Place, Space, and the Fabric of Reality

Archi-textures: study-model for the Vaxjo Tennis Hall, architectural competition. Alessandro Calvi Rollino Architetto, 2009.

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 things and bodies exist and move.[1] This continuum is the invisible substrate we should think about when we speak of the arena or background of our lives: it is 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, explicated by terms like above, below, inside, outside, beyond, next to, near, far, etc.); (ii) metrics (order of position, or situation, between things or bodies explicated by means of distances reducible to abstract dimensional units); (iii) temporality (order of succession between things or bodies, explicated by means of their reciprocal presentation and duration: one before or after the other; one simultaneous to the other, etc.).[2] It is a continuum, properly, in virtue of the seamless continuity that exists not only between place (or space according to many) and time but also between place (or space), time and matter; thereby the material aspect is included in this sea of continuity. Obviously, and most importantly, this continuity also relates the object to the subject, and this is another fundamental reason why we call it a continuum. In the end, the continuum objectivates the relations between entities and give them 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 continuum – then, the refutation of the canonical division between matter and place, or space – is a relatively recent finding; actually,  a ‘re-finding’ if we consider the history of the continuum and the modes through which we have expressed it in the different epochs. In the current epoch, from a physical perspective, the continuum has taken the shape and the name of ‘physical field, and matter is no more considered a localized entity, but a field of localization participating in the extended existence of the continuum itself. We will see the implications that this type of vision has on the traditional concepts of space, place and matter. Conversely, spacetime is an example of a dimensional continuum, properly. It is a dimensional continuum since spacetime expresses a tetra-dimensional continuum, where the continuum is mainly considered according to the three basic spatial dimensions, or extensions (width, height, and length), and one temporal dimension (which is an extension as well; this fact should alert us on the intrinsic connection between time, space and matter: in different times, from different authors, we have read that extension can be considered as the defining character of space, or place, time or even matter), severed from matter.

If we go back to the time when this debate on the fundamental state of reality we are inquiring into started, we see that such a fundamental state was probably identified and represented by different terms: chaos, apeiron, pneuma apeiron, kenon, chōra, topos, anaphés phusis, spatium, locus, absolute space, ether, spacetime, etc. Of course, each of these terms puts a different focus on the different intelligible aspects related to the continuum: spatial, placial, material, or even immaterial aspects.

Now, the main question I would like to answer to is the following one: given that the continuum referred to the order of the things and bodies is a true and a real datum beyond any reasonable doubt (it is beyond any doubt the fact that the actual reality we live in is an ordered system), are all of the different modes of expressing the continuum equally true, real and effective? I mean: 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‘ any time I’m present in this room, and the same holds for anyone who enters this room, in every moment.[3] Then, without appealing to the Cartesian ‘I’, there is no doubt that, while I’m writing these notes, I am here, now, in this place that I call ‘room‘. Yet, I ask: is it equally real, true and effective if I say that I am in a physical space, the same way I can say that I am in this place – the room, properly -, now?  When I use the expression ‘true, real and effective’ to describe the physical reality I’m living right here and now, I basically intend to find a correlation between the term that I have used to describe the continuum (that is: space, spacetime, place, etc.) and the actual continuum itself, which is the basic component of reality, the arena or background of our lives. This means that I consider terms and concepts ‘true, real and effective’ when they are correlated with the ongoing reality of events that occur in a certain place and time, beyond any reasonable doubt. Conversely, if concepts and terms that aim at describing the ongoing reality fail to be reasonably correlated with them, we should say that these terms/concepts are less effective, or they are not effective at all. This may be the case for certain ideal, imaginary, or even abstract terms and concepts. For instance, I cannot say that the term unicorn is an effective word to represent an animal that exists ‘out there’. In fact, the term unicorn refers to an abstract, ideal, or imaginary concept (an imaginary animal), which does not correlate with the ongoing reality of facts. ‘Out there’ there is no unicorn that kicks me back. It is an abstract entity, a fantasy, precisely. The same holds for Gotham City, or many other fantastic, ideal, or abstract terms and conceptualizations. These are all cases where there is not a direct correlation between the terms/concepts that we used to define reality and the concrete reality of facts. Whenever we find out that the terms or concepts we used to describe the continuum of reality have not the correlation we expected, we should treat those terms or concepts as imaginary data cast on reality, or as terms/concepts that are not effective for that purpose: those terms, or concepts, break the fundamental epistemological correlation that actually exists between the subject and the physical world of objects. Ultimately, they may halt the progress of knowledge, or, even worse, as it was the case for the concept of space – we will see it soon.

By anticipating the answer to the aforementioned question about the modes of describing the continuum, contrary to appearances and old presuppositions, I maintain that the concept of space is not an effective term to describe the continuum, if this is intended as the ultimate datum of physical reality. Space is an imaginary concept, a shadow cast on reality by our imagination; it is not a fully-effective term to deal with the continuum as a concrete fact of nature; rather, it is a deceitful concept. Conversely, a term that I consider to be ‘true, real and effective’ to express the concept of the continuum, as a fact, is place: it is a shadow as well (language has intrinsic epistemological limits), yet this shadow is real, actual, given that it is cast on reality by the actual entity – I mean the actual physical continuum – which keeps reality together and ordered.  Of course, in this game of mirrors and reflections which hinges on language, the expression ‘physical continuum’ – or even ‘dimensional continuum’, and the likes – acts in the guise of the actual entity that keeps things together and ordered, therefore it is a shadow as well. However, that shadow is an actual shadow, cast by the actual entity that we identify by that expression (the continuum); it is not a shadow cast by our imagination severed from physical reality; or, to put it another way, it is not a fantasy, an illusion, hallucination or a daydream. [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, namely: place is an appropriate and effective term to indicate the continuum of reality, that is the continuum that keeps reality together (order of co-existence between physical elements) and ordered (order of succession between physical elements). Space only exists within the domain of our imagination (it is an abstract term, a figment of our imagination): it is not a proper term to define the actual continuum in which everything exists and happens.  Yet, we must be careful: we can invent any term, at any moment, and say that such a term ‘really’ represents something ‘out there’. That’s fine: this is a basic function of language, in the end. However, what I’m questioning here is the historical primacy of certain concepts – what concerns us, here, is the primacy of place against space for the definition of the continuum -, and the different ‘effectiveness’ or ‘appropriateness’ of certain terms to convey an adequate meaning with respect to which those terms are signs. My interest in questions of space and place had a burgeoning escalation as soon as I understood that space was not an adequate term (ironically, a limited term…) to deal with the fundamental states of reality, as it was supposed to do, especially since the time of Newton. Therefore, there are two related questions, here: one concerning the nature of space and place from the historical perspective; another from the linguistic perspective (and in it, I include the etymological and the philological perspective). It is my conviction that without engaging with such questions no philosophical or scientific inquiry about space and place can lead to convincing results.

The inquiry into the nature of the continuum and its linguistic aspects we have already started is situated in-between epistemology and metaphysics, or ontology. It is certainly a difficult and unusual domain for architects, but I believe architects should become used to such a domain in the coming future (at least, they should know its basic outline), given that the fundamental terms and concepts through which it is possible to investigate this domain – I mean the concepts of space, place, matter, the void, motion and time, to begin with – besides being primary concepts for philosophers and physicists, are also basic ingredients for the activity of architects. And, I repeat it: it was my direct experience as an architect working intuitively on space, place, matter and time that took me to inquiry into the  meaning of those concepts by going back to the sources whence those meanings stemmed from, as soon as I understood that the traditional meanings attributed to those concepts had many ‘grey areas’ that needed to be elucidated if architects wanted to be more aware of the basic theoretical tools of their profession.

