[buh-rohk; French ba-rawk]
The proposition is that Hersey’s work on Baroque geometry is, ironically, baroque itself in the sense of the dictionary listings numbers 3 and 6. They are ‘ornate, florid, and convoluted’ inventions, ‘extravagantly ornamented’ so as to prove the point being assumed. Hersey seems to be forcing fabrications, faking proofs with naive manipulations that appear structured to purposefully confuse and convince at the same time. Why is Hersey unable to say that, e.g., Borromini’s dome (Fig. 5.32) is similar to the Columbine flower, (Fig. 5.33), rather than asserting that, as on p.129-130: It seems to me that the thought behind Borromini’s design is botanical. The two juxtaposed rotations seem to mimic the alternating petals and sepals you find in certain flowers – for example, the columbine pictured in figure 5.33.
Is it merely that Hersey would like it to have been this way? Why try to pompously guess at Borromini’s thought processes when the origin of the dome forms could easily have been otherwise, perhaps generated by some straightforward, or alternatively, some more complex planning decisions and/or a simple decorative desire. The similarity in the forms might merely be chance, serendipitous, like a lot in this world. But no; Hersey has to ‘prove’ his reading is so, citing some abstract geometrical rotation, perhaps to make things appear somewhat ‘scientific.’ Is it a matter of prestige; a yearning for academic stature? The outcome reduces any academic standing by its excess of hopeful manipulation and the lack of review and testing. It is mere conjecture without any clarifying refutation. Does Hersey fear that such an off-handed observation about this work might change perceptions of his heroically original book on things Baroque? Hersey notes that he is unaware of anyone who has explored such geometry in art history. Is there a reason for this? Is he claiming originality? Does he have to prove his unique approach has substance to confirm his brilliance?
p. 125 I will here mention Descartes’s theories about vortices, namely that they filled the heavens and were everywhere on Earth – in the air, invisibly, as well as visibly in water and other fluids. Such thoughts expanded the importance of vortices and spirals in Baroque thought. Yet I’ve never seen any art-historical comment on these aspects of Solomonic columns. (But then I’ve never seen any art-historical comment on most of the subjects raised in this book.)
So let’s push onwards.
The piece, APPROXIMATE ARCHITECTURAL THEORIES – GEHRY GUESSING, used the example of the proportions of St. Peter’s to show how precise theories were based on broad generalities: see - http://voussoirs.blogspot.com.au/2015/03/approximate-architectural-theories.html
George L. Hersey, in his book Architecture and Geometry in the Age of the Baroque, The University of Chicago Press, Chicago, 2000 has published many diagrams to prove his thesis suggested in the title: that geometry lies at the root of Baroque architectural design. One does not have to delve too deeply into this book to find the first worrying illustration. On page 14 there are two identical main elevations of St. Peters in Rome. A small photograph that has been reproduced twice has been used to illustrate how the proportions of this building, well this portion of it, involve two systems: a double golden section rectangle and a double sesquiquartoquintal rectangle. It becomes obvious that Hersey loves obscure Latin and Greek labels.
These somewhat blurred, faded grey photographs are identical, about 85mm long and 30mm high. The coloured lines, blue and red, that have been drawn over this image to illustrate the idea being discussed have a width that is about one quarter of the width of one of the main doorways. At a quick guess, the line might be, if scaled, about 600mm wide. Now this in itself is not really a problem, as we are dealing with proportions. The rectangle formed by the outer edge of this frame, however thick it might be, has the same proportion as that defined by the inner edge. It is what the line is trying to relate to on the photograph that is the critical issue, either inside or out, because this is the significant point being highlighted by Hersey: that the accumulated parts of this building have been planned using specific, related dimensions, in this case, a clever twin set of proportions. The concern is that a 600mm pointer is being used to identify the precise locations of the dimensions to confirm the claim. It is like waving one’s hand at a group of cups to indicate which particular one has the pebble under it, to prove that one knows exactly where the elusive stone might be. The detail is all very rubbery.
