Concepts of Space in Vitruvius

The previous article — Place Space and the Unicorn — could be seen as a prologue to this one, as it lays out the premises and reasons that led me to analyze Vitruvius’s ancient text De Architectura, written by the Roman architect in the first century B.C., in order to understand how the concept of space was interpreted across the different eras. In the final part of that article I questioned whether, beyond 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, which views the so-called background space as an inert container of things, bodies and events, emerged after the invention of Cartesian geometry and the introduction of Newtonian absolute space. I also sought to explore how the metaphorical understanding and diffused use of the concept ‘space’, associated with the notion of pure extensiveness, spread.

When I began specific readings to deepen my knowledge of the concepts of space and place, one of the most disconcerting things that initially struck my attention was the significant ambiguity in how different authors used the terms ‘space’ and ‘place’; furthermore, I was surprised by the ambiguities in translating ancient texts, particularly with regards to spatial terms. There were countless instances where the same word – whether it was the Greek topos, chōra, or kenon, or the Latin locus, spatium, and vacuum – was translated as ‘space’ by one author and as ‘place’ by another, or vice versa. Although it sounds good to consider the context where a term belongs to determine its proper translation, it remains somewhat elusive, as we always operate within interpretative hypotheses, shifting our interpretative tools from the term to its context, and thus, subjective and questionable interpretations persist. I realized that things aren’t that easy when disentangling questions of space and place, as these millenary concepts have been interpreted differently throughout the ages, with varying connotations from one epoch to another. This raises the risk of anachronistic interpretations when analyzing ancient texts, since cultures and societies constantly evolve, and a person’s mindset is always shaped by their own time. I began to think that a philological interpretation of an ancient text couldn’t lead to any definitive conclusions, but rather provide some useful indications or tendencies to compare with traditional historical analyses.

To initiate this philologically-based inquiry I chose Vitruvius’s De Architectura – Libri Decem (The Ten Books on Architecture) for three reasons: first, I was already familiar with the book from my undergraduate studies at the Politecnico di Milano, as it is a well-known introduction to the discipline of architecture for aspiring architects. Second, a study of Vitruvius’s concept of space could provide insight into the relationship between architecture and space in general, as well as shed some light on the the differences in the concept’s meaning across various historical periods, including Classical Greek, Roman, and Modern epochs. Finally, the choice of an ancient Latin text could be especially useful for my specific scope, as it can help elucidate the meanings and different interpretations of space, given that the English term ‘space’ originates from the mediaeval Latin term ‘spacium’, which is a modification of the old Latin term ‘spatium’. As if to say: there is only one degree of separation between the two words. Conversely, it is more challenging 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 often used interchangeably to translate the concepts of space and place. However, despite the direct relation between the English term ‘space’ and its Latin descendant ‘spatium’, it is crucial to consider the issue of anachronism I mentioned earlier: when dealing with the original Latin term ‘spatium’ as space, we must keep in mind the specific literary and historical contexts in which the term was used. Whenever we encounter the term ‘spatium’ in the Treatise, we cannot assume that Vitruvius had an idea of space as a neutral container or background like the three-dimensional immersive entity we are familiar with today. The idea of an abstract container and, consequently, the idea of a background space are often considered modern ideas. With this important consideration in 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 that Cartesian geometry and Newtonian physics originated the idea of three-dimensional space would need to be reevaluated. Otherwise, apart from indirectly confirming the reliability of historical studies sensitive to this question (at this regard, Casey’s textThe Fate of Place is an exemplary work), we could explore another interesting area of investigation to understand how the interpretation of space has changed over time. In the context of architecture, it is worth exploring how the concept of space (spatium / spacium / spazio / espace, etc.) and other spatial notions are employed (if at all) in the works of architects and critics such as 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 more contemporary architects and critics like Charles Jencks, Peter Eisenmann, Bernard Tschumi, Rem Koolhaas, and Zaha Hadid. Answering that question could provide valuable insights into the nature of space and other spatial concepts, as well as their development, not only within architectural circles but also beyond, considering that architecture is a complex system of knowledge influenced by sociocultural and symbolic dynamics. Additionally, it could reveal the impact of architecture on the evolution and dissemination of space-related concepts.

