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Maths
and Music
An excellent way to kill a conversation is to say you are a
mathematician. Tell others you are also a musician, however, and they will be
hooked. Although there are obvious similarities between mathematical and
musical activity, there is no direct evidence for the kind of magical
connection many people seem to believe in.
I'm partly referring here to the "Mozart effect",
where children who have been played Mozart compositions are supposedly more
intelligent, including at maths, than other children. It is not hard to see why
such a theory would be popular: we would all like to become better at maths
without putting in any effort. But the conclusions of the experiment that
expressed the belief in the Mozart effect were much more modest. If you want
your brain to work better, you clearly have to put in hard work. As for
learning to play the piano, it also takes effort.
Surely a connection is quite reasonable. Both maths and
music deal with abstract structures, so if you become good at one, then it is
likely that you become good at something more general that helps you with the
other. If this is correct, it would show a connection between mathematical and
musical ability. It would be more like the connection between abilities at
football and tennis. To become better at one, you need to improve your fitness
and coordination (协调). That makes you better at sport and probably helps with
the other.
Abstract structures don't exist only in maths and music. If
you learn a language then you need to understand its abstract structures like
grammar. Yet we don't hear people asking about a connection between
mathematical and linguistic (语言的) ability. Maybe this is because
grammar feels mathematical, so it wouldn't be surprising that mathematicians
were better at learning grammar. Music, however, is strongly tied up with
feelings and can be enjoyed even by people who know little about it. As such,
it seems different from maths, so there wouldn't be any connection between the
two.
Let's see how we solve problems of the "A is to B as C
is to D" kind. These appear in intelligence tests but they are
also central to both music and maths. Consider the opening of Mozart's Eine Kleine Nachtmusik (小夜曲). The second phrase is a clear answer to the first. The
listener thinks: "The first phrase goes upward and uses the notes of a G
major chord (和弦); what would be the corresponding phrase that goes downward
and uses the notes of a D7?" Music is full of puzzles like this. If you
are good at them, expectations will constantly be set up in your mind. The best
moments surprise you by being unexpected, but we need the expectations in the
first place.