The loose use of preferred ideas continues throughout the Hersey book, Architecture and Geometry in the Age of the Baroque, leaves one a little bewildered: why was it published by such a prestigious university press? It is not as though Hersey is trying to keep his guessing game concealed. Theoretical studies like these do nothing to generate any respect for rigour in the architectural profession. They allow others to mock matters architectural that merely support the romance of imagery with some flippant flare of flimsy ‘maybes’ and ‘perhaps’ that drive today’s efforts in the shaping of fanciful form. We need to do better than this. Hersey writes:
Let us look at the work of a late Baroque architect who did this - ‘make use if the faces of Archimedean and rhombic solids . . . in the plans of buildings’ - (though he dressed his Baroque bodies in neoclassic trimmings): William Halfpenny. Halfpenny was the author of numerous villa books, including A New and Complete System of Architecture (1794). In that book, the plan of house no. 31 (fig. 4.26) consists of a central equilateral triangle with, on each side, a 4:3 rectangle (the latter are not all exactly the same size, but never mind). For simplicity’s sake I will ignore the three circular rooms at each corner of the triangle.
. . . I will also note, if Halfpenny’s “faces” were to be extended – that is, if other clusters of the same shapes were added – it would then fold into a hexakaiicosohedron, a 20-sided Archimedean solid with 8 equilateral triangles and 18 squares.
It seems that for the sake of confirming his idea that Archimedean patterns have been used, Hersey is prepared to ‘simplify’ and ‘ignore.’ As for the unequal 4:3 rectangles that appear to become ‘squares’ to make the solid if ‘extended’ appropriately, perhaps approximately, to make an Archimedean form with such an obscure Greek name, (as I said, Hersey likes these complicated names: more ‘academic’?), Hersey seems to be as liberal here with his hopeful interpretations and disregard as he has been with the reading of the plans – ‘never mind’? It is all, apparently, for simplicity!
Hersey does make an interesting point: that these plans have a set of cumulative geometrical relationships similar to those displayed in the Kepler solids if ‘developed’ - flattened out into one plane; but this is all. To continue what he likes to present as his detailed analysis of this observation, his proof, Hersey, (unfortunately close to ‘heresy’ and ‘hearsay’), has to manipulate, ignore and simplify matters in the very worst example of scientific rationalism that struggles to prove a point by creating the proof rooted in a set of ‘appropriate’ dismissive assumptions and ad hoc conjectures. Hersey is forcing the outcome he has chosen to be the case, rather than exposing his ideas to the testing questioning of scientific method as identified by Karl Popper in his Conjectures and Refutations.
Rhombic and Archimedean patterns of just these types, and variant forms of them, frequently appear in the coffers and ribs of Baroque domes. Guarini’s dome at San Lorenzo, Turin (1668-80; fig. 4.24), while it is not one of the 13 classic Archimedean solids, is a set of repeated tiled geometric faces formed into a sphere segment. . . . A dome like this could only be the work of someone, like Guarini, who had studied rhombic solids.
One has to ask: why might this be so? The photographic image (fig. 4.24) shows a dome lined with four sets of twin arches rotated 45 degrees to each other, making this display of what Hersey reads as ‘tiles’ within their intersections, the spaces between the arches. It is as though Hersey is ignoring the obvious - the arches. His diagram of the pattern to ‘prove’ his point, fig. 4.25, shows a set of triangles arrayed around an octagon inside a circle. It is a pattern that appears to ignore the clear relationship between the intersecting arches and the shaping, the integral making of the octagon: four pairs of lines rotated at 45 degrees make an octagon. In the Hersey diagram, the octagon stands alone as an isolated, complete form like the outer circle, without any precise relationship with the geometry of the surrounding triangles that are arrayed independently as a zigzag between these two shapes with no necessary alignments - but ‘never mind’? Hersey appears intent on reading the spaces between the lines rather than the lines themselves, the bold arched forms that generate the octagon and all of the other spaces between. These semi-circular arches are similar to the ‘Islamic’ style of decoration where complexity is generated by a strict and rigorous simplicity. Is Hersey completely unaware of the dome of the Mezquita in Cordoba, Spain? It looks as though Hersey had to yet again manipulate matters, his interpretations, his explanations, to make a fit with ‘his’ story, and read the image only as a tiling pattern. It is not this.
p.83 – 84
But how does architecture come into it? - ‘Tilings that use more than one shape are known as Archimedean tilings’ – My answer is that Kepler’s patterns (fig. 4.4) show that the Liber architectonicus was well named. Many of the diagrams look like Baroque and Rococo church plans, or like the polygonal palace plans one sees in the mathematically architectural treatises such as Juan Caramuel Lobkowitz’s Arquitectura civil, tecta y obliqua and Guarini’s book.
