Concepts of Space in Vitruvius

Elaboration on an illustration by Palladio, 1556, concerning the hypothetical reconstruction of the Basilica di Fano by Vitruvius (source image: Centro Studi Vitruviani).

The previous article could be read as a prologue to the present one: that article — Place Space and the Unicorn — unveils the premises and the reasons which took me to analyze an ancient text like De Architectura, written by the Roman architect Vitruvius in the first century B.C.,  to understand how the notion of space was interpreted during the different epochs. As I said in the final part of that article I wanted to know if apart from or in addition to the traditional historical analyses and studies on the concepts of space — e.g. Space and Place: A Philosophical History, or Space and Place: A Scientific History – Part One and Part Two —,  there was another way to test the hypothesis that the volumetric interpretation of space (that is the conceptualization of the so-called background space as an inert container of things, bodies and events) was a conceptualization concocted after Cartesian geometry was invented and the Newtonian innovation — absolute space — introduced; and I also wanted to know if there could be a way to cast some light on the diffusion of the metaphorical understanding and use of the concept ‘space’ associated to the notion of pure extensiveness.

When I began specific readings to deepen my knowledge on the concepts of space and place, one of the most disconcerting things that initially stroke my attention was the great ambiguity in the use of the terms space and place between different authors;  even more, I was stroke by the ambiguities concerning the translations of ancient texts, their words and concepts. The cases where the same word — either the Greek topos, chōra or kenon,  or the Latin locus, spatium, and vacuum  —  was translated as space by an author and place by another author, or vice versa, were countless. The wise indication to look at the context where one term belongs to establish the appropriate translation sounded good, although a bit elusive in the end, given that we always remain within interpretative hypotheses, moving our interpretative tools from one term to its context: still, subjective and questionable interpretations remain. I began to think that things are not that easy when we have to disentangle questions of space and place since those are millenary concepts and each epoch developed a particular interpretation, with different connotations from one epoch to the other; therefore,  the danger of anachronistic interpretations is intrinsic in the analysis of ancient texts given that cultures and societies always change, while a mind is always the product of its own epoch. I began to think that I couldn’t draw any dogmatic conclusion from the philological interpretation of an ancient text, just some useful indication or tendency to compare with the more traditional historical analyses.

To inaugurate this kind of philologically-based inquiry, my choice fell on Vitruvius’ De Architectura – Libri Decem (The Ten Books on Architecture) for three reasons: first, I already knew that book since the time I was an undergraduate student at the Politecnico di Milano, given that Vitruvius’ De Architectura is a well-known introduction to the discipline of architecture for anyone who wants to become an architect. Second, an investigation into Vitruvius’ concept of space could shed some light on the relation between architecture and space at large; and it could also shed some light on the many Histories of Architecture, which make almost no distinction between what the concept of space could mean in the Classical Greek epoch and the Roman epoch, or the Modern one. Finally, the choice of an ancient Latin text could be especially useful for my specific scope to elucidate the meanings and the different interpretations of space, since the English term ‘space’ comes directly from the mediaeval Latin term ‘spacium’, which is, in turn, a slight modification of the old Latin term ‘spatium’.  As if to say: there is just one degree of separation between the two words. Conversely,  it is more difficult to find a direct correspondence between the concept expressed by the English term ‘space’ and those ancient Greek terms like chōra, topos or even kenon, which are commonly, and often interchangeably, used to translate the concepts of space and place. However, despite the direct relationship between the English term ‘space’ and its Latin descendant ‘spatium’, it is critical to keep in mind the question of anachronism I mentioned above: whenever we deal with the original Latin term ‘spatium’-as-space we should keep in mind the particular literary and historical contexts in which the term was used; every time we read the term ‘spatium’ in the Treatise, we cannot automatically ascribe to Vitruvius an idea of space as a neutral container or background (that is space as a three-dimensional immersive entity), like the one we are now used to; the idea of an abstract container and, consequently, the idea of a background space are modern ideas. Having that important question well settled in my mind, I thought that if there was clear evidence that Vitruvius might have used the term space with a similar purpose and in similar circumstances with respect to a modern author — namely an architect — the hypothesis on the fundamental role of Cartesian geometry and Newtonian physics as the originators of the idea of three-dimensional space had to be called into question. In the opposite case, apart from an indirect confirmation of the reliability of those historical studies which are particularly sensitive to this question (Casey’s text is exemplary at this regard), we could have another interesting field of investigation to understand how the interpretation of space could have changed through the different epochs. And with particular reference to architecture, we could also ask: how is the term space (spatium / spacium /spazio / espace, etc.) used in the Treatises and works of Leon Battisti Alberti, Sebastiano Serlio, or Andrea Palladio, with respect to more modern architects and critics like Claude Perrault, Étienne-Louis Boullée, Claude-Nicolas Ledoux, Robert Morris, John Ruskin, Gottfried Semper…  Louis Sullivan, Frank Lloyd Wright, LeCorbusier, Mies van der Rohe, Alvar Aalto or even with respect to more contemporary architects and critics like Charles Jencks, Peter Eisenmann, Bernard Tschumi, Rem Koolhaas, or Zaha Hadid? Answering that question could give us some useful indication on the nature of space, its development, hopefully even outside of architectural circles if we consider that architecture is a complex system of knowledge where sociocultural and symbolic processes play a major role; and, in parallel, it could give us indications on the influence that Architecture could have had on the different elaborations of the concepts of space and their diffusion, especially.

Image 1: Cénotaphe à Newton, by Étienne-Louis Boullée, 1784 (source: wikipedia.it). Hanging from the roof of the cenotaph, at the center of the composition we find an armillary sphere, which is for me the supreme symbol that symbolizes the deep entanglement between questions of place and space as such (astronomical space is one among the many connotations of space).