Image 1: Cénotaphe à Newton, by Étienne-Louis Boullée, 1784. 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 previous articles, although spatial and placial concepts had significant milestones tied to the works of Aristotle, Descartes, Newton and Einstein, those works represent symbolic watersheds behind which we find the concurrent efforts of many individuals who helped create an environment conducive to the widespread adoption of certain spatial and placial concepts. Can we overlook the role played by the invention of geometric perspective (to which geometers, mathematicians, architects and painters gave important and converging contributions) to the elaboration of the first geometrical and quasi-physical modes of understanding space as a three-dimensional entity? Or, even before, can we overlook the role of ancient astronomy and astronomers in shaping the modern concept of space, so beautifully described by Julian Barbour (see Space and Place: A Scientific History – Part One)? Why can’t we also acknowledge the recent contributions of social scientists in enhancing our understanding of the concepts of place and space? After all, according to the systemic placial( )spatial perspective that I call for here, physicochemical, biological, social and symbolic patterns of reality have equal dignity and footing, 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 present brief excerpts from Vitruvius’s Latin Treatise that contain the term ‘space’ (including its declensions such as ‘spatium’, ‘spatii’, ‘spatio’, ‘spatia’, ‘spatiorum’, ‘spatiis’, in the original version) relying on two English and Italian translations to understand, from different linguistic perspectives, the context in which Vitruvius used these terms.^[1] Following this, I will provide brief comments on the excerpts before summarizing the different senses of ‘space’ and their usage in the Treatise in a concluding paragraph. For brevity, I have selected one representative excerpt for each sense of ‘space’ (e.g., space as distance, as region, as time, as astronomical expanse, etc.), and will indicate the relevant sections of the text where Vitruvius used the term ‘spatium-space’ or its variations as an attribute (e.g., 3,5,8, that is: Book III, Chapter V, Section 8).

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 speak 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 for the benefit of architecture students and those interested in architectural issues; indeed, Vitruvius’s De Architectura has shaped the academic training of many generations of architects (at least here in Italy) and remains widely known or cited after more than two millennia. Readers interested solely in the linguistic use of the term ‘space-spatium‘ in Vitruvius’s Treatise can proceed to the paragraph On The Use of the Term ‘Space’ (i.e., spatium) in Vitruvius: An Overview, skipping the next two paragraphs.

Book I

Architecti est scientia pluribus disciplinis et variis eruditionibus ornata, cuius iudicio probantur omnia quae ab ceteris artibus perficiuntur opera. Ea nascitur ex fabrica et ratiocinatione
Vitruvius

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 derive), 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.

Image 3: Landscape with Trees and Figures, drawing attributed to a member of the Sangallo family; in Vitruvius’s DeArchitectura Libri Decem, Book 1, Chapter 6, Section 2 (date: 1530–45): remarks on the Winds and the Lay-out of the City.

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 commences 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 a noun 114 times throughout Vitruvius’s text De Architectura. In addition, as an adjective with attributes like ‘spatiosus’, ‘spatiosis’, ‘spatiosae’ etc. it was used 10 times, with 3 of those instances being 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 — consists of about 58000 words, which means a ratio bigger than 450 concerning the times the term space — either as a noun or adjective — was used throughout the text compared to other words. I considered this aspect — the ratio — because when we compare this ancient architectural treatise to a contemporary work written by a modern architect we find a huge difference between the two ratios, with modern authors, especially architects, showing a strong bias towards using this term in comparison to an ancient text like De Architectura.^[9] This provides further proof of the fundamental modern human bias towards abstraction (space is an abstract concept) as a mode of understanding and describing physical reality. Apart from architecture, this modern tendency to use the term ‘space’ as a privileged mode of expression and description of different environmental situations is well attested by my parallel research — a photographic report of how the concepts of space and place are used with communicative intent in the streets of Milano, the city where I live (see Spatiophilia): the approximate ratio between the use of the two words is 5 to 1 (the word ‘space’ used in signs, billboards, shop windows, public warnings, street banners, description of activities, etc. is five times more recurrent than the word ‘place’).