If we come back to the phrase I have used in a previous passage – ‘I am in this room, now’ – we have to start reasoning about: (i) the proposition ‘I am’ – the physical entity-as- subject that truly exits as a concrete, material entity related to other material entities; (ii) the proposition ‘in this room’- the container/incubator of events, things and bodies (I come back to the main question: what is the appropriate name for describing the continuum of events that is intrinsic ‘in this room’? from a concrete perspective, can this room be epitomized as place or as space? What is the difference if we understand the continuum that is intrinsic in this room as space or as place?); (iii) the term ‘now’, intended as temporal dimension/extension – a duration, properly -, which guarantees the existence and the ordered relation of the physical entities we are considering. At the very least, if the proposition ‘I am’ is the representation of an actual material entity (my body, its presence), and the ‘now’ represent the temporal dimension concerning the duration of the material entities included in the scene we are considering (or to put it in different terms, the ‘now’ regards the duration of the processes in which/out of which the physical entities emerge, exist and behave), then, as a first approximation, we could generally affirm that the here and the where of the proposition ‘in this room’ may also represent the continuum (a portion of/in the continuum, actually) that offers a concrete, and a seemingly stable existence to the entities, in the interval of time considered. Hereinafter, the step is short before we can conceive the possibility of extending the material character of the things to the room itself intended as part of/in the continuum (this happens by correlating the where of the room – intended as geographical region or spatial/local expanse – to the what of the room – intended as physical entity made up by walls, floor and ceiling -, and by fusing them together into a whole, or unicum).

Once again, in order to put a deeper focus on the question regarding the modes of knowledge of the continuum and the way it can be represented trying to avoid epistemological traps, I will make use of a historical excursus: this has the scope to sum up and condense into a personal narration the past three articles concerning the historico-philosophical and the historico-scientific perspectives on space, place and matter.

Before proceeding with the historical argumentation, I would like to reflect a little bit more on the preliminary investigation of the terms I have used as the title of the paragraph: the fabric of reality and the continuum.

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Image 3: The Fabric of Reality is the physical continuum that keeps entities together and related according to their order of position and succession.

By the words fabric of reality I refer to how reality is made – I mean its fundamental essence -, according to the human perspective at the beginning of the new millennium.[5] Figuratively, the terminology fabric of reality also puts the focus on the critical interweaving between the basic concepts used by many scholars during different epochs, (I mainly refer to the concepts of matter – or, more appropriately, of substance, from the Latin etymology of the verb sub-stare, that which stands under what appears – place, space, and time) to offer an interpretation of the fundamentals of reality. I believe that such fundamental texture or fabric of reality can be interpreted as a constitutive and connective fabric, a sort of invisible glue that keeps things and bodies related and ordered. The very terms that we use to characterize the fundamental nature of things – in primis: matter, place, space and time – are constitutive parts of that continuum, an almost inextricable continuum, which also correlates objects to subjects whenever they emerge at larger scales. This means that the continuum, by holding together names and things, also guarantees the possibility for human knowledge. To investigate the fundamental nature of the continuum through our rational faculties implies a high degree of abstraction: we lose something in authenticity concerning the nature of things and physical reality, but we earn in communication. To sum up, we could say that the fabric of reality is the invisible glue that holds things and bodies together, connects them and gives them the apparent sense of continuity and stability that we see all around us. Without such a glue that supports the apparent continuity of events and phenomena, reality would be like living in a surrealist painting: there would be no certainty about the disposition of elements and no certainty about the physical forces that act upon them. There would be no certainty either concerning the duration of events; without it, that which comes after could precede that which comes before.

I believe the image concerning the unifying structure of reality – the fabric of reality – understood as the ultimate place that, ab origine, can simultaneously develop physical/material, positional (or locational), and temporal properties is a prolific and effective image to describe the fundamental structure of reality. In fact, there is no material entity, or physical substance, which is not in relation with other entities ingrained in that continuum and emerging through it. Then, from the very beginning, and in every phase of its existence, each physical entity – what we generally term ‘physical matter’ – is a condensate of (i) substance (the entity having non-zero intensity or extension), (ii) localization, and (iii) temporality, which appear simultaneously. Then, we could understand the term matter – or physical matter – as the generic word that, all at once, encompasses physical substance (the product of intensive or extensive forces acting in the continuum), localization and duration; it is the pure physical existence of the entity that manifests to the world.

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Image 4:  Physical Matter understood as the place of physical processes after which substantial, positional and temporal properties emerge through the continuum.
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Image 5: The Fabric of Reality can be interpreted as a physical continuum since it guarantees the seeming continuity and stability of the relations of order and succession between the entities that emerge through and exist within the fabric.

Dimensionality, understood as physical extension, is intrinsic to matter: at least, this is also what Descartes intended by the formula res-extensa, as stated in Part II, Principle IV, of his Principles of Philosophy, according to which ‘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]

Considering this question more in detail, I would say that matter and dimension (in the sense of physical extension) are literally taken under the same umbrella – that is, they are unified and transformed into a concrete entity having non-zero dimension – by an intrinsic force, a tension properly, acting in the continuum: when this tension acts inwards from a certain region of the continuum, we speak of intension  properly (intensio, from the Latin verb intendo,ere, where the ‘in’ defines an original insideness, thereby an inward tension), and we have a compression of – or a higher density in – the continuum (in this regard, we can speak about intensive continuum, properly); this results in a higher density (mass) and energy of the concretized entity: a material entity (Image 6, below).

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Image 6:  Physical Matter understood as the concretization of intensive forces acting in the continuum.

Conversely, when tensive forces act outwards, we properly speak of extension (ex-tensio from the Latin verb extendo,-ere, where the prefix ‘ex’ defines an original outsideness, that is a tension directed outward, a stretching out, properly), and we have a rarefaction of matter; when such forces are extreme they imply a very dim or almost null visibility of traditional matter, which disappears into the continuum, and, consequently, is epitomized as space: an ‘extensive continuum’ (image 7, below).

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Image 7:  Physical Matter understood as the concretization of extensive forces acting in the continuum.

Then, at the one extremity of the gradient, or spectrum, of tensions we have the maximum rarefaction of the continuum, after which physical matter – as a discernible localized physical entity – dissolves within the continuum itself:[7] this state of matter and/or energy tends to zero. At the other side of the gradient of tension, we have a concentration of matter and/or energy tending toward a positive and infinite value. The concept of the void, or space belongs to the former extreme (what is space if not a pure extension?); at the other extremity, we have a state of maximum aggregation or density of matter: this is the place of maximum material intensity. Such an extreme state of matter is a place where the compression and density is so high that nothing can escape its attraction. In-between the two extremes we find usual forms of matter, which our mind-and-body is naturally correlated with (this is the common phenomenological dimension of the res-extensa). Now, I think we have a clue for the reason why by the expression extensive continuum we often mean space: this is the extremity, or the part of the tensional spectrum of forces acting in the continuum, where matter/energy seems to be absent (it is certainly absent for the physiological possibilities of the human body, which can only detect matter/energy within certain ranges). Conversely, at the other extremity of the spectrum, where intensive forces prevail over extensive forces, matter certainly presents before our eyes: that’s why physical matter can be easily associated with the intensive part of the continuum. In spite of the apparent differences, both states – the extensive and the intensive -, given that they are physically existent and present (they have intension or extension), are logically characterized by having a non-zero dimension (or dimensions): in this sense, both extension and intension are dimensional facts. 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: extension and intension are just two different names for the same fundamental phenomenon concerning the tension in/of the continuum. That’s why Descartes says that space and matter are not different, in the end: he refers to the fundamental state of reality – the continuum as a non-zero tensional state – that subtends the maximum rarefied state of matter (what we are accustomed to conceiving as space) as well its most compressed state (what we are accustomed to conceiving as matter).[8]  Such a continuum as a non-zero tensional state is, therefore, a plenum: reality is a plenum, even in those remote regions – places – where matter is maximally rarefied, invisible, and, too often, mistaken for the void, or for (empty) space. Besides Descartes, this is also what Aristotle believed in: according to them, reality is definitely a plenum.

