In Luke Syson and Dora Thornton’s Objects of Virtue there is a nice comparative illustration of a carved ivory knife handle after Francesco Salviati (Fig. 1) and a print by Cherubino Alberti of two designs of knife handles by Salviati of 1583 (Fig. 2). The actual knife handle corresponds approximately to the left design, and depicts a griffin on top of two back-to-back caryatids. The authors question the usual assumption that the actual handle postdated the print—was copied from it—implying either that the print is based on the actual handle or, more probably, that both are derived from an original drawing by Salviati conceived as an exercise in disegno. (The other design is interesting in that it shows the classical figure of Marsyas about to be flayed, with an older and smaller hook-nosed man between his legs grasping ‘Marsyas’ where it hurts (Fig. 3).)
But what struck me about the two images is how the figure of the griffin in the knife handle is, to my eyes, so much more powerful than the engraved one (Fig. 4). The engraved one is more fluid and naturalistic (Fig. 5), with more convincing wings, but the ivory one has the superb geometry of the inner neck, a near-perfect arc that terminates in the beak on one side and (as the engraving makes clear) a tuft of neck hair on the other. This responds to the arch of the beak and head, which flows in one continious curve to the back of the neck and its knobbly hairs. The dark background to the photo makes these arcs stand out. Following this observation around, we see that the chest and front left profile has some of this geometrical power, but the back has rather less, although, compared to the print, the wings are more closely tied to the profile of the back.
Another instance of such organic geometry that I used to show my undergraduate students is the area of the breast and belt of Judith’s maid in the Judith and Holofernes in Michelangelo’s Sistine ceiling (Fig. 6). This is just like the torus, fillet, and scotia mouldings of one of Michelangelo’s architectural drawings. This would sometimes get a laugh from students, but it was not intended by me as a joke, nor yet my Michelangelo who would certainly have been aware of what he was doing. The Renaissance study of anatomy, including the famous écorché statue of Cigoli, saw the human body in engineering terms, the external contours being the result of the stresses within the tendons and muscles beneath, and ultimately geometrical.
One of the greatest things in art is this tension between geometry and naturalism, between the operations of the mind and mere likeness. Excessive naturalistic skill in the Renaissance could be at the expense of what is most important in art. The low point came with the concept of a picture as a photograph of a stage with frozen actors, as with Poussin. To be sure, naturalism can be transcendent, as with still-life painting. Earlier periods were in many ways more satisfactory, as with Romanesque animals that are similar to the ivory griffin but not the engraved one. Early modernist sculptors, quite self-consciously, returned to this problem of the balance between naturalism and geometry, and for a little while kept both balls in the air. But modernism had its own fatal flaw, which was not excessive naturalism, but the teleological fallacy. Having got to this point artists believed that their destiny was to keep moving further and further away from naturalism, failing to realise that the point of their early successes was this balance, not their contribution to artistic progress. We see this throughout the post-Impressionist-modernist trajectory. In sculpture Early Brancusi held representation and geometry in balance, but his later works are emptily geometrical, which opened the way for the even drearier Anthony Caro and his ilk. Cézanne realised that what mattered in landscape was the tension between surface and depth, and developed some extraordinary techniques to realise this. The early Cubism of Picasso and Braque ran with this but allowed modernist teleology to destroy it, making it into something crude and obvious, and worse, a ‘movement’. Braque recovered from this and went on to produce brilliant still life paintings that no-body is interested in any more, while Picasso draw the conclusion that all that matters was to be clever, which worked, because everyone is still interested in him. And for twenty years in the 1920s and 1930s Cubism provided the crucial tools for handling the geometry/representation balance in the decorative arts, which is where this period is most rich artistically. Otto Wagner reached a point of balance between historical forms and abstract ones during his Sezession phase which got him through to the Postsparkasse, after which he and every other architect lost the plot.
But back to the knife handle. The artisan responsible, it must be said, only half-grasps the problem. Although the naturalism of the wings is tamed, their geometry is pedestrian rather than transcendent, while the thighs are shapeless blobs. How would a Romanesque or early modernist sculptor have proceeded, having discovered the arcs of the head and neck? They would, I think, have worked on the silhouette, which shows promise. One problem area is the negative space between the paws, thighs and forelegs. This needs more emphasis, while the paws need strengthening geometrically with stronger repetition between the two (sets of) paws. The other problem area is the wings. Their attachment to the shoulders is messy, while their outer profile is too much subordinated to the curve of the back. What to do with them? This depends on the sculptor’s mode of working in three dimensions. The driving aesthetic so far has been two-dimensional. Does the sculptor work in planes, relying on superimposed shapes that generate linear shadows? Or do they work in masses that require it to viewed from above and behind? In other words, do that, like the Romanesque sculptor, start with a cubical block, or, as here, what is essentially a drawing. Either way, the knuckles of the wing could be brought forward to cover the blandness of the lower neck: this is done much better in the engraving, which hints at the profile of the wings being a series of humps and reflex curves. The engraver uses shadows to separate the wings from the body, as if they are about to unfurl. The sculptor does take this path, because he is confined within a planar conception. A sculptor in solids would start to spread the wings; a sculptor in planes would enrich the profile and superimpose them (it) on the body.
 After Francesco Salviati, knife handle. Italy, mid-sixteenth century. Florence, Bargello. After Luke Syson and Dora Thornton, Objects of Virtue. Art in Renaissance Italy, London: British Museum Press, 2001, fig. 156
 Cherubino Alberti after Francesco Salviati, Two designs for knife handles composing grotesques and naked male figures, 1583. Engraving, 249 x 102 mm. London, British Museum, 1872,1012.870. Lettered above ‘Frac Salviat in’, on the base of the handle of the knife at left ‘1583’ on blade ‘Secura …convivivum’, and Alberti’s monogram ‘CA’, at left ‘Cum privilegio sumi pontificis’. Curator’s comments: ‘An impression in the Bibliothèque Nationale, Paris BN (Estampes, B3a res) shows that this engraving and P&D 1872,1012.869 are printed from a single plate. (Information supplied by James Grantham Turner, February, 2015). Bartsch XVII.111.171. Images of other copies are available online, including a copyright-free image from the Cooper-Hewitt.
 Syson and Thornton, 2001, pp. 168-169.