Let us now examine the specific parts of the text where the term space-spatium is used and the various meanings it can convey. Before proceeding, I want to clarify that my interpretation of the term space-spatium is not exhaustive, as it can be ambiguous and open to multiple meanings due to its inherent semantic openness. Furthermore, considering the stratification of meanings that this notion acquired over the past two millennia, we can appreciate the philological challenges involved in this type of classification and the risks of anachronism. Despite 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 where 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 spatio’ that 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 the cases in which the term space was used figuratively to mean a simple generic distance we can also identify 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).

In all the cases we’ve examined so far, we can say that behind the term ‘spatium’-as-space we find the idea of a simple distance, extension, or interval whether 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 reflected 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 a linear, continuous extension is so powerfully and comprehensibly conveyed 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 in the text, specifically 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 are a couple of examples: ‘Larix (…) longo spatio tarde comburitur’, which means ‘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).

As a first summary, space as a ‘simple’ extension, distance, or interval (1D) to describe a real or figurative situation was used 48 times. To this number, we must add 14 instances where ‘space’ referred to a temporal (linear) extension. 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 spatial or temporal.

Besides using the term ‘spatium’ to convey the idea of a simple extension, distance, interval, or temporal duration, independently of the fact that that conceptualization is applied to astronomical, geographical, architectural, geometrical or to other contexts, Vitruvius often employs the term ‘spatium’-as-space to denote something more complex and richer than a simple extension, referring to areas or regions. Then the term ‘spatium’-as-space is particularly useful for describing two-dimensional areas, surfaces, regions, etc. (2D), as opposed to simple extensions (1D). These are the specific cases I am referring to:

2) Space as an area, surface or region referred to the description of things, objects or physical bodies — like a building or a clock — was used a total of 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 a two-dimensional sense, I cite the following passage: ‘conlocantur in extremis partibus earum supra alterae transversae, quae circomcludunt medium spatium habitationis, which means, ‘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 interpreting the space for dwelling as a specific portion of the ground or of the floor (2D) rather than as a three-dimensional expanse (3D) in the modern or contemporary sense we are now used to (see also Image 6, below).

2.1) Space as a 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 (1.6.13_1-2). 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.

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 an 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’ll use the following passage as an example: ‘Sol autem signi spatium, quod est duodecuma pars mundi, mense vertente vadens transit’ which translates to ‘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 must note that the cosmological model prevalent during Vitruvius’s time — the Aristotelian model — consisted of concentric spheres revolving around a central sphere, the Earth, with heavenly bodies moving in perfect circular trajectories on the surface of each sphere; this basic model was the foundation for ancient astronomical models, including Ptolemy’s model (which I discussed in the article Space and Place: A Scientific History – Part One, see Image 10). Therefore, the space-spatium Vitruvius refers to is a portion of the surface of a sphere where the stars, comprising the twelve signs of the zodiac, were thought to be located. What is the surface of a sphere if not a two-dimensional region? We must remember that the ultimate issue at hand is not the existence of a multidimensional extensive (as well as intensive) character of the Cosmos — which we, modern people, take for granted —, but how humanity has understood and described it throughout history, the names given to it in different epochs by different people. This is not merely a semantic question, as the adoption of a particular term or description is rooted in distinct ontological and epistemological perspectives and cosmologies. The concepts of space and place are inherently tied to these fundamental questions or worldviews, which is why it’s essential to understand and use these notions correctly, as they reflect our ultimate understanding of the world’s phenomena.