reality is a plenum

As you have probably already noted, by using this kind of terminology, a sort of inversion happens: when the tension in the regions of the continuum tends to the maximum and is directed outward (maximum ex-tension) we will have the minimum extension of the usual forms of physical matter (that is, we have its maximum rarefaction); beyond that maximum value of tension directed outward any trace of physical matter dissolves in the continuum, and we can only speculate on what happens after, or beyond, that state. Literally, we are entering metaphysical speculations (without even appealing to Aristotle’s works, metaphysics means after physics, then, we are speaking of the state after/beyond the physical). ‘After’ the physical, that is, after that which is concrete and ‘bounded’ (that’s why the realm of the physical is a place, if we stick to Aristotle’s definition of topos-as-place) – we find that which has not a limit, literally the unboundedto apeiron in Greek -, and/or, for semantic affinity, the voidto kenon in Greek -, or, even, space. Actually, it is from the above-mentioned maximum value of rarefaction of matter, almost a dissolution into an apparent nothingness, that the idea of space as pure extension arises: this is the block of glass without glass that Barbour spoke about by referring to the Newtonian concept of absolute space; or, we add, this is the intangible substance anaphés phusis – Epicurus spoke about in antiquity: pure dimensionality, or even distance, interval between things (diastēma). In fact, as I have tried to show in the article Back to the Origins of Space and Place, from a linguistic perspective, space enters the debate as a distance, properly: such is the Greek spadion, or stadion. To come back to the nature of the continuum in-between physics and metaphysics, our speculations on what may exist after/beyond the place of maximum ex-tension can also regard the nature of the chaos, the primordial confused state out of which the ordered cosmos emerged. In this case too, that which is unbounded may be interpreted as an indistinct, or even indeterminate material mass without any sensible form (apeiron); that’s why, apart from Aristotle’s definition of place/topos as a bounded entity, it is appropriate to speak of that which is sensible – that which is physical, ultimately – as something ‘bounded‘, to distinguish it from that which is unbounded, chaotic (but intelligible). To put it briefly, we are questioning on the difference between that which has a limit (peras) – this is the nature of place, according to Aristotle -, and that which has not a limit, like the apeiron of Anaximander, properly, or the void, or even space; or, again, the chaos, if we remind of Casey’s initial chapters in The Fate of Place, where we have seen that many antique mythologies and cosmologies consider place the first ordered state of existence after the chaos (the cosmos as a whole – literally, an ordered state – is a place made of places emerging from the chaos). It is evident the logical and psychological necessity to cling to matter as an ordered state to describe the fundamental physical state of reality.

It is from the extremity of the gradient belonging to that which exists but tends to zero (a nearly-zero form of energy we have also said) that the short circuit between matter and place, matter and space or matter and the void appears in its entirety. I believe the most appropriate concept to reveal that short circuit is place. It is place that allows the presence of matter in the physical world as an ordered state, which is a the same time sensible and intelligible: a material datum, or fact. For me, place – in the reformed and extended meaning that I’m proposing here – transcends dimensionality in the sense that it encompasses both the minimum and the maximum dimensions, besides incorporating that which has not a physical dimension at all (ideal or intelligible place). To identify the substrate, I mean the continuum  – what Plato calls hupodochē or even chōra -, as a place of processes, is a way to justify the entire genealogy of that which exists as an aggregate – a concretion, properly – of material substance (ex/in-tension) , localization and duration: the physical entity as the place of its own existence. Only from places can other places be generated: that’s why I think it is possible to interpret the Platonic chōra as an ultimate place, rather than a space or a typology of space. Like the platonic chōra, this place I’m speaking of preserves both material and immaterial dimensions; this does not hold for space which only corresponds to immaterial dimensions. [9]

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Image 8:  Reality and its continuum: in-between physics and metaphysics

Then, given that the continuum can be intended either as an intensive or an extensive continuum (other than temporal continuum), more generally, it can be intended as if it is subtended to the presence/existence of matter as well as to its apparent and hypothetical absence: while, in the first case, we can speak of physical or sensible matter as a matter of fact, in the second case – the seeming absence of physical matter – we can only speak or reason in abstract, through words and concepts that are projections of our imagination into the actual reality of facts (in a passage before, I have spoken of imaginary shadows cast on the actual reality); however, it may happen – and it happens frequently – that in the process of knowledge the imagination of someone is able to anticipate or imagine before others that which no one else is able to see or to imagine, but which ‘really’ exists ‘out there’: when this happens it means that someone has been able to fully correlate his/her imagination to the actual reality of facts, thereby extending the edge of knowledge.

Chōra and, sometimes, hupodochē was the name attributed by Plato to that pristine place, or original substrate. Topos was the name given by Aristotle to define the continuum that actively determines the movements of physical matter (material bodies): this is the natural place where matter, in the form of bodies, exists and moves. To kenon – the void – was the name chosen by the early Atomists, to whom Aristotle opposes his theories.

But allow me a final consideration before continuing with the historical argumentation concerning the continuum and its names. This is the way I see reality or, better, the fabrics of reality, its intimate texture: a place that encompasses physical matter as well as its duration.[10] It is this encompassing embrace, of physical in/ex-tension, localization and duration into a single entity, that I call place. Henceforth, a place – any place – is, at once, a unicum and a continuum, which goes far beyond the simple character of location that is traditionally associated with a physical entity. The character of ‘simple location‘ is a misleading abstraction (it is misleading since it abstracts what cannot be abstracted: it abstracts location from the material in/ex-tension and duration that is intrinsic to that location; from this misplaced abstraction – which is exactly the reverse of the fallacy of misplaced concreteness concerning space – derives the traditional understanding of place as simple location or localization, which is a concept I reject and which I’m currently questioning – this is the scope of this website, ultimately). Such an encompassing embrace puts focus on the opportunity and the difficulty of distinguishing a line of demarcation between matter, localization and temporalization: as a matter of fact, this can only be done in abstract and a-posteriori. Any entity, I mean any physical entity, is before all a unicum in which matter, place and time (as duration) co-exist in a seamless continuity. It is man or, better, it is the highly abstracting cognitive faculty of man that is able to dissect reality with a rational knife, thereby reducing to parts that original unicum; that’s how, at a certain historical moment, we found matter on one side, place (or space) on another side and time, on a different side again. But, most of all, by focusing our attention on matter, place (or space) and time as single/individual characters or properties, we have forgotten their intrinsic relationships. Using these basic concepts – place or space, matter and time – scholars of any epoch tried to solve the fundamental phenomenon concerning the existence and behaviour of material entities. So it seemed that – and it still seems that – our bodies and the objects around us are immersed in what we now call a dimensional continuum that guarantees a stable order to the world and its appearances, and gives an account of that original continuity, indeed by obscuring, silencing and hiding it. This operation of disguise concerns a reality that in the origins is undivided –  a whole -, but which is understood, interpreted and described as dualistic and/or divided into parts (of which, I repeat, we have forgotten the intrinsic relationships): this gap between reality and knowledge is the source of many incomprehension and tragedies as well. [11]

To recover the primordial sense of the continuum and to understand the passages that took to its dissection into different parts (matter, place, space and time to begin with), is a mandatory task for us. To do that, we have to analyse history (the history of thought). As I briefly mentioned before, what follows is my synthesis of the three preceding articles that focused on the historico-philosophical and the historico-scientific perspectives concerning questions of place, space and matter. These are the concepts through which it is possible to start investigating the fundamentals of reality.

