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Architecture by numbers JEREMY MELVIN Architectonics of Humanism: Essays on Number in Architecture by Lionel March. Academy Editions (John Wiley), 1999. £24.95

All the ingenuity and diligent detective work which Lionel March achieves in his Architectonics of Humanism depends on one surmise. 'Where are the musicologists or the linguists of architecture?' he asks in the prologue. 'Even the formal studies of languages themselves have far more to offer than vague and shallow metaphors appropriated by architectural apologists.'

This is a challenging thesis, but March sets out to prove that such analysis is possible. Essentially he presents a programme for architectural theory based on numbers, introducing a variety of numerical relationships which show far greater range than the fetishised musical proportions or golden section.

However, music, to paraphrase Perrault, is not architecture. It is possible to have a theory of music based on numerical relationships because music has an internal consistency. Literature too can benefit, for the different reason of its infinite complexity: its analysis has to start somewhere. These internal discourses are what characterise the outward perception of music and literature; to borrow a tired term, their form and function are inseparable.

Architecture, it needs hardly be said, is different. Form and function are separable. Also, architecture is partly structural and physical and partly experiential, lacking either the consistency of music or the inconsistency of language. Moreover, the theory of architecture has to be historical; because history is the only academic discipline which deals with the sequence of events, ideas, motivations and circumstances which impinge on architecture and provide its core dynamic.

But March's work here is so thorough and detailed that it almost convinces. He shows how fecund the numerical, proportional and arithmetic sequences were, and how they formed part of an intellectual discourse which connected Pythagoras and Euclid with the thinkers of the Renaissance. Music was only a small part of the greater discipline. He also shows, in many empirical examples, how these numbers were embedded in buildings, and how they can be decoded.

So, the dimensions of Vitruvius' bath house at Fano, in one way of counting at least, spell out the name Marcus Terentius Varro, the Roman polymath who March suggests 'invented' Vitruvius as an intellectual game, and an admonition to younger architects who were less inventive and rigorous.

In the Renaissance, Alberti was up to the same tricks, interweaving layers of complexity which might be interpreted as uniting Christian and Classical traditions. Palladio, too, encrypted his name into several buildings, including the cruciform central hall at the Villa Malcontenta; its proportions baffled Wittkower because he was looking purely at musical proportion (in Architectural Principles in the Age of Humanism, now 50 years old and the only real precedent for March's work).

The sheer weight of the examples which March describes is impressive, even if he has a worrying tendency to use his own numerical discoveries as the sole evidence for making suggestions such as the non-existence of Vitruvius. Indeed, it is almost more difficult to accept some of his conclusions because, for me at least, to wade through so much mathematical and tabular notation lends to number blindness.

March's stated aim was to produce an equivalent to erudite literary or musical theory, but in the process he shows up an even more serious problem than the lack of such criticism: namely, the lack of genres with which music and literature abound - symphonies, novels, quartets, tragedy. They should be the conceptual frameworks within which to place architecture, and within which March's speculations and discoveries might really be able to shine.

Jeremy Melvin is a writer and teacher

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