As I have said in the past articles, even if spatial/placial concepts had some turning points that we can associate to the works of Aristotle, Descartes-Newton and Einstein, these represent symbolic watersheds behind which we find the concurrent works of many people who contributed to creating the appropriate milieu to the overall diffusion of certain spatial/placial conceptualizations. Can we neglect the role of perspective (to which geometers, mathematicians, architects and painters gave important and converging contributes) to the elaboration of the first geometrical and quasi-physical modes of understanding space as a three-dimensional fact? Or, even before, can we neglect the role of ancient astronomy and astronomers in the elaboration of the modern concept of space, so beautifully narrated by Julian Barbour? And why cannot we say the same with respect to the recent contributes of social scientists concerning our understanding of the concepts of place and space at large? After all, within the systemic placial( )spatial perspective that I call for here, physicochemical, biological, social and symbolic patterns of reality have equal dignity, and, to state it with Robert M. Pirsig, ‘there is no intellectual requirement that any level dominate the other three‘ (see On the Structure of Reality).

In the remaining parts of this article, after introducing some biographical notes on Vitruvius and delineating the arguments of his Treatise, I will report in the form of brief excerpts those parts of Vitruvius’ Latin Treatise containing the term space (that is ‘spatium’, or any of its declensions — e.g.spatii’, ‘spatio’, ‘spatia’, ‘spatiorum’, ‘spatiis’ in the original version) relying on two different English and Italian translations to understand, from different linguistic perspectives, the context in which Vitruvius used those terms. [1] I will make some brief comments on those excerpts before making final considerations in a concluding paragraph, which is a summary of the different senses of space and the times it was used in the Treatise. For the sake of brevity, I’ve decided to publish only one representative excerpt for each of the different senses that can be attributed to the term ‘space’ (that is: space as distance, as region, as time, as astronomical expanse, etc.), and to indicate by means of a reference (e.g. 3,5,8, that is: Book III, Chapter V, Section 8) those parts of the text where Vitruvius used the term spatium-space, in any of its declensions or variations when used as an attribute.

Vitruvius, De Architectura Libri Decem

A few biographical notes on Marcus Vitruvius Pollio, commonly known as Vitruvius. We have scant information available on him: he was probably born in the first decades of the I century B.C., but we have no certainties about the place where he was born; from time to time, different sources speaks about different places: Verona, Ravenna, Piacenza, Fano and other cities in the Italian peninsula.[2] As regards his famous Treatise — De Architectura, Libri Decem — it is the only complete treatise on architecture to survive from antiquity. However,  we do not have the original manuscript, just different copies and editions (the first press edition — the so-called editio princeps — dating back 1486).[3] The argument is about public and private buildings and it also contains descriptions of building materials and the machinery used for constructions.

Image 2: DeArchitectura Libri Decem, by Vitruvius, 1567 edition with a commentary by Daniele Barbaro.

It was probably written in the period between 27 and 23 B.C.[4] In the Treatise rules were given to let people understand the quality of existing buildings or projects. The Treatise is divided into ten books, each containing a preface and different chapters, which, in turn,  are divided into sections. From an architectural point of view, I believe the first part of Book I is probably the most important one — an everlasting one for architects, I would say. In virtue of this fact, I will give a summary of each chapter of Book I to the advantage of the students of architecture and those who are interested in architectural related questions; as a matter of fact, Vitruvius’ De Architectura has influenced the academic training of many generations of architects (at least here in Italy) and is still widely known or cited after more than two millennia. Those who are only interested in the linguistic use of the term space-spatium in Vitruvius’ Treatise can skip the next two paragraphs and go to the paragraph On The Use of the Term ‘Space’ (i.e. spatium) in Vitruvius: An Overview.

Book I

In Chapter 1, Vitruvius speaks about the education of the architect, who ‘should be equipped with knowledge of many branches of study and varied kinds of learning’[5] from drawing, to geometry, from history to philosophy (from which ethics precepts derives), from physics to music and mathematics, from medicine to astronomy, in order to let the convenience and beauty of a building coincide. What Vitruvius had in mind was an interdisciplinary approach to the discipline, which is an approach I also maintain. Today this argument — a systemic, interdisciplinary approach to architecture — is still far from being accepted by the entire community of architects: within a reductionist perspective of the processes and phenomena of the world, many architects believe architecture to be a fully-fledged independent discipline, a system of knowledge with its own rules and regulations, with precise epistemological and disciplinary limits. Yet, things changed a lot in the last couple of decades: it seems to me, the number of those fundamentalists of architecture has greatly decreased, especially since the coming into evidence of the environmental question, which is obliging architects to a more pragmatic and open attitude towards the discipline.  That fundamentalist position was alien to Vitruvius: from the very beginning of his Treatise, Vitruvius understands architecture as a difficult discipline in the middle ground between art and science.[6]

In Chapter 2, Vitruvius introduces the six Fundamental Principles of Architecture: Order – which ‘gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole’ . Arrangement – which ‘includes the putting of things in their proper places and the elegance of effect’. Eurhythmy, that is, ‘beauty and fitness in the adjustments of the members’. Symmetry, the ‘proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme’. Propriety: ‘that perfection of style which comes when a work is authoritatively constructed on approved principles’ , and Economy‘the proper management of materials and of site, as well as a thrifty balancing of cost and common sense in the construction of works’.[7]

In Chapter 3, Vitruvius presents the three departments into which architecture was divided at his time: the art of building, the making of timepieces (that is, the art of making instruments to measure the passing of time, like sundials, water clocks, sand clocks, etc.), and the construction of machinery for buildings or military purposes. It is at this point, in Section 2,  that Vitruvius introduces his famous three principles — the Vitruvian triad — to which any building must comply with: firmitas, utilitas and venustas,  or durability, convenience, and beauty, that is: any building should be solid, useful and beautiful.

