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Letter to Arthur Miller


Dear Professor Miller

I liked your Einstein/Picasso book very much. It touches on many questions I think are very important but what I liked particularly is that you take the artists seriously in this domain. Much of the existing literature (even the great work of Linda Henderson) tends to assume that the artists couldn't understand any of it so their references to terms taken from physics was just a piece of fashionable pretentiousness. Princet has been dismissed (Kahnweiler has a lot to answer for in this respect) as what the French would call a 'farfelu'. Even Poincaré is sometimes treated as a mere 'vulgarisateur' on the grounds apparently that he was widely read. I'm hoping to be able to follow up Einstein/Picasso by looking at what you've done on Poincaré. Part of the problem is that most of what's been written so far has of course been done by people like myself, on the artistic/cultural side, who have an inferiority complex with regard to physics. Your background in physics gives you a bit of an edge.

I want while its still fresh in my mind to jot down some of the thoughts your book has prompted, and I hope you'll excuse me doing it in the form of a letter to you. Also if I put the emphasis on points of disagreement, or at least question marks. That's just because, alas! in the way of things its easier to write about contentious matters than non-contentious matters.

Beginning with Ernst Mach. I was surprised at your characterising Mach as a 'positivist'. I first came across him in Lenin's Materialism and Empirio-Criticism, which attacks him for 'Idealism', which I understand to be the view that we cannot know 'nature' as something external to ourselves; we can only know our sensations. Positivism I take to be the view that our sensations can be trusted. It is an act of faith that the real world corresponds to our experience of it. Materialism I take to mean the view that the consciousness that observes this external world is itself an epiphenomenon of the world it is observing. It has evolved on the basis of unconscious matter.

Lenin's book was written in opposition to a little group in the Bolshevik movement centred on Alexander Bogdanov and Anatoly Lunacharsky. Lunacharsky was later to be Lenin's commissar for education and culture and played an important role in supporting the Constructivist and Suprematist artists. This group - nicknamed the 'God-builders' - greatly admired Mach. At the same time that Lenin was attacking them they were also being attacked, from outside the Bolshevik circle, by the doyen of Russian Marxist philosophers, Grigory Plekhanov. In the course of this polemic, Plekhanov published a book called Art and Social Life, a sort of manifesto for what was later to become Socialist Realism which includes a polemic against the Du "Cubisme" of Gleizes and Metzinger.

Forgive me if you know all this.

The essence of Mach's argument as I understand it is that 'nature' as such is fundamentally incomprehensible and it is only very approximately that any of its operations can be reduced to predictable mathematical formulae. In nature there is only the particular event which is shaped by a quantity of variable factors so great as to be immeasurable (I can't remember what he has to say about the Sun coming up every morning ...)

What the scientist does is to 'abstract' from nature certain operations and reproduce them under conditions that are essentially artificial. In these circumstances they 'work' - ie produce predictable results. But we are no longer talking about nature. We are now talking about 'mechanics'. Nature in Mach's scheme (and this was the idea that was picked up by Bogdanov, for example in his Utopian novel about life on Mars, The Red Star) is 'uneconomical'. The general tendency of human history is away from nature and towards the 'economy' of 'mechanics'. And this is a process of 'abstraction'.

This notion is, I think, very different from that of Einstein as you describe it; but the difference isn't that Mach is more 'positivist' than Einstein. It is rather that Einstein thought that in abstracting simple principles out of nature, he was coming to a closer understanding of nature; where Mach would say he was moving away from nature and towards mechanics. To put it crudely, e = mc2 is useless as a device for understanding any of the real operations of nature; but very useful as a device for building an atomic bomb. Or, perhaps better: pretending that time is a fourth dimension of space helps us to solve certain problems that arise when we try to develop a mathematical account of events in time. But this does not at all mean that time IS a fourth dimension of space.

