Cube of Knowledges [1986/2014]

The Cube of Knowledges: Towards a Symbolic Library

 

Murdo Macdonald

Professor of History of Scottish Art

DJCAD

University of Dundee.

 

mjsmacdonald@dundee.ac.uk

 

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Preamble: Towards an ecology of art and science[1]

This work finds its starting point in PhD research carried out in the Department of Psychology of the University of Edinburgh in the 1980s. The current paper stems directly from one published in 1989 in the art journal Alba, under the title ‘A Pattern of Thought’.[2] What I was concerned with then were the ways of thinking that characterise different arts and sciences. How are these ways of thinking shared, or not? Can the assumptions of different areas be inter-translated, or are they incommensurable? If they are incommensurable, is this a difficulty, or an opportunity for wider insight? I suppose I was concerned with the possibilities and subtleties of knowledge transfer and interdisciplinary illumination, not just in a social setting, but within an individual. How does one area of thinking inform another? And how can one area of thinking inform another? These are questions that can be asked both in a room full of people of diverse views, and with respect to the unique combination of cognitive styles characteristic to one person. I revisited this work in the context of an interdisciplinary project. This project, a collaboration between researchers at the universities of Dundee and Aberdeen sought to illuminate creativity and learning.[3] It had a strong undercurrent of interest in the relationships between arts and sciences. I acknowledge here the interdisciplinary environment created by members of that research group: the artist and anthropologist Wendy Gunn, the anthropologist Tim Ingold, the artist Arthur Watson, the artist Sandra McNeil and the architect Ray Lucas.[4]

 

What my 1989 paper did was to propose a comprehensive model that linked and differentiated arts and sciences, shed light on significant activities of childhood (drawing, building, narrating, playing) and at the same time suggested relationships between the cultural style descriptions empirical, rational, classical and romantic.

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What I want to do here is to explore again my thinking in the 1980s and to situate it with respect to the later project, particularly in the light of an invited paper given by the anthropologist James Leach at Dundee Contemporary Arts under the auspices of our own project and the Visual Research Centre.[5] It was entitled ‘Disciplinary specialisation and collaborative endeavour: some challenges presented by sci-art projects’. That paper was characterised by a rejection of easy assumptions about the relationship between arts and sciences, and it led me to look again at my own work.

 

The necessity of generalism

The specific questions addressed in my 1989 paper can be summarised as follows: What do we mean by art? What do we mean by science? And, crucially, how are these two areas of activity related? In addressing these largish issues I noted Polya’s reminder that general questions can be more easy to solve:

The more ambitious plan may have more chance of success. This sounds paradoxical, yet when passing from one problem to another, we may often observe that the new problem is easier to handle than the original problem. More questions may be easier to answer than one question. The more comprehensive theorem may be easier to prove, the more general problem may be easier to solve.[6]

 

Quite so. Another comment which had bearing on the task came from the anthropologist Gregory Bateson. He wrote of ‘the pattern which connects the items of learning’ and of how breaking that pattern was to ‘necessarily destroy all quality’.[7] Polya’s ‘more general problem’ provided me with an ethos, a context for thinking, Bateson’s ‘pattern which connects’ provided me with a motto. As a kind of caveat I noted these lines from the poet Borges: ‘To reach it, a ladder has to be set up. / There is no stair. /What can we be looking for in the attic / but the accumulation of disorder?’[8]

 

 

Three related questions

The relationship between art and science is, on closer examination a number of often conflated issues. These concern (at the very least), first of all the relationship of arts as practised (painting, music, literature, etc) to sciences; secondly, the links between humanities (i.e. arts as institutionally described in faculties of arts) and sciences; and, thirdly, aesthetic aspects of science.

 

Art and science as overlapping insights: C. H. Waddington

An explorer of the first issue, that is to say the relationship of arts as practised to sciences, was the geneticist C. H. Waddington who concluded his 1969 discourse on modernist art, Behind Appearance, with the words:

 

We have been led, by a consideration of one apparent discontinuity in human experience, that between painting and natural science, to recognize that there is a continuity between them after all, and that this continuity extends out into wider fields …. the conclusion we have come to is that man is an Argus with innumerable eyes, all yielding their overlapping insights to his one being, that struggles to accept them in all their variety and richness.[9]

 

Waddington was a pioneering mid-20th-century biologist with a passionate interest in contemporary art. Perhaps it was his breadth of vision that led him to give little credence to philosophers of science who characterise scientific method in a rigid manner:

 

The mistake made by both sets of philosophers – those who asked for verification and those who would settle for falsification – is that they demand 100 per cent certainty; and that is something we can never have in the real world. All science can do is to show that some things are very likely, others unlikely. Its picture of the world is more like a portrait drawn by a painter than a precise theorem in logic.[10]

Waddington’s message is that however analytical science may be, by virtue of its contact with the real world, it demands a form of expression that may reflect some of the ambiguous characteristics of art. This is a useful antidote to the scientism that undermines so much of our current discourse on method.