2. The intuition of the physical continuum according to Aristotle

The intuition of the physical continuum that surrounds us, and in which we live, is something difficult to describe through words. I believe some terms are opportune to describe that concept, other terms are not. That question is as old as the history of philosophy. As far as we know, among the first men that investigated the relation between physical bodies and the continuum within which such entities seemed to exist and move, we find Plato and Aristotle. Very succinctly – and, inevitably, a bit roughly – chōra was the name used by Plato to describe that original ‘within which’. Topos was the name used by Aristotle. Yet, probably, it was Anaximander who described that initial state before anyone else: apeiron was the name used by the Milesian, but there are very scant written sources about that. Of course, there are hidden meanings or shades of meanings behind those original concepts, and while some of them may match our expectations with respect to the image we have of the continuum, other may not.[12] Aristotle was quite direct in his writings: his definition of topos – which I would generically translate into English as place rather than space – was rationally devised to challenge the theories of the early Atomists – Leucippus, Democritus and their disciples – according to whom, the ultimate reality was composed of indivisible pieces of matter – the atoms – moving through the voidto kenon. For the ancient people, the concept of the void was an untenable notion from a psychological point of view: after all, this is what the ancient cosmogonies have said (we have seen it through the narration made by Edward Casey, in the past article Place and Space: A Philosophical History). And this is also the reason why the first atomistic theories were rejected in favour of Aristotle’s theory, who considered the ultimate reality as a plenum, and not as a void. The most complicate theorization was the one devised by Plato – I consider Plato’s theory, expressed in the Timeus, the most appropriate one, yet it was too ambiguous and open to different and difficult interpretations;[13] Plato took into consideration the appearances within which bodies seemed to be located. As far as I know, this is the first ancient theory with respect to which we can speak about the correlation between epistemological and ontological factors through which it is possible to investigate the fundamental nature of reality: that which exists as the ultimate reality and the knowledge we have of such reality. Yet, it was too ambiguous and so complex that the theory was abandoned – we were almost at the beginning of what could be generically termed ‘the dawn of abstract thinking’. The debate on the nature of physical existence was won by Aristotle, ultimately: for well over a millennium, ancient astronomers based their observations on Aristotle’s cosmology, to offer the first scientific framework through which considering the order of things and its continuum.

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Image 9: The Cosmology of Aristotle: a theory of place (topos), matter and motion.

For this is exactly what we are speaking about: the order of things, that is, the cosmos as a world ordered according to the coexistence and succession of things and bodies; a stable and intelligible order, that’s what the term ‘cosmos‘ means in the origin. The cosmos – an ordered world or universe – understood as the counterpart of the chaos – the utter disorder. But even if the debate was ultimately won by Aristotle, his theory was strongly criticized since the beginnings; in fact, the modern concept of space springs, develops, and becomes mature after centuries of discussions on the Aristotelian notion of topos. Evidently, that term – after the definition given by Aristotle – did not meet all the requirements that were necessary to exhaustively define the nature of physical reality and its continuum.

Since the time I became interested in the debate about the nature of place and space, I have read a certain number of scientific and philosophical texts: I have noticed that many scientists – physicists, especially – are prone to interpret the Aristotelian topos as space; conversely, those scholars who are more responsive to the intricate mix of physical, philosophical and philological questions that determine the meaning of words, are more inclined to consider topos as place, or, at most, to interpret its meaning according to the context. This difference of interpretation concerning the term topos, which, in the end, is an interpretation that concerns the nature of the continuum – is it place? Is it space? Is it a vacuum? – is highly debatable, given that Aristotle’s vision of reality was the vision of a plenist; a vision that opposed the conceptions of the Atomists and their idea of the void as ‘that in which/through which’ atoms exist and move. Now, if we attain to logic and assume that my synthetic narration, in its broad outline, is true, we find ourself in the middle of an incongruence concerning the relation that we, modern people, have with the terms that we use to describe the intuition of the physical continuum all around us: how can we attribute Aristotle a theory of space (a concept that, since its appearance, is paired with the idea of distance, extension or interval between things, suggesting us the idea of the void), if the idea of Aristotle is that of describing physical reality understood as a plenum? As a matter of fact, it seems to me that the Aristotelian topos is both physically and, most of all, ontologically connected to its content, that is, it is connected/correlated to the matter (material bodies) whose topos offers the possibility to exist (there is no matter without place: this is a fundamental axiom for Aristotle, I have already written about that in one of my previous articles, by borrowing an argument already considered by Edward Casey).[14]  In my opinion, that ancient concept – topos – is as much distant from the concept of the void as it is distant from the concept of space (yet, there is little doubt about the semantic affinity between the void and space). ‘That’s what place (topos) is: the first unchangeable limit (peras) of that which surrounds’: this is Aristotle’s definition of place.[15] From the logical and ontological perspectives, it seems to me that understanding topos as place is an opportune linguistic choice, before than an appropriate choice from the historical and philological perspectives.

To sum up this paragraph, the first debates on the nature of physical existence and the continuum in which physical entities exist and move, were solved by the theory of place devised by Aristotle: according to the ancient people, that immersive extent (the physical environment as the stage where all things exist and events happen), that invisible something that surrounds things and bodies and guarantees their stable order has to be interpreted as place, not as space.

3. The dimensional continuum according to Descartes and Newton

After Aristotle’s definition of place (topos), there was ground enough for criticism concerning the dynamical and dimensional characters of that definition, especially. As regards the first argumentation, according to Aristotle, bodies in the sublunar region moved upwards or downwards, in a straight line, according to their tendency to reach for their natural places (that which is heavy – i.e. a rock – goes down, that which is light or very light – i.e. the fire – goes up); conversely, bodies in the celestial regions moved according to perfect circular paths through the aether (see image 9, above). We have already analysed the different historical passages that determined the abandonment of Aristotle’s cosmological vision: at this regard, the activity of the astronomers was decisive not only to dismiss the credibility of Aristotle’s cosmology, but also, as a consequence, to dismiss the concept of natural place and natural motion (I redirect you to the article Space and Place: A Scientific History – Part I, focused on the book The Discovery of Dynamics, by Julian Barbour). As to the second type of criticism regarding the Aristotelian definition of place – its dimensional character -, according to the very definition of place (topos) given by Aristotle, place ought to be considered as a two-dimensional entity. Since the beginnings, that seemed almost a contradiction in a world that appeared to have more than two dimensions (i.e.: front-rear, left-right, above-below, or, by abstraction, length, width, and height). Yet, at this regard, we must be careful: to say that the intuition of the notion of three-dimensionality belongs to the pre-scientific way of thinking, does not mean to say that ancient people had already intuited, let alone elaborated, a notion of space as immersive extent of the kind modern people is accustomed to (very often, we incur into this highly debatable, yet immediate and – I believe – deceitful way of thinking: Einstein himself regarded space as an intuitive notion, already available to the ancient people).[16] I will go right to the point: it is hard to believe that people in antiquity already possessed a notion of space as immersive three dimensional entity like the one we usually think about, otherwise it would be difficult to understand the reason why we have to wait the Renaissance period before we arrive at forms of spatial representations that are systematically three-dimensional; it would be difficult to understand why Egyptians pictures representing men at the time of the pharaohs were represented in profile and almost flattened without any depth; or the reason why the rooms and the external environment represented by Giotto in Assisi almost lacked any sense of precise depth and proportions that, on the contrary,  is present in almost any paintings of a century later, when the geometrical perspective was invented; I do not even linger on the explanation offered by the Swiss epistemologist and psychologist Jean Piaget (1896; 1980) on the genetic and psychological mechanisms and phases that lead a (modern) child to appropriate the conception of space – an explanation that I consider very appropriate and plausible.[17] I redirect you to my introductive article Preliminary Notes for a more detailed treatment of these questions. It is not the fact that men before the Renaissance period lacked manual and calculation skills to represent the world around us with the correct spatial depth and proportions; it is anything but that. What they lacked was the very concept of space as a unitary structure which can to put together, according to an organic conception, the three directions/dimensions of the physical continuum as a container of objects that is apparently before everybody’s eyes. In confirmation of the fact that space interpreted as a three-dimensional extent (space as background) is a relatively late achievement – a modern achievement, properly – I would also bear some evidence from a study that I conducted on some Latin texts, where the concept of space (spatium) is specially interpreted as a simple (mono-dimensional) extension or distance, as a region or area (two-dimensional extension), as an astronomical object, actually the place were bodies are located (here, it is evident the legacy of the stadion – the ancient unit of measurement for astronomical distances, as if the sum of an infinity of distances can be synthesized into a whole, which is a locational place, and not an indistinct immersive space as in the modern vein), or as time (i.e. in the space of a year, a month, etc.). [18]

At least, two outstanding steps were necessary before the concept of space conceived in the modern vein could be formalized (I mean the three-dimensional entity, space as the background, or arena of happenings). We are at a crucial point of the debate concerning the continuum: this is the second and decisive historical passage (the first one has to be attributed to Aristotle), which was necessary to understand the notion of space in the modern sense: a dimensional continuum, properly. The first step was undertaken by René Descartes, when he invented geometrical space – the three-dimensional entity that put together the three dimensions (represented by three different axis x, y, z) into a coherent system; a conception that nobody had envisioned before (contrarily to a commonplace, which is also surprisingly diffused among scientists, Euclidean geometry, before Descartes, was a discipline where no entity-space as such was present: only relations of contact between forms or figures existed, as we apprehend it directly from Albert Einstein). [19]

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’;[20] 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 not in a physical domain, but we are in an abstract domain: this is an abstract background space for geometrical entities (see also the paragraph on Descartes, in the article Space and Place: A Scientific History – Part I).

