I. Accuracy, precision, and building methods.
While modern contractors measure precisely and accurately, we have no reason to assume that the ancients either did or could measure so precisely. See these sources for further discussion of the precision/accuracy issue: Harrison Eiteljorg, II, "Measuring with Precision and Accuracy," CSA Newsletter, XV, 1; Spring, 2002; http://csanet.org/newsletter/spring02/nls0206.html; Harrison Eiteljorg, II, "How Should We Measure an Ancient Structure?," Nexus Network Journal, , vol. 4, no. 4 (Autumn 2002), http://www.nexusjournal.com/Eiteljorg.html; and Harrison Eiteljorg, II, The CSA CAD Guide for Archaeologists and Architectural Historians, II, "Data Gathering," http://csanet.org/inftech/cadgd/cadgdtwo.html. That is not to say that the ancients were or intended to be inaccurate, but their ability to measure, so far as we know, was limited. It is far more likely that one stone could be and was matched to another with the aid of calipers, for instance, than that two stones could be and were cut to the same size through the use of careful measurement of distances longer than an ancient foot or so.
This means that, when examining an ancient structure, one should worry less about abstract measurements and more about matching things that must, in the end, be properly related to one another. For instance, a temple's columns must be the same height as its walls so that the beams passing over the open space between will be horizontal. It is far less important that they be a particular height than that they be the same height. Thus, a minor discrepancy between the elevation of the top of a column and the elevation of the nearby wall top is far more significant that a larger discrepancy between the lengths of blocks in the same course of a wall.
This is an important distinction because ignoring it can cloud the judgment of those of us who must examine buildings after they have been completed. If we look for dimensional regularity rather than something somewhat less tangible, we may find that we have carefully attended to matters of lesser importance. For example, is it possible that ancient temples were occasionally built colonnade first, as suggested by the temple at Segesta, because the builders thought that adjusting the columns to be of equal height first and matching the walls to that height was a better way of making walls and columns come out correctly at the same height?
We cannot know the answers to question such as the last about Segesta, but we are more likely to find answers if we put aside our expectations for dimensioned parts designed to be put together like so many cinder blocks. As the ancients did not use mortar, so they did not construct large buildings as we do. Nor, one suspects, did they fret about blocks of standard size as much as we might expect, knowing that, in the end, most would be cut to match other stones rather than to match abstract dimensions or that an overlong block could always be accounted for by inserting a slightly short one in the same course. It is important to keep that in mind.
II. Contracts and other inscriptions provide information of note concerning the design and building processes.
A. Contracts (which are later in date than the Propylaea) indicate a four-stage process to shape building stones.
1. The blocks are quarried at the architect's specified size PLUS something called an apergon (ἀπεργον), an unspecified extra amount that would apparently permit some minor damage during transit without yielding a block too small for the final specified size. It is generally assumed that the apergon was defined by custom since it is not defined by specific measurements in surviving inscriptions.
2. The blocks are then cut, on site (and therefore after transit), to the specified sizes. That is, the apergon is removed and all edges and corners are made properly right-angled. At this point the anathyrosis band/bands is/are also carved as required. However, so-called lifting bosses are included at this point. (Lifting boss is an unfortunate term that has been widely-used. Deemed a questionable notion by many scholars, the idea that the protrusions on ancient blocks were used to permit ropes to hold and lift blocks has now been thoroughly discredited by A. Trevor Hodge in "Bosses Reappraised," in Stephan T.A.M. Mols and Eric M. Moorman, eds., Omni pede stare. Saggi architettonici e circumvesuviani in memoriam Jos de Waele. Studi della Soprintendenza archeologica di Pompei 9, Electa Napoli and Ministero per i Beni e le Attività Culturali, 2005, 45-52.)
3. The blocks are put on the wall, one course at a time; when a course has been completed, the tops of all blocks of that course are smoothed before the next course is erected. This provides a finished horizontal bed for each new course. This process reduces the height of the course by some amount, perhaps as much as a centimeter, depending on the circumstances.
4. The sides of the blocks are trimmed (apparently about one cm. on each side, judging by the Propylaea) so that both interior and exterior wall surfaces are absolutely smooth and uniform. This is one of the very last things done to a building. The walls are trimmed to the surface level of the peritenia band (see #1 above).
