What Did They Know and When did They Know It?

Scholastic Interpretations of Architectural Dynamics.

by Thomas Boothby and Steven Walton

Presented at the AVISTA session at Kalamazoo, May 2006.

Intro

Powerpoint Slides (as a PDF)

[slide[1]]  Exploring medieval architecture is largely the domain of art and architectural historians, and historians of science have rarely looked into the field.  If, it is assumed, the medieval architects were laboring under the manifestly absurd precepts of Aristotelian physics, then any rational understanding of building design from a structural point of view seems a inherent contradiction.  Of course in terms of the geometrical design, we know a great deal, and it is clear that the medieval architects were above all else certainly master masons.  But is that sufficient?  Can we say that their complex quadratures were so deftly made into three dimensional edifices in stone and that was that?  Did they have no further concept of solidity, or stability?  Did they look at the rubble of a collapsed vault or entire church and not ask ‘Hmm… I wonder why that happened?’

Of course, we think they did and it is our intention here to use 14^th-century “expertises”– the meetings of experts brought in to discuss structural problems in cathedrals – to question how medieval architects understood their structures “scientifically”.

To speak of “science” in the modern sense in the Middle Ages, is, of course, an anachronism.  More properly, we should speak of “natural philosophy” and as soon as that phrase is uttered, [slide[2]] we know that it will be in the framework of Aristotelian natural philosophy that these questions must be answered.  Further, let us be clear that we are not claiming to have divined a medieval science of architecture or in any way to put the medieval master masons in the same category as a modern practicing engineer with calculus, finite element models, or materials science.  Rather we are arguing that we do not believe that there was no intellectual framework in play when they conceived of how or why buildings stood, and stood soundly.

[slide[3]] The 14^th-century “expertises” that we have examined – from Charters, Florence, and Milan – do not contain any “smoking guns” of these architects working “scientifically”, but they do contain numerous allusions to their “scientific” framework or reasoning.  Before proceeding to the analysis of the expertises, it is my task to provide a framework of how the Scholastics spoke about nature and in particular about falling bodies and bodies in equilibrium before Tom will look at specific cathedrals and specific design criteria and evaluations.  Ultimately, we argue for three points:

1. the architects and experts were in fact peripatetic to the core as that was the de facto philosophical understanding of the world at the time.
2. Although we do not claim to find a science of architecture, or really even a physics of architecture in the modern, predictive, sense, we will argue that architectural technology was understood within the Aristotelian set of concepts.
3. Medieval architecture in their terms must be understood dynamically.

Scholastic Building Sites

So, to conclude my portion of this talk.  One other consideration is often forgotten by architectural historians we think: the intimacy that scholastic masters would have had with building construction. It was they who requisitioned the churches, it was they who paid for them, it was they who lived among them as they rose, and in some sense at least, it was they who had to agree on how they were built.  Take for example, the rebuilding of Canterbury in 1174.  Although William of Sens, the master mason in charge of rebuilding, was not a monk himself and we have no indication whether or not he had been Scholastically educated (we assume little if at all), when he had to break the news to the monks that the Cathedral had to be rebuilt from the ground up,

he ventured to confess that the pillars rent with the fire and all that they supported must be destroyed if the monks wished to have a safe and excellent building.  At length they agreed, being convinced by reason and wishing to have the work as good as he promised.[i]

The use of the term “convinced by reason” (ratione convicti) should not be taken lightly.  To convince a group of monks by reason suggests that William of Sens was not arguing by model or by simple demonstration.  Rather, it implies that he had some cogent, logical plan of reasoning that would convince a set of Scholastically-trained churchmen.

Scholastic Architecture

[slide[4]] First, a basic review of Aristotelian physis,  or as it means literally in the Greek, “nature”.  Their understanding of motion—or as they would say, ‘local motion’ or change (motus) in place (locus)—: [slide[5]] for ‘earthy’ matter, natural motion was necessarily in a straight line downwards and ‘violent’ motion was in any other direction: up or laterally or curved.  For The Philosopher, the concept of falling bodies as Galileo (and we) conceive of it did not exist. Instead he spoke of motion towards or away from the center.[ii] Strictly speaking, Aristotle did think about the relative motions of bodies near the earth—suggesting, for example, that bodies (‘earth’, as he put it) move more quickly the nearer they are to the center, an idea later overturned by the medieval thinkers on motion (of which more shortly)[iii]—but nowhere do we find a clear modern physical understanding of falling bodies.  What we do find, however, in Aristotle is an enunciation of a equilibrium relationship of objects in balance:

The agent itself is acted up on by that which acts; thus that which cuts is blunted by that which is cut by it, that which heats is cooled by that which is heated by it, and in general the moving or efficient cause… does itself receive some motion in return; e.g., what pushes is itself in a way pushed again…[iv]

Although not action-reaction in the Newtonian sense, the core of the idea is there and it will be this relatively simple understanding that will drive much of later commentators’ interpretations, particularly in the ‘science of weights’, or, the scientia de ponderibus.