2.3) Space as a geographical region was used 4 times, 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’ which means, ‘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).

We can now make a second summary: we have just interpreted spatium-as-space in terms of two-dimensional extensions (2D) — area, region, or surface — 41 times out of 114. If we combine the times the word ‘spatium’-space was used as a simple extension (62 times) with those where ‘spatium’-space was used as a two-dimensional extension, area, surface, or region (41 times), we get a grand total of 103 times out of 114. While there are certainly cases where the interpretation is ambiguous, to me, the numbers remain quite impressive overall: today, when we discuss space, almost everyone instinctively understands it as a three-dimensional arena where events occur and things or bodies are located (an immersive arena or space, that is a background space), rather than as a two-dimensional region or simple distance; in our conversations, we automatically associate space with the idea of three dimensions. Then, when does this latter conceptualization of space emerge? In my opinion, this study suggests that the conceptualization of space as a complex (multidimensional) object comes certainly after the Greek and Roman classical period. Whether this ‘object’ — space — is viewed 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. This serves as further proof that the hypothesis — that we had to wait for Descartes and Newton to develop a fully-fledged three-dimensional understanding of space — is well-founded.

So far, we have observed that the term space-spatium has been used in 103 out of 114 instances to describe one-dimensional extensions, whether spatial or temporal, or two-dimensional extensions, such as an area, surface, or region. The introduction of the concept of space-spatium referring to a geometrical region, raises the important question of ‘architectural space’ and, more broadly, space as a three-dimensional expanse — the immersive arena for objects and bodies. As I have often said, it is an obvious fact for both architects and ordinary people today that space can be understood as a three-dimensional expanse, whether physical or ideal. Initially, we rejected the idea of 3D space as an astronomical hypothesis due to the prevailing cosmological model popular during Vitruvius’ time. Additionally, it is essential to recall that prior to Descartes, Euclidean geometry, the basis of that cosmological model, was strictly a two-dimensional system comprising axioms and postulates that focused on the position of elements such as points, lines, angles, and shapes like triangles and circles. There was no idea of space as a containing entity within the domain of Euclidean geometry before Descartes. Then, the question we are now approaching is the following one: is it possible to attribute to Vitruvius some kind of three-dimensional understanding of spatium-space (as in the modern sense) in the remaining cases we need to analyze? Or is such an interpretation merely our own, and thus a kind of anachronism?

Before exploring this possibility, let’s revisit a passage in the text where Vitruvius discusses how establish proportions for a private house: ‘Igitur statuenda est primum ratio symmetriarum, [a qua sumatur sine dubitatione commutatio] deinde explicetur operis futuri locorum imum spatium longitudinis (et latitudinis)’, which translates to English as: ‘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). Undoubtedly, in this case, the ‘space’ of architecture is confined to a generic two-dimensional area on the ground, specifically ‘the ground lines of the length and breadth’, which is essentially a surface or area.

Image 6: drawing attributed to a member of the Sangallo family; in Vitruvius’s DeArchitectura Libri Decem, Book 3, Chapter 2 (date: 1530–45).

Another important passage to read in conjunction with the one we’ve just analyzed is the following one: ‘… uti nullum parietem tangant circaque habeant locum vacuum et ab summo capite spatium’, which translates to ‘… 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 the area around the bronze vessels on the floor as ‘locum vacuum’, that is, a place free from objects and obstacles; while he uses the term ‘spatium’ to refer to the vertical extent above those vessels — ‘ab summo capite spatium’. This distinction suggests that, for Vitruvius, the horizontal dimensions have a different character or connotation than the vertical dimension, which is why he uses two different words — ‘locum vacuum’ and ‘spatium’ — to describe what could have been described with just one word — spatium-as-space — had he understood space the same way we understand it now (indeed, 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 treats the three spatial dimensions as separate (two horizontal dimensions described as ‘locuum vacuum’ and one vertical dimension described as ‘spatium’) suggests that he may not have had a fully developed concept of space as a single, integrated entity comprising all three dimensions, as we do today. This interpretation is further supported by instances in the text where Vitruvius uses the term space-spatium to describe a horizontal region (as seen in the previous quotation 6.2.5). In this passage, since he is discussing all three dimensions at the same moment, instead of using the same term ‘spatium’, he uses the proposition ‘locuum vacuum’ to define the two horizontal dimensions and ‘spatium’ to define the vertical dimension (in this regard, it is evident the legacy of the ancient Greek ‘stadion’ — from which the Latin ‘spatium’ is derived — 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 — I redirect readers to the article Back to the Origins of Space and Place).

