Margaret Koehler, Poetry
of Attention in the Eighteenth Century
...Compare Newton, Leibniz, and Cardan: “When we read about the behaviour of Newton we notice some features that unmistakenly point to something like schizophrenia ― a kind of "perpetual distraction" where he seemed lost to the world at large for hours, sitting in his bed the whole day forgetting to dress and to eat. He himself tells us that he solved the problem by fixing in his mind until a little crack of light broke through and until the whole problem was seen in full light ... In the case of Cardan we find the same schizophrenic symptoms, accompanied by communications with demons and spirits telling him the secrets into which he desired to penetrate. At all the points of transition in the evolution of mathematics I believe that we should find such symptoms ... Leibniz ... In the Nouveaux Essais ... discussing the actual experience of innate ideas ... says that "other modem philosophers have given them beautiful names, especially Julius Scaliger who has called them Seminae Aeternitatis and also Zopyra, sparks, as if he intended to say (Leibniz's interpretation): living fire, lightning traces, hidden within us but which, on meeting the senses appear as the sparks of shooting guns..." (Jurij Moskvitin, op. cit., p.191. On the origin of the Calculus see pages 188-191). Compare Platonic 'forms' or 'Ideas' and the daemons (See...). We have also mentioned Georg Cantor's guiding Voice or mathematical-mystical Muse (Page...). "Discoveries of any great moment in mathematics and other disciplines, once they are discovered, are seen to be extremely simple and obvious, and make everybody, including their discoverer, appear foolish for not having discovered them before. It is all too often forgotten that the ancient symbol for the prenascence of the world is a fool, and that foolishness, being a divine state, is not a condition to be either proud or ashamed of ... To arrive at the simplest truth, as Newton knew and practiced, requires years as of contemplation. Not activity. Not reasoning. Not calculating. Not busy behaviour of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are being continually thrust upon them .. In these circumstances, the discoveries that any person is able to undertake represent the places where, in the face of induced psychosis, he has, by his own faltering and unaided efforts, returned to sanity. Painfully, and even dangerously, maybe. But nonetheless returned, however furtively" (G. Spencer Brown, Laws of Form, London: George Allen and Unwin Ltd., 1969, pp.109-110.
As Jurij Moskvitin describes it, "The principle of the calculus is a synthesis of several of the other fundamental discoveries... The fundamental concept of the limiting position of a tangent is only geometrical, and in the translation of the "limit" concept into terms of logic where the lower dimensions are discarded we have a clear example of what I have called intrusion into the logical space of R-o [...a certain ground-level, coinciding with, or having a frontier common with, the space described by the axioms of Aristotelian logic...]. What made the calculus so difficult to understand for the contemporaries of Leibnitz and Newton, and what still makes it difficult for some children capable of thought and preferring to think instead of imitating, is the violation of all the fundamental algebraical rules which they have just bothered to pick up... The logic is visual and not deductive. After the discovery had been introduced, the next centuries were busy systematizing it and finding and defining all its fields of application... All these examples represent the general development from a vision to an ever more formalized form, and in most of the cases the steps may be followed minutely... When such an intrusion has taken place the various devices may be treated in terms of mechanical and causal logic. Thoughts which would otherwise have been inaccessible to the average mind now become the property of this mind... Also for various reasons it is the final form of the discoveries that remains and which is accessible to the average mind, which of course obscures the source... In the case of Leibniz we know from his own texts how often he describes the solution of long theological arguments – for instance the transcendent problem of the existence of God – as an infinite line or an infinite series of causes, the solution being the angle of the line on infinity – the series differentiated. Again we find that the solution of the problem is the visualization of the whole thought-sequence. Leibniz's Monadology is built on the idea that thoughts become clearer according to the degree and the intensity of the introspective process" (Jurij Moskvitin , Essay on the Origin of Thought , Ohio University Press, 1974, pp.188-191, ).