I have always felt that the Romans made better sculpted portraits than the classical Greeks. I very much like their emphasis on 3D geometry as the basis of their vision of the individual. I wanted to explain this to my students at Wimbledon Art School. There were 4 or 5 busts at the British Museum that were good examples. I chose Hadrian.

I made an analysis of the geometry by which the museum's bust was cut from a block of marble. There were probably many versions of the emperor's portrait made during his reign. Many likenesses have survived. I guess that the original would have been modelled in clay by a master sculptor from the emperor himself. This would have been fired and preserved as a terracotta, which was then sent to the carving workshop and reproduced on demand. This one in the British Museum is very similar to one in the Uffizzi which would have resulted in the same geometric analysis. The Ufizzi version wears a toga and looks in the opposite direction. Most extant versions of Hadrian are recognisably from the same workshop and very easily recognised as Hadrian. The Romans were much more concerned with the individual likeness rather than an idealised hero that satisfied the Greeks during the classical period.

The process of copying from a modelled original was a standard practice in Greece and Rome. We know this for certain because there are many examples where a measuring boss has not been removed in the final sculpture. A boss takes the form of a protrusion on the top middle of the forehead which has a cross engraved upon its surface. This is the point from which measurements would have been made with calipers or plumb-line. In the case of Hadrian the boss has been removed but it is obvious that it had been in the standard place, there is a prominent curl there (see video below). I only needed to hold a board up touching the width of his lower chest and a curl on the right side of his head to be quite sure that this was the front face of the original block. My certainty rested on the fact that the whole of that side of his face was parallel with the blocks surface. Such things do not happen by chance.

The first Roman step would be to get an apprentice to remove the unwanted stone above the shoulders thus leaving a smaller block for the head. If we think of this block as a box in which the head exists, then the left side of the face has the same parallelism with that side of the box as we noted for the right.

The nose is found within the near right hand corner as we face the block. This is a very good trick which was discovered around 100 AD. It obviates the need to remove a lot of stone in order to find the nose. Furthermore, the corner of the smaller block usefully establishes the axis of symmetry from the beginning, the diagonal between right front corner and left back establishes the axis in depth. These clearly established coordinates are a great convenience to the carver as it makes symmetrical measuring much easier. The Roman emperors from this period onwards tend to look left or right as a consequence of this method of putting the nose in the corner of the smaller block.

Next a measuring boss would be fixed above the nose and an egg-shape would be carved for the head. The axes of symmetry for the egg following the corners of the block as above. When I pointed these things out to a fellow sculptor he described it as frozen music which I find very apt. Hadrian's head exists in the middle of geometric solids - cuboids, polyhedra and ovoids – each superimposed in space. All resulting from the businesslike approach of the carver to his task. All the geometry visibly hovers in the final result: the likeness to music.

The Romans came to love the geometry for its own sake. See how Hadrian's frown and the corners of his mouth are in the same planes as the side of his nose, thus emphasising the geometry. Many subsequent carvers have followed the Roman example. When perspective came to allow painters and draftsmen to follow they did so, perhaps subconsciously.

Insofar as I admired Roman portraits and based my own drawing on them, long before I made this analysis it could be said that I was sleepwalking towards the concept of geometric space patterning. I think many artists did the same, Holbein and Rembrandt among them. Rembrandt owned thirty Roman portraits and filled two books with drawings of them (unfortunately, these books have been lost but they were noted in his bankruptcy inventory of 1656). I suggest the subconscious in this respect because no critic or drawing book refers to the geometric approach directly though Bridgman refers to block construction which is along the same lines. Seeing the Roman precedent and its complexity seems important to me because it is a different cast of mind to the Greek based forms. These are usually the basis of academic drawing, inherited from Renaissance drawing. One cannot use the same criteria for two such different approaches.

The folly of talking about the quality of line is particularly apparent when using the geometric method. This method depends upon placing the high points (the angles where the planes meet) in a defined space. Lines define planes but what counts in a geometrically conceived work is where these points are placed in space. It is the relationship of these points that defines volume and how that volume is tilted in space.

Few heads are actually egg-shaped, an assemblage of polyhedra is infinitely more flexible and therefore can define the variety of nature better. The folly of concentrating on the style of lines in a drawing rather than the conception of volume and space has led to the Rembrandt disaster dealt with in chapter 9.

Classical line as used by the Renaissance masters has to distinguish between where it runs along the length and then turns to run round the section of a limb. Even in the hands of a master this distinction tends to become vague and the volumes suffer. Consider a diagram of a cylinder.

This deals with lines along the length of the cylinder and those that run round the section. With a cylinder the distinction is clear; with a leg or arm less clear and more difficult to achieve. This is another reason why I prefer the geometric method. Thinking in this way is more precise. I can confidently sculpt a portrait in the round from a Holbein drawing; much less surely from a Raphael.

The complete analysis of Hadrian can be found in the Apollo Magazine of August 1972 or the YouTube video above. The bust is now on show in room 70. Unfortunately, since I made this analysis the British Museum has seen fit to repair the chips in Hadrian's ears (the best proof of my hypothesis). Unfortunately one can scarcely see the repair any longer. The chips can be seen on old plaster casts from the museum.