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The Man who mistook his wife for a hat – Oliver Sacks

I believe the twins, who have extraordinary ‘feeling’ for numbers, without being able to calculate at all, are allied not to Buxton but to Toch in this matter. Except – and this we ordinary people find so difficult to imagine – except that they do not ‘convert’ numbers into music, but actually feel them, in themselves, as forms, as ‘tones’, like the multitudinous forms that compose nature itself.

They are not calculators, and their numeracy is ‘iconic’. They summon up, they dwell among, strange scenes of numbers; they wander freely in great landscapes of numbers; they create dramaturgically, a whole world made of numbers. They have, I believe a most singular imagination – and not least of its singularities is that it can imagine only numbers. They do not seem to operate with numbers, non iconically, like a calculator; they ‘see’ them, directly as a vast natural scene…

The twins hear the world symphony, I conjecture, but hear it entirely in the form of numbers.

The twins, I believe, have not just a strange faculty – but a sensibility, a harmonic sensibility, perhaps allied to that of music.

One might speak of it, very naturally, as a Pythagorean sensibility – and what is odd is not its existence, but that it is apparently so rare. Perhaps the need to find or feel some ultimate harmony or order is a universal of the mind, whatever its powers and whatever form it takes. Mathematics has always been called the ‘queen of sciences’ and mathematicians have always felt number as the great mystery, and the world as organised, mysteriously by the power of number…

They do not approach numbers lightly, as most calculators do. They are not interested in, have no capacity for, cannot comprehend calculations. They are, rather, serene contemplators of numbers – and approach numbers with a sense of reverence and awe. Numbers for them are holy, fraught with significance.

This is their way of apprehending the First Composer.