 

The real world. What an intriguing idea. Now what is that? For Waddington it seems to hover as a kind of mid-term between art and science, to which each somehow refers. Wittgenstein notes ‘I read: “philosophers are no nearer to the meaning of ‘Reality’ than Plato got.” What a strange situation. How extraordinary that Plato could have got even as far as he did! Or that we could not get any further! Was it because Plato was so extremely clever?’ [11]

 

Humanities and sciences: C. P. Snow, George Davie, Patrick Geddes

Most discussion of the relationships between arts and sciences has centred on the second issue, that is to say the links and schisms between the humanities and the sciences. Perhaps the most widely known discussion is that of C.P. Snow, indeed in the wake of Snow’s eponymous article of 1956, it has been known as the ‘two cultures’ debate.[12] Snow’s view of the past is of a period dominated by the literary culture of the traditional arts faculties. For Snow in the future science will come into its own ‘certain that history is on its side’. Understandably, such views led Aldous Huxley to describe Snow’s writing as ‘bland scientism’.[13] But one must concede that Snow is at least implicitly aware of the problem of scientism, indeed one could argue that it is this that leads him to seek a rapprochement between science and literary culture in the first place. The problem with his view is that by seeing science as having ‘history on its side’ – implying that it is somehow a more ‘advanced’ type of knowledge than literature – he brings his scientism to the fore and makes any such rapprochement difficult. Thus for Snow literature is important, but not as important as science. He has a ‘one and a half cultures’ problem, so to speak.

 

A more considered view of the relationship between humanities and sciences is to be found in the work of the philosopher and historian of ideas George Davie (1961, 1986).[14] Davie takes his cue from the St Andrews classicist John Burnet, paraphrasing him as follows:

 

the most important side of any department of knowledge is the side on which it comes into contact with every other department. To insist on this is the true function of humanism.[15]

 

Davie’s approach is informed by historical understanding. In The Democratic Intellect (1961) he explores the dynamics of Scottish nineteenth-century education in terms of the encroachment of specialisation on the generalist tradition of Scottish education. Davie notes that in nineteenth-century Scotland it was taken for granted that one area of thought or expertise benefited from the illumination of another and, of course, vice versa. With respect to this I have commented elsewhere that:

 

any aspect of knowledge, culture, society, or whatever, benefited from the illumination of other aspects. The task of education was to facilitate such processes.[16] This social approach to knowledge, which takes for granted the role of the wider community in the process of establishing and maintaining bodies of knowledge, also implies that different and perhaps incommensurable disciplines should be juxtaposed for mutual illumination, rather than … kept in watertight compartments.[17]

 

The notion of incommensurable disciplines being juxtaposed in order to illuminate the blindspots in one another is fundamental to Davie’s philosophy. It challenges the assumption that evaluation criteria can be easily transferred across disciplines.

 

My comment about watertight compartments derives from an essay by the poet Hugh MacDiarmid. MacDiarmid was a friend of George Davie, and wrote about his work, but this quotation is to be found in his assessment of another generalist thinker, Patrick Geddes, and it is worth quoting at more length:

 

[Geddes’s] constant effort was ‘to help people to think for themselves, and to think round the whole circle, not in scraps and bits.’ He knew that watertight compartments are useful only to a sinking ship, and traversed all the boundaries of separate subjects.[18]

 

Mention of Geddes allows me to make a further point. One finds in Geddes’s work, not least in his comprehensive Notation of Life, a high value assigned to arts as practised, alongside humanities, social science and natural sciences.[19] Thus one can argue that Patrick Geddes unites the perspectives of Snow, Davie and Waddington, or at least provides a context.