In Chapter 4, Vitruvius writes about the site of a city and its choice according to some principles related to the health of humans and animals (exposure with respect to the sun and winds, the presence of water, the levels of temperature, humidity, etc.). It is important to point out that Vitruvius looks at nature — the health of birds, fishes, land animals or even pastures — and at more traditional systems to find indications on how to determine the choice of a site (if wild animals and the vegetal kingdom are in good conditions and healthy, it means the place is good for human dwellings).

In Chapter 5, Vitruvius, after the choice of the site is made, tells where to lay the foundation of the city walls and its towers; then he introduces some architectural principles to be followed in their construction. It is properly in Section 7 that Vitruvius uses the term space — i.e. the Latin spatium —  for the very first time in his Treatise: ‘Item interiore parte substructionis fundamentum distans ab exteriore introrsus amplo spatio ita uti cohortes…’ (1.5.7).

In Chapter 6, Vitruvius speaks about the direction of the streets within the walls of the city, making some remarks on the direction of Winds.

Image3: Landscape with Trees and Figures, drawing attributed to a member of the Sangallo family; in Vitruvius’ DeArchitectura Libri Decem, Book 1, Chapter 6, Section 2 (date: 1530–45): remarks on the Winds and the Lay-out of the City. Pen and dark brown ink  (metmuseum.org).

Finally, in Chapter 7, the last chapter of Book I, Vitruvius’s argumentation is about the choice of the convenient place for public meetings, or assemblies, and sacred buildings.

The Other Books in Brief

In Book II, Vitruvius begins by telling a story about Dinocrates of Rhodes, a Greek architect and technical adviser for Alexander the Great; he also gives a brief account on the origin of architecture. But he mostly explains the types and qualities of materials used for the construction of buildings: bricks, sand, lime, concrete, etc. After having explained the preliminaries about building constructions, in the remaining books Vitruvius treats the different typologies of buildings and orders of architecture. Book III is about temples and their proportions. In Book IV, Vitruvius explains the proportions of Doric and Corinthians temples, their differences and peculiarities; he gives some indications on the orientation of temples with respect to the sun or the city and gives indications about doors and altars. Finally, he presents the Tuscan order. In Book V, Vitruvius writes about the construction of public buildings. In Book VI, Vitruvius considers private houses, their conveniences and proportions with regard to the three principles — utilitas, firmitas and venustas. In Book VII, Vitruvius’s argumentation is about the different kinds of polished finishings (to make buildings elegant and durable), their preparation and installation. Book VIII is about water supplies and aqueducts. In Book IX, Vitruvius writes about sundials, about the principles of timepieces — like water clocks or sand clocks — and their construction. Finally, in Book X, Vitruvius explains the principles, use and construction of machines like hoisting machines, engines for raising waters, water wheels and watermills, pumps, odometers, siege machines like catapults, scorpions, ballistae, and so forth.

On The Use of the Term Space (i.e. spatium) in Vitruvius: An Overview

The Latin term ‘spatium’ — in any of its declensions either in singular or plural form — was used as noun 114 times throughout Vitruvius’ text De Architectura. Moreover, in the form of an adjective — with attributes like ‘spatiosus’, ‘spatiosis’, ‘spatiosae’ etc. — it was used 10 times;  3 times out of 10 it was used as a comparative adjective (e.g.spatiosora’ or ‘spatiosores’). No verbal or adverbial forms of space (spatium) were used in the text.

The entire text — De Architectura — counts about 58000 words, which means a ratio bigger than 450 with respect to the times the term space — either as a noun or adjective — was used throughout the text. I have taken account of this aspect — the ratio — because if we compare this ancient architectural Treatise with a contemporary work written by a modern architect we will find that there is an enormous difference between the two ratios, that is: there is a huge difference in number between the times the word ‘space’ is used by a modern or contemporary author with respect to an ancient text like De Architectura.[9] We, modern people and especially modern architects, have a special bias toward the use of the term space; this is another consonant proof of the fundamental human bias towards abstraction — space is an abstract concept — as a mode of understanding and describing physical reality.

Now, let us consider the specific parts of the text where the term spatium-space was used and the different meanings that can be attributed to the term. Before that, a remark: the interpretation I give to the term spatium-space is by no means exhaustive; there is a number of cases in which the interpretation is ambiguous and open to different interpretations due to the inherent semantic openness of the term ‘space’. If we also consider the stratification of meanings that that spatial notion acquired during the two millennia after the Treatise was composed, we can imagine the philological difficulty behind this type of classification and the risks of stumbling into an anachronism. Anyway, considered these difficulties, this inquiry into Vitruvius’s Treatise should be considered as an attempt to look at the concepts of space from a different perspective; an attempt to investigate the original meanings of the term space-spatium with respect to the Roman and Greek classical cultures (as I have said in the article Back to the Origins of Space and Place, the Mediterranean area was the place of a huge network of exchanges, at social, cultural and economic levels).

1) Space as a simple denotative distance, or extension, was used 5 times in the following occasions: 6.3.5; 10.9.1; 10.9.4; 10.9.7; 10.15.6. By way of the proposition ‘simple denotative distance, or extension’ I mean using the term spatium-as-space to denote a precise one-dimensional extension, or a linear extension, as when in the Latin text the author says: ‘habentes inter se palmipedalia spatia that is, according to the English translation by M. H. Morgan ‘…[cables were bound] a foot and a quarter apart’ (10.15.6). Or again, when the Latin author says: spatia pedum milia quinque’, that is ‘a distance of five thousand feet’ according to the English translator (10.9.4). In both cases, those ‘spatia’ — that is, those ‘spaces’ — denote a precise distance: in the above-quoted examples those distances were measured by means of feet and palms.