In the context of an architectural explanation, there is another passage where Vitruvius employs the term ‘spatium’ to draw a distinction between the horizontal plane, which defines a two-dimensional region — referred to as ‘locus’ — and the vertical dimension — referred to as ‘spatium’. The passage reads: ‘non est alienum in angustis locis et in concluso spatio’, which translates to, ‘it is not improper, in narrow quarters or where the space is enclosed…’ (4.4.3). Again, in my opinion, the English translation can be reinterpreted to better align with what I think is Vitruvius’s understanding of spatium-space in this context, as the translator overlooks that Vitruvius is describing the same spatial/placial (environing) situation which results from ‘angustis locis’, a limited horizontal plane or region (the ground-floor) and — note the original Latin conjunction ‘et’, which has a different sense from the English disjunctive ‘or’, used by Morgan — the vertical dimension/extension associated with that region referred to as ‘concluso spatio’ (this interpretation is similar to the one mentioned at 5.5.1, where the horizontal dimensions define an area and the vertical dimension defines the vertical closure above our heads, two distinct names).

Similar to the passage we have just analyzed, but even more ambiguous, another passage features the term ‘spatium’-space is in the middle ground between a region and a vertical dimension/extension (see excerpt 5.9.5, in the section below); it is precisely this ambiguity that could have inspired Vitruvius, with a leap of imagination, to envision space-spatium as a three-dimensional concept in a modern sense. This may seem like a suggestion influenced by a modern mind biased towards three-dimensional space, but to me, the situations Vitruvius describes using the term space have a distinct flavor, differing from the interpretations of space we’ve analyzed so far:

3) Space as an expanse, (also in architectural sense) in the following two passages: ‘Media vero spatia, quae erunt subdiu inter porticus, adornanda viridibus videntur’, which means, ‘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’, which means ‘… which will give the lever man a convenient amount of space’ (6.6.3). Passage 5.9.5 might suggest a close relationship between architecture, the concept of space, and the possibility of assigning space a three-dimensional sense (in addition to the cases already analysed suggesting one-dimensional and two-dimensional senses) by integrating the three dimensions described separately by Vitruvius in 5.5.1; this would represent a dimensional ‘upgrade’ in the conceptualization of space from a simple one- or two-dimensional understanding to a three-dimensional conception, where the three extensions (two horizontal, one vertical) are unified into a new entity.

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

In fact, aside from the specific interpretation of that single passage in Vitruvius’s text (5.9.5), this is a hypothetical possibility for architects of the Roman period and the subsequent epochs: they could have envisioned before others the deep connection between the dimensions of height, depth, and width, which, taken together, form a coherent system of dimensions that enable a three-dimensional understanding of the world. It is true that philosophers, physicists, and mathematicians/geometers have explored the fundamental spatial/placial nature of reality since the origins of Western Thought, but architects, with their daily involvement in geometrical drawings and actual constructions in between theory and practice, the ideal and the physical, more than others have had a unique opportunity to stay in close touch with the three extensions/dimensions, which they had in front of their eyes and nose every day in their working activities (as I mentioned in the Preliminary Notes, architects played a significant role in developing linear perspective, a three-dimensional representation of space). However, I’m also well aware that having something right in front of us is one thing, but attributing a certain meaning to it, or even an unforeseen or unexpected one, is quite another. I experienced this first-hand as an undergraduate student. I read several books on architecture and discovered it was a question of space, but understanding what that truly meant was a different story. I compare the moment I finally grasped the significance of space in architecture to Paul Klee’s epiphany about the role of color in painting:^[11] it was a revelatory experience, a kind of epiphany that had little to do with what we have in front of us; it is as if our perspective is turned upside down in the blink of an eye, and we begin to see what had been invisible until then. It’s not easy to ‘see’ space… Eureka!