[slide[6]] The second element of review is that of causes: material (that from which it is made), formal (that shape in which it is made), efficient or accidental (that which made it), and final (the reason for which it was made).  To the Aristotelian, these more philosophical questions concerning why (final and accidental) are much more interesting than the more mundane what or how (formal or material) that an architect or mason might be concerned with.  But as we shall see, it is in this realm of causes that some of the peril to cathedrals was understood.

In terms of architecture itself, Aristotle offers nothing explicit.  Despite his remarkable attention to sense experience and the natural world, and his semi-rejection of Platonic ideal forms, Aristotle was remarkably poor on dealing with artificalia, that which included technology such as architecture.  Although no architect or engineer himself, Aristotle was not hostile to analyzing their products.  In the Physics he offers a clear distinction between mathematicians and physicists:

The mathematician, though he too treats [surfaces and volumes, lines and points], nevertheless does not treat of them as the limits of a physical body; nor does he consider the attributes indicated as the attributes of such bodies.  That is why he separates them; for in thought they are separable from motion, and it makes no difference [to the mathematician], nor does any falsity result, if they are separated. …

Physicists, however, one of whom Aristotle would claim to be, do consider the real physical bodies, and he uses the analogy of branches of physics to prove his point:

While geometry investigates physical lines but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical.^[v]

More importantly, when he comes to offer an example? “If… art imitates nature,” he says, then it would be the job of physics to know “nature in both its senses,” just as “the builder [knows] both of the form of the house and of the matter, namely that it is bricks and beams”.

[slide[7]] And if this distinction is true in Aristotle, even if he then does not go much father in the physical mathematical sciences, it is even more true in his medieval commentators, who had fully absorbed the Greek tradition of the Physics (and its Arabic commentators) by the mid 13^th century.[vi]  Virtually all Scholastics who comment on the Physics take up this passage.  Grosseteste, for example, in a discussion of “whether nature is determined by of [our] manner of talking about it,” argues that (paraphrasing), mathematicians and physicists look at the world differently, and although each can be the other (i.e., work as the other does), “physicists truly do not demonstrate the magnitudes of accidentals as magnitudes of how great simple magnitudes happen to be, but show of physical bodies the magnitude according to their shape because how great the physical body is a part of them qua physical” – that is, they deal with the real world.[vii]  Similarly, Aquinas, Duns Scotus, William of Ockham, Albertus Magnus and the rest of the who’s who of Scholastic physics treat this passage, arguing that we must understand the world as matter, and matter as it behaves in the real world, not as merely mathematics in the ideal world. Aquinas is explicit: “Knowledge is the principle of operation in art [and] in artificial things we work to a likeness of natural things.”[viii]  Architecture, then, while not a fully mathematical art, was part of physis rather than mathesis.

Boethius warned that proper philosophy proceeded from the practical to the speculative, not he other way around.[ix] [slide[8]] In addition, it is worth remembering that Vitruvius exerted a considerable influence on the Middle Ages, not often as a practical building manual, but usually as a framework for understanding building.[x]  Historians of science have noted that, for all their Aristotelian posturing, the medieval philosophers when working on the ‘science of weights’—which seem to have been primarily developed for practical, not speculative, reasons[xi]—show a distinct tradition within the genre focusing on the Vitruvian massa (‘lump or mass’) rather than the Aristotelian ponus or gravitas (‘weight’).[xii]  And when we read from the Florentine experts that “the design of the masters and painters is il piu bello e piu utile e honorevole e forte”—the most beautiful and useful and praiseworthy and strong—“than any other design they’ve seen”, [xiii] can we not be reminded of Vitruvius’ follwing clear dictum?: buildings “must be made such that they have a plan/nature [ratio] that is firmitatis, utilitatis, and venustatis,” — “solid, and useful, and beautiful”?[xiv]

Finally, here I can do no more than mention in passing the occasional awareness of the Scholastic authors to architecture:

• Hugh of St. Victor in his Didascalicon compares Divine Scripture to a building, noting that both must have “a smoothly proportioned construction”– in effect, he uses these ideas of opposition of stones and bearing weights and what a modern engineer would term a “load path”, as a model for Scriptural understanding.[xv]
• From the 12^th century on, the classification of the sciences blossomed and the categories of the seven liberal arts and their seven sister mechanical arts were extended, elaborated, and discussed, including architecture as a subspecies of mechanics, or of geometry.[xvi]
• Alexander Neckam, in his De rerum natura of c.1200 made a brief digression into the physics of buildings, arguing, for example, that the walls of a building are never parallel in that they must necessarily diverge slightly if both walls are ”natural” rays pointing to the center of the earth. From a strictly geometrical point of view, Neckam is correct; from a structural point of view, the divergence is on the order of micrometers; from our point of view, Neckam was attempting to understand the architecture within the intellectual framework of Aristotelian natural philosophy.[xvii]
• Although St. Augustine had classified architecture as craft, and warned that knowledge of it was only “to be acquired casually and superficially in the ordinary course of life unless a particular office demands a more profound knowledge,” or so that a Churchman could use them to judge Scriptural metaphor based upon them,[xviii] by the late 13^th century, the Archbishop of Canterbury, Robert Kilwardby, legitimated architecture and the mechanical arts by noting that “the making of… architecture… [is] much supported by physics, and physics makes known the propter quid of many things about which [architecture] only provides the quia sunt.”  That is, architecture makes known “that which is” while the physics behind it shows us “that by which” those things exist; architecture does, physics tells us why.[xix]

It would appear, then, that there is reason to believe that architecture appeared on the radar of Scholastics, and as we shall suggest below, Scholasticism similarly appeared on the radar of architects (or at least Scholastically-trained architectural experts).

On “Power and Place” in architecture

Finally, before Tom takes over with particulars, there are two of concepts in Scholastic physics that became (ahem!) the cornerstone for architectural physics in the high Middle Ages. In the Euclidean concept of weights and of their equilibrium, it is interesting to note that the medieval commentators almost exclusively speak in terms of two concepts: the virtus of weights and their gravitas secundum situm.

Virtus is most ably translated as “power”, which should remind us that in the Middle Ages, it was not forces that mattered–as would become the case when accelerations and mass became paramount in Cartesian and Newtonian physics – but rather work , or in this case the potential or potency to do work, which was fundamental.[xx]  Thus we find postulates such as: “the proportion of one space to the other is as the proportion of the power of the motion (virtuts motus) of [one] to the power of the motion of… [the] other.”[xxi]  We should be also careful of understanding the use of ‘power’ here as roughly synonymous with a physical “motive force”, however.  For Aristotle, virtus cannot be a cause; in Physics IV.1, Aristotle explicitly says that “None of the four modes of causation can be ascribed to [place]” and effectively says that the power of place cannot be thought of in the sense of our modern “attractive power.”[xxii]  Although I don’t have time to derive the full set of connections here, Claggett and Moody summarize nicely: in this tradition, “the statical assumptions used in the theorems on the Roman Balance are given a foundation of generalized nature, resting on postulates of a dynamical character.”[xxiii] The “virtue” theory as Clagett refers to had a brief vogue in explaining Aristotelian projectile motion under people like Roger Bacon and Aquinas, but as they discarded this ‘none is moved except by the virtus of the mover’ idea in favor of the impetus theory of motion by the early 14^th century, the concept of virtus remained useful only for those bodies which remained in contact with each other (my emphasis).[xxiv]

Second, gravitas secundum situm, literally the “weight according to position/place”, or as we should say, “positional gravity”, is an idea that predates the 13^th century and figures prominently in the work of Jordanus de Nemour.[xxv] [slide[9]] It is defined as “the component of the force of a body’s natural gravity directed along whatever path of movement the body can take as constrained by its connections with other bodies in a single system.”[xxvi]  Thus, when the medieval commentators on statics speak of bodies in those constrained systems, they speak of a body being “heavier positionally” when their path of descent is less oblique – that is, the gravity of an object moving laterally is less gravitas than that one falling vertically.[xxvii]  Or, to invert the idea, when a body is constrained that it can only move vertically, it is considered the heaviest, and by extension, the most stable. This, combined with the concept of “power” may be interpreted in an Aristotelian state by saying that the “power of a place” is also “the power to confer rest” to the stones in question.[xxviii]  And rest for the stones in a cathedral, of course, is stability.

It is in this context, of constrained bodies, that the understanding of the ‘ruin, harm, and peril’ of the cathedrals must be understood.  For as Jordanus said, “Since the science of weights is subalternate both to geometry and to natural philosophy, certain things in this science need to be proved in a philosophical manner, and certain things in a geometrical manner.”[xxix]

Powerpoint Slides (as a PDF)

Slides: