionality by encompassing both minimum and maximum dimensions, while also incorporating that which has no physical dimension at all (ideal or intelligible place). To identify the substrate—the continuum—as place (hupodochē or chōra, in Plato’s terms) is to justify the genealogy of existence itself, understood as the inseparable concretion of material substance (ex/in-tension), localization, and duration. In this sense, each physical entity is the place of its own existence. From potential places, actual places are generated; hence, Plato’s chōra can be interpreted not as space, but as an ultimate place. Like the Platonic chōra, the place I describe at RSaP—Rethinking Space and Place preserves both material and immaterial, physical and metaphysical dimensions—something space, strictly immaterial, cannot do.[9]
As I have argued elsewhere, from the bounded standpoint of place we can also reason about the unbounded. Place, by definition bounded or limited, implicitly includes the unbounded as its correlative possibility. In this way, place includes space, not the other way around. Ultimately, place can be both concrete and abstract, actual and potential, physically bounded and ideally unbounded. By saying reality is a place of processes, we include both the potential and actual states of reality within the overarching compass of place.
Image 8: Reality and its continuum between physics and metaphysics.
Given that the continuum can be understood as intensive, extensive, or temporal, it may be conceived as underlying both the presence of matter and its apparent or hypothetical absence. In the first case, we speak of matter as a fact (physical or sensible matter); in the second, we reason only in the abstract, through words and concepts that are projections of imagination onto the reality of facts. Yet imagination sometimes anticipates reality: one may ‘see’ what no one else can yet see, and later it proves to exist. This happens when imagination correlates fully with the reality of facts, thereby extending the edge of knowledge (a fact well known to physicists).
Plato called this primal substrate chōra or hupodochē. Aristotle named it topos, the natural place in which matter (in the form of bodies) actually exists and moves. The Atomists, in contrast, called it kenon—the void—against which Aristotle argued.
Before continuing with the historical discussion of the continuum and its various names, let me add one final reflection. This is how I see reality—or better, the fabrics of reality, its intimate texture: as a place that embraces physical matter and its duration.[10] This embrace—of material in/ex-tension, localization, and duration within a single entity—is what I call place. Thus every place is at once a unicum and a continuum, far more than the simple aspect of ‘location’ to which place has too often been reduced. The notion of ‘simple location’ is a misleading abstraction. It severs location from the material in/ex-tension and duration that intrinsically belong to it. From this misplaced abstraction derives the modern concept of place as mere localization—a notion I reject and which this project seeks to question. In truth, matter, localization, and temporalization cannot be separated in reality, only abstracted a posteriori. Every physical entity is first and foremost a unicum in which matter, place, and time co-exist in seamless continuity. It is only the human faculty of abstraction that dissects this unity into parts, yielding matter on one side, place or space on another, and time on yet another. In doing so, we have forgotten their intrinsic interrelations. Using these concepts—place/space, matter, and time—thinkers across history have tried to explain the existence and behavior of material entities. It has seemed, and still seems, that bodies and objects are immersed in a dimensional continuum that guarantees order and stability. Yet this very continuum, while securing order, also obscures the original unity of reality. What was at the origin an indivisible whole has been interpreted and described as divided, dualistic, fragmented. The gap between reality and knowledge is thus born—a gap that has led, as history shows, to misunderstandings and even tragedies.[11]
To recover the primordial sense of the physical continuum of reality, and to understand the historical process by which it was dissected into matter, place, space, and time, is an essential task. Only by retracing this history of thought can we grasp how the continuum was eventually reduced to a merely dimensional or extensive concept—modern space—and how much was lost in that reduction.
2. The Intuition of the Physical Continuum from Aristotle to Descartes and Newton
The intuition of the physical continuum that surrounds us, and within which we live, is difficult to express in words. I believe some terms are well suited to describe this concept (such as chōra, place, or field), while others are not (such as space or spacetime). This question is as old as physics and philosophy themselves. Among the first thinkers to investigate the relation between physical bodies and the continuum within which they exist and move, we find Plato and Aristotle. Very succinctly—and inevitably somewhat roughly—chōra was the name Plato used to describe that original ‘within which’ of things, which also carried a metaphysical connotation: the ‘out of which’ things emerge. Topos was the name Aristotle employed, which bore a more distinctly physical meaning. Yet even earlier, Anaximander described that primordial locative and generative state of nature: apeiron was the name he gave it (an abstract concept), though only scant sources survive.
Naturally, these concepts carry different shades of meaning. Some resonate with our modern understanding of the continuum, while others diverge.[12] Aristotle, however, was unambiguous: his definition of topos—which I would translate as place rather than space as many still do—was formulated to challenge the Atomists, such as Leucippus and Democritus. For them, ultimate reality consisted of indivisible atoms moving in the void (to kenon). Yet for ancient people, the void was psychologically untenable (also logically untenable, according to Aristotle). As the cosmogonies suggested (as Edward Casey has described, see Place and Space: A Philosophical History), the world had to be full, not empty. Hence the Atomists’ theory of the void was largely rejected, while Aristotle’s conception of reality as a plenum prevailed.
