Showing posts with label greeks. Show all posts
Showing posts with label greeks. Show all posts

Wednesday, 16 April 2008

Quote Of The Day (16/04/08)

'The early Greeks were uncertain as to whether 2 was a number at all, observing that it has, as it were, a beginning and an end but no middle. More mathematically, they pointed out that 2 + 2 = 2 x 2, or indeed that any number multiplied by 2 is equal to the same number added to itself. Since they expected multiplication to do more than mere addition, they considered 2 an exceptional case. Whether 2 qualified as a proper number or not, it was considered to be female, as were all even numbers, in contrast to odd numbers, which were male.

Division into 2 parts. dichotomy, is more significant psychologically and more frequent in practice than any other classification. The commonest symmetry is bilateral, 2 sided about a single axis, and is of order 2. Our bodies are bilaterally symmetrical, and we naturally distinguish right from left, up from down, in front from behind. Night is separated from day, there are 2 sexes, the seasons are expressed in pairs of pairs, summer and winter separated by spring and autumn, and comparisons are most commonly dichotomous, such as stronger or weaker than, better or worse than, youth versus age and so on'.




David Wells; The Penguin Dictionary of Curious and Interesting Numbers (revised edition)

Tuesday, 25 March 2008

Quote Of The Day (25/03/08)



'Perhaps mistakenly, the ancient Greeks attributed to the association of music and numbers a predominant place in the philosophy of of the cosmos. Perhaps equally mistakenly, some composers of the Forties and Fifties tried to build music entirely by numbers. But regardless of the rights and wrongs of such beliefs, there are incontrovertible mathematical facts which must be outlined, however briefly.

Other numerical data less closely associated with musical reality, but forming a basis for modern composition, are also worth a mention, even though they only demonstrate man`s subconcious awareness that there is beauty in numbers, and that they in turn can make beauty of out chaos.'

Introduction to chapter 6; 'Numbers' of The New Music: The Avant Garde since 1945 by Reginald Smith Brindle.