1.2) Space as a simple figurative distance or extension  was used 29 times in the following occasions: 1.5.7; 2.1.42; 3.3.2; 3.3.6; 3.3.11; 3.5.9; 4.3.6; 4.4.3; 5.1.5; 5.5.1; 6.3.42; 6.7.12; 6.7.13; 6.8.2; 6.8.41; 6.8.6; 6.8.7; 7.3.1; 7.5.2; 8.3.2; 8.6.5; 10.3.9; 10.6.11; 10.6.12; 10.6.21; 10.6.22; 10.6.4; 10.10.2; 10.12.1. With the proposition ‘simple figurative distance, or extension’ I mean using the term space — i.e. the Latin ‘spatium’ or any of its declensions — to suggest the idea of a generic (one-) dimensional distance, or extension, as when Vitruvius says: ‘Item interiore parte substructionis fundamentum distans ab exteriore introrsus amplo spatiothat is ‘then within this substructure, lay a second foundation, far enough inside the first’ (1.5.7); or when the author says: ‘planis dextra, ac sinistra in terra positis, spatio inter eas relicto quanto arborum longitudines patiuntur’ that is — in the English translation by M.H. Morgan — ‘they lay down entire trees flat on the ground to the right and the left, leaving between them a space to suit the length of the trees’ (2.1.41).

Among all of the cases in which the term space was used with figurative intentions to mean a simple generic distance we can also distinguish other connotations:

1.3) Space as a geometrical distance or extension; such interpretation of the term may be applied 4 times in the following passages: 3.5.6; 4.1.11; 4.2.1; 9.7.2, as when the author gives a geometrical explanation on how to build the convoluted forms of the Ionic capital: ‘Tunc ab summo sub abaco inceptum (schema volutae) in singulis tetrantorum actionibus dimidiatum oculi spatium minuatur’ that is, ‘then, in describing the quadrants, let the size of each (quadrant) be successively less, by half the diameter of the eye’ (3.5.6).

1.4) Space as an astronomical distance, or extension, used 7 times throughout the text in the following passages: 9.1.2; 9.1.14; 9.2.21; 9.2.41; 9.2.42; 9.3.11; 9.3.31. Example: ‘Item reliquae stellae, quo maiore absunt spatio ab extremo caelo’, that is ‘likewise with the rest of these stars: the farther they are from the outer most limits of the heaven…’ (9.1.14)

1.5) Space as an interval to indicate an extension between two or more bodies far apart, was used 3 times — in 3.2.6; 3.3.1; 10.4.1 —, as when Vitruvius speaks about the extension that must be left in between the structures of a temple or in between the columns: such is the meaning of spatiis intercolumniorum’ translated by the English author as ‘intercolumniations’, that is, the distance between columns (3.3.1).

Image 4: Temple Types: Peripteral, drawing attributed to a member of the Sangallo family; in Vitruvius’ DeArchitectura Libri Decem, Book 3, Chapter 2, Section 5 (date: 1530–45). Pen and dark brown ink  (metmuseum.org).

In all of the cases we have examined so far, we can say that behind the term ‘spatium’-as-space we find the idea of a simple distance, extension or interval either that distance, extension or interval is understood as a denotative or connotative entity. Denotative distances, as well as geometrical and astronomical distances, extensions and intervals, are the most immediate conceptualizations that the term space can describe (this is the Greek origin of the term space as spadion/stadion after all —  see the article Back to the Origins of Space and Place).  The simple idea of extension is so powerfully and comprehensibly described by the term space that the very term space was often used by Vitruvius to denote a temporal extension, duration or interval of time:

1.6) Space as an interval of time was used 14 times throughout the text in the following occasions: 2.9.141; 5. Introduction. 3; 5. Introduction 4; 8.2.9; 9. Introduction 15; 9.2.43; 9.3.12; 9.3.32; 9.3.33; 9.8.8; 9.8.9; 9.8.131; 9.8.132; 9.8.133. Here a couple of examples: ‘Larix (…) longo spatio tarde comburitur’ that is, ‘The larch (…) after a long time it slowly consumes away’ (2.9.141); or again: ‘brevi spatio fit frigida’ that is ‘in a short time (water) becomes cold’ (8.2.9).

To make a first recognition, space as a ‘simple’ extension, distance or interval (1D)  to describe a real (denotative) or figurative (connotative) situation was used 48 times. To such number, we have to add the times ‘space’ was used to describe a temporal extension: 14 times. This makes a grand total of 62 times: in the Latin text ‘De Architectura’, 62 times out of 114, the term ‘spatium’-as-space can be interpreted as a simple — one-dimensional — extension, either that extension is spatial or temporal.

Besides using the term ‘spatium’ to communicate the idea of a simple extension, distance, interval or temporal duration, independently of the fact that that conceptualization can be applied to astronomical, geographical, architectural, geometrical or to other contexts, Vitruvius often uses the term ‘spatium’-as-space to denote something more complex and richer than a simple extension: he also uses that term to refer to areas or regions. Then ‘spatium’-as-space is a very useful word to describe two-dimensional areas, surfaces, regions, etc. (2D), other than simple extensions (1D). These are the cases I’m referring to:

2) Space as area, surface or region referred to the description of things, objects or physical bodies — like a building or a clock — was used 15 times in the following passages: 2.1.42; 2.8.171; 2.8.172; 4.3.81; 4.3.82; 4.7.2;  5.5.12; 5.6.8; 6.3.10; 9.8.12; 9.8.141; 9.8.142; 9.8.143; 9.8.15; 10.4.2. As an example of this kind of interpretation of the term ‘spatium’-as-space in two-dimensional sense, I take the following passage: ‘conlocantur in estremis partibus earum supra alterae transversae, quae circomcludunt medium spatium habitationis, that is, ‘and then (they) place above these (trees) another pair of trees, resting on the ends of the former and at right angles with them. These four trees enclose the space for the dwelling’ (2.1.42). By reading this passage in the appropriate context — see also the passage 2.1.41,which directly precedes this one (trans: ‘they lay down entire trees flat on the ground to the right and the left, leaving between them a space to suit the length of the trees’) — I believe few doubts can arise in the interpretation of the space for dwelling as a specific portion of the ground or of the floor (2D) rather than as a three-dimensional expanse in a modern sense.