Plato’s theory in the Timaeus was, in my view, more nuanced—conceiving the continuum as an entity in between the metaphysical and the physical—but it was also notoriously ambiguous and open to conflicting interpretations.[13] This complexity made it difficult to sustain, and ultimately Aristotle’s vision won out. For well over a millennium, ancient astronomers relied on Aristotle’s cosmology, which offered the first systematic scientific framework for understanding the order of things and their continuum. The term cosmos itself reveals this view: an ordered universe (the counterpart to chaos) characterized by the coexistence and succession of things.
Image 9: The Cosmology of Aristotle: a theory of place (topos), matter and motion.
Still, Aristotle’s theory was criticized from the start. In fact, the modern concept of space emerged only through centuries of debate over the nature of the Aristotelian topos. For this reason, I find it problematic when scientists—physicists in particular—interpret topos as space. Scholars attentive to the mix of philological, philosophical, and historical issues are more inclined to render topos as place, or at least to vary its translation by context. The distinction is crucial: Aristotle rejected the void, so it is inconsistent to attribute to him a notion of space that implies pure extension, or emptiness as such, which are akin to the void. For Aristotle, topos was inseparable from matter: there is no body without place, no place without body.[14] In this sense, topos is as far from ‘space’ as it is from ‘the void.’ To cite Aristotle’s own words: ‘That’s what place (topos) is: the first unchangeable limit (peras) of that which surrounds’: this is Aristotle’s definition of place.[15] From both logical and ontological perspectives, rendering topos as place seems the most accurate choice—before even considering philology or history.
In short, the earliest debates on the continuum and physical existence were resolved, for the ancients, by Aristotle’s theory of place. The medium that sustains order, that immersive extent in which things exist and events occur, was understood not as space (which is a notion that did not exist in antiquity except as a linear distance, a temporal extension, or an area—see notes 18 and 19, below), but as place.
Yet Aristotle’s definition of topos left room for critique. Dynamically, he held that bodies in the sublunar realm moved in straight lines toward their natural places (heavy things downward, light things upward), while celestial bodies moved in perfect circles through the aether (see Image 9, above). These assumptions eventually collapsed under astronomical observation, along with the concepts of natural place and natural motion—I redirect readers to the article Space and Place: A Scientific History – Part One, focused on the book The Discovery of Dynamics, by Julian Barbour.
The issue of dimensionality posed another difficulty: Aristotle defined place as two-dimensional: the limit of that which surrounds—this is the definition of place according to Aristotle—is a surface, after all. But the world obviously seemed to possess three dimensions—front–back, left–right, above–below. Still, we should be cautious here: the intuition of three-dimensionality belongs to pre-scientific thought, but that does not mean ancient people possessed a fully-fledged concept of space as a three-dimensional immersive extent similar to the modern concept (what people, including Einstein, often call ‘intuitive space’).[16] On the contrary, the lack of systematic three-dimensional representation in pre-Renaissance art suggests otherwise. Giotto’s frescoes, for instance, show depth only vaguely, while Renaissance perspective brought a fully geometrical conception of space for the first time. Space is everything but ‘intuitive’.
Confirming this, the Swiss psychologist and epistemologist Jean Piaget argued that even modern children must pass through specific cognitive stages before they can construct the concept of space as we know it now—a finding that suggests it is neither innate nor timeless or ‘intuitive’.[17] Likewise, Latin texts use spatium mainly to mean a linear distance or extension, an area or surface, or a stretch of time—[18]not an immersive three-dimensional background, at least not before the fourteenth century as philosopher Ivor Leclec also observed.[19]
Two decisive steps were needed before the modern concept of space could take shape. The first came with René Descartes, who invented geometrical space: a coherent three-dimensional system defined by the axes x, y, z. Contrary to common belief—even among scientists—Euclidean geometry contained no notion of space as such, only relations between figures (see Image 10, below). As Einstein himself observed, the very idea of space as an entity arose with Descartes.[20]
Image 10: The Origin of geometrical space. ‘Let AB, AD, EF, GH… be any number of straight lines given in position…’; in Descartes’s Geometry – which first appeared as an appendix to the Discours de la Methode (1637) – ‘lines given in position but not in length… becomes lines of reference or coordinate axes’;[21] This is the first step necessary to define an abstract space of mathematical origin with respect to which geometrical elements can be located.
With geometrical space, we are no longer in the physical domain but in an abstract one: an ideal background for geometrical entities (see also the paragraph on Descartes in the article Space and Place: A Scientific History – Part One).
The second step—bolder and more ambitious—was taken by Isaac Newton, who reified that abstract concept by endowing it with physical properties. As we saw in the previous article, he materialized abstract space when he realized that his laws of motion were untenable without it (the question is open whether that act of reification is entirely due to Newton or to his interpreters—see paragraph 7 Concepts of Space in Place, Space and the Philosophy of Nature). This marks the formal birth of physical space: a logical consequence of Newton’s notion of absolute space.
Thanks to Descartes and Newton, the continuum became a dimensional continuum proper: extension or dimensionality—the possibility of defining the continuum by measure—emerged as its decisive property. This is absolute, infinite space. We moved from a concept physically and qualitatively tied to matter (Aristotle’s topos-as-place) to one that originated as an abstraction (space as stadion/spadion, denoting distance, extension, or a unit of measure) and was later reified into physical substance passing through mathematical abstraction. It is now a quantitative, measurable concept: its stability and durability with respect to measuring defines the very nature of absolute space as infinite, both spatially and temporally.
This is the concept deeply ingrained in our thinking: when we say ‘space’, we usually imagine an indefinite, empty extension surrounding us—pure extension, pure dimensionality abstracted from everything else. The concept is so deeply embedded in our thought that it feels ‘naturally integrated’, physiologically and psychologically ingrained in our minds (as Kant also believed), and even mistaken by many for ‘intuitive space’. Yet, as I argued in earlier articles, there is no such thing as ‘intuitive space’. At best, one may intuit certain aspects of place—including its dimensional character—but that is quite different. Place is all-embracing: dimensionality cannot be apprehended apart from materiality and temporality. Space, by contrast, is exclusive and reductive: it requires a highly sophisticated mind to abstract dimensionality from matter and time. In nature, those aspects are always given together. It took more than two millennia of debate and reasoning to separate extension from materiality and temporality, and thus arrive at the modern concept of space—the three-dimensional background we know today. Place is intuitive; space is not.
There is no such a thing as intuitive space… Place is intuitive, space is not.
Physical space, born from absolute space, became for Newton—and especially his interpreters—something real and concrete. Thus arose a short circuit between reality and its representation, one we still live with. This short circuit was memorably captured by Alfred North Whitehead’s phrase ‘fallacy of misplaced concreteness’: mistaking the abstract for the concrete. With Newton, the new vision of the world was complete: the Aristotelian cosmos of places as a plenum gave way to a scientific cosmos of bodies moving through absolute space, a material void (!), a neutral container—or, as Julian Barbour put it, ‘a perfectly uniform and translucent block of glass extending from infinity to infinity and has all the properties of such a block of glass except the glass!’[22]
Image 11: The Newtonian concept of absolute space; a perfectly uniform and translucent block of glass… without glass.
To sum up the second part of the story concerning the continuum, two of history’s greatest minds, Descartes and Newton, were needed before we could conceive of space as an actual three-dimensional continuum. Our understanding of the cosmos, until the early 20th century, rested on this conception. Contrary to appearances, the modern notion of space did not arise suddenly from a single insight. For Descartes’s and Newton’s theories to appear, nearly two millennia of debates were required. From Aristotle’s theory of place and natural motion to Newton’s system of absolute space and mathematical laws (which erased the distinction between terrestrial and celestial motions), the spatial debate—the question of the continuum in which bodies exist and move—unfolded slowly, shaped by astronomers, mathematicians, philosophers, alchemists, architects, painters, rulers, and priests alike. Intellectual processes always intersect with sociocultural ones; each transforms the other. After two millennia of debates, place—Aristotle’s topos—was transformed into space, or rather reduced to a mere location within an infinite extension: absolute space.
3. Relativity, Quantum Mechanics, and the Question of the Continuum
The debate concerning the nature of the continuum in which bodies exist and move opened with Plato’s chōra and Aristotle’s theory of place (topos) and culminated—at least provisionally—with Newton’s theory of absolute space, which reduced place to a mere location for bodies in space: Locus est pars spatii quam corpus occupat—‘place is a part of space which a body takes up.’[23] Despite the rapid ascendancy of the concept of absolute space, I believe we have inherited several unresolved questions: is space real or ideal? (Here, by ‘real’ I mean the concreteness of a physical entity with non-zero energy or mass.) Closely related: what is the relation between space and place? Any answer that diverges from Newton’s inevitably entails a reformulation of space, place, matter, and time.
In broad strokes, the passage from Aristotle to Newton led from a simple, intuitive or phenomenological cosmology—aligned with the senses, where place and matter were visible and time a derivative measure of change—to a sophisticated vision of reality divided into space, matter, and time. Space and time, invisible entities, became the necessary background for physical laws, laws defined to comply with absolute space, a ‘concrete’ framework as elusive as the void or as intangible as an idea. Abstract yet indispensable, space was treated as if it were real for purposes of calculation—an oxymoronic entity without mass or energy, difficult to sustain logically or epistemologically, yet extraordinarily effective in practice. That effectiveness transformed the modes of thought: a passage from concreteness to abstraction as the privileged mode of inquiry into nature, symbolized by the transformation of place into space. The continuum under investigation remained the same, but the terms and concepts shifted radically, with emphasis placed on dimensionality as its defining trait. The Scientific Revolution finalized by Newton was the prelude to the Industrial Revolution, after which mankind entered the contemporary epoch.
From the perspective that space is an abstraction—a construct of the imagination dealing with the extensive (dimensional) aspect of reality—I would argue that, just as the pre-Socratics marked the passage from mythos to logos, so too the transition from Aristotelian topos to Newtonian spatium marked the affirmation of logos not merely as philosophical fact, as in the beginning of Western thinking, but as scientific fact.
Yet in this long historical trajectory, a ‘final passage’ seems necessary: one that reconnects the original logos—the philosophical mode of speculation on place—with the logos inherited from Descartes and Newton—the physical-mathematical mode of abstraction. Such a passage aims at a more encompassing understanding of the continuum, surpassing dualistic, reductionist, and mechanistic views of the cosmos. It envisions instead a unitary, holistic whole: a plenum not reducible to its parts, thus re-establishing connections with Aristotle’s older organic model.[24]
As in the past, this new passage emerges from intertwined historical episodes awaiting a systematization comparable to those of Aristotle and Newton. Abstract thought, sharpened by scientific precision, remains the privileged mode of inquiry into nature and the continuum. Yet without a convergence between humanistic and scientific modes of knowledge, no systematization of comparable depth can be achieved.
Continuing our synthesis of the main stages in this debate, immediately after Newton’s triumph we must note the contributions of Leibniz, Locke, Berkeley, and Huygens (especially the first three philosophical). They opposed Newton’s absolute space with the idea of a relative space or continuum, determined by relations among material entities. But Newton’s absolute space would dominate for more than two centuries, until Einstein. Meanwhile, the study of electromagnetic phenomena introduced another concept—the field—which suggested new ways to understand the continuum. The pioneering works of Faraday and Maxwell, along with Lorenz, Mach, and Einstein, proved decisive.
It was Einstein who decisively challenged Newton. His 1905 Special Theory of Relativity dissolved absolute space into relative spacetime, coupling space with time as a single entity, as Minkowski formalized. A decade later, the General Theory of Relativity redefined the continuum again, as a physical field intrinsically coupled to time and matter.[25] Many scholars interpret this as Einstein’s final vision: the continuum as a relative ether, an interpretation he continued to pursue in his unified field theory until his death in 1955.[26]
Yet it was also the field of quantum mechanics—developed in the same decades—that transformed the debate further. By probing phenomena from the atomic scale down to the Planck scale, it suggested that the continuum itself may be discontinuous (a discontinuum) at its most fundamental level. The very term ‘quantum’ signals this shift: a discrete structure underlying what appears continuous. At these scales, reality seems discontinuous, while the apparent continuity of the cosmos emerges as an ordered property at higher levels.
after of the birth and development of quantum mechanics new modes of interpreting the continuum became possible. The very term ‘quantum’ signals this shift: a discrete structure (a discontinuum) underlying what appears continuous.
Thus, just as Einstein showed that space and time are bound together, and spacetime bound to matter (as field), quantum mechanics in its development as quantum gravity introduced a new horizon: the unification of spacetime with quantum fields, the spatial, temporal, and material folded into one encompassing entity: covariant quantum fields (see image 12 below). Could this be the ultimate ‘place’ of physical processes?
Image 12: ‘What is the world made of?’ The Italian theoretical physicist Carlo Rovelli argues that it is made of only one ingredient: covariant quantum fields. By interpreting these fields as physical states of place—the first in a chain of concrescent states of place (physicochemical, biological, social, and symbolic)—I suggest that the concept of place can regain the fundamental ontological status it held at its origin: to exist is, first of all, to exist in some place (Image adapted from Carlo Rovelli’s Reality Is Not What It Seems, with my addition of the blue row concerning Aristotle).[27]
So, to recap: if Aristotle and Newton formalized the placial/spatial question in line with the intellectual needs of their times—and if from those modes of thinking about the order of the cosmos two very different cosmologies emerged, guiding Western societies and their social, political, economic, religious, cultural, and technological trajectories for nearly two and a half millennia—then today, as modern people of a global village, we find ourselves awaiting a third systematization of knowledge. That is, a new mode of understanding the cosmos and its laws.
This would be a systemic mode of understanding, one that conceives the order of the cosmos as the outcome of interwoven processes operating at different but equally fundamental levels—physicochemical, biological, sociocultural, and intellectual or symbolic. In this vision, the field concept may well become the primary category for representing the physical and dimensional continuum (or discontinuum) in which living and non-living beings exist, intertwined as physicochemical, biological, sociocultural, and intellectual entities. It is such a unifying, totalizing vision of reality, understood as a whole, that we are now trying to formalize.
And with this new Weltanschauung—this systemic understanding of the cosmos—comes a rethinking of place, space, matter, and time. From the perspective of one specifically interested in the meanings of spaces and places, I argue that a reformed understanding of place, of the kind I have been sketching at RSaP—Rethinking Space and Place, can subsume the physical concept of the field, offering a more comprehensive vision of reality both around and within us (hence, a concept of place broad enough to encompass physical and metaphysical levels of existence). Within such a systemic vision, every concrete entity is the place where certain processes actualize into matter. Place and matter are therefore co-extensive: there is no place without matter, and no matter without place. This is in agreement with the new physics. In this sense, the field concept used by physicists can be understood as a physical state of place. I have already stated it: in an ascending order of complexity, from inorganic matter to thought, actual entities can be considered places where physicochemical, biological, sociocultural, and symbolic (or intellectual) processes become concrete (see On the Structure of Reality). Needless to say, this comprehensive understanding of place goes far beyond the old notion of location or position, which has too often been reductively equated with place.