To illustrate: In figures 4.5 amd 4.6, first, is another of Kepler’s tilings, a set of five stellated decagons arranged in a pentagonal footprint, with a central smaller pentagon serving as the centrepiece. The little spaces between the rays of the decagonal stars are also pentagons. Already this could almost be a church plan, with five chapels and a central pentagonal nave. Specifically, it could be compared with Johann Santin-Archel’s plan of St. John Nepomuk, near Saar in Slovakia, dating from 1719-21 (figs. 4.7 and 4.8). That too has a pentagonal footprint with a central nave – though in this case the chapels are ellipses rather than stellate decagons, and the central nave is circular instead of pentagonal. But these differences are trivial. The chief point remains that the tiling and the plan are instances of Kepler’s “congruent” conjunctions of polygons – his tilings.
‘. . . as if this might be necessarily so?’ (Wittgenstein, Philosophical Investigations). Does Hersey decide what is important and what is ‘trivial’ on the basis of his theories and readings, to create the best ‘fit’ through specific exclusions? The mathematics of tiling patterns is precise and certain. There is no sloppiness or any random choice of forms or fits here. Hersey seems to want to prove his concepts just too much. Maybe he should be content with the simple, loose analogy that says that Kepler tiling patterns might have stimulated an interest in cluttering various geometrical shapes into the one plan pattern? Hersey seems happy to leave the Wren steeple and bell tower of St. Bride’s, Fleet Street in London, p.93, as being . . . thus like that other Baroque artefact, the telescope, which also opens up into a set of contiguous cylinders, without pressing the point further or extending the analogy in any other manner. It is an interesting observation that might have no real sense of beginning or origin in the manner suggested. It might be just that this similarity has happened: ‘it looks like a . .’ - like viewing clouds. Why is he so insistent on other ‘proofs’?
His reading of the multiple, stacked domes of the Baroque era as being like the layered lenses of the recently invented magic lantern, telescope and microscope, p.60, is likewise interesting, as these dome forms cleverly play with light and, symbolically, with celestial projections too. Unfortunately, Hersey seems to get carried away with mathematical forms called catenoids, a surface generated by the 360 degree rotation of a catenary. He even gives the formula for the catenary: x = (a/2)(e x/a + e x/a).
He writes. p.69:
. . . St. Paul’s, the masterpiece of Sir Christopher Wren (1675-1710; fig. 3.17). There, however, one finds not a true paraboloid, (unlike previous domes), but a set of three domes. The outer dome is a flattened hemisphere – half an oblate spheroid, one might say, perhaps as a bow to Wren’s colleague Newton. Then, within, are catenoids. These form the two inner domes supporting the outer. . . . catenaries had just recently been distinguished from parabolas (they have different formulas), notably by Jacobus Bernoulli in 1691.
The proximity in dates seems to have persuaded Hersey that Wren must have used catenoids. He even illustrates this with coloured lines drawn over the section of the dome. While the outer and innermost domes appear to confirm his vision, it is the middle ‘dome’ that seems to have been faked. The only other explanation is that the lines are as casual in their placement as those previously illustrating proportions on St. Peter’s. The red line that illustrates the catenoid profile is drawn over a masonry structure that is conical in form with a segmented hemispherical cap. It is not a catenoid. The sides are sloping straight lines, conical. The red ‘catenoid’ line does not even follow the sectional lines of this masonry structure other than at the beginning and the end of the side of the cone; but Hersey claims that it does? Is he relying only on the illustration and the misreading of it, perhaps as a misprint, for this outcome? This seems to confirm that yet again Hersey is determined to ‘prove’ his thesis, come hell or high water.