2.1) Space as geometrical area, surface or region, was used 11 times in the text: 1.6.131; 1.6.132; 1.6.133; 1.6.134; 4.4.1; 4.7.1; 4.7.3; 4.8.6; 6.2.5; 6.3.3; 9.8.102. Example: ‘quod erit spatium ab G ad H, erit spatium venti austri et partis meridianae’ that is ‘the space from G to H will belong to Auster and the South (winds)’ reports Vitruvius in his description about the subdivision of a geometric circular diagram — the wind rose — to express the distribution of the Winds (1.6.131-2). Within this category, I also consider the cases in which Vitruvius speaks about the space of buildings like temples, houses, arenas, and the likes, with an evident reference to dimensions, proportions, symmetry and reciprocal disposition of architectural elements, which can only be attained by means of geometrical and mathematical relations between the parts of a building. Example: ‘tertium, uti latitudo in quadrato paribus lateribus describatur inque eo quadrato diagonios linea ducatur, et quantum spatium habuerit ea linea diagonii, tanta longitudo atrio detur’, that is ‘the third (class of atriums is laid out) by using the width to describe a square figure with equal sides, drawing a diagonal line in this square, and giving the atrium the length of this diagonal line’ (6.3.3).

Image 5: DeArchitectura Libri Decem, edition translated by Daniele Barbaro, with illustrations by Palladio, 1557 (abebooks.it).

It seems to me, this connotation of space is somewhat different from the previous one (2.1.42) and the others, which follow:

2.2) Space as astronomical region was used 11 times, in the following passages: 1.6.8; 6.6.6; 9.1.61; 9.1.62; 9.1.63; 9.1.8; 9.1.9; 9.1.10; 9.2.2; 9.3.1; 9.8.10. I take the following passage as example: ‘Sol autem signi spatium, quod est duodecuma pars mundi, mense vertente vadens transit’ that is, according to the English translation:  ‘The sun takes a full month to move across the space of one sign, that is, one twelfth of the firmament’ (9.6.61). To properly consider this kind of interpretation of the term spatium-space within its astronomical context, we have to remark that the cosmological model acknowledged at the time of Vitruvius — that is the Aristotelian Cosmology — was made of concentric spheres revolving around a central sphere — the Earth — and that on the surface of each sphere heavenly bodies moved with perfect circular trajectories: on this basic model, the astronomical models of antiquity were conformed, specifically the model of Ptolemy (I’ve spoken about that in the article Space and Place: A Scientific History – Part  One, see Image 10); then, the spatium-space Vitruvius speaks about is a portion of the surface of a sphere on which the stars, composing the twelve signs of the zodiac, were thought to be located. What is the surface of a sphere if not a two-dimensional region? Remember the ultimate problem we are dealing about, is not the existence of a multidimensional extensive (as well as intensive) character of the Cosmos — which we, modern people, take for granted —, but the way man understands and describes it, the names that were given to it, through the different epochs, by different people. Of course, this is not a semantic question only: behind the adoption of a term or another, behind one description or the other, there are different ontological and epistemological perspectives and a different cosmology, in the end. Concepts of space and place are inherently connected to such ultimate questions, or visions of the world: that’s why it is important the way we understand and use those notions: they express our ultimate understanding of the phenomena of the world.

2.3) Space as a geographical region was used 4 times throughout the text in the following passages: 1.6.9; 6.1.1; 6.1.6; 6.1.10. Example: ‘veros inter spatium totius orbis terrarum regionesque medio mundi populus Romanus possidet fines’ that is, ‘the truly perfect territory, situated under the middle of the heaven, and having on each side the entire extent of the world and its countries, is that which is occupied by the Roman people’ (6.1.10).

Now, we can make a second recognition of the text: we have just interpreted spatium-as-space by way of two-dimensional extensions (2D) — area, region, or surface — 41 times out of 114. If we sum the times the word ‘spatium’- space was used as a simple extension — 62 times — to the times ‘spatium’-space was used as a two-dimensional extension, area, surface or region, — 41 times — that makes a grand total of 103 times out of 114. There are certainly cases where the interpretation is ambiguous but, to me, in the overall, those numbers remain quite impressive: today, when we speak about space, almost everybody understands it as a three-dimensional (or four-dimensional) arena where things happen and bodies are located (an immersive arena or space, that is a background space); its understanding as a two-dimensional region, portion or area or, even less, its understanding as a simple distance or extension is considerably minor in number; in our talks, we instinctively and instantaneously associate space to the idea of three dimensions. Then, when does this latter conceptualization of space emerge? It seems to me, the prevailing tendency of this study is consistent with the idea that the conceptualization of space as a complex (multidimensional) object, comes certainly after the Greek and Roman classical period. Either this ‘object’ —space — is conceived of as ideal or physical, I believe that the conceptualization of space as a three-dimensional medium is closer to our times rather than to the time of Vitruvius. The hypothesis that we have to wait for Descartes and Newton to have an understanding of space as a fully-fledged three-dimensional concept is well-grounded.

