Design essence: David Dunster, who co-edited this issue of the AR, introduces its theme, the diagram. In the pages that follow, architects describe the role of diagrams in their own work, and examples they admire by others.

What do we mean by a diagram? Two quotations--any building should be described by three or four lines says Stefan Behnisch; a century ago Daniel Burnham is alleged to have said that only a noble diagram can capture men's minds. (1) Such a diagram lay behind his and Edward Bennett's Plan of Chicago produced in 1909--radial lines cutting through concentric rings over a rude grid. Though not the first use of the term diagram, (2) these citations suggest a further idea: that the diagram, as part of the process of design, is inherent to the project of Modernism in architecture. (And further that the strong questioning of Modernism over the past twenty years might have made the diagram redundant as computer-aided design dominates.) For an architect to find a satisfactory diagram has been taken as proof that an idea was born.

So rather than begin at a precise definition I prefer to ask what purposes diagrams satisfy inside the processes of architects' designing? Can one drill down into the geological history of the uses of diagrams and ask: what does the diagram cover? What can and cannot be represented within its linear, two-dimensional nature? And finally, is the day of the diagram over as the Modern Project decays into who knows what?

In the period of neo-functionalist Brutalism (the 1950s and '60s), the fundamentals of routes, how progress was to be made into and through a building, was the content of many diagrams. A logic of choice and topological possibility structured the development of a scheme until it had reached diagrammatic clarity. Choices were to be avoided or signalled only by volumetric or compositional means. Tom Ellis, senior partner in the office of Lyons Israel Ellis which employed, among others, James Gowan, James Stirling, Alan Colquhoun and John Miller, described how the route as an organising principle was to be found in many of the Modern Movement's most significant buildings, especially for him in the works of Le Corbusier and Alvar Aalto, in the only two articles he ever wrote. (3) While the route had been critical to the axial control exercised in Beaux-Arts planning, Ellis argued that people could now navigate asymmetrical plan organisations by architectural means alone--volume, material, and perception. Most of his office's work at that time was built for growing educational requirements; schools and universities had precisely the newer kinds of needs for which Modernism, in its more functionalist mode, could offer most. The corridors of older educational buildings became the street and the hall became an almost urban space.

Of greater functional complexity was the modern hospital. Nonetheless the diagram was circulation, NOT form. Diagrams from the Heroic period of Modernism (I use the Smithsons' romantic term) were, however, more formal, more concerned with exterior apprehension. The diagram embodying circulation patterns, as befitted a neo-functionalist approach, left the outside of the building to become the result, the outcome, of a play of forces which in the hands of a hard-line rationalist like John Weeks was reportedly indifferent to composition or character, the evil twins of historicist thinking. In Northwick Park near Harrow, north-west London, and in the women's hospital at the Queen Elizabeth, Birmingham, this indifference presented Weeks with a conundrum. Form could not be denied, either as mnemonic, symbol or semiotic, yet composition smacked of an anti-scientific approach which Weeks' partner Richard Llewellyn Davies, coming from an engineering, research and pragmatic background, foreswore. Weeks, more fascinated by the fine arts, drew not only upon abstract art through his friends Harold and Mary Martin (with whom he had collaborated on the influential This is Tomorrow exhibition), but closely followed the musical avant-garde in their embrace of chance, and of structure. Aleatorics, most extreme in the work of the American John Cage, and partly introduced into the Western tradition by Pierre Boulez and Karlheinz Stockhausen among others, offered Weeks support for his own design work. So the structure of the wings at Northwick Park was designed to be spaced according to the weight they carried. However, this would have required that each floor of the hospital be uniquely structured too, and therefore a standard floor system could not be used. Consequently the mullions, which are indeed irregularly spaced, now act as sun louvres and behind them sits a rather too standard curtain wall.

The corridors at the Dominican Monastery of La Tourette, connecting the various monkish functions to the Chapel, were based upon the Fibonacci series, and laid out by Yannis Xenakis, the composer, then an architect working in Le Corbusier's office. Weeks was aware of that detail. (4) But unlike La Tourette, Northwick had no formal diagram, no avowedly poetic or therapeutic aim. He wrote: 'Whether or not this was the intention at La Tourette (the control of glare by the spacing of the louvres), this control is achieved here (at Northwick Park).' But Weeks' diagram is in many ways the simplest form of organisational diagram--a spine, or street, off which discrete entities crowd and expand as and when need arises. For all the references, however, the most delicious statement in his lecture still seems to be 'We did not know, until the engineer had calculated the stress patterns, what each building would look like'. Towards the conclusion he drew an interesting and informative parallel: 'Stravinsky has said of his music, now usually serial in form, that he is interested not in harmony but in related densities of intervals. There seems to be a parallel here: varying densities of intervals are the visual characteristics of the elevations at Northwick Park, rather than a proportional harmony'. Music helping Architecture again.