I understand the story to be that during construction Wren realised that the footings were inadequate to support the load of a full masonry dome. He redesigned the structure, placing a conical masonry form over the inner dome that would support a wooden-framed outer dome, reducing the loads without unnecessarily loading the inner dome. The sections of St. Paul’s published by others confirm this, (see, e.g., Bannister Fletcher). Surely Hersey must have known that the red line did not accurately follow the alignment of the sectional profile of this inner form? Did he just think that it didn’t matter - ‘never mind’: all for ‘simplicity’? Was it considered ‘trivial’ – or that he could ignore such minor discrepancies? Was it just a close enough fit? It is this sloppy lack of precision and logical argument that makes Hersey’s work weak - hopeful guesswork that would like the world to be seen in a certain ordered manner: his ‘academic’ way, in spite of all the evidence that leaves matters ‘suggestive’ at the very best - loose guesswork.
It is not as tough this might be a simple mistake or misconception. Hersey later asserts by way of summary:
And of the three nested domes of St. Paul’s, two are even more exotic. Two are cubical catenoids and one is parabolic.
One can look at any section of St. Paul’s dome. It is clear that the inner dome is conical. Indeed, Wikipedia describes its sectional illustration unequivocally:
‘Cross-section showing the brick cone between the inner and outer domes’
Hersey seems determined to see the inner dome as a catenoid. Why? Unbeleivably he draws a catenoid over the cone in order to offer visual confirmation, but, even with smothering misalignments of the thick, coloured line, the discrepancies are more than obvious.
His intuitive readings are not without interest; but they might suggest simple serendipity rather than any self-conscious manipulation or scientific adaptation of other inventions and mathematical studies of the times. Why not be happy to leave things like this? There are other circumstances that have seen inventions occur in parallel: e.g., calculus (Newton; Leibniz); and the filament light bulb (Edison; Swan). No one seeks to resolve these inexplicably surprising events with some pseudo-rational explanations. Hersey’s efforts to create some sense of music out of his seemingly almost random allocations of notation by ‘adjusting’ some notes, again highlights his self-conscious manipulations and adaptations that seek to illustrate some inherent order, when they are merely superimposed guesses, perhaps, or maybes.
In figure 2.25 I have rewritten the two tunes into a single melody. I’m cheating, I suppose. I make use of the entrenched and necessary musical tradition whereby a given note can be transposed an octave without overly damaging the musical sense (but which of course changes its number ratio since it changes its interval). But in this way we can make the baldacchino’s original melodies more acceptable. Anyway the old ratios and the new ones do remain linked, musically, even though the numbers change. This is because when we transpose a note up or down an octave, or even several octaves, it remains harmonically the same note.
Hersey unabashedly confesses his manipulations and boldly, almost brazenly, seeks to justify them. Why?
Architectural theory needs to be more thorough and exact. We have to overcome our lazy tolerance with ‘Gehry guessing/Hersey hoping’ that indulges in much the same carefree world as that of selfies, centred on my image, visions and hopes, when there are larger, broader, deeper, more significant things that are seeking in all humility to be represented otherwise. If our ideas are sloppy, then there is little hope for anything based on them being otherwise: they will all be other than wise. We need careful rigour and responsibility in all that we do rather than playing the game of the over-confident, over-satisfied, smiling television presenter, grinning with apparent superfluous contentment at the entertaining delight of life and its extremes, promoting this vision as an ambition for all: life as one great laugh, where everything different and flippant will let one stand out from the pleasure-seeking crowd looking, as tourists do, for the next distracting ‘high’ for folk to applaud - see: http://springbrooklocale.blogspot.com.au/2012/06/who-or-what-is-tourist.html
But there is more. Deeper into the book, Heresy has another example of his preferred geometrical graphic patterns overlaying an illustration, this time a plan drawing, to document another idea of his interests: the nine-square plan, the 3x3 lattice.
p.120 - 121
While as it stands the Invalides’ nave/chancel complex does not possess more than the most primitive bilateral reflection, the composition is nonetheless formed from a matrix that very clearly is a 3x3 lattice. That is, by removing the plan’s symmetry-breaking elements – its main entrance with its steps and columns, and the chancel extending the church to the east, all of which split the plan into heterodox shapes, the rest of the plan then turns directly into a square building with central cupola, four flanking domical transepts, four corner chapels, and four entrance massings, all identical in form and placement.