Note that the result of this process is that the only block dimension supplied by the architect that survives the construction process is the length of a given block. The height is changed when the top of the block is trimmed prior to erecting the next course. The thickness is changed when the wall surfaces are trimmed at the conclusion of the construction process.
B. The Arsenal of Philon inscription shows that the architect understood implicit mathematical relationships among the parts (The inscription is considerably later than the Propylaea.)
The Arsenal of Philon inscription includes an interesting but not obvious mathematical relationship that relates to planning. For many years after the discovery of the inscription scholars debated the width of the triglyph in the frieze, and those who assumed the height of the frieze was to be three Greek feet eventually settled, more or less, on a width of the triglyph of two and one-quarter feet. That dimension descended from arguments based upon the standard proportions to be found in contemporary structures. As I demonstrated in my dissertation nearly thirty years ago, however, the width of the triglyph, assuming the same relationship between interior colonnade and exterior frieze used for the standard calculations, depended entirely on two dimensions, the diameter of the columns in the colonnade and the thickness of the exterior wall. The width of the triglyph must be twice the difference between the radius of a column and the thickness of the wall. (This is true because the difference between a standard interaxial and the space from the center of the last column to the exterior surface of the wall must be half the width of a triglyph. Further, that difference is the difference between a column radius and the wall thickness.) That number is two and one-quarter feet, the same width arrived at by arguments based on proportions.
To me, this indicates that the architect understood exactly how the parts of the structure interacted, what the mathematical cause-and-effect relationships were between and among the parts, and how to design the whole and the individual parts together so that there were no conflicts.
III. The Arsenal of Philon inscription shows that the architect understood implicit mathematical relationships of the parts to the whole
In the Arsenal inscription the way the architect laid out the plan in terms of block lengths is very telling. While he indicated that there should be openings in the walls for ventilation, he specified the sizes of the blocks of the euthynteria and the length and width of the course (by implication, based on the building dimensions, block thickness for the courses, and standard practice of centering each course on the one below when the thickness of the blocks changed).
The building was to be, at the euthynteria level, 405 1/2 feet long and 55 1/2 feet wide - 405 x 55 at the wall-block level plus the additions because the euthynteria blocks were to be 1/2 foot thicker than the wall blocks. He also specified standard block lengths of 4 feet and non-standard block lengths for the corners of 4 1/2 feet, without saying precisely how the corner blocks should be arrayed. That is, he did not indicate whether the longer corner blocks should be used on both the long and short walls or on only the long or short walls. These dimensions for the total length of the euthynteria and the individual blocks had to be sensible together; it must be possible to build a wall of the right total length with the blocks of the specified individual lengths. As it turns out, there is one and only one way to arrange the blocks so that
1. the ordinary blocks are all the specified size
2. all corner blocks are longer
3. the total length and width work out correctly.
If and only if there are extra-long blocks on both the long and short walls and the long walls pass beyond the short ones, the block lengths and course size work out correctly. The length of 405 1/2 feet consist of 99 blocks 4 feet long and two blocks 4 3/4 feet long. The short walls consist of 10 blocks 4 feet long plus two blocks 4 3/4 feet long plus the widths of the blocks from the long wall, two of them, each 3 feet thick.
This seems to indicate, to me at least, that the architect had not only thought about the rather general aspects of the building but had carefully worked out the subsidiary parts as well. I see this as an indication of a level of careful planning that is too easily missed. There is no complex math here, nothing more complex than multiplication, but the result of one and only one layout is precisely as it ought to be according to the architect’s various specifications.
IV. Intersecting Walls
The ways that walls intersect (not abut, intersect) has a bearing on planning in my view. I am putting this discussion on its own separate page because the drawings require so much space. Please look at this page about Intersecting Walls to see what I am thinking about in this area. (My apologies in advance. You will need to open up your browser page so that this over-wide presentation works, but I thought it important to put the drawings up in a way that lets them be seen side-by-side.)
The original text about intersecting walls strikes me now, after some intervening time, as impenetrable. Let me try again to approach this issue. If you would like to see the original text, please follow the old link above. For the new discusion, however, please see http://propylaea.org/architect/intwalls2.html.
To the Propylaea Matters page.
To the Discussion page.