As we have seen with Casey, one of the great merits of philosophical, scientific, and sociocultural inquiry has been to revise the concept of place since the early twentieth century—a process that continues (Place and Space: A Philosophical History). Physics, in its own way, has been undergoing a parallel revision, if we understand the field concept as the primordial place of physical processes (as suggested, more or less explicitly, in Barbour, Jammer, and Weinberg—see Space and Place: A Scientific History – Part One and Part Two). Thus, as I often say, we can close with this conviction: only through the joint contributions of different forms of knowledge—scientific and humanistic—can we hope to achieve a new, shared formalization of the laws and concepts that ground our understanding of the order of things, or nature.
4. Conclusion
The ways of thinking about the physical continuum—the substrate that holds things together in order and succession—are in perpetual evolution. We now know that, at the limits of physical existence (the Planck scale), what we once believed to be a continuum no longer appears continuous. We also know that, according to current physics, the most appropriate term for this continuum/discontinuum is not space, nor even spacetime, but field (more precisely, covariant quantum fields). At the physical level, fields are the most fundamental entities that exist: they are at once material, temporal, and locally extended, woven into one single substance—the very fabric of reality (i.e., the ultimate place of processes that actualize into physical substance).
From the systemic perspective I advocate at RSaP—Rethinking Space and Place, and through which all phenomena—not just physical ones—can be analyzed, the concept of place regains primacy as a fundamental and operative category. Place can be understood both as the actualized state of things that emerge from the continuum and as the potential state that nurtures any such actualization. Ultimately, place is the substrate of reality itself—the continuum. Reality’s fabric is nothing other than a place of processes.
At the physical level, this fabric can be described as a set of fields: fields themselves are nothing other than physical states of place. Higher-order phenomena—physicochemical, biological, sociocultural, symbolic—are likewise different states of place: emerging from, yet irreducible to, the states that preceded them. The totality of these states defines reality as a whole place. Thus, place is both the seat of possibility and the actuality of finite, discrete elements. It embraces potentiality and actuality alike, becoming and being. Before all else, reality is place. The old Archytian axiom is vindicated.
Notes
[1] I use the term thing in its most general sense: to refer to any entity, particularly physical or concrete ones, unless otherwise specified.
[2] Leibniz understood the order of things as an order of coexistences (space) and an order of successions (time): ‘As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is – that I hold it to be an order of coexistences, as time is an order of successions’, said Leibniz in his third letter to Clarke ; see: Leibniz G. W. and Clarke S., Correspondence, ed. Roger Ariew (Indianapolis: Hackett Publishing Company, Inc., 2000), 14.
[3] The expression ‘reality kicks back’ refers to the famous episode of Dr. Samuel Johnson, the eighteenth-century English man of letters, who, during a discussion on Berkeley’s idealism, kicked a large stone so hard that his foot rebounded, exclaiming: ‘I refute it, thus’. The incident indeed demonstrates the reality of the stone, yet since its reality is shown only through perception (the rebound of the foot), it does not actually disprove Berkeley’s central claim—that matter cannot exist independently of its perception.
[4] I will often rely on the following interpretation of the Allegory of the Cave (see image 1): the knowledge we have of actual reality—the ongoing and multifarious phenomena of the world—is necessarily limited by our physiological and mental apparatus. We may extend this natural apparatus by means of artificial tools (whose efficiency we can usually verify), and ultimately through imagination and creativity (whose reliability, when correlated to reality, cannot always be verified). In general, we can say that knowledge is true, real, and effective, even if limited compared with the infinity of phenomena composing the actual world. More precisely, knowledge is true whenever there is a verified correlation between the subject and the object of knowledge. When this correlation is interrupted—as in fantasies, hallucinations, or misplaced concreteness—knowledge loses efficacy, creating a gap between subject and object (objective reality), from which countless problems arise.
The reason we can still affirm the objective (or, more properly, superjective—a Whiteheadian neologism) value of knowledge is this: although our knowledge is intrinsically limited, it is limited in the same way that a shadow is limited with respect to the processes that cast it. Just as a real object produces a real shadow, our knowledge, when correlated to actual processes, is real knowledge. I speak of the superjective value of knowledge because this value arises from the historical (evolutionary) correlation between object and subject. The subject comes after the object—it emerges from the world, as Whitehead observed—and thus should be called a superject rather than a subject (see Alfred N. Whitehead, Process and Reality: An Essay in Cosmology [New York: The Free Press, 1978], 88). For this reason, our knowledge of the real world rests on the correlation between what precedes us—the place of physicochemical processes from which reality-as-place emerges—and ourselves, as interpreters of that primal place. We are, first of all, the place where physicochemical and biological processes converge, before sociocultural and symbolic processes arise. To express this in Whitehead’s terms: I stand by the ‘reformed subjectivist principle’ (Process and Reality, 166–67), which overturns the Kantian relation between object and subject while preserving the truth that no knowledge exists apart from the experience of the subject, and that all knowledge requires correlation between subject and object. This principle restores the original meaning of the terms subject and object, prior to the Cartesian inversion of sense, as Heidegger showed in What is a Thing? (South Bend: Gateway Editions, 1967), 105: “Until Descartes every thing present-at-hand for itself was a “subject”; but now the “I” becomes the special subject, that with regard to which all remaining things first determine themselves as such… The things themselves become “objects”.’
[5] Henry Lefebvre used the term ‘archi-textures’, in the following passage: ‘One might say that practical activity writes upon nature, albeit in a scrawling hand, and that this writing implies a particular representation of space. Places are marked, noted, named. Between them, within the ‘holes in the net’, are blank or marginal spaces. Besides Holzwege, or woodland paths, there are paths through fields and pastures. Paths are more important than the traffic they bear, because they are what endures in the form of the reticular patterns left by animals, both wild and domestic, and by people (in and around the houses of village or small town, as in the town’s immediate environs). Always distinct and dearly indicated, such traces embody the ‘values’ assigned to particular routes: danger, safety, waiting, promise. This graphic aspect, which was obviously not apparent to the original ‘actors’ but which becomes quite dear with the aid of modern-day cartography, has more in common with a spider’s web than with a drawing or plan. Could it be called a text, or a message? Possibly, but the analogy would serve no particularly useful purpose, and it would make more sense to speak of texture rather than of texts in this connection. Similarly, it is helpful to think of architectures as ‘archi-textures’, to treat each monument or building, viewed in its surroundings and context, in the populated area and associated networks in which it is set down, as part of a particular production of space.’ In Henry Lefebvre, The Production of Space (Oxford: Blackwell Editions, 1991), 118.
In my architectural works, I extended Lefebvre’s networks of physical space to include immaterial perceptual relations (reified through lines, wires, threads, etc.) that bind subject to environment (object). In short, I correlated existing patterns of action and movement with new perceptual patterns (visual, tactile, auditory, olfactory, kinesthetic) of the subject situated within the environment destined to host a new architecture. These new patterns altered the existing place, context, and surroundings. Hence, architecture is always a correlation between space (the space of the project) and place (the actual site in which the project is realized). Yet it took nearly a decade of research for me to understand the deeper correlation between place and space, and, more broadly, between reality and knowledge: place is actual and concrete, the result of physicochemical, biological, social, and symbolic processes; whereas space is ideal and abstract, belonging solely to the symbolic domain. Unless we reconsider the entire range of processes involved, place and space remain outworn concepts. The images in this note (from my thesis with architect Davide Benini), along with Image 3b, the Featured Image for the post Václav Havel on Education, and the video Chōra, are examples of these Archi-textures.
[6] René Descartes, Principles of Philosophy, translated by V.R. Miller and R.P. Miller, (Dordrecht: D. Reidel Publishing Company, 1982), p. 40.
[7] We do not have to misplace the processes pertaining the emergence of a definite, and localized physical entity (generically, matter or the material entity), with the continuum itself which subtends the totality of matter, is diffused everywhere, and persists when matter emerges through it.
[8] In Principle X, Part II of the Principles of Philosophy, Descartes says: ‘nor in fact does space, or internal place, differ from the corporeal substance contained in it, except in the way in which we are accustomed to conceive them. For, in fact, the extension in length, breadth, and depth which constitutes the space occupied by a body, is exactly the same as that which constitutes the body…’, René Descartes, Principles of Philosophy , translated by V.R. Miller and R.P. Miller (Dordrecht: D. Reidel Publishing Company, 1982), 43.
[9] From its origin, place (topos) can be understood both as an abstract linguistic entity (a term fortuitously invented to denote location, as John Chadwick suggests in Lexicographica Graeca—see also my article Back to the Origins of Space and Place) and as a philosophical, other than physical entity, in Aristotle’s sense (the physical entity to which place gives location). By contrast, space (stadion/spadion) entered discourse as an abstract entity—an abstract term for an abstract measure of distance or extension. Only much later, after more than two millennia, did space acquire apparent substantiality. Yet this late ‘reification’ was, in truth, a fallacy. For space, as an abstract term denoting an abstract relation, cannot simply be transformed into a concrete entity by reason, as Newton and his interpreters attempted, to safeguard a physical theory (see the article on Julian Barbour’s The Discovery of Dynamics—Space and Place: A Scientific History – Part One). Accordingly, while it may be appropriate to understand chōra as place—which, as I have argued, has a double nature, at once abstract and concrete—it is misleading to equate chōra with space, since space is strictly abstract. This proposition may face resistance, given the centuries of contrary assumption and the intellectual inertia that, like physical inertia, requires time and energy to be overcome.