Accompanying these words are two illustrations, Fig. 5.22 and Fig. 5.23. Fig. 5.22 is a hazy, rather blotchy plan of the Invalides, Paris by Mansart, erected 1679-91. Fig. 5.23 is supposed to be the same plan, modified by truncations and deletions. This plan drawing is more indistinct and does not appear to be the same illustration that has had the entry and chancel removed. The forms of the various parts differ in shape and detail. Still, Hersey presses on with his ‘proof.’ He draws a square divided into four in red and the same square divided into nine in green over this plan to illustrate his theory. The red and green lines are very thick. They must be at least one metre wide to scale. But what is strange is that the symmetries and alignments that Hersey seems to suggest might be there are not. Central columns sit askew around the perfect symmetry of the red lines, while the green ones slice through the masonry masses at what look like random points that have no mirroring sense or sensibility. There is such a sloppiness here that one cannot believe that Hersey is serious. Are the red and green lines so bold as to appear to want to assert this proof just too much? Is Hersey trying to bluff us with the certainty of brash, thick colour overlaying a fuzzy, indistinct diagram that is not even a reproduction of the adjacent ground floor plan being referenced? The thick, coloured bands clearly define the proportional divisions, but even with such generous tolerances, they do not illustrate what Hersey is suggesting. Some of the relationships between the building parts and these broad, overlaying graphics are not even close.
On p.122 he says it more clearly: My doctored version of the Invalides plan in figure 5.23, for example, . . . Yes, he is ‘doctoring’ the proofs to suit himself. Hersey is constantly manipulating matters to achieve his proofs.
Why does Heresy consider his approach to be acceptable?
(Leonardo’s famous drawing, illustrating this passage, proves that while the circle originates at the navel, the square will have its origin at the penis. As an origin-point or generator, however, a penis is just as appropriate as a navel, perhaps more so.) Anyway, throughout the Renaissance and Baroque periods, the male body was thus seen as an aspect of cubices rationes, fathering geometric and architectural forms.
One might imagine a point being the centre of the navel, like a circle referencing its centre, but where on earth might one begin to locate a point of generation in or on the penis? Does Hersey acquire his inspiration for generalities and vague diagrams from Fig. 4.1 that illustrates correspondences between macrocosm and microcosm from Robert Fludd’s Utriusque, 1619? This illustration shows the penis as the ‘Centrum’ – the generating point – with a line that passes under the overhanging penis and in front of the scrotum, tucked up somewhere in the intimacies of this sheltered location. Where is this generating point? Has it a location or is it merely a metaphor: seed; growth; fertility; futures? Is Hersey doing the same in his study – making broad certainties out of generalities and maybes anchored in geometrical analogies: making facts out of poetic fictions that can themselves touch reality obliquely, but with an elusive certainty too? The geometry is not without interest, but we need to avoid the suggestion of any sense of rigour when there really is very little, in the same way that drawing approximate diagrams to prove certainties must be avoided if we are ever to understand our world and our place in it beyond what we envisage it to be. No other profession other than perhaps astrology could get away with such sloppiness.
Hersey might be hopeful, but fabricating ‘baroque’ theories is neither poetic nor factual, not emotionally, or in any other manner. It merely creates a fantasy of possibilities that highlights Heresy’s hearsay; his heresy. Academics must do better than this if they want respect. Architecture needs better too.
One is left wondering:
Is Hersey too casual with his subject; too easily distracted with matters interestingly geometrical and their internal rigours? On p.130-131 he notes: The whole subject (spirals) stands as a fascinating challenge for architectural writers. And not just in Baroque architecture. Any architect who uses continuous curves – Antonio Gaudi and Frank Gehry are only two of the many who come to mind – can be studied for their use of spiral symmetry.
This observation leaves one a little amazed, but when the previous lines are read, ‘spiral symmetry’ can be seen to include anything: Archimedean, golden section, Pythagorean, dynamic-symmetry, random, and fractal spirals. They also discuss spirals with what is called broken symmetry. One could also mention that there are parabolic, hyperbolic, and cornu spirals.
