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What are the scientific deductive systems that could be used in psychoanalysis? What form would a calculus take? Can it be found in Euclid? That is certainly what I suspect. That is to say that the problem would be associated with the three-kneed thing with equal legs; and this would provoke the search, as described by Poincaré, for the harmonizing fact to be selected. What then?
If this is correct, then one would suppose that the scene described by ‘blood everywhere’ might be formalized, say, as ‘the looking-glass murder’ – rather like a film being projected end first so that the scene of bloodshed would depict itself as one in which the ‘blood everywhere’ was being reabsorbed through the original route. Cubism might be a kind of attempt to geometrize a scene: in this way the looking-glass murder would need to be formalized – but how? Do Lewis Carroll's chess rules for Alice Through the Looking-Glass give a clue?
The clue is in the translation of an isosceles triangle as the three-kneed thing with equal legs (A. D. Ritchie, Studies in the History and Methods of the Sciences, p. 28) and then the astounding fact – and yet I expected it and was looking for it – of the popular names for the Euclidean propositions, and in particular for I.5 and I.47, the Pons Asinorum and the Theorem of the Bride (Heath, Euclid, vol. I, p. 415).
The question that arises at once is that which I have already formulated about Poincaré's statement of a need to find a fact that harmonizes as a method of coping with the intolerable paranoid-schizoid position (Poincaré, Science and Method, p. 30). Is the mathematical discovery reassuring by virtue of its being an external creative attempt that can be set against the internal stress of depressive or paranoidschizoid positions? Or is a formula produced which itself brings into being a calculus (and the s.d.s. it represents) that is of ‘importance in various branches of science’, including in particular the relationship of paranoid-schizoid to the d