[10] The very existence of matter—its actuality as the materialization of a series of processes—should be considered a phenomenal event. Matter, as the place of processes that concretely realize themselves, is therefore both a place and an event. It is self-evident that every place is the manifestation of an event (or phenomenon, properly speaking).
[11] Misunderstandings may appear at an academic level, as if speaking about space, time, matter, or place concerned only a few specialists—physicists, philosophers, architects, sociologists, geographers, artists, and so on. Conversely, the tragic consequences of such misunderstandings affect everyone. This is my thesis: from the original act of substituting and dissecting a complex, unified reality into its abstract model—divided into parts and conceived as easier to handle (machanicism and reductionism)—arose unforeseen outcomes that affect all (e.g., climatic issues). From abstract economic and social models to urban and architectural schemes, many kinds of planning strategies severed from the logic and functioning of real systems—combinations of physical, chemical, biological, ecological, social, cultural, and symbolic processes—can negatively impact people’s daily lives and the environment.
[12] The images I have used to represent the continuum are one way to visualize the terms that described it across epochs (topos, chōra, apeiron kenon, spatium/space, locus/place, spacetime, field, etc.). Still, no picture or image can capture the full epistemological and ontological connotations behind those terms. Furthermore, any interpretation of ancient concepts is necessarily a posteriori and offers no complete guarantee of the original meanings—or their nuances—in the minds of ancient authors and their contemporaries. Precisely because of this fundamental ambiguity, the debate about space and place has lasted so long, and it is unlikely ever to reach a definite conclusion.
[13] This ambiguity is encapsulated by the term ‘bastard’, Plato’s epithet for the mixed nature of the continuum. More precisely, he says that the receptacle (another translation of the Greek hupodochē, often identified with chōra—the continuum in which everything exists) must be grasped through a kind of ‘bastard reasoning.’ See Edward S. Casey, The Fate of Place: A Philosophical History (Berkeley: University of California Press, 1997), 37.
[14] Edward S. Casey, The Fate of Place: A Philosophical History, 71.
[15] Edward S. Casey, The Fate of Place: A Philosophical History, 55.
[16] See Einstein’s article ‘The Problem of Space, Ether, and the Field in Physics’.
[17] Jean Piaget and Barbel Inhelder, The Child’s Conception of Space (London, Routledge & K. Paul,1956).
[18] In this regard, I undertook a specific analysis of Vitruvius’s De Architectura Libri Decem. More generally, I observed that in many Greek and Latin texts, when classical authors used the terms locus or topos (closer to the materiality of place than to the immateriality of space), modern translators often render them as ‘space.’ This raises an obvious question: how could the ancients possess a concept of space as we usually conceive it today—an immersive background—if they had no word to denote it? Heidegger already observed that ‘the Greeks had no word for space’ (Introduction to Metaphysics, New Haven & London: Yale University Press, 2000, 69). A quick check of translations confirms that the ancient sources for ‘space’ are usually topos, sometimes chōra, and locus. Contrary to common assumptions, the modern notion of space as a background container for objects and bodies was unavailable to the ancients. This point is expressed explicitly and convincingly by the mathematician Salomon Bochner in his entry ‘Space’ for the Dictionary of the History of Ideas, where he writes that the concept of ‘background space’—the continuum in which things exist—did not belong to the ancients, but emerged gradually, culminating in the works of Descartes and Newton (Vol. IV, New York: Charles Scribner’s Sons, 1973, 295). This also reflects my own view of the evolution of the concept of space.
[19] ‘Until the seventeenth century, the word “space” had the general meaning of “extent”, and in English, back to the fourteenth century, was used in two main specific senses, one in regard to time, an extent or lapse or interval of time, and the other in respect of linear distance, an extent or interval between two or more points, and consequently also a superficial extent or area.’ Ivor Leclerc, ‘Concepts of Space’, in Probability, Time, and Space in Eighteenth-Century Literature, ed. Paula R. Backscheider (New York: AMS Press, Inc., 1979), 209-216.
[20] Einstein wrote: ‘Euclid’s mathematics, however, knew nothing of this concept [space] as such; it confined itself to the concepts of the object, and the spatial relations between objects. The point, the plane, the straight line, the segment are solid objects idealized. All spatial relations are reduced to those of contact (the intersection of straight lines and planes, points lying on straight lines, etc.). Space as a continuum does not figure in the conceptual system at all. This concept was first introduced by Descartes, when he described the point-in-space by its coordinates. Here for the first time geometrical figures appear, in a way, as parts of infinite space, which is conceived as a three-dimensional continuum’. See Einstein’s 1934 article: ‘The Problem Of Space, Ether, and The Field in Physics’. In Ideas and Opinions (New York: Crown Publishers, Inc., 1954), 279.
[21] René Descartes, La Geometrie – The Geometry of René Descartes, translated by D. E. Smith and M. L. Latham, (New York: Dover Publications, Inc., 1954), 26, 27.
[22] Julian B. Barbour, The Discovery of Dynamics (New York: Oxford University Press Inc., 2001), 618.