Up to now, we have seen the many different circumstances —103 out of 114 — in which the term spatium-space was used to express the idea of one-dimensional extensions (either spatial or temporal extensions), or two-dimensional extensions, such as an area, surface or region. The introduction of the notion of ‘spatium’-space to connote a geometrical region, also introduces the important question of ‘architectural space’ and consequently the more general question of space understood as a three-dimensional expanse — the immersive arena for objects and bodies. As I have repeatedly stated, for the architect as well as for the man in the street of the present time, it is an obvious fact to understand space as an expanse in three-dimensional sense (either physical or ideal). From a first recognition, we discarded the interpretation of 3D space as an astronomical hypothesis because of the prevailing cosmological model in vogue at the time of Vitruvius. Moreover, we also have to remember that before Descartes, Euclidean geometry, on which that cosmological model was conformed, was exclusively a two dimensional kind of geometry consisting of axioms and postulates dealing with the position of elements like points, lines, angles, or shapes like triangles, circles and the likes. There was no idea of space as a containing or referential entity within the domain of Euclidean geometry before Descartes.  Then, now, the question we are approaching is the following one: is it possible to attribute to Vitruvius some kind of three-dimensional understanding of spatium-space (in the modern sense) for the remaining cases we have to analyse? Or is such interpretation our own interpretation, therefore a sort of anachronism?

Before introducing this possibility, we have to go back to a passage in the text where Vitruvius speaks about how to set up the proportions for the private house: ‘Igitur statuenda est primum ratio symmetriarum, [a qua sumatur sine dubitatione commutatio] deinde explicetur operis futuri locorum imum spatium longitudinis (et latitudinis)’, that is, in English: ‘hence, the first thing to settle is the standard of symmetry, from which we need not hesitate to vary. Then, lay out the ground lines of the length and breadth of the work proposed’ (6.2.5). Here, the term ‘spatium’ clearly defines architectural space as the two dimensions — ‘longitudinis et latitudinis’ — which make up an area or surface on a plan, or on the ground (floor). No doubt: in this case, the ‘space’ of architecture is limited to a generic two-dimensional region on the ground — ‘the ground lines of the length and breadth’ —, that is, an area or surface.

Image 6:, drawing attributed to a member of the Sangallo family; in Vitruvius’ DeArchitectura Libri Decem, Book 3, Chapter 2 (date: 1530–45). Pen and dark brown ink on laid paper(drawingmatter.org).

Another important passage, to read in combination with the one we have just analysed, is the following one: ‘… uti nullum parietem tangant circaque habeant locum vacuum et ab summo capite spatium’, that is, ‘… in such a way that they (the bronze vessels) nowhere touch the wall, but have a clear space all round them and room over their tops’ (5.5.1). Apart from the English translation, which I consider a weak translation, Vitruvius literally describes as ‘place’ (!) free from objects and obstacles — locum vacuum — the area on the floor all around the bronze vessels, while he uses the term ‘spatium’ to refer to the vertical extent over those vessels  – ‘ab summo capite spatium’. In this circumstance, it seems for Vitruvius the two dimensions on the horizontal plan have a different character, or connotation, from the vertical dimension: that’s why he uses two different words — ‘locum vacuum’ and ‘spatium’  — to describe what he could have described using just one word — spatium-as-space — had he understood space the same way we understand it now (as a matter of fact this is exactly what the Italian translator does — ‘… senza che – i vasi di bronzo – siano a contatto  con qualche parete, ma abbiano piuttosto uno spazio vuoto tutt’ attorno e sopra’ — that is, he used just one term: space-spazio).[10] After all, for a modern man, what is an empty place if not a space? The fact that Vitruvius considers the three spatial dimensions disjoined (2 horizontal dimensions described as ‘locuum vacuum’ + 1 vertical dimension described as ‘spatium’ ) means that he hasn’t probably already developed an organic or fully-fledged idea of space, understood as single entity or system made up by the three integrated dimensions, like the one we possess. This is all the more so if we consider that there are other occasions in the text where Vitruvius generically describes a horizontal region as space/’spatium’ (it suffices to see the previous quotation 6.2.5); in this case, since he has to speak of the three dimensions at the same moment within the same passage, instead of using the same term ‘spatium’, to avoid confusion, he uses the proposition ‘locuum vacuum’ to define the two horizontal dimensions and ‘spatium’ to define the vertical dimension (at this regards it is evident the legacy from the old Greek ‘stadion’ — from which the Latin ‘spatium’ derives — as the well-known unit of measurement especially used to define vertical or astronomical distances, like the distance from the Earth to the Sun or to the Moon).

There is another case in the context of an architectural explanation, where Vitruvius uses the term ‘spatium’ to draw a distinction between the horizontal plane, which defines a two-dimensional region — now described as ‘locus’ — and the vertical dimension — described as ‘spatium’. This is the passage: ‘non est alienum in angustis locis et in concluso spatio’,  that is, ‘it is not improper, in narrow quarters or where the space is enclosed…’ (4.4.3). Again, I believe the English translation can be interpreted differently and closer to what I think is Vitruvius’ understanding of spatium-space in this occasion since the translator overlooks that Vitruvius is speaking about the same spatial/placial (environing) situation which results from ‘angustis locis’, that is a limited horizontal plane or region (the ground-floor) and — this ‘and’, which is a conjunction, is the Latin ‘et’, not the English ‘or’, used by Morgan, which means a disjunction or an alternative — the vertical dimension/extension, which is associated to that region and which Vitruvius refers to as ‘concluso spatio’ (in this way we are closer to the aforementioned interpretation at 5.5.1, where the horizontal dimensions defining an area, and the vertical dimension, defining the vertical closure above our heads, have two different names).

