Passage 16, from John Barrow, Pi in the Sky:
Suppose that instead of spending this chapter discussing the nature of mathematics we had picked upon music. We could then have debated whether musicians invented new tunes and rhythms or whether they discovered them in some world of universal musical entities. Indeed, the comparison is rather interesting because the Pythagoreans regarded music and mathematics as closely linked because of the mathematical relations between what are now called musical intervals.
The discovery of the simple numerical ratios linking the musical scale with the ‘harmonic’ progression of string lengths was probably one of the key motivations for the Pythagoreans to conclude that everything was imbued by number. The formalists and constructivists could lay down definite rules of harmony and composition, but there would always be musicians who wish to innovate and improvise and break the rules.
The real difference between the structures of mathematics and music is that, whereas there is no basic condition which tells whether or not something is music, irrespective of whether we happen to like the sound of it, there is such a criterion in mathematics. Inconsistency is sufficient to disqualify a prospective mathematical structure. It is this appeal to something that feels objective that is responsible for the suspicions that there is an aspect to be discovered, regardless of how much that element may subsequently be embroidered by human constructions. (p. 268)
okay and just for kicks:
QUESTION 16
Which of the following is the best statement of the point Barrow makes concerning music and mathematics in passage 16?
A) Mathematics is closely related to music. This fact was discovered first by the ancient Pythagoreans, who discovered the specific ratios linking the musical scale with the ‘harmonic’ progression of string lengths.
B) The question – invention or discovery? – that can be asked of mathematics can be
asked of music. And the cases may seem similar. Yet it is reasonable to regard
mathematics as a better candidate for discovery than musical tunes. For mathematics is governed by the need for consistency as music is not.
C) There are suspicions that there is an element of discovery in mathematics, regardless of how much that element may subsequently be embroidered by human musical
constructions.
D) One can lay down formal rules for musical composition, just as one can lay down formal rules for proof in mathematics. It does not follow that music is mathematics, as the Pythagoreans believed. For in order to get from music to mathematics, one must add the crucial element of consistency.
E) Mathematics feels objective, whereas music feels subjective. Yet mathematics and
music have much in common. The source of the difference in our feelings towards the
two must be due to the one difference between them: namely, the demand for
consistency in mathematics, which is absent from music.
the correct answer is hidden here -> B in white :D highlight it to get it!
and.. i hope you enjoyed this like i did. :D
jess
...making music for GOD!
