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I know of no source in which Coomaraswamy engages with the details of Gleizes's thought but there are several letters in which he recommends his books - notably Vie et mort and La Forme et l'histoire - to his correspondents, and they appear in the footnotes and bibliographies of several of his essays. [13] He tried to arrange reviews of Gleizes's books in the New York based Art Bulletin. [14] At one point he was proposing to send his teenage son Rama to stay with Gleizes as well as with Walter Shewring and Eric Gill at Ditchling but in the event Rama went travelling in the Himalayas with the principle Buddhist member of the 'traditionalist' circle, Marco Pallis. [15]

[13]  Letters to Dr James Marshall Plumer, 36/1/1937 (Singam 1976); Miss Ad'e Bethune, 22/11/1939 (Singam 1972); Robin Field, April 1945 (Singam 1975). Footnotes in The Philosophy of Mediaeval and Oriental Art, Lipsey 1977, vol i, p.53; Le Symbolisme de l'épée, English translation in Lipsey 1977, vol i. p.438. For a more detailed account see the bibliography. See also Symbols and The Interpretation of Symbols, not published in Coomaraswamy's lifetime but available in Coomaraswamy (ed) 2004 and widely available on the internet.

[14] Coomaraswamy to Gleizes 20/12/1936 includes a letter from A.Philip McMahon, Chairman of the Dept of Fine Arts, New York University saying he knows Gleizes's books and hopes to publish an article for the Art Bulletin. The only article I have seen in the Art Bulletin is Shapley 1937.

[15] Coomaraswamy to Walter Shewring, 19/3/1946 in Singam 1974.

Perhaps the most interesting of Coomaraswamy's references to Gleizes comes in his essay Philosophy of Mediaeval and Oriental Art, published in Mircea Eliade's shortlived journal Zalmoxis in 1938. Giving La Forme et l'histoire as his reference he says: 'We hail the shift from form to figure that marked the "Renaissance" out of which our own materialism and sentimentality are only the inevitable and more complete development ... ' [16]

[16] Lipsey 1977, vol i, p.53

The distinction between 'form' and 'figure' is central to Gleizes's thought - it can be seen quite clearly in the way he uses the words in Active Tradition. For Gleizes, the 'figure' is a geometrical expression, entirely static and spatial, while the 'form' is ultimately sensed in the whole rhythmic movement of the work. 'Form' is a word to be used in the singular - there is only one Form, it is universal and is best expressed by the circle. The variety of our works of art is only possible because the absolute circular Form is unattainable - happily, he says, for the artist! [17] Gleizes does not pose a choice between form and figure as two mutually incompatible entities. The figure has its proper place in the work of art but it is, so to speak, the lowest place. The painting, the painter and the person contemplating the work rise from the figure (the appearance of the Buddha, of Christ or whatever) through the spiralling cadence to the overall circular completeness of the Form, 'the truth of the rhythm, form-light, perfectly incorporeal yet nonetheless complete ...' [18] 

[17] Gleizes 1998, p. 85
[18] Gleizes 1937, p. 180

But we may wonder if Coomaraswamy and Gleizes understood these terms in quite the same way. Coomaraswamy understood 'form' in a Platonic sense as the artist's apprehension of a divine idea. The 'figure' on the other hand is the external, one might say 'photographic', appearance of an object we encounter in the world about us. In this understanding most of the 'forms' admired by Coomaraswamy may be only figures. The artist's apprehension of the divine idea may not be a copy of the external appearances in nature but it is still 'figurative', the appearance of the Buddha, Christ or whatever remains its most important feature.

The passage in Philosophy of Mediaeval and Oriental Art continues:

'We do not realise that the ideas which he ["primitive man" - PB] expressed with such austere precision by means of his spirals, for example ... are only meaningless to us because we no longer understand them.'  

I do not know Coomaraswamy's earlier writings sufficiently well to be able to say with certainty that he never before evoked 'spirals' in quite this way before but a central argument of La Forme et l'histoire is that the spirals and concentric curved lines which characterise the drapery in early mediaeval and much oriental statuary have the same role - of propelling the viewer into a state of contemplation in time and movement - as the similar spirals and concentric curved lines to be found on the megaliths of Ireland and Brittany - again the argument can be found in Active Tradition. Coomaraswamy also evokes the spiral in his essay The Christian and oriental, or true, philosophy of art: 'The artist's spirals are the forms of life, and not only of this or that life; the form of the crozier was not suggested by that of a fern frond. The superficial resemblances of art to "nature" are accidental; and when they are deliberately sought, the art is already in its anecdotage.' [19]

[19] Coomaraswamy 1956, pp.34-5.

The punning word 'anecdotage' is notable in this context. 'Anecdote' is the word Gleizes uses, nearly always dismissively, to refer to the subject matter of the work of art, the story it tells. I feel pretty confident that Coomaraswamy in this passage has Gleizes's use of the word in mind but again I am not sure that the two men understood it in quite the same way. The 'story' behind the painting is precisely what interested Coomaraswamy and Guénon. Gleizes, Guénon and Coomaraswamy were all agreed that it was only as religious, and from within a religious mind-frame, that religious art could be understood. But for the writers of Études Traditionnelles, religion was to be understood first and foremost as doctrine. For Gleizes the religious meaning or inner life of the painting was essentially non-representational. It was through the organisation of planes, lines, colours, not through the iconography, that the painting became a 'support for contemplation'.