Similar to the passage we have just analysed, but even more ambiguous in its interpretation, there is another passage where the term ‘spatium’-space is in the middle ground between a region and a vertical dimension/extension (see the excerpt 5.9.5, in the section below); it is precisely from such an ambiguous situation that, with a leap of imagination, Vitruvius could have been put in the right direction to imagine spatium-space as a three-dimensional notion in a modern sense. This can be my suggestion, but, it seems to me, the following situations, described by Vitruvius by means of the term ‘spatium’-space, have a flavour which is somewhat different from the interpretations of space we have analysed so far:

3) Space as an architectural expanse, or, simply, space as an expanse, in the 2 following passages: ‘Media vero spatia, quae erunt subdiu inter porticus, adornanda viridibus videntur’, that is, ‘the space in the middle, between the colonnades and open to the sky, ought to be embellished with green things’ (5.9.5). Or again: ‘ita enim erit vectiario spatium expeditum’, that is ‘… which will give the lever man a convenient amount of space’ (6.6.3). The passage 5.9.5 is important since it is about the close relationship between architecture, the concept of space, and the possibility to assign space a three-dimensional sense (in addition to the already analysed one-dimensional and two-dimensional senses) by drawing together the 3 different dimensions that Vitruvius described separately in 5.5.1; a sort of dimensional ‘upgrade’ to the conceptualization of space: from a simple dimensional or two-dimensional understanding of the term to a three-dimensional fully-fledged conception, where the three extensions (two horizontal, one vertical) are fused together into a new integrated entity.

Image 7:, I made this sketch to sum up the different senses of space and place (spatium, locus) contained in Vitruvius’ De Architectura in the passages at 4.4.3, 5.5.1, and 5.9.5.

As a matter of fact, apart from the specific interpretation of that passage in Vitruvius’s text, this is a possibility that I see for any architect of the Roman period, or even for architects of the coming epochs: the possibility to understand before than others the deep entanglement between the dimensions of height, depth and width, which, taken together, make up space as a congruent stucture, a coherent system of dimensions allowing for a spatial understanding of the world in a (modern) three-dimensional sense. It is true that philosophers and physicists or mathematicians/geometers investigated the fundamental spatial/placial nature of reality for the sake of knowledge since the origins of Western Thought; but, architects, in their daily routines in between geometrical drawings and actual constructions, in between theory and practice, more than others had the possibility to stay in close touch with those three extensions/dimensions, which they had in front of their eyes and nose every day in their working activities. However, I’m also aware that one thing is to have something in front of our nose, another thing is to attribute that ‘something’ a certain meaning or, even more difficult, an unforeseen or an unexpected meaning. I experienced this fact first-hand: when I was an undergraduate student I soon learned that architecture was a question of space, by reading a number of books; yet to understand what that really meant was something different; I like to compare the precise moment in which I really understood what space meant for architecture to the precise moment in which Paul Klee really understood what colour meant for painting:[11] it was an enlightening experience, a sort of epiphany, which has almost nothing to do with what we have in front of our nose; it is as if our perspective is turned upside down in a blink of an eye… and we start seeing what we didn’t see until that moment. Eureka! 

There are other ambiguous passages concerning the interpretation of the term space-spatium in the text, but, in the overall, they do not change the tendency we have seen so far with respect to its interpretation as a one-dimensional or two-dimensional entity.

3.1) Space as a figurative gap or cavity referred to existing objects or material, was used 9 times in the following passages: 2.1.5; 2.9.142; 4.2.4; 5.1.7; 5.12.3; 6.3.41; 10.8.2; 10.8.5; 10.11.2. Example: ‘aere implent spatia modiolorum’ that is‘filling the interiors (of the cymbals) with air’ (10.8.5).

4) Space as an attribute of distance, extension or region wasused10 times in the following passages: 5.1.21; 5.3.5; 5.10.4; 5.11.2; 6.3.2; 6.3.8; 6.5.2; 6.7.1; 6.7.3; 8.8.4. In all of the mentioned cases, we are in the context of an architectural explanation: the dimension to which the spatial attribute is referred to is, from time to time, a simple distance or extension (e.g.: spatiosiora intercolumnia’ — ‘let the intercolumniations… be pretty wide’ in 5.1.21; or ‘intinera faciunt latitudinibus non spatiosis — ‘… the Greeks… make passage-ways… not very wide’ in6.7.1), an area or a region which defines an architectural room or locale, in analogy to what we have already considered at 6.2.5 and 6.3.3. — see images 5 and 6 above — rather than an indefinite space in the modern sense (e.g.: spatiosae habitationes’  — ‘large rooms’ , in 6.3.2; or ‘oeci corinthii tetrastylique… spatiosores’ — ‘Corinthian and tetrastyle oeci… should be ampler’, in 6.3.8).

Summary

The following table summarizes the times the term spatium-as-space was used in the Treatise ‘De Architectura’ by Vitruvius, and the meanings attributed to it:

GRAND TOTAL 124 TIMES
As noun 114 times
As adjective 10 times
As denotative distance or extension 5 times
As figurative distance or extension 29 times
As geometrical distance or estension 4 times
As astronomical distance or extension7 times
As simple interval 3 times
As temporal interval or extension 14 times
As an area, surface or region (of objects, things, bodies, etc.)
15 times
As a geometrical area, surface, region11 times
As astronomical region 11 times
As geographical region 4 times
As figurative expanse (architectural too)2 times
As figurative gap or cavity 9 times
Table 1: Summary table concerning the use of the term space-spatium in Vitruvius’s DeArchitectura (Alessandro Calvi Rollino Architetto).