This idea of abstracting from the essential chaos of nature those characteristics that are useful and desirable is one of the fundamental driving ideas of the early history of twentieth century art, and many of the artists concerned (especially in Holland, Germany and the Russian Empire/USSR) were perfectly conscious of the relation with Mach. Both the Constructivists and Suprematists would have subscribed to Mach's notion of 'economy' ­ the terminology is used by Malevich - and abstraction from nature. The difference between them was that the Constructivists were subjecting art to non-'artistic', functional ends; while the Suprematists continued to believe in art as having its own disinterested value, but still in the overall context of a human victory over nature (hence their name).

I tried to tease all that out in a little pamphlet I wrote some time ago comparing Gleizes (who, in the end, refused this rejection of 'nature', but was very conscious of it) and Malevich (who embraced it wholeheartedly but who - necessarily - understood the drive towards economy/mechanics as itself an evolution of nature - since the human mind is of course itself a part of nature).

When Plekhanov attacks Gleizes and Metzinger, he sees them as 'Idealists' (as Lenin saw Bogdanov, Lunacharsky and, behind them, Mach), basically because they start off from the Berkeley-Kant-Schopenhauer, anti-positivist assumption that it is only as sensation, as a phenomenon of consciousness, that the world can be known. Consequently, a painter painting a landscape is engaging in what might be called a 'psychological' event - an event in the realm of consciousness - rather than recording the 'truth' of an event that is external to himself. The same feeling of distrust with regard to the act of recording the happenings of the external world informs Poincaré's notion of 'conventions'. You say (p.169) that whereas Poincaré maintains that all the conventions are of equal value, Gleizes and Metzinger state 'dogmatically' that there is one which is superior - 'our own'; but I don't see a contradiction here. Clearly when we act in relation to nature we choose the convention that suits us. It becomes, temporarily at least, superior (much later, Gleizes was to write on the subject of preferring one manner of painting to another: 'il faut être injuste pour agir').

My understanding of the theories of relativity is that they are an attempt to reconcile the conflicts that arise between different ways of accounting for certain measurable aspects of the world which we assume to be external to ourselves. As you say in your interesting fn 79 to ch 8: 'the name "relativity theory" is a misnomer because on a deeper level it reveals how the laws of nature remain the same in all reference points'. I accept Mach's view that it is only a very minimal aspect of the external world that can be accounted for in this manner ­ one that actually excludes everything that comes under the title 'aesthetic', which in its proper meaning (as in the word 'anaesthetic') refers to sensations ­ colour, sound, quality of touch etc. None of this exists for Einstein as physicist, whatever about Einstein the musician. His sense of beauty (the love of simplicity ­ Mach's 'economy' in fact) is entirely unaesthetic, ie separate from the work of the senses. And consequently, I would suggest, unsatisfying for the human sensibility in its completeness in which, of course, the senses are included.

The problem is very real and practical since the conversion of the natural world (in which the senses are stimulated and delighted constantly) into the mechanical world is leaving the senses starved and frustrated. It is a problem for artists since that is their domain; but at the moment I think they are dealing with it very badly largely because they too have followed the general tendency away from the aesthetic to the conceptual, from the 'natural' to the mechanical (the tendency is typified by Marcel Duchamp).

There is certainly a parallel to be drawn between Einstein's attempt to reconcile the different viewpoints from which mathematical calculations can be made ('all reference points') and the multiple perspective of the Cubists, attempting to establish what Metzinger called (in 1910) a 'total image'. In both cases, however, I think it can be said that what was achieved was not the longed for reconciliation of the conventions but simply the addition of another convention - very shortlived in the case of the artists (though Gleizes much later remarked to his friend Walter Firpo that the painters had been in too much of a hurry to abandon multiple perspective. There was still a lot that could have been done with it - and in fact Firpo himself continued to practice it to some extent).