The second step, which was even bolder and ambitious than the previous one, was taken by Isaac Newton, who reified that abstract, immersive concept by endowing it with physical properties. Precisely, as we have seen in the previous article, he materialized that abstract space when he understood that his physical theory – I mean the laws of motion – was untenable without it. This is how the idea of physical space was born, formally: as a logical consequence of the Newtonian formalization of absolute space.

Then, thanks to the works of Descartes and Newton the continuum became a dimensional continuum, properly: extension or dimensionality – the possibility to define the continuum by measure – becomes the characterizing property that unambiguously identifies the continuum: this is absolute, infinite space. We have passed from a concept that was physically, intimately and qualitatively connected to matter (this was the Aristotelian topos-as-place), to a concept that was born abstract (space-as-spadion/stadion, originally identified distance, extension or a unit of measure as well) and has been turned into something concrete; a concept based on quantity and measure: it is its stability and durability with respect to measuring that defines the very nature of absolute space as infinite, either spatially or temporally. This is precisely the concept that is still ingrained within our minds: anytime we use the term space, we simply think at an indefinite, void extension all around us. Pure extension, pure dimensionality abstracted from everything else. This concept is now so perfectly integrated with our modes of thinking to appear ‘naturally integrated’ (that is, physiologically and psychologically ingrained within our minds, as also Kant believed), and misplaced for intuitive space. However – I’ve already said it in the past articles -, strictly speaking, I believe there is no such a thing as intuitive space: at best, there can be an intuition of the main characters of place, included its dimensional character, which is quite different.

I believe there is no such a thing as intuitive space

Place is an embracing concept (dimensionality cannot be apprehended apart from materiality and temporality); space is an exclusive and reductive concept, which allows a highly sophisticated mind to discern and abstract the character of dimensionality from materiality and temporality. In nature those characters are given all at once; to learn how to rationally divide extension from matter and time, occurred more than two millennia of debate and reasoning: the modern concept of space (the pure three-dimensional extent, or the so-called background space) is anything but intuitive. Place is intuitive; space is not.

Place is intuitive; space is not.

I have said that physical space was an idea born out of absolute space: for Newton and his followers, that idea represented something concrete and real (actual). In this way, a short circuit between reality and its representation was formalized; a short circuit into which we are still dispersed (this short circuit was remarkably seized by the expression ‘fallacy of misplaced concreteness’, by the Anglo-American philosopher Alfred N. Whitehead).

Thanks to Newton, the new vision of the world was completed: we passed from the Aristotelian Cosmology – based on the idea of place as plenum – to a scientific vision of the cosmos composed of physical bodies moving through absolute space, a material void, a neutral container, or, as Barbour said ‘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!’[21]

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 the most brilliant minds of all time were necessary before we could speak of space as a three-dimensional continuum. Our comprehension of the cosmos, until the beginning of the XX century, was based on that conceptualization. Contrarily to appearances, the emergence of the modern conception of space did not appear all of a sudden: it was not the intuition of a single mind. For Descartes’s and Newton’s ground-breaking theories and concepts to appear, almost two millennia of debates were necessary; two millennia before the spatial debate, or, otherwise said, the question concerning the nature of the continuum in which bodies exist and behave (at first a physical continuum, after Descartes and Newton a dimensional continuum, properly), could be put on the table by Aristotle – as a theory of place and natural motions – and solved by Newton, according to whom bodies moved in an absolute space according to precise mathematical laws – a concept that removed any distinction between terrestrial and celestial motions. Two millennia in which the more or less hidden contribute of astronomers, alchemists, mathematicians, and physicists intersected with that of philosophers, architects, painters, man of religion and power, etc. (it is not a minor thing to observe that intellectual, or symbolic processes always interact with sociocultural processes to change our vision of the world; there is a two-way correlation between those two orders of processes). Two millennia after which place – the Aristotelian topos – has been transformed into space, or, better, reduced to a simple location within a space of infinite extent: this is absolute space.

4. The continuum at the epoch of the theories of Relativity and Quantum Mechanics (is it really a continuum?)

The debate concerning the nature of the continuum in which bodies exist and move opened with Aristotle’s theory of place, and concluded with the temporary affirmation of Newton’s theory of absolute space, which reduced place into a simple location for bodies in space – ‘Locus est pars spatii quam corpus occupat’: ‘place is a part of space which a body takes up’ -,[22] thereby divesting the old placial concept of any residual ontological interpretation. In spite of the rapid affirmation of the concept of absolute space, I believe we have inherited a couple of unresolved questions: is space a real or is it an ideal entity? (by the term ‘real’ I mean the concreteness of the physical entity that possesses a non-zero energy or mass). Moreover, another related and highly relevant question arises: what is the relation between the concept of space and the concept of place?  Needless to say, any answer different from the one offered by Newton not only implies a reformulation of space but also of place, matter and time. We will see it soon. To summarize the passage from Aristotle to Newton, we passed from a vision of the cosmos which was quite simple and intuitive, in agreement with our senses (place and matter are visible entities, while time was considered a derivative notion: a number for the changes occurring to matter), to a highly sophisticated vision of reality, split into space, matter and time (space and time are invisible entities); a vision with respect to which physical entities moved according to perfect mathematical laws, that were valid in, and defined to comply with absolute space – the concrete background for those laws, an entity as elusive and intangible as the void, nothingness, or as an idea can be. An elusive entity turned into something concrete for calculation purposes; an entity whose substantial nature was impossible to investigate directly, until modern times. A sort of ether (the ether, another highly controversial philosophical/scientific entity, as old as the Aristotelian topos) devoid of materiality. Or, again, a physical entity without any mass or energy, that is, an oxymoron from the linguistic and the physical point of view, if not a real contradiction in terms, difficult to be sustained from an epistemological perspective. And this difficulty will drive modern physicists to explore other possibilities and concepts to describe the nature of the continuum. In spite of these difficulties, that idea – I mean absolute space – worked very well. It definitely worked so well that new models of organization, in many different fields of knowledge, were based on the geometrization and spatialization of physical reality obtained through the methods of mathematical abstraction. That was a real revolution of the modes of thinking and knowledge: a true Scientific Revolution, prelude to the Industrial Revolution, after which mankind entered the contemporary epoch. Human societies came out completely transformed from that unprecedented combination of sociocultural and intellectual processes: it is the very nature of man that came out transformed. The modes of thinking changed: the passage from concreteness to abstraction as the typical mode of inquiring nature was accomplished. I believe this passage can be symbolically emphasized by the transformation of place into space: the entity under investigation was the same – the physical continuum that keeps things related and ordered -, but the terms and the concept used to express that entity changed radically. And, of course, it changed the focus with respect to which analysing that concept: a focus that was especially – if nor exclusively – put on the dimensional character of the continuum.

From the perspective of one who thinks that space is an abstract concept – a fiction of the imagination, which especially deals with the so-called extensive (or dimensional) character of reality -, I believe it is possible to sustain that just like the passage from ‘mythos’ to ‘logos’ was accomplished with the pre-Socratics, almost two millennia and a half ago, now, with the passage from the Aristotelian ‘topos’ to the Newtonian ‘spatium’, another critical passage was done: the affirmation of ‘logos’ as a scientific fact rather than as a philosophical fact, as it was in the beginnings.