 

Aesthetics and physics: Paul Dirac

Like good art, good science in prone to conceptual elegance. Consider the following: ‘It is tempting to go one step further and speculate that the entire universe evolved from literally nothing.’[20] This is a minimalism worthy of the painting of a Zen master. But these words were written by physicists. Thus the third question, aesthetic aspects of science, is an interesting one not least because by noting what scientists say one can dispose of the notion that the aesthetic is the province of art alone, or that it is somehow art’s contribution to science. The point is made succinctly by the physicist Paul Dirac when he writes that ‘it is more important to have beauty in one’s equations than to have them fit experiment.’[21] Here Dirac is reflecting on Schrodinger’s wave equation, one of the cornerstones of quantum physics. Elsewhere he notes, with respect to Einstein that ‘his entire procedure was to search for a beautiful theory’ expanding this as follows:

 

He was guided only by the requirement that his theory should have the beauty and the elegance which one would expect to be provided by any fundamental description of nature. He was working entirely from these ideas of what nature ought to be like and not from the requirement to account for certain experimental results.[22]

 

Similar points have been made by other writers, for example:

 

It should, however, be pointed out that, mathematically, Einstein’s theory is extremely simple and beautiful. The competing theories are not. If beauty and simplicity are in some way a measure of validity, we may continue with confidence in assuming Einstein was right.[23]

 

 

A model, then a library

To get some sort of grip on these questions of art, science and the aesthetic, I developed a model. This consisted of a three-dimensional surface capable of expressing a sufficient number of links and separations between disciplines or ways of thinking. For convenience of mapping I used a cube. This model is a crude but useful classification device. It organizes a significant body of information, but more than that it generates new thinking about the interactions and continuities between different or not so different cognitive domains. My first publication of it was in an architecture research journal and on the basis of the model I was consulted by an architectural partnership on a competition entry for the proposed new library at Alexandria.[24] I would like to think that my efforts resonate with Schopenhauer when he notes:

 

As the biggest library if it is in disorder is not so useful as a small but well arranged one, so you may accumulate a vast amount of knowledge but it will be of far less value to you than a much smaller amount if you have not thought it over for yourself; because only through ordering what you know by comparing every truth with every other truth can you take complete possession of your knowledge.[25]

 

This notion of ‘comparing every truth with every other truth’ interested me. But I would resist the notion of ‘complete possession’. What I intended the model to reflect was something like the generative interactions that Herman Hesse explores in The Glass Bead Game. Hesse writes of ‘every rapprochement between the exact and the more liberal disciplines, every effort towards reconciliation between science and art or science and religion’ and then refers to ‘the dream of capturing the universe of the intellect in concentric systems, and pairing the living beauty of thought and art with the magical expressiveness of the exact sciences.’[26]

 

But, remembering Borges, I bore in mind this equivocal caveat from Michael Moorcock:

 

[He] let his mind drift about in time, encompassing past, present and future and forming it into a whole – a pattern. He was suspicious of pattern, disliking shape, for he did not trust it. To him, life was chaotic, chance-dominated, unpredictable. It was a trick, an illusion, of the mind, to be able to see a pattern to it.[27]

 

Perhaps so, nevertheless I had got that far, more or less, in the 1980s. What struck me when working on the Learning is Understanding in Practice project was how material that I was encountering in that context seemed to gloss aspects of the model. For example, thanks to my anthropologist colleagues I became aware of the classification of modes of production stemming from the voice as distinct from those stemming from the hand.[28] The point of this distinction is that it does not necessarily correspond to the final medium of expression. For example literature stems from the voice, not from the hand, even if it is hand-written. I saw that these notions were closely linked to the one of the complementarities I had used in my model, namely ‘development’ versus ‘extension’.

 

 

 

 

A model of ways of thinking

So, things began to fall into place when I started trying to map arts and sciences onto a three dimensional shape, namely a cube.[29] There are substantial difficulties in communicating an unfamiliar model, but suppose you were faced with the task of designing a general library, so that the inter-relationships of the areas of thought covered by that library were reflected in the structure of the building itself. The design would only be satisfactory if it enabled people to progress from one subject area directly to any other closely related subject area. It would not be satisfactory if people could not go directly from, for example, social science to, on the one hand, history, and to biology on the other. Similarly it would not be satisfactory if people could not go easily from music to painting or to literature.

 

The question is this: what shape would such a library be? The answer is: the same shape as a coherent model of ways of thinking. It is interesting to reflect that since the model proposed is three dimensional, such a library could in fact be built. One day, no doubt, it will be.