Is this not the curse of the diagram--always seeking an authority outside architectural traditions? The example of Weeks's hospital diagrams polarises the use of diagram. In extremis, this version looks to the rational diagram to generate an architecture that is automatically generated, or rather generated out of pure materialistic reason with no recourse to aesthetics or notions of harmony, totality and poise. As Stravinsky commented that he was merely the vehicle through which his music passed, from God to His people presumably, so Weeks sought to make what would be recognised as architecture, but architecture generated from a deep understanding and approaching in form the perfect and utterly transparent language which Umberto Eco has recently shown to have been a preoccupation since the Tower of Babel. (5) In such a language, a building communicates and demonstrates its uses and pertinence entirely through mechanisms that can be read by a civilised and educated mind. No metaphysics, no aristocratic preoccupation with elitist codes, this would truly be, as Banham called it in The New Brutalism, an architecture autre. As such, Weeks would indeed build a diagram, a built diagram he believed so close to the most coherent array of uses that it would be universally understood. The diagram describes the essence of the building. Essence in this sense: that this set of lines stands for the least, the most economical and restrained delineation of the architectural idea; in this case a diagram which will be heavily dependent upon simple structure and the extensive use of glass.

Why is the diagram so important for Modernism? Is it a guarantee of authenticity because there is no 'other' any more? If there is a diagram, which can be repeated to friends and colleagues, even used in a future monograph, then there is a mnemonic, something to remember, an easily repeatable set of lines. Do diagrams, their inevitable lines, relative dispositions and perhaps even their intersections, offer some strangely comforting support in the empty wilderness of invention? One of the greater mysteries of designing, after functionalism had been enunciated as a creed, is that creativity is always associated with one or more moments after all functional considerations appear to have been absorbed within the analytical process. Thus they are no longer the defining parameters of the process but the sine qua non of it. At this point, and only really at this point, is there enough personal sense of security and assuredness that a possibility might arise, through all the mists of critical analysis, of an object whose logic will be sufficient to allow it to surface in public, ex vitro, out of the confines of the designer's laboratory. The search that the diagram says is nearly over is a search therefore which seeks the inevitability of immanence, (6) which seeks the 'Es muss sein'. (7) This was immanence in practice--Beethoven, rather like Martin Luther, could do no other. Precisely the point any real architect would wish to reach, a point not only where every decision made, but every line drawn, is doubly determined (doubly in the sense that if one reason is removed then there still remains one other compelling reason for the action). In psychoanalytic terms this is almost overdetermination, a condition easily pointing towards neurosis. In architecture this is also the point or moment from which the actual construction appears to design itself, to take over the pen, pencil or computer of the architect to make every move compelled, inexorable, inevitable, immanent to the process. In this way, Modernism was able to offer a complex sense of security, a process instead of a father-figure of language or history.

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Somewhere between aphorisms and icons, the early architects--Loos, Le Corbusier, Mies and Gropius--parlayed between the demands of emerging post-First World War social democracy (replace slums via an industry-led housing boom) and the urge to bring to the fore a new formal language which could stand architecture within the revolutionary changes which were happening in music, literature and above all painting. If the diagram appeared to be one design tool that was internal to the practice of architecture, wordless, meaningless even, then the repeated diagram failed to excite anyone. Mechanical repetition of a diagram lost the complex psychological investment that the individual diagram needed. The individuality which functionalism sought to celebrate, to each according to his need, could not obtain within the political context of housing need, slum replacement, and post-war rebuilding. Did the use of diagram, then, assist within that larger scale, the scale of city planning?

If diagrams in architectural thinking relate process to ideation, then their role within city planning is even more contentious. Certainly in the twentieth century, too many architects thought that designing a city was merely part of a design continuum extending at all scales from the design of a building to cities at the largest scale and doorknobs at the smallest. Alles ist Architektur declared Hans Hollein. This view, multum in parvo (the world in the detail), is not only a delusion, but also confuses a final object, which can only be some warped utopia, with the process of designing cities as well as the historical forces which change them. It is almost a battle between one icon produced by theistic religion, and a conflicted partial solution continuously changed by a democratic and atheist process.