In this millenary process of evolution concerning human knowledge a final passage is left concerning the debate on place, space, or the continuum all around us; a passage which is able to reconnect the original ‘logos’ – the place of philosophical and rational speculation – to the ‘logos’ we have inherited from Descartes and Newton (I use these two names as the outstanding symbols of an entire epoch) – the place of physical and/or mathematical speculation. A final passage which aims at recovering a more encompassing mode of understanding the continuum upon which reality is built. A final passage which – it seems to me – is trying to surpass the image of the bifurcated reality we have inherited from the atomistic tradition and from some questionable interpretations of Descartes’s philosophy. This new vision, by surpassing outworn forms of dualism, reductionism, and the mechanistic view of the cosmos, is trying to offer a unitary and holistic vision of it, understood as a unique and complex system, which cannot be reduced to the simple addition of its constitutive parts; a cosmos understood as a plenum, thereby a vision that re-establishes some connections with the old Aristotelian model. [23]

As it was in the past, this final passage that takes us to the present time is the result of many interlaced historical episodes waiting for a systematization of the kind Aristotle and Newton were protagonists. Even more than ever before, the different modes of abstract thinking, driven by the precision of scientific language, are the privileged modes of inquiry into the secrets of nature, hence, into the nature of the continuum. Yet, until we cannot find a convergence between humanistic and scientific modes of knowledge and thinking, I believe no real systematization of knowledge comparable to the past can be obtained.

Continuing on with our synthetic analysis of the main historical passages concerning the modes of understanding the continuum, immediately after the success of Newton’s absolutist theory, we have to point out the contributes of Leibniz, Locke, Berkeley and Huygens – philosophical contributes, especially, if we exclude Huygens – who embraced the hypothesis of relative space as a working concept contrary to the idea of absolute space concocted by Newton (therefore, they promoted the idea of a relative continuum determined by the relations between material entities, rather than the idea of an absolute continuum that existed independently of matter). Yet, before the concept of absolute space was surpassed by new physical theories – I mean Einstein’s theories of relativity -, more than two centuries passed. In this interval of time, we also have to mention the studies concerning the nature of electromagnetic phenomena, which were accompanied by the introduction of a new physical concept – the field concept, which opened up the possibility to understanding the continuum differently from the past. Then, we have to recall the pioneering studies made by Faraday and Maxwell, but also to the contributions of Lorenz and, of course, Mach and Einstein.

It was properly thanks to Einstein’s genius that the physical and the mathematical limits of the Newtonian concept of absolute space could be reconsidered: this happened after the introduction of the Special Theory of Relativity, in 1905, and after the General Theory of Relativity, in 1915. Once again, these two theories changed the mode of understanding the continuum: in consequence of the special theory of relativity, the old Newtonian concept of absolute space was dismissed in favour of a new conceptualization: relative spacetime (space was coupled to time, forming a new entity, after the interpretation that the mathematician Hermann Minkowski gave to Special Relativity). But this was just the first step; in fact, with the General theory of relativity, the understanding of the continuum changed again: its interpretation as a physical quantity related to matter (or intrinsically coupled to it as well as coupled to time, according to certain late-interpretations of the theory),[24] contributed to transforming the tetra-dimensional continuum into another, more encompassing entity: a physical field, or a kind of relative ether. As far as I understand the complicate debate in between physical and philosophical argumentation that still divide many scholars, the latter interpretation, is the final interpretation of the continuum that Einstein had in mind few years before his death, in 1956, when he was still working at his unified field theory. [25]

But it will be the contribution of a new field of knowledge that Einstein contributed to set up, which will be decisive to offer even more different interpretations of the continuum: I’m speaking of quantum mechanics, the discipline that investigates the phenomena of physical reality in a range from the atomic scale to the inferior limit of applicability of the physical laws – the so-called Planck scale (I believe the Planck length could be identified with the ‘inferior limit’ I was talking about in the previous paragraph, when I was speaking about the minimal tensional state of the continuum for the existence of the continuum itself, and with it, for the existence of matter – see also images 6, 7 above). [26] It was properly after of the birth and development of this new branch of physics, which is currently formalized into the Standard Model of Physical Particles and Interactions, that new modes of interpreting the continuum, in which matter exists and moves, became possible. The very meaning of the term quantum could be an indication of the new way of understanding the continuum: a discrete entity rather than something continuous. Then, the fundamental structure of what we have called ‘continuum’ (in virtue of its characteristic action of creating a seemingly stable and continuous order between physical entities), when investigated at the scale of micro phenomena – and precisely at the Planck scale – appears to be a dis-continuum! This linguistic discrepancy may also suggest us the possibility that order – the ordered cosmos we are plunged into with the stable physical processes after which we have determined certain physical laws – is an emergent property and that the generic proposition fabric of reality can be said discontinuous or continuous according to the level of investigation.

If thanks to Einstein the relation between space and time (after special relativity), and between space and matter (after general relativity) were seen under a different  light, and new interpretations were offered to understand the continuum – from absolute space to relative spacetime; from spacetime to the field concept, a relative field, precisely, after Einstein -, now, with quantum mechanics and the necessity to understand what happens when gravitational effects come into play at infinitesimal scale, a new possibility of thinking about the continuum entered the debate. In fact, the present programme of physics is to see what happens when such physical fields are subject to the laws of general relativity: the most straightforward way to see that long-awaited (and final?) unification between quantum mechanics and general relativity is the unification of spacetime and physical fields (quantum fields) into an encompassing entity that incorporates the spatial the temporal and the material under the same structure (see image 12, below). Cannot such an encompassing entity be the ultimate place of intelligible processes?

Image 12: What is the world made of?’ The Italian theoretical physicist Carlo Rovelli says it is made of only one ingredient: covariant quantum fields. By interpreting those fields as physical states of place (the first of a chain of concrescent states of place – physicochemical, biological, social, and symbolic states of place, to begin with), I say that the concept of place may regain the basic ontological status it had at its origin: first of all, to exist is to exist in some place (image adapted from Carlo Rovelli’s book – Reality Is Not What It Seems – I have added the blue row concerning Aristotle). [27]

So, to recap, if Aristotle and Newton formalized the placial/spatial question in agreement with the instances of their times (and out of those different modes of thinking about the order of the cosmos emerged two different cosmologies which have guided the different stories of Western people and their different forms of social, political, economic, religious, cultural and technological organization, for nearly two millennia and a half), now, as modern people of a global village and reality, we are waiting for the third systematization of knowledge, that is, a new mode of understanding the order of the cosmos and its laws. A new mode of understanding the order of the cosmos as the result of a different series of interweaving processes that happen at different scales and/or stages (physicochemical, biological, social and cultural); a mode of understanding where the field concept will probably be the concept deputised to represent the physical and dimensional continuum (or discontinuum) we come from and we are plunged into as complex systems –  we are seamless physicochemical, biological, sociocultural and intellectual entities – together with and correlated  to every other system either simple or complex. It is such a unifying and totalizing vision of reality understood as a whole, which we are trying to formalize in the current epoch. And to this new vision – a new weltanschauung – will correspond a new mode of understanding the concepts of place, space, matter and time. From the perspective of one who is specifically interested in the analyses of spaces, places and their meanings, I will try to show that a reformed understanding of the concept of place will be able to encompass the field concept of physics so that we could have a more comprehensive vision of reality, which is all around, within and without us. I use to say that the field concept that physicists speak about is nothing other than a physical state of place, within a systemic vision of reality where any concrete entity is the place of certain processes, or, better the place where certain processes concretize into matter (than matter and place are correlate entity, there is no place without matter and vice versa). We have already said it: in strict order of growing complexity and dynamism, from inorganic matter to thought, actual entities can be considered the place where physicochemical, biological, sociocultural and symbolic – or intellectual – processes become concrete. Needless to say, such a comprehensive understanding of place encompasses (but is not limited to) the old notion of location, or position, which is often univocally – and inappropriately – associated to place. We have seen it with Casey: it is a special merit of philosophical and social scientific thinking if the concept of place has been a subject of revision since the beginnings of the last century. A process of revision that is still ongoing. The same attitude of revision has been adopted by physics if we also understand the field concept as the primordial place of physical processes: more or less directly, we have seen it with Barbour, Jammer and Weinberg. Thereby, as I often say, we can conclude this article with the hope that only by means of the joint contribution of different types of knowledge – the scientific and the humanistic – will be possible to reach for a new shared formalization of the laws and the concepts that are fundamental to understand the order of things.