In addition to the passages mentioned, there are other ambiguous passages in the text concerning the interpretation of the term space-spatium, but they do not alter the overall trend of interpreting it 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’, that is ‘let the intercolumniations… be pretty wide’ in 5.1.2₁; or ‘intinera faciunt latitudinibus non spatiosis’ that is ‘… 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’ that is ‘large rooms’ , in 6.3.2; or ‘oeci corinthii tetrastylique… spatiosores’ that is ‘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 a noun	114 times
As an adjective	10 times
As a denotative distance or extension	5 times
As a figurative distance or extension	29 times
As a geometrical distance or estension	4 times
As an astronomical distance or extension	7 times
As a simple interval	3 times
As a temporal interval or extension	14 times
As an area, surface or region (of objects, things, bodies, etc.)	15 times
As a geometrical area, surface, region	11 times
As an astronomical region	11 times
As a geographical region	4 times
As an expanse	2 times
As a figurative gap or cavity	9 times

Table 1: Summary table concerning the use of the term space-spatium in Vitruvius’s De Architectura.

The text contains several passages where the term can be interpreted in different ways, and what is particularly relevant is the distinct sense of dimensionality that ‘spatium’-as-space takes on each time, depending on the context in which it is used. In particular, when explaining architectural concepts related to buildings or their parts, the interpretation of space (a linear distance between parts? A region or an area on the ground or floor? A three-dimensional expanse?) needs a careful inspection. Similarly, when interpreting ‘spatium’-space in an astronomical context caution is necessary, as ‘space’ must be understood in light of the prevailing cosmological and geometrical models of Vitruvius’ time. Overall, apart from the reasons I mentioned regarding to the interpretation of some important passages such as 6.2.5, 5.5.1 and 4.4.3 — which suggested a bias towards a two-dimensional understanding of ‘spatium’-as-space in architectural contexts — it is undeniable that Vitruvius’ concept of space differs significantly from the modern concept of space as a three-dimensional (or tetra-dimensional) arena where objects and bodies are situated. During Vitruvius’ time, the term ‘spatium’-space primarily referred to a simple (linear) extension, a temporal extension, and a two-dimensional concept used to define regions, surfaces, areas or territories in various contexts (geometric, architectural, geographical, astronomical, etc.). However, it’s essential to note that this doesn’t mean people in the pre-scientific era lacked an understanding of reality as a three-dimensional fact (a continuum); rather, they didn’t have the cultural and social conditions to express or communicate that idea through a fully developed concept of space like the one we modern people are familiar with. That immersive and neutral conceptualization of reality as a three-dimensional space became clear only after space-as ‘spatium’ (or ‘spacium’) acquired a stratification of meanings in the course of history, and especially in the last four hundred years with the important contributions of Descartes and Newton, even if one of the first explicit pronouncements on the three-dimensional nature of space, in the modern sense (space explicitly understood as a neutral, integrated system of three dimensions containing bodies), can be probably traced back to Giordano Bruno, at the end of the XVI century (some also attribute that primacy to the ‘intangible substance’ of Epicurus).^[12] I believe that architecture, as a social and cultural endeavour that accompanies people’s daily lives, might have played an important role in transforming and/or diffusing the concept of space from a simple (one-) dimensional fact to a more complex dimensional concept. The fact that Roman architecture is often recognized as an ‘architecture of (interior) space’, whereas Egyptian and Greek Architectures are often recognized as ‘architectures of place’, may suggest this possible leap of imagination that could have led 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, EG.

