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John Venn

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We endeavour to employ only symmetrical figures, such as should not only be an aid to reasoning, through the sense of sight, but should also be to some extent elegant in themselves.
--
Symbolic Logic (1881)

 
John Venn

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Do you think it interests me that this painting represents two figures? These two figures existed, they exist no more. The sight of them gave me an initial emotion, little by little their real presence grew indistinct they became a fiction for me, then they disappeared, or rather, were turned into problems of all kinds. For me they are no longer two figures but shapes and colours, donít misunderstand me, shapes and colours, though, that sum up the idea of the two figures and preserve the vibration of their existence.

 
Pablo Picasso
 

Elegance is necessarily unnatural, only achieveable at great expense. If you just do something, it won't be elegant, but if you do it and then see what might be more elegant, and do it again, you might, after an unknown number of iterations, get something that is very elegant.

 
Erik Naggum
 

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

 
Alan Turing
 

This gift... which God gave us in order to enable us to perfect ourselves, to learn and to teach, must not be employed in doing that which is for us most degrading and perfectly disgraceful... Those who employ the faculty of thinking and speaking in the service of that sense which is no honour to us, who think more than necessary of drink and love, or even sing of these things; they employ and use the divine gift in acts of rebellion against the Giver, and in transgression of his commandments.

 
Maimonides
 

This intersecting of inherently non-symmetrical diatonic elements with inherently non-diatonic symmetrical elements seems to me the defining principle of the musical language of Le Sacre and the source of the unparalleled tension and conflicted energy of the work.

 
George Perle
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