5. Conclusion

The modes of thinking about the continuum that keeps things together and related according to an order of position and succession are in perpetual evolution. We have learnt that at the utmost limits of what physically exists (I mean at the Planck scale) that which we have always called a continuum doesn’t seem to be continuous at all. We have also learnt that, according to the present state of scientific knowledge, the convenient term to identify the continuum/discontinuum, is not space and not even spacetime, but field (covariant quantum fields, is the technical term suggested by physicists). At fundamental level, fields are the only entities that actually exist: it is these physical entities that constitute the fabric of reality, which is probably the most appropriate term to identify the basic substrate of reality – which is, all at once, a material, temporal and locally-extended substrate; a substrate through which any phenomena of reality appear and in which exist. Space, in any of its semblance – absolute space, geometrical space, relative spacetime, etc. – is a fiction of our imagination, a very useful idea that we have used to partly represent the happenings of that fundamental substrate or of that which emerges through it. Therefore, space, or its updated version – spacetime -, does not exist as an actual entity (as a res extensa Descartes would have said), but is an ideal, or abstract entity; an invention (of the human mind) which improperly abstracts some aspects of the fundamental state of reality (dimensional and locational aspects) from other aspects (material and temporal aspects) that are connaturated to the former. According to the systemic perspective through which analysing all of the phenomena of reality – not just physical phenomena – it is possible to reconsider the concept of place as a fundamental and operative concept for each emerging reality that exists in or emerges through the physical substrate, or fabric of reality. In fact, that basic fabric or texture we have spoken about in this article can certainly be understood as a set of fields, but, before all, that fabric is a place: more appropriately, physical fields are nothing other than a physical state of place. Phenomena of superior order (generically, inorganic phenomena, organic phenomena, social and symbolic phenomena) are nothing other than other different states of place, which are correlated to the preceding states out of which they emerge, but with which they are in contrast to affirm their autonomy and irreducibility. The totality of the states of place (physicochemical, biological, social and symbolic states of place) defines reality, as well as its fundamental fabric, as a place.


[1] I’m going to use the term ‘thing’ in its most general sense: to refer to any entity, especially to physical or concrete entities, if not otherwise specified.

[2] Similarly, Leibniz understood the order of things like 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 concerning the fact that ‘reality kicks back’ is referred to the famous episode of Dr Samuel Johnson, an English literate of the XVIII century, who, during a discussion about the possibility to refute Berkeley’s idealism, kicked a big stone so that his foot rebounded, thereby exclaiming ‘I refute it, thus’. It is true that the episode proves the reality of the thing-stone, yet, by proving its existence in correlation with perception (again, the ‘reaction’ of the stone that causes the rebound of the foot is a question of perception), it fails to disprove the main point of Berkeley, for whom matter cannot exist as an independent entity separated from the perception of it.

[4] I will often refer to the following interpretation of the Allegory of the Cave (or Plato’s Cave), which is represented in image 1: the knowledge we have of the actual reality – the knowledge of the ongoing, multifarious phenomena of reality – is certainly limited to our physiological and mental apparatus, or, otherwise said: knowledge is ingrained in our body-and-mind. We can extend such natural apparatus by mean of many artificial tools and devises (of which we can verify the good or bad efficiency) and, in the end, by our imagination and creativity (of which we cannot always verify its reliability and efficiency whenever we want our imagination/creation be correlated to the actual reality of facts). In general, we can say that the knowledge we have of the world can be true, real and effective, even if it is limited with respect to the infinity of data and phenomena the actual world is made up. More appropriately, we could say that knowledge is true, real and effective whenever there is an ascertained correlation between the subject and the object of knowledge; in the case the subject interrupts such correlation – this is the case of fantasies, hallucinations, misplaced concreteness, etc. – our knowledge of the world loses efficacy, and the result is an emerging gap between the subject and the object – or the objective reality -, so that an infinity of problems may arise. The reason why we can be sure about the objective value of knowledge (as a matter of fact we should use a Whiteheadian neologism and replace the term objective with superjective) is the following one: our knowledge of reality is indeed intrinsically limited (because of the aforementioned natural/biological limits), however, such knowledge is limited the same way a real shadow is limited with respect to the entire set of processes that determine that shadow. Therefore, the same way a shadow belonging to a real object is a real or an actual shadow, so our knowledge is real knowledgeobjective someone would say, albeit somewhat improperly – given that a shadow, whenever is cast by real objects, is objective, something that cannot be severed from the actuality of the physical object.

I have spoken of superjective value of knowledge, since this value is given by the historical (evolutionary) correlation between the object and the subject: actually, the subject is the one who is ‘thrown out there’ after the object, or, to put it another way, the subject naturally comes after the object, to which is correlated. As Whitehead affirmed ‘the subject emerges from the world’, therefore it should be termed ‘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 is founded on the correlation between that which exists before us – the place of physicochemical processes in which/out of which concrete reality-as-place emerges – and us, as the interpreters of that pristine place; then, to begin with, we are the place where physicochemical and biological processes meet before social, cultural and intellectual or symbolic processes come into play. To express this position of mine through an expression taken by Alfred Whitehead, I stand by the so-called ‘reformed subjectivist principle see: Alfred N. Whitehead,  Process and Reality – An Essay in Cosmology (New York: The Free Press, 1978), 166, 167 , which overturns the Kantian relation between the object and the subject  without questioning the fundamental truth that there is no knowledge apart from the experience of the subject and that no knowledge is attainable without understanding the correlation between the object and the subject (the ‘reformed subjectivist principle’ reinstates the correct relation and the original meaning of the terms subject and object, before the Cartesian inversion of sense between those terms occurred, as Heidegger showed in his essay – What is a Thing?. Heidegger says: ‘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 the remaining things first determine themselves as such… The things themselves become “objects” in Martin Heidegger,  What is a Thing? (South Bend: Gateway Editions LTD, 1967),  105.