Image 9: The Acropolis of Athens, GR.

Image 10: The Pantheon in Rome, IT.

From a semantic perspective, the Latin term spatium likely had a broader range of meanings and connotations than classical Greek concepts like ‘topos’ and ‘chōra’, which, by the start of the Christian era, were part of a declining civilization, whereas the Roman world was on the rise. In our analysis of the Latin text De Architectura, we have encountered a few ambiguous passages where the term spatium-space might suggest a three-dimensional interpretation to us; this ambiguity demonstrates the versatility of the term, as it could transcend its original one-dimensional nature and take on more complex meanings. The term spatium-as-space (rather than the Greek terms topos or chōra) was likely adopted by scholastic philosophers, from early and late Renaissance Italian naturalists to Descartes, and Newton (Einstein ‘received’ the concept elaborated by Newton), precisely because of its semantic openness, which enabled them to describe reality as a dimensional fact in spatial or spatiotemporal terms. Will the concept of space adapt to the impact of time over millennia, potentially changing its nature again in the future? As we enter a new millennium, we await fresh, innovative spatial interpretations of reality, and, consequently, new meanings for spatial concepts.

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: Archive.org and Wikisource.org

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, Perseus.tufts.edu

[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). This is the extended English translation, by Morris Hicky Morgan, of the original Latin phrase opening this section: “The architect should be equipped with knowledge of many branches of study and varied kinds of learning, for it is by his judgement that all work done by other arts is put to test. This knowledge is child of practice and theory”. The interpretation of architecture as a ‘Science’ stems from that original statement by Vitruvius (the Latin word ‘scientia‘ is translated as ‘knowledge‘).

[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’s 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: ‘Colour 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: Colour and I are one. I am a painter’. I like to think that I became an architect when I really understood what space meant for architecture, and not when I got my degree or license (which happened a few years later my epiphany with space). ‘Space and I are one. I am an architect’, I immediately thought when I became acquainted with Klee’s episode.

[12] ‘ Est ergo spacium, quantitas quaedam continua physica triplici dimensione constans, in qua corporum magnitudo capiatur, natura ante omnia corpora, citra omnia corpora consistens, indifferenter omnia recipiens, citra actionis passionisque conditiones, immiscibile, impenetrabile, non formabile, illocabile, extra et omnia corpora comprehendens, et incomprehensibiliter intus omnia continens’, that is: ‘Space therefore is a certain continuous physical quantity consisting of a triple dimension, in which the magnitude of bodies is captured, by nature before bodies, and subsisting without all bodies, indifferently receiving all things, without conditions of action and passion, intermixed, impenetrable, not formable, not locatable, exteriorly embracing all bodies, and incomprehensibly within, containing all bodies.’ The original Latin statement is included in Giordano Bruno’s De Immenso (I, 8). This statement and its English translation are reported in Ivor Leclerc, The Nature of Physical Existence (London: George Allen & Unwin Ltd, 1972), 162.

Concerning the primacy attributed to Epicurus, in Casey’s book The Fate of Place (page 83), we find a quote, elaborated on a statement from Long and Sedley, according to whom Epicurus was ‘the first ancient thinker to isolate space in the broadest sense’. Yet, here the question requires some elucidation because ‘space’ was neither a term nor a concept available to the ancient Greeks: in a passage from Sextus Empiricus and reported in Casey’s The Fate of Place, Epicurus refers to an ‘intangible substance’ (anaphes phusis), as he calls it, which is named ‘void’ (kenon), ‘place’ (topos), or ‘room’ (chōra) according to whether that substance is empty of all body, is occupied by a body, or bodies roam through it. There are not irrelevant metaphysical, physical, epistemological and historical questions to disentangle before we can attribute that ‘intangible substance’ the same conceptualization behind the term ‘space’.