It is curious, therefore, to find this conflict already present in Renaissance writings about city building. The drawn musings on parchment of Francesco di Giorgio and narratives by Filarete discuss the process of how to build a city, in both cases under the umbrella of reflected religious dogma. An ideal city would by definition be a city of God, one formed as if to imitate Heaven, however its structure might be construed. While di Giorgio was the more graphic, Filarete spoke more of the process than the outcome and thereby is the first architect to discuss the process of design. It is, to say the least, a sexually charged view, even in the 1965 translation by John R. Spencer. Having established that a building is like a man and so needs to be conceived and then born, Filarete describes how 'the building cannot be conceived by one man alone. As it cannot be done alone without a woman, so he who wishes to build needs an architect. He conceives it with him and then the architect carries it. When the architect has given birth, he becomes the mother of the building'. Later Filarete describes how Alexander met Zenocrates, ('he was a handsome person, well built [and] had a handsome face') which I mention to show that Filarete surely understood something about role play in the architect/client relationship. Filarete's city, which he describes in considerable detail, is not then a devotional practice but an earthly, potentially erotic (even homoerotic) process. If indeed they can be traced back this far, may we not adduce this to a condition of all city planning, though some may well emerge that differentiate the possibilities of city planning from architecture.

Throughout the history of urban planning, the idea expressed later by Daniel Burnham, that only noble diagram can capture men's minds, plays upon the diagrammatic as seminal. Only in the twentieth century was the nature of the diagrammatic approach to be questioned, by Christopher Alexander in his paper 'A city is not a tree' (instead a semi-lattice). A tree structure is indeed a god-like source, branching into districts, into villages, into streets, possibly zones even, in a hierarchic and hieratic way. Alexander argues that Modernist views of cities, from Abercrombie through Goodman and Costa to Le Corbusier, all fail utterly to achieve anything more than a tree-like separation of activities, whereas the cities we admire all bear the characteristic of enjoying overlapping functions, not their separation. In this he follows Jane Jacobs who had argued, in The Life and Death of the Great American City that mixed uses were infinitely superior for sustaining (sustainable was thankfully not part of her vocabulary) city life than zoning.

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In advocating the semi-lattice, Alexander followed two great theoreticians of urban planning who arrived at their results simultaneously but unknown to each other--Losch (8) and Christaller. (9) The theory of central places, Christaller's contribution, was based upon an analysis of telephone traffic between cities and towns in southern Germany--a predominantly more agricultural area than the industrial north. Christaller produced a diagram that showed two overlapping hexagonal grids. He read this as showing a hierarchy between settlements with more important nodal points (bigger towns) surrounded by smaller nodes (villages) but then each larger town node is related to other towns. In the 1960s, Melvin Webber read the same diagram as a model that could be applied to Los Angeles, and in enunciating the 'non-place urban realm' appeared to legitimate car-domination over pedestrian and public transport. Coming to the problems of city planning from transport studies himself, Webber's argument, and all his subsequent published work, used no illustrations at all, unlike Christaller, or Losch or Alexander. His influence was said to be powerful in the White House so is held partly responsible for the under-funding of all public transport in the US. His constructive influence in the UK came from his consultancy to Llewellyn Davies Weeks as planners for the new town of Milton Keynes. Here a diagram so simple that it can be almost adequately described in words suggested that the new city did not need a centre, but indeed read diagrams like Christaller's as a mesh, with little or no hierarchy and no centre. Los Angeles, then considered by many to be the single most powerful example of the future city, had many centres and lacked that homogeneous and contiguous mix of business and shopping which the West came to regard as the urban centre.

Two of the most amazing diagrams of cities are not design projections at all, but are in everyday use as means of navigating a city that already exists. These are Harry Beck's map of the London Underground and Phyllis Pearsall's A-Z of the same city. While the story of the Underground map is fairly well-known--a kind of topological resolution employing the conventions of electric circuit diagrams--the A-Z is not so well known. Without going into the tortuous process by which Mrs Pearsall traipsed all over London in order to be able to locate house numbers in streets and roads, the most extraordinary feature of the A-Z is how it distorts London. While all maps distort, as J. B. Harley (10) and Mark Monmonier argue, (11) what the A-Z does to central London is to shrink block sizes as given by the Ordnance Survey in order to be able to incorporate a hierarchy of type sizes which expresses the relative importance of streets. So the Euston/Marylebone Road is a street of the highest importance and is spelled out in the largest type, while a nearby street like Luxborough Street (where I used to live) is very much a minor street and therefore has the smallest type. However, even that type size means that graphically, and to maintain the relative position of streets through their centre lines, the block between Luxborough Street and the mews behind it is little more than a line on the page. In fact the block is at least 20 metres from front to back but shows as if it were a sliver.