[5] This is indeed the theoretical position of an architect like me who ‘concretely and abstractly’ worked with space, place and matter for more than a decade, before putting those concepts under closer scrutiny through different humanistic and scientific readings, to find the ultimate sources out of which the meanings of those concepts derive. The phrasing and some of the theoretical content behind the proposition fabric of reality has an echo in the work of two physicists: in 1997 the British physicist David Deutsch wrote the book ‘The Fabric of Reality – The Science of Parallel Universes and Its Implications’, in which the fundamental state of reality was interpreted according to the quite recent discoveries of Quantum Mechanics. Fundamentally, I agree with the systemic approach of that book, according to which reality cannot be reduced to an ultimate principle – that is, it cannot be reduced to an ultimate physical principle; rather, it is the emerging result of a complex system of interacting principles: ‘four strands’, according to the author, that is physical, computational, epistemological and biological/evolutionary principles that mutually operate to determine the meaning and the appearance of reality. This position has analogies to what I also argue for in this website: in the wake of the philosopher and novelist Robert M. Pirsig, I also say that physical reality is made up of four interacting strands or principles, which I call physicochemical, biological, social and symbolic (see the post On the Structure of Reality). In 2004, the American physicist Brian Greene, famous strings theorist and scientific populariser, wrote the book ‘The Fabric of the Cosmos – Space, Time, and the Texture of Reality’, a scientific narration focused on the Physics of the last century and on the concepts through which it is possible to express the fundamental state of reality (space, time, spacetime, physical fields, strings, branes, etc.). Some of the concepts and terms that I use in my texts take a cue from those two authors. However, the basic concept  ‘fabric, or texture of reality’ – understood as a fundamental constitutive element of reality – was a concept that I already used – as an intuitive concept – in my works as a student of architecture and post-graduated architect, well before reading those two texts. Precisely, I was using the term texture, in an architectural context, to define the fundamental intricate structure that sustains the emergence of (phenomenological) space as a basic element for architecture: I’m referring to the series of theoretical studies that I eventually called ‘archi-textures’, a term which, with some opportune distinctions, I started using after having read the book The Production of Space, written by the French philosopher and sociologist Henri Lefebvre, who used that term 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 my architectural works, I extended those physically existing networks, which defined space according to Lefebvre, to include the immaterial perceptual relations (reified through lines, wires, threads etc.) that bind the subject to the environment (-as object). To put it briefly, I correlated the existing physical patterns of actions and movements to the modified patterns and the new perceptual patterns (visual, tactile, auditory, olfactory patterns and patterns of motion) of the subject thrown into the existing environment that was going to host a new architecture, with its new functions, which would have modified the existing place, context and surroundings. That’s why, in the end, architecture is a correlation between space (the space of the project) and place (the current place where the project is plunged into or reified – in the case the project is built); but it took me almost a decade of painstaking research to understand the correlation between place and space, and between the nature of reality and knowledge: place is actual and concrete, the result of concrescent physicochemical, biological, social and symbolic processes; while space is ideal and abstract, and it only pertains to a symbolic domain (symbolic processes). If we do not reconsider the whole gamut of those processes when we think about place and space, then place and space remain outworn terms and concepts. The images above in this note, which are from my thesis-work (with architect Davide Benini), the featured image of this article, and the related video Chōra are some examples of 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] Since its origin, place (topos) can be understood as an abstract linguistic entity (an abstract name, a fortuitous linguistic invention to denote location, as suggested by John Chadwick in Lexicographica Graeca, see also the article Back to the Origins of Space and Place), other than as a philosophical entity correlated to that which is concrete – I’m referring to its rational definition given by Aristotle, that is the physical entity to which place offers location; conversely, space, since it came into the scene as ‘stadion/spadion’, it came as an abstract entity – an abstract term – that defined an abstract entity (a distance, or extension between visible entities, which became a unit of measurement). Only after well more than two millennia space acquired a substantial character, apparently, all of a sudden. Yet, this sort of late-reification was an unconvincing operation, a fallacy, in the end; a fallacy of misplaced concreteness, is the proper name for this fallacy, given that space, since its origin, was an abstract term defining an abstract/immaterial entity like a distance or an extension between visible entities can be, and it could not simply transform into a concrete entity in virtue of an act of will aiming at preserving the validity of a physical theory (this is what Newton have done – we have already seen it by examining the text of Julian Barbour). Therefore, while it can be appropriate to understand chōra as place (which has an intrinsic double nature as I have said above and as my reformed understanding of place shows), since we preserve the double character – bastard nature – that is intrinsic to chōra, I think it can be deceitful to understand chōra as space, since space can only be understood as abstract. I think the latter proposition may encounter many obstacles before being accepted, given that we come from a few centuries in which things appear contrary to what I’m saying, and the inertia of thinking – just like the inertia of any physical body – requires energy (and time) to be reversed.

[10] The very existence of matter, its being actual as the emergence of a series of processes, should be considered a phenomenal event. Therefore, matter qua place of processes that realize themselves, concretely, is a place and an event as well. It is self-evident that a place, any place, is the manifestation of an event (a phenomenon, properly).

[11] Incomprehension may regard an academic level of discussion, as if speaking about space, time, matter or place is a question concerning a few individuals, or a determined category – physicists, philosophers, architects, sociologists, geographers, artists, etc. Conversely, tragedies regard everybody since – this is my thesis – from that original operation of substitution and dissection of a complex and unitary reality into its abstract model, divided into parts and conceived of as easier to handle and ménage (reductionism), derived unexpected consequences that run over everybody: from the elaboration of abstract economic and social models to the elaboration of urban and architectural models, there are many ways in which different kind of planning strategies, severed from the logic and functioning of the real systems that compose reality – a combination of physical, chemical, biological, ecological, social, cultural and symbolic processes -, may negatively impact the daily life of people.

[12] The images through which I have represented the continuum are a possible way to understand the terms that described such a continuum through the different epochs (topos, chōra, apeiron kenon, spatium/space, locus/place, spacetime, field etc.); in spite of that, a picture, or image, cannot certainly render all of the different epistemological and ontological connotations that exist behind those terms. Moreover, any interpretation of ancient terms and concepts is an interpretation a-posteriori that offers no complete guarantee about the original meanings (and shades of meaning) in the intentions of the ancient authors and of those living at that time. It is properly in virtue of this fundamental ambiguity that the spatial/placial debate lasted so long and is still alive today, without any credible chance that it can come to a definite end.

[13] This ambiguity is explicated by the term ‘bastard’,  the epitome used by Plato to define the nature of the continuum. More appropriately, Plato says that the nature of the receptacle (this is also another translation for the Greek term hupodochē, which we also have identified with chōrathe continuum) in which everything exists, has to be apprehended by a sort 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] At this regard, I made a specific analysis of Vitruvius’s text ‘De Architectura Libri Decem’. More generally, with respect to this spatial/placial question, I could observe that in many Latin or Greek texts, where the classical authors used the terms locus or topos (terms that are certainly closer to materiality of place rather than to the immateriality of space), they are very often translated by modern translators as space. A question arises quite spontaneously: how could the ancients possess the concept of space like the one we usually think about today (that sort of immersive background), if they did not even have a term to indicate that conceptualization? I do not think we need Heidegger’s assistance to find that ‘the Greeks had no word for space see Martin Heidegger, Introduction to Metaphysics (New Haven & London: Yale University Press, 2000), 69; a quick verification of the translations used by modern translators, will usually lead us to topos (and some time to chōra) and locus, as the ancient sources for the term space. Contrarily to what is frequently assumed, the concept of space intended in the modern vein – that sort of background space that contains objects and bodies – was not a concept at the disposition of the ancient people. This conviction of mine is also rendered quite explicitly and effectively  by the American mathematician Salomon Bochner in his Introduction to the voice ‘space’, in the Dictionary of the History of Ideas, where he says that the concept of ‘background space’ – the continuum we are speaking about, in which things exist – did not belong to the ancients, but it was the result of a long historical process that reached its climax in the modern era with the works of Descartes and Newton see: Solomon Bochner, “Space”, in the Dictionary of the History of Ideas, Volume IV (New York: Charles Scribner’s Son, 1973), 295. This is also the way I see (the evolution of) the concept of space.

[19] 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.

[20] 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.

[21] Julian B. Barbour, The Discovery of Dynamics (New York: Oxford University Press Inc., 2001), 618.

[22] Isaac Newton, Newton’s Principia – The Mathematical Principles of Natural Philosophy, trans. A. Motte (New York: published by Daniel Adee, 1846), 78.

[23] 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 I).

[24] 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.

[25] The different interpretations of the continuum conceived of 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).

[26] I want to reconnect to note number 7. Figuratively, I think the continuum can be interpreted similarly to the lines of force that define an electromagnetic field: those lines are energy linkages embedded in the field itself.

[27] From the blue row concerning Aristotle, which I have added to the original image that we find in Carlo Rovelli’s book Reality is not what it seems (Italian edition: La realtà non è come ci appare, Milano: Raffaello Cortina Editore,  p. 167), two related things stand out: first, that Aristotle’s conception of time is not a primary concept; in fact, according to Aristotle, time is the measurement of change: that change obviously regards things that move from place to place. Matter and place are the primary concerns for Aristotle to oppose his view against the cosmological account of the Atomists, who believed in indivisible pieces of matter – atoms – moving through the void, which was a concept that Aristotle rejected resolutely. Second: the concept of place (topos) is intrinsically richer than what we usually call space; it includes that portion of time which, if correlated with matter, explains the concept of time itself  as the measurement of the change (of place) of a material entity. That is another reason why it is reductive – and, I believe, wrong in the end – to understand the Aristotelian topos as space. Since its origins space had a dimensional meaning (an extension between points, things or objects, hence a distance or interval); conversely, place – the Aristotelian topos – has a more encompassing meaning that is intimately correlated to the material and the temporal, besides being in itself a dimensional fact (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. 

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.