 

In examining the diagrams and descriptions below it may help to keep this ‘coherently related library’ analogy in mind. Imagining a journey round such a library may be of particular value. Bear in mind that the library will have a highly efficient stair, escalator and lift system connecting nearby areas to each other. Thus in your journey ignore gravity, which would otherwise bias the structure of the library by making it more easy to travel horizontally than vertically.

 

 

The Development of the Model

The initial insight was, therefore, that a three dimensional model had an explanatory power in some way appropriate to the problem of relating the arts and sciences. What are these ‘dimensions’?

 

I approached this problem by giving working labels to the surfaces of the cube. With time I was able to give more precise labels to the surfaces. But in a real sense these labels are provisional. That is to say they are ‘to meet necessity’. The model does not originate in them.

 

The dimensions were characterised by the following complementarities:

(i) the idea of interpretation – one or many – which I characterised by the terms ‘analysis’ and ‘ambiguity’ respectively; (this reflects the usual science – art distinction);

(ii) the idea of relation – internal or external – which I characterised as ‘form’ and ‘likeness’; (broadly reflecting the difference between activities like, for example, mathematics and music on the one hand and biology and portraiture on the other);

(iii) the idea of direction – one or many – which I termed as ‘development’ and ‘extension’; (broadly reflecting the contrast between time-dependent sciences like psychology and sciences like physics where time can even be reversed in a space-like way, and between time-dependent arts like literature and space dependent ones like painting).

 

Thus, analysis is closely involved in what we call sciences. Each work depends on being interpreted in only one way (or at least that is the goal). Typical analytical activities are biology, social science, mathematics and physical science. Ambiguity is very much involved in art; each work has many possible appropriate interpretations. Typical activities concerned with ambiguity are music, plastic arts, mythology and literature. Another way of noting this distinction is Measurable versus Measureless.

 

Development is to do with what one might call a timespace, or following Waddington, a chreod, rather than a spacetime. The irreversible order of events is of paramount importance. Novels, studies of development, chess, and biographies do not make sense backwards. Activities typifying this element of thought are social sciences, history, literature and games. It contrasts with Space, which is to do with potential reversibility and the implications of such multi-directionality. Even time is thought of in this radically spatial way in physics, for example its treatment as a dimension, or the backward time of Feynman diagrams. Typical activities are plastic arts, physical sciences, design and depiction. Another way of noting this distinction is to simply call it Time-space versus Space-time.

 

Resemblance is to do with, not so much what something is, but what it is like, that is to say it is to do with a relation external to the thing. Activities that depend heavily on this concept are history, biology, depiction and mythology. In contrast, Form is to do with internal relations. The relations with such a formal work count for more than what it is like. This element of thinking is typified by the activities of design, music, games and mathematics.

 

These concepts can be seen as three sets of complementarities or polarities. These are the dimensions of the model. They can be called categories of meaning. These three categories are: definitional, that is to say one or many interpretations (analysis vs ambiguity); directional: irreversible or reversible (development vs space); and relational: internal or external (form vs resemblance).

 

The convention adopted here is that the development/space polarity is represented

vertically, the analysis/ambiguity polarity is represented from left to right, and the resemblance/form polarity is represented from front to back.

 

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This structure makes sense of a substantial body of ways of thinking. These are most accurately described by the concepts that characterise them (eg ‘thinking about development and ambiguity’) however each way of thinking is also typified by an identifiable approach to knowledge, an identifiable activity.

 

Thus thinking about development and ambiguity is typified by the production of literature. Similarly, thinking about form and analysis is typified by the production of mathematics, while thinking about form and development is typified by games.

 

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Style and creativity

The model also gives insight into the relationship between the style words classical, romantic, empirical and rational. Thus a rational approach unites form and analysis; a classical approach unites form and ambiguity; a romantic approach unites ambiguity and resemblance; an empirical approach unites resemblance and analysis.

 

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The model also sheds light on the relationship of the key creative activities upon which both arts and sciences depend, namely playing, narrating, depicting and designing. Play, narrate, depict, design. Our intellectual tool kit.This situates areas such as design, games, depiction and history in the central plane of the model, making them areas that relate strongly to thinking that underlies both science and art.