In the text there is a number of passages where the term can be interpreted in different ways; what is especially relevant is the different sense of dimensionality that each time can be attributed to ‘spatium’-as-space according to the context in which it is used. In particular, when we are in the context of an architectural explanation regarding buildings or some parts of them, the interpretation of space (a region or an area on the ground or floor? a three-dimensional expanse?) needs a careful inspection. The same caution is needed for any interpretation of ‘spatium’-as-space, when we are in an astronomical context: here ‘space’ has to be understood in the light of the cosmological and geometrical models prevailing at the time of Vitruvius. In the overall, apart from the reasons I showed you with regard to the interpretation of some important passages at 6.2.5, 5.5.1 and 4.4.3, — which gave me a bias in favour of a two-dimensional interpretation of the concept of ‘spatium’-as-space when applied to an architectural context — , it seems to me it is undeniable the fact that the concept of space in Vitruvius is very different from the modern concept of space intended as a three-dimensional (or tetra-dimensional) arena where things and bodies are located. At the time of Vitruvius, by means of the term ‘spatium’, space was mainly understood as a simple extension (linear), as a temporal extension, and as a region, surface, area or territory to be used in different contexts (geometric, architectural geographical, astronomical, etc.). Yet, we must be careful: this fact does not mean that people in the pre-scientific era, had no cognition of reality as a three-dimensional fact (at least); I’m just saying that people in antiquity were not in the appropriate cultural and social conditions to express or to communicate that idea by means of a fully-fledged concept of space like the concept we, modern people, usually think about; this immersive and neutral conceptualization of reality-as-space became clear only after space acquired a stratification of meanings in the course of history, and especially in the last four hundred years with the important contributes of Descartes and Newton. I believe that architecture — as a social and cultural enterprise which accompanies the daily life of people — can have played an important role in transforming and/or diffusing the concept of space from a simple (one-) dimensional fact to a complex multidimensional concept. The very fact that Roman architecture is often acknowledged for being an ‘architecture of (interior) space’,  while, conversely, we could better understand Egyptian and Greek Architectures as ‘architectures of place’, may testify this possible leap of imagination that could have pushed, at first, Roman people and architects to embrace new cultural and social models to understand physical reality in a different way (a spatial mode of understanding reality) with respect to the past. Roman architecture was certainly the concretization of critical cultural and social changes in the Western World.

Image 8: The three main pyramids at Giza plateau, EGYPT (Image by Carmen Estrada, @Pixabay.com).
Image 9: The Acropolis of Athens, GREECE (Image by Markus Winkler, @Pexels.com).
Image 10: The Pantheon in Roma, ITALY (Image by Daniel Farkaš, @Pixabay.com).

From a semantic point of view, the Latin term spatium-space was probably open enough to accept within itself more complex meanings and connotations with respect to other classical Greek concepts (especially ‘topos’ and ‘chōra’), which, at the beginning of the Christian era, belonged to a decaying civilization if compared to the emerging Roman world. As we have seen in the analysis of the Latin text DeArchitectura there are passages where the term ‘spatium’-space might suggest us an interpretation in a three-dimensional sense;  the fact that the term spatium-as-space was open to different interpretations is a proof of the versatility of that term, which takes within itself the possibility to transcend its simple dimensional nature into more complex characters. It was also in virtue of such different yet coherent possibilities of interpretation, that the term ‘spatium’-as-space (and not the Greek topos or chōra) was precisely adopted by the Roman Catholic culture and the scholastic philosophers, down to the Italian naturalists of the early and late Renaissance, until Descartes, Newton, and later, Einstein, to express our understanding of reality as a spatial or spatiotemporal fact. Will the concept of space comply with the impact of time across millennia changing its nature once again in future? Here we are, at the beginning of a millennium waiting for new different spatial (or placial) interpretations of reality.

Notes

[1] English edition: Vitruvius, ‘The Ten Books on Architecture’, translated by Morris Hicky Morgan. London: Humphrey Milford Oxford University Press, 1914. Here a couple of links to that work, now in the public domain:

https://archive.org/details/vitruviustenbook00vitruoft

https://en.wikisource.org/wiki/Index:Vitruvius_the_Ten_Books_on_Architecture.djvu

Italian edition: Vitruvio, Marco Pollione. ‘De Architectura’, translated by Luciano Migotto. Pordenone: Edizione Studio Tesi srl., 1990.

While the aforementioned English edition only presents the translation by Morgan, the Italian edition I have considered also includes the original Latin version, on which I have based the Latin excerpts for the present article. A Latin version of De Architectura can be found at this link:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0072

[2] Vitruvio, Marco Pollione. ‘De Architectura’, translated by L. Migotto (Pordenone: Edizione Studio Tesi srl., 1990), xxix.

[3] Ibid., xxxi.

[4] Ibid., xxix.

[5] Book I, Chapter 1, Section 1 (1,1,1).

[6] Book I, Chapter I, Section 11 (1,1,11).

[7] Book I, Chapter II, Sections 1, 2, 3, 4, 5, 8 (1,2, 1-2-3-4-5-8).

[8] Then within this substructure, lay a second foundation, far enough inside the first to leave ample room for cohorts…’ (1,5,7).

[9] For instance, in the books The Autopoiesis of Architecture Vol.1 and Vol.2, (2010), written by the German architect Patrick Schumacher (Zaha Hadid Architects),  we find a frequency three times greater than in Vitruvius’ text. If we consider that we, modern people, understand space almost univocally as a three-dimensional (or tetra-dimensional) expanse in which bodies are located, while, as we are noting, for the ancient author space had multiple meanings (one-dimensional extension, two-dimensional region, time, interval, etc.) we can understand how big is the difference between the conceptions of space of modern people with respect to ancient people. The mind of the modern man is certainly a spatialized mind, where ‘space’ corresponds to an absolute or even relative frame of reference understood as an immersive entity where things and bodies move and are located.

[10] Vitruvio, Marco Pollione. ‘De Architectura’, translated by L. Migotto (Pordenone: Edizione Studio Tesi srl., 1990), 213.

[11] ‘Die Farbe hat mich’. During his journey in Tunisia, on April 16, 1914, Paul Klee wrote on his notebook: ‘Color possesses me. I don’t have to pursue it. It will possess me always, I know it. That is the meaning of this happy hour: Color and I are one. I am a painter’.

Works Cited

Vitruvio, Marco Pollione. ‘De Architectura’, traslated by Luciano Migotto. Pordenone: Edizione Studio Tesi srl., 1990.

Vitruvius. ‘The Ten Books on Architecture’,  translated by Morris Hicky Morgan. London: Humphrey Milford Oxford University Press, 1914.