[23] Isaac Newton, Newton’s Principia – The Mathematical Principles of Natural Philosophy, trans. A. Motte (New York: published by Daniel Adee, 1846), 78.
[24] in this sense we have to interpret the analogies between Aristotle and Ernst Mach pointed out by Julian Barbour, when he introduced the work of Aristotle – Chapter 2, The Discovery of Dynamics (see also my presentation of that book in the article: Space and Place: A Scientific History – Part One).
[25] At this regard, as Jammer said ‘because matter cannot be understood apart from knowledge of space-time, then matter as source of the field become part of the field’, in Max Jammer, Concepts of Space – The History of Theories of Space in Physics (New York: Dover Publications, Inc., 1993), 198.
[26] The different interpretations of the continuum envisioned by Einstein in his entire career, are the subject of an interesting book forwarded by Jammer and written by the physicist and philosopher of science Ludwik Kostro, Professor at the University of Gdańsk: Ludwik Kostro, Einstein and the Ether (Montreal: Apeiron, 2000).
[27] From the blue row I added to Carlo Rovelli’s scheme in Reality is Not What It Seems (Italian edition: La realtà non è come ci appare, Milano: Raffaello Cortina Editore, p. 167), two things emerge. First, Aristotle does not regard time as a primary concept; for him, time is the measurement of change, and change always concerns things moving from place to place. Matter (as “formed matter”—since for Aristotle physical matter is inseparable from form, see The Nature of Physical Existence: PART II – The Concept of the Physical in the article Concepts of Place, Space, Matter, and the Nature of Physical Existence) and place are primary for Aristotle, in opposition to the Atomists, who posited indivisible atoms moving through the void—an idea he firmly rejected. Second, the concept of place (topos) is intrinsically richer than what we call space. It includes that dimension of time which, when correlated with matter, explains time itself as the measurement of change (of place) of a material entity. This is another reason why it is reductive—and ultimately mistaken—to equate Aristotelian topos with space. From its origins, space carried a dimensional sense (an extension between points, objects, or bodies—thus a distance or interval). By contrast, place—Aristotle’s topos—had a more encompassing meaning, intimately bound to the material and the temporal, while still being dimensional (res extensa).
Works Cited
Barbour, Julian B. The Discovery of Dynamics: A Study from a Machian Point of View of the Discovery and the Structure of Dynamical Theories. New York: Oxford University Press Inc., 2001.
Bochner, Salomon. “Space“. In Dictionary of the History of Ideas, Volume IV. New York: Charles Scribner’s Son, 1973.
Casey, Edward S. The Fate of Place: A Philosophical History. Berkeley: University of California Press, 1997.
Descartes, René. Principles of Philosophy, translated by V.R. Miller and R.P. Miller. Dordrecht: D. Reidel Publishing Company, 1982.
Deutsch, David. The Fabric of Reality; The Science of Parallel Universes and Its Implications. New York: Penguin Books, 1997.
Einstein, Albert. “The Problem of Space, Ether, and the Field in Physics”. In Ideas and Opinions. New York: Crown Publishers, Inc., 1954.
Greene, Brian. The Fabric of the Cosmos – Space, Time, and the Texture of Reality. New York: Alfred A. Knopf, 2004.
Heidegger, Martin. What is a Thing? South Bend: Gateway Editions LTD, 1967.
—. Introduction to Metaphysics. New Haven & London: Yale University Press, 2000.
Jammer, Max. Concepts of Space – The History of Theories of Space in Physics. New York: Dover Publications, Inc., 1993.
Leclerc, Ivor. ‘Concepts of Space’. In Probability, Time, and Space in Eighteenth-Century Literature, edited by Paula R. Backscheider, 209-216. New York: AMS Press, Inc., 1979.
Lefebvre, Henry. The Production of Space. Oxford: Blackwell Editions, 1991.
Leibniz, G.W., and Clarke S. Correspondence, edited by Roger Ariew. Indianapolis: Hackett Publishing Company, Inc., 2000.
Newton, Isaac, Newton’s Principia – The Mathematical Principles of Natural Philosophy, translated by A. Motte. New York: published by Daniel Adee, 1846.
Piaget, Jean, and Inhelder, Barbel. The Child’s Conception of Space. London, Routledge & K. Paul,1956.
Rovelli, Carlo. La realtà non è come ci appare. Milano: Raffaello Cortina Editore, 2014.
Weinberg, Steven. “The Search for Unity: Notes for a History of Quantum Field Theories”. Daedalus, Vol. 106, 1977.
Whitehead, Alfred North. Process and Reality – An Essay in Cosmology. New York: The Free Press, Corrected edition, 1978.
Image Credits
Featured Image: Tomás Saraceno, ‘Social… Quasi Social… Solitary… Spiders… On Hybrid Cosmic Webs’, 2013. Installation, detail.
Images 03, 03b, 04, 05, 06, 07, 08, 09, 12 and Images in Note [5] by Alessandro Calvi Rollino, CC BY-NC-SA