Screen Shot 2015-05-29 at 10.42.05

 

An ecology of art and science

What I think I am beginning to look at here is what one might call a cultural ecology or, to use a more current phrase, an ecological anthropology, of art and science. Just as Polya and Bateson gave me lines of approaching my initial questions, a way of approaching this notion of a wider ecology of thinking comes from Novalis: ‘What is nature? An encyclopaedic, systematic index or plan of our spirit.’ Thus: not mind interpreting nature, but mind and nature, to employ another of Bateson’s concise and effective expressions.[30]

 

 

 

 

Bibliography

Bateson, G., 1973, Steps to an Ecology of Mind, London: Paladin.

Bateson, G., 1979, Mind and Nature, London: Wildwood House.

Boardman, P., 1978, The Worlds of Patrick Geddes, London: Routledge and Kegan Paul.

Borges, J. L., 1972, trans. Reid, A., 1977, The Gold of the Tigers New York: Dutton.

D’Avoine Fitton Horne & Papa, competition entry for Bibliotheca Alexandrina, 1988-1989, in Patel, P., Taylor, A., & Hull, P., 1989, Bibliotheca Alexandrina: UNESCO: The British Entrants, London: RIBA.

Davie, G. E., 1961, The Democratic Intellect, Edinburgh: Edinburgh University Press.

Davie, G. E., 1986, The Crisis of the Democratic Intellect, Edinburgh: Polygon.

Dirac, P. A. M., 1963, ‘The Evolution of the Physicist’s Picture of Nature’

Scientific American, 208:45-53.

Dirac, P. A. M., 1979, ‘The test of time’ in The Unesco Courier, 75, June, pp.17-23. reprinted as ‘The Test of Einstein’ in Brown, S., Flauvel, J., and Finnegan, R., eds. 1981, Conceptions of Inquiry, London: Methuen, 88-93.

Gardner, P., 1963, Schopenhauer, Harmondsworth: Penguin

Guth, A. H. & Steinhardt, P. J., 1984, ‘The Inflationary Universe’ Scientific American, 250:98-102.

Hesse, H., 1943, trans. Winston, R. & C., 1970, The Glass Bead Game, London: Johnathan Cape.

Huxley, A., 1963, Literature and Science, New York: Harper & Row.

Kaufmann, W. J., 1977, Relativity and Cosmology, 2e, New York: Harper and Row.

MacDiarmid, H., 1966, The Company I’ve Kept, London: Hutchison.

Macdonald, M., 1985, ‘A Basis for Library Design’ Edinburgh Architecture Research, (Dept. of Architecture, Univ. of Edinburgh), 12, 1985, 104-113.

Macdonald, M., 1985, ‘A Model of the Relationships between Art and Science’, Edinburgh Review, 71, 1985, 81-90.

Macdonald M. J. S., 1986, Birth Order, Art and Science: A Study of Ways of Thinking, PhD thesis, University of Edinburgh.

Macdonald, M., 1987, ‘Types of Thinking’, Common Sense, 1, May 1987, 22-25.

Macdonald, M., 1989, ‘A Pattern of Thought’, Alba, Spring, 15-17.

Macdonald, M., 2000, ‘Patrick Geddes and Scottish Generalism’ in V. Welter & J. Lawson, eds., The City after Patrick Geddes, Berne: Peter Lang.

Macdonald, M., ed., 1993, Edinburgh Review, ‘Democracy and Curriculum’ Issue, No 90, 1993.

Macdonald, M., 2005, ‘Towards an Ecology of Art and Science’ in M. Macdonald and J. Leach Two Papers about Art and Science, Creativity and Practice Research Papers, Visual Research Centre, University Dundee, 2005, 2-10.

Moorcock, M., 1965, Stormbringer, London: Herbert Jenkins.

Polya, G., 1957, How To Solve It, 2e, Princeton: Princeton University Press.

Snow, C. P., 1956, ‘The Two Cultures’, The New Statesman and Nation, 6 October.

Snow, C. P., 1959, The Two Cultures and the Scientific Revolution, Rede Lecture, Cambridge: Cambridge University Press.

Tedlock, B. & Tedlock, D., 1985, ‘Text and Textile: Language and Technology in the Arts of the Quiché Maya’, J. of Anthropological Research, Vol. 41, No. 2, 121-146.

Waddington, C. H., 1969, Behind Appearance, Edinburgh: Edinburgh University Press.

Waddington, C.H., 1977, Tools for Thought, London: Cape.