It seems that the whole Hersey world is spiralling out into some romantically unpredictable spin. So this is how Gaudi and Gehry can be mentioned in the one breath, in the context of matters beautifully Baroque. Gaudi had rigour in his forms using hyperbolic surfaces because these are formed by straight lines – the lines of light itself: symbolically ‘the light of the world,’ of God himself. Embarrassingly, Gehry might be seen to fit more into the no-man’s-land of the ‘random’ and ‘broken’ aspects of spirals, if at all. Analogies and references to war zones seem to fit Gehry’s work very well: see http://voussoirs.blogspot.com.au/2013/12/new-gehry-projects-in-aleppo.html It seems strange to try to justify anything Gehry-like when there appears to be such a disregard for anything and anyone in his work – other than himself, of course, and his reputation, no matter what comes up.
But what is this? Hersey knows about his fudges! After claiming that he can use Serlio’s system to make ovals that simultaneously come remarkably close to ellipses, adding that One can, with sufficient care, reduce the bumpiness to a near zero level, (p.138); he continues on p.139 after illustrating precisely how this can be done with: I admit that scientifically my pseudo-ellipse falls apart into a bumpy Serlio oval if the procedure is redone with thinner, more exact lines. Mathematically a Serlio oval can never be a true ellipse. Its elliptical nature is really the result of the thick, therefore ambiguous, lines that construct it. But then, of course, when you’re constructing a building, these are just the ambiguities you face.
It seems that Hersey is unable to help himself. He still continues to explain and excuse himself in order to prove that he is correct, ‘near enough,’ even knowing that ‘scientifically’ he is wrong, just for things to fit his ideas and theories. Given this, one can only assume that Hersey’s work is all merely simple, unproved conjecture, schematic fabrications, and that he is fully aware of this. Did Hersey try just too hard to make one last substantial book out of a set of simple, yet interesting observations collected over the years, noting that ‘this looks like that’? He was 73 when Architecture and Geometry in the Age of the Baroque was published and would/should have known better. Is Hersey’s work nothing more than a child’s game of seeing things in shadows? That my hands can make a rabbit shadow on the wall does not establish any essential ‘rabbit’ quality for my hands or my thinking. Trying to impose some mental stance on a Baroque architect through some apparent parallel in form and geometry is taking things far too far. Attempting to reform Wren’s dome to match his own personally preferred ideas is unforgivable. In short, Architecture and Geometry in the Age of the Baroque is close to hypothetical nonsense masquerading as a learned, academic study.
There is one thing: on p.130 Hersey notes that, on the matter of spirals, The whole subject stands as a fascinating challenge for architectural writers. Maybe that is the best one can say about this book – it offers many ‘challenges’ for others to explore, test, question and develop. It is a real shame that it knowingly, almost desperately, tries so hard to be otherwise; but geometry is like that: it entrances with its own special abstracted magic.
But this is not all: on p. 141 Hersey comments on Borromini’s plan, that it has both a visible and a physical pseudo-ellipse: We are dealing here with the sort of coincidences that arise independently in the course of geometrical play. This sums the whole book up. It is a shame that Hersey is so selective in his understandings, so blind to possibilities of chance encounters. Hersey is grasping at phantoms. On p.153 he talks of up-down symmetry: This happens when the buildings are up-down reflected – for example, in water or on wet streets; and notes how this dual form matches some floor plans – again at Sant’ Agnese. He sums up ‘pseudo-scientifically’ on p.155: . . dihedral reflective symmetry of both left-right and, at least on rainy days or in canal cities, the up-down sort. This is a real ‘up-down sort’ of book that comes close to being a farce. If you do happen to pick it up by mistake, put it straight down again and spend your time more productively and creatively watching clouds and observing the surprising reflections in our world, both in nature and our built environment.
15 February 2015
Hersey’s erratic rashness never fails to surprise. While being prepared to ignore the possibilities of serendipitous occurrences earlier in the book and make outrageous assumptions and claims, it is not until the very last section that he recognises the possibility that might have made his book a better study had it been recognised at the beginning of the work:
I am far from suggesting that Le Corbusier or Maillard were consciously concerned with Robert Fludd. But Fludd’s microcosm is nonetheless the modulor man’s Baroque ancestor. It is less a question of conscious influence than of geometric genes. Both results were independently generated -