This incidentally (just another convention) is how it, or rather the business of walking round a model to see it from different angles, is treated in Du "Cubisme". You take this as the central idea in Du "Cubisme" (p.258) but, although it is certainly one of the central ideas in Metzinger's 1910 Note sur la Peinture, in Du "Cubisme" its just treated as another convention which has shocked the public but which the public will eventually come to accept as they came to accept the 'atomist' presentation of the world as a multitude of dots of primary colour. I would say the basic idea in Du "Cubisme" is that just as each colour is modified by the relations of the colours around it (the basic idea of Neo-Impressionist colour theory) so each form is modified by the forms that surround it. It is a development of, and reply to, Signac's D'Eugène Delacroix au néo-impressionisme, extending the argument to deal with questions of form.

Its not entirely true to say the book doesn't mention Picasso and Braque. No painters are mentioned by name in the theoretical discussion but Picasso and Braque appear in the illustrations and their pioneering role is affirmed in the fact that they appear first.

You quote Lhote in 1935 describing Princet arguing against the perspective trapezoid in favour of the 'real' rectangle of the table surface. You may be interested to know that almost exactly the same description of the intentions of the Cubists is to be found in Severini's Du Cubisme au Classicisme (1921. He doesn't mention Princet. I've published an English translation of it as second in the series that began with Gleizes' Art and Religion). There is also a letter from Lhote to Gleizes, obviously in preparation for Huyghe's essay, asking him to confirm that he had heard Princet using this argument. Unfortunately I haven't Gleizes' reply, but he gives his own variation on it in an essay written in 1928, Peinture et Perspective Descriptive (which I've translated but not yet published) and in Art et Science in 1932 (p.79). Here he shows Cézanne preferring the full circle of the bowl to the perspective ellipse not because it is a more accurate representation (pace Lhote, Severini, Princet) but because it is more beautiful; it corresponds to the nature of our senses; we want to look at a circle not an ellipse. And this is clearly manifested in the art of so-called 'primitive' peoples who were not prone to the illusion that the aim of art is the futile effort to copy the appearances of the external world.

I think we may question whether Princet really was arguing for this (the rectangle not the trapezoid) as a more 'accurate' way of depicting the world. Or at least question if he really was arguing for a more 'conceptual' art, in opposition to the senses, in line with what you present, rightly I think, as Einstein's anti-positivist approach (what you see isn't what you get).

It is very frustrating, I'm sure you'll agree, to be told all the time that Picasso, Braque and their circle were having these wonderful high powered intellectual discussions and then to find that so little of it has come down to us in writing. Both Picasso and Braque prefer to express themselves in sibylline aphorisms; Salmon is quite useless; Apollinaire is interesting but his best thinking comes in relation to Delaunay not Picasso; Jacob is in my estimation one of the loveliest men who ever lived and I suspect one might find more philosophy in him than one thinks but I haven't yet tried; Princet published practically nothing. Except, as you say, the preface to an exhibition by Delaunay in 1912. Which has been reproduced in the big Centre Pompidou exhibition catalogue of 1999 (p.242). I think its very good and leaves us regretting that he didn't write more (what happened to him? He has this long life, makes pots of money, but doesn't even seem to feature as an important collector). He says:

'Our sensations are born in spite of us; it is neither the surrounding world (milieu) nor the climate that develop them; they are almost the consequences of our personality. It is a vain effort to try to provoke them artificially. We must arrange them systematically in our mind, free them from the fog which surrounds them to reveal them in their clear logic, to those who come to admire them.'

The emphasis here is on the 'clear logic' of 'sensations', and these sensations are not just an automatic reaction to the external world. Which is to say that two people looking at a cow in a field will experience it very differently. Both will be able to state that it is a cow in a field, but the 'sensation' will be utterly different and these sensations are facts, as objectively real as the facts of the cow's measurements, of its atomic structure, or of its capacity to produce milk.