Wittgenstein L, trans. Miles A. & C., 1979, Remarks on Frazer’s Golden Bough, Retford: Byrnmill.

 

 

 

Acknowledgments

Acknowledgment is due to all those involved in the AHRB-funded Learning is understanding in practice project based at the Universities of Dundee and Aberdeen (2003=2005). This paper looks again at my PhD work, so I also acknowledge my teachers at the University of Edinburgh, in particular the psychologists Halla Beloff and Tom Bower, and the philosopher George Davie. Particular thanks also to James Pattison, my colleague at Duncan of Jordanstone College of Art and Design, University of Dundee, for the digital versions of the images, made in 2010.

 

 

 

 

Updated 28/09/2011 (minor revisions, 13/04/2014)

 

 

 

 

 


Appendix:

 

A note from a visiting professor[31]

 

By John Douglas

 

I feel I must give some account here of my visit to the College of the Necessary Path (formerly known as the Chreodic College). Its four faculties are the traditional ones. The first, sited above the main campus in several field stations, is the Faculty of Mountain Gravity (which incorporates the schools of Epigenetic Landscape Studies and Ecological Physics). More centrally placed on the campus is the Faculty of Highland Space. Gunn-Sesshu contemplative methodologies are widely adopted here, although Stevensonian and even Humean views are also common. The dominant school is that of Waterfall Studies, but that is complemented by the School of the Carefully Placed Stone. Also based here is the Cloud Chamber project (Wilsonian). The third faculty occupies the well-resourced studio complex, which makes such a visual impact as one clears the last hairpin bend on the approach to the college. This is the Faculty of Hand and Eye, which incorporates the School of Ecology of Mind. Close by is the cafeteria in its marvellous limestone cavern. Many of you will remember the views of the archipelago from there. The final stop on my visit was the Faculty of Stairs and Labyrinths. Deep within this faculty lies the hexahedral library that defines the knowledge handling of the college by specifying the relationships between different styles. Within that library one can see how the School of Empiricism depends on its co-schools of Rationalism, Classicism and Romanticism. My visit concluded with a reception on the terrace above the sea, followed by a sound sleep in the tented village.

 

[1] The use of the word ‘ecology’ in this context is an allusion to Gregory Bateson. See, e.g., Bateson, G., 1972, Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution and Epistemology, San Francisco: Chandler.

[2] This work was developed from my PhD thesis (Murdo Macdonald, University of Edinburgh, 1986). See Murdo Macdonald: (i) A Basis for Library Design. Edinburgh Architecture Research. Vol. 12, 104-13 (1985); (ii) A Model of the Relationships between Art and Science. Edinburgh Review. Issue 71, 81-9 (1985); (iii) Birth Order, Art and Science: A Study of Ways of Thinking. PhD Thesis, University of Edinburgh (1986); (iv) Types of Thinking. Common Sense. No. 1, 22-5 (1987); (v) ‘A Pattern of Thought’, Alba, Spring 1989, 15-17.

[3] Learning is Understanding in Practice: exploring the relations between perception, creativity and skill. Funded over three years by the Arts and Humanities Research Board (AHRB), this was a joint venture of the School of Fine Art of Duncan of Jordanstone College of Art and Design (DJCAD), University of Dundee, and the Department of Anthropology, University of Aberdeen. The first part of this current paper is linked to a paper written as part of that project, ‘Towards an Ecology of Art and Science’ in M. Macdonald and J. Leach Two Papers about Art and Science, Creativity and Practice Research Papers, Visual Research Centre, University Dundee, 2005, 2-10.

[4] Further interchange of ideas (in both words and images) came from a then PhD student at DJCAD who started his work because of this project, Dr Paul Harrison, and from the project research assistant Suzanne Holland.

[5] 18 February 2004.

[6] Polya, G., 1957, How to Solve it: A New Aspect of Mathematical Method, Princeton: Princeton University Press; p.121.

[7] Bateson, G., 1979, Mind and Nature: A Necessary Unity, New York: Dutton; 8.

[8] From ‘Inventory’ by Jorge Luis Borges, in Borges, J. L., trans. Reid, A., 1977, The Gold of the Tigers, New York: Dutton.

[9] Waddington, C.H., 1969, Behind Appearance: A Study of the Relations Between Painting and the Natural Sciences in this Century, Edinburgh: Edinburgh University Press,1969; 243.