This kind of distortion does not hinder our use of the A-Z, because, as someone looking for a particular address, what we need are the coordinates, street names, junctions and finally house numbers, knowing that usually in the UK odd numbers are on one side, even on the opposite. From this simple information the A-Z, originally only printed in a run of 250, has now sold millions and is a model used throughout the UK. This map is a diagram of the city, like Beck's underground map. It reduces the city, as all maps must, to a two-dimensional representation of a three-dimensional construct; not only do maps leave out the third dimension, they also leave out information any walker would receive on perambulation. They are in this way diagrams, abstracts of reality for a particular purpose or agenda. A diagram of a city is merely a further abstraction or simplification, which leaves out information so that a proposition can be more clearly understood. Moreover that information, presented in graphic form, is more understandable as an image/diagram than as a written description, which is always ambiguous. Written directions (turn left at the pub, take the third on the right) lack the immediacy of a map.

Beck's legendary drawing for the London Underground followed radical changes already introduced to the system by Frank Pick, who not only commissioned Charles Holden to design a series of new Underground stations, but also brought the distinctive roundel into public sight lettered in the sans serif face specifically drawn up by Edward Johnston for all publicity. Beck reduced the geographic chaos that the tube lines produced when mapped between the stations on a normal map, to an electrical switch system which equalised distances between stations, made interchanges clear and through graphic means alone made clearer which names referred to which stations. (This related to a system that included at least five per cent more stations in the centre than we know today--where are Down Street and Dover Street, Praed Street and British Museum?)

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This may now be the only way in which diagrams function within cities. No town plans are being produced whose ambition resembles in any way that of Webber, Burnham or others. Instead, where the market does not entirely dominate, then two cosmetic applications are suggested--BIG, or GRID. As car navigation becomes automated, no longer paper-map based, even the diagram of the city, its map in whatever form, ceases to be material and becomes virtual. In this state it is beyond any creative process, a mere factoid engineered without inspiration. And architecture? The diagram may persist where movement dominates the architectural process and its resolution; elsewhere, and hopefully only for a brief period, the social goals with which this tool of process were associated need to be revived to recover that sense of adventure that attracted people to Modernism.

David Dunster is Roscoe Professor of Architecture at Liverpool University.

1 Thomas Hines in his biography of Burnham clearly states that he could find no evidence that Burnham actually wrote down that thought and traces it to a memorial postcard from Willis Polk after Burnham's death in 1912. It certainly sounds Swedenborgian.

2 The OED quotes no architectural writer in defining six senses of the term.

3 In Architectural Design, 1960, Nov, Vol 30, pp481-482 and Oct, Vol 36, pp511-517.

4 See his lecture 'Indeterminate Architecture', Transactions of the Bartlett Society, Vol 2, 1963-64, p83-106.

5 See Umberto Eco, The Search for a Perfect Language, Blackwell Publishing, Oxford, 1995.

6 Again a Banham reference with respect to Charles Eames--that Eames discovered the lore of the operation.

7 Muss es sein? Es muss sein! Es muss sein! (Must it be? It must be! It must be!): Ludwig van Beethoven, comment written on the finale of his String Quartet in F Major, Op 135, copying perhaps Handel's Jephtha 'it must be so' (in German 'So muss es sein'), Gerald Silverman, The Musical Times, Autumn 2003. It would be a lengthy footnote that followed through the role of immanence in design methods as much as in art history, see Otto Pasch, The Practice of Art History, Harvey Miller, London, 1999 or philosophy, Gilles Deleuze in particular has much to say on the topic. See Pure Immanence, Zone Books, New York, 2001, pp25-32.

8 Losch, August (1906-1945), 'The Nature of Economic Regions', Southern Economic Journal, Vol 5, No 1, July 1938, pp71-78. The Economics of Location (English translation, Yale University Press, New Haven, 1954, first edition Die raumliche Ordnung der Wirtschaft, Gustav Fischer, Jena, 1939).

9 Walter Christaller, 1893-1969, the author of Central Place theory as published in Central Places in Southern Germany in 1933 (in English 1966), see diagram p30, bottom left.

10 J. B. Harley, The New Nature of Maps, Baltimore, Johns Hopkins University Press, 2001.

11 Mark Monmonier, How to Lie with Maps, Chicago, University of Chicago Press, 1991.