I would suggest that this emphasis on 'sensations' puts Princet into the line of the man whom I regard as the key figure in the physics/art dialogue, especially in France ­ Charles Henry, friend of Seurat (and incidentally of Félix Fénéon who you say came to see the Demoiselles with Matisse and laughed at them. I hope he didn't) in the 1880s and of Gleizes in the 1920s - though I can't get a grasp on what he was doing in the actual 'Cubist epoch'. I can't believe he didn't find it interesting.

But this opens up what is for me a very big field (I discuss Henry in the introductions both to Art and Religion and From Cubism to Classicism and in my Yale book on Gleizes. I have a notion of trying to publish a translation of his writings. Which are voluminous, but heavy going especially for a non mathematician). Very briefly, since this letter's obviously getting out of hand, he was the French representative of the German school of 'psycho-physics' associated with the name of Gustav Fechner. For the psycho-physicists, especially Henry, mathematics and geometry were important not because they describe external reality (the 'real' circle of the opening of the fruitbowl) but because they correspond to the structure of the mind (the circle that we find, in and of itself, pleasing); and they 'work' in physics because the physical world can only be known as sensation and consequently can only be known insofar as it too corresponds to the (mathematical) structure of the mind. And this at whatever scale of magnitudes, including the infinitely large or infinitely small, we choose to study it.

Through the Henry-Seurat-Fénéon connection ­ and also through the Sérusier-Peter Lenz connection, which I'm working on at the present time ­ the idea is well established among the French painters that painting can be expressed mathematically, both in terms of colour and of form; and this mathematical expression gives it an objective truth which is independent of and perhaps more compelling than, the objective truth of the thing represented.

But this immediately poses two problems. Given that the Neo-Impressionists may be thought to have succeeded in establishing an objective scientific basis in the domain of colour, what about the domain of form? And given that it works quite well for massively still, hieratic subjects, what about dynamic subjects? Seurat attempted to address both problems in his late works (circus, dancers) and William Innes Homer has shown that they are structured following the proportions and angles proposed by Henry.

All the leading Cubist painters, with the exception of Picasso (and, as it happens, Gleizes. And Gris, but he was a late comer) came from Neo-Impressionism; and the Futurists too started with Neo-Impressionism, believing it to be a discovery of scientific, objective validity. It is partly this conviction that a scientific basis had been established for painting that then leaves the painters vulnerable to the critique of scientific objectivity that was being made in their different ways by Mach and Poincaré. And it was the desire to take account of movement in painting that then poses the question if it could be done,as the mathematicians were proposing, by treating time as a fourth dimension. All these questions are continuous from the nineteenth century and I believe they would have been posed even without the contribution of Picasso, which comes from outside the line (the Blue and Pink periods are in a completely different intellectual realm), though he may well have had a necessary catalyzing effect.

I just want to finish with a last word which is not developed as it should be. I was interested to learn that Nils Bohr had Metzinger's Femme à Cheval. You say this is 'the earliest direct interaction of the new art with the new physics.' It might be more justifiable to say that its the first manifestation of interest in the new art on the part of a leading representative of the new physics, but (leaving Princet and Henry out of consideration for the moment) I would suggest that the first direct interaction comes in the conversations Gleizes had with Langevin about 1920. Unfortunately I haven't a clear impression of what Langevin thought about it all. I'd also like to indicate that in 1922, Gleizes adopted the terms 'translation' and 'rotation' to describe the two operations, one in space the other in time, involved in the manner of painting he had developed on the basis of what had been achieved during the war by Gris and Metzinger (going well beyond multiple perspective. And the importance of the Gris-Metzinger relationship is one of the most closely guarded secrets of the history of twentieth century painting). These terms are of course hardly unprecedented. They appear in Aristotle and in an essay (very interesting from your point of view) Severini wrote in 1917. But I still think it may be significant that they are used by Henry in an essay he published in 1922 on Les travaux français sur les problèmes de la théorie de la relativité, in a discussion of the Michelson-Morley experiment ...

Best wishes and thanks for a stimulating read