[10] Waddington, C. H., 1977, Tools for Thought, London: John Murray; 121.

[11] Wittgenstein, L., trans. Miles, A. C., 1979, Remarks on Frazer’s Golden Bough, Nottingham: Brynmill Press.

[12] Snow, C. P., 1956, ‘The Two Cultures’, New Statesman, 6 October 1956; see also Snow, C. P., 1959, The Two Cultures and the Scientific Revolution, The Rede Lecture, Cambridge: Cambridge University Press.

[13] Huxley, A., 1963, Literature and Science; New York: Harper and Row; 1.

[14] Although Davie’s view may be more considered than that of Snow, Snow was quick to praised Davie’s Democratic Intellect on its publication in 1961. Davie, G. E., 1961, The Democratic Intellect: Scotland and her Universities in the Nineteenth Century, Edinburgh: Edinburgh University Press. The Robbins Report on the universities was also influenced by Davie’s book.

[15] Quoted by Davie, G. E., 1986, The Crisis of the Democratic Intellect, Edinburgh: Polygon; 15.

[16] For further consideration of this point see Macdonald, ed., 1993, Edinburgh Review: Democracy and Curriculum, 1993.

[17] Macdonald, M., 2000, Patrick Geddes: Generalist’ in Welter, V., & Lawson, J., eds., The City after Patrick Geddes, Berne: Peter Lang.

[18] MacDiarmid, H., 1963, The Company I’ve Kept, London: Hutchison; 83.

[19] See, for example, the appendix to Boardman, P., 1978, The Worlds of Patrick Geddes, London: RKP.

[20] Guth, A. & Steinhardt, P., 1984, ‘The Inflationary Universe’, Scientific American, May 1984.

[21] Dirac, P., 1963, ‘The Evolution of the Physicist’s Picture of Nature’, Scientific American 208 (5); 47.

[22] Dirac, P. A. M., 1979, ‘The test of time’ in The Unesco Courier, 75, June, pp.17-23. reprinted as ‘The Test of Einstein’ in Brown, S., Flauvel, J. & Finnegan, R., eds. 1981, Conceptions of Inquiry, London: Methuen, 88-93; 92.

[23] Kaufmann, 1977, Relativity and Cosmology, 2nd edition, New York: Harper and Row.

[24] D’Avoine Fitton Horne & Papa, competition entry for Bibliotheca Alexandrina, 1988-1989. in P. Patel, A. Taylor & P. Hull, 1989. The model was also used as the basis of an architectural project by Julian Cowie. With respect to the Alexandria library, things have now come full circle, through my colleague on the Learning is Understanding in Practice project, Dr Wendy Gunn. Gunn’s doctoral thesis, ‘The social and environmental impact of incorporating computer aided design technologies into an architectural design process’ (University of Manchester, 2002) includes a detailed case study of how CAD technologies were incorporated into an architectural design and construction process: namely, the winning entry by the Norwegian practice Snohetta for the Alexandria Library Project in Egypt.

[25] Gardner. P., 1963, Schopenhauer, Harmondsworth: Penguin.

[26] Hesse, H., trans. Winston, 1970, The Glass Bead Game, Harmondsworth: Penguin;19.

[27] Moorcock, M., 1965, Stormbringer, London: Herbert Jenkins.

[28] Tedlock, B. & Tedlock, D., 1985, ‘Text and Textile: Language and Technology in the Arts of the Quiché Maya’, J. of Anthropological Research, Vol. 41, No. 2, 121-146.

[29] Why I started using this three dimensional structure I don’t know, however it may be related to the fact I had been thinking of art/science differences with respect to hemispheric specialization, and had just been using Bogen’s (1969) propositonal/appositional distinction to try and sort them out. It may be that my thinking of a three dimensional structure like the brain carried over into my thinking on art and science in general. I mention all this to try and avoid the usual practice of pretending that present work is the logically necessary outcome of all that has preceded it. The pattern of autobiography in this case seems more helpful than the pattern of logic.

[30] Bateson, G., 1979, Mind and Nature, New York: Dutton.

[31] Pseudonymous text piece: John Douglas (aka Murdo Macdonald) ‘A Note from a visiting professor’ for Clementine Deliss, ed., Metronome 11: What is to be Done? Tokyo, Paris: Metronome Press, 2007. Exhibited magazine, Documenta 12, Kassell.