Some of my favourite passages
Mathematical analysis and computer modelling are
revealing to us that the shapes and processes we
encounter in nature - the way that plants grow, the way
that mountains erode or rivers flow, the way that
snowflakes or islands achieve their shapes, the way that
light plays on a surface, the way the milk folds and
spins into your coffee as you stir it, the way that
laughter sweeps through a crowd of people - all these
things in their seemingly magical complexity can be
described by the interaction of mathematical processes
that are, if anything, even more magical in their
Dirk Gently's Holistic Detective Agency
Shapes that we think of as random are in fact the
products of complex shifting webs of numbers obeying
simple rules. The very word "natural" that we have
often taken to mean "unstructured", in fact describes
shapes and processes that appear so unfathomably
complex that we cannot consciously perceive the simple
natural laws at work.
They can all be described by numbers.
We know, however, that the mind is capable of
understanding these matters in all their complexity and
in all their simplicity. A ball flying through the air is
responding to the force and direction with which it was
thrown, the action of gravity, the friction of the air
which it must expend its energy on overcoming, the
turbulence of the air around its surface, and the rate and
direction of the ball's spin.
And yet, someone who might have difficulty
consciously trying to work out what 3 x 4 x 5 comes to
would have no trouble in doing differential calculus and
a whole host of related calculations so astoundingly fast
that they can actually catch a flying ball.
People who call this "instinct" are merely giving the
phenomenon a name, not explaining anything.
I think that the closest that human beings come to
expressing our understanding of these natural
complexities is in music. It is the most abstract of the
arts - it has no meaning or purpose other than to be
Every single aspect of a piece of music can be
represented by numbers. From the organisation of
movements in a whole symphony, down through the
patterns of pitch and rhythm that make up the melodies
and harmonies, the dynamics that shape the
performance, all the way down to the timbres of the
notes themselves, their harmonics, the way they change
over time, in short, all the elements of a noise that
distinguish between the sound of one person piping on
a piccolo and another one thumping a drum - all of
these things can be expressed by patterns and
hierarchies of numbers.
And in my experience the more internal relationships
there are between the patterns of numbers at different
levels of the hierarchy, however complex and subtle
those relationships may be, the more satisfying and,
well, whole, the music will seem to be.
In fact the more subtle and complex those
relationships, and the further they are beyond the grasp
of the conscious mind, the more the instinctive part of
your mind - by which I mean that part of your mind that
can do differential calculus so astoundingly fast that it
will put your hand in the right place to catch a flying
- the more that part of your brain revels in it.
Music of any complexity (and even "Three Blind
Mice" is complex in its way by the time someone has
actually performed it on an instrument with its own
individual timbre and articulation) passes beyond your
conscious mind into the arms of your own private
mathematical genius who dwells in your unconscious
responding to all the inner complexities and
relationships and proportions that we think we know
Some people object to such a view of music, saying
that if you reduce music to mathematics, where does the
emotion come into it? I would say that it's never been
out of it.
The things by which our emotions can be moved - the
shape of a flower or a Grecian urn, the way a baby
grows, the way the wind brushes across your face, the
way clouds move, their shapes, the way light dances on
the water, or daffodils flutter in the breeze, the way in
which the person you love moves their head, the way
their hair follows that movement, the curve described by
the dying fall of the last chord of a piece of music - all
these things can be described by the complex flow of
That's not a reduction of it, that's the beauty of it.
Ask the poet (Keats) who said that what the
imagination seizes as beauty must be truth.
He might also have said that what the hand seizes as a
ball must be truth, but he didn't, because he was a poet
and preferred loafing about under trees with a bottle of
laudanum and a notebook to playing cricket, but it
would have been equally true.
Because that is at the heart of the relationship between
on the one hand our "instinctive" understanding of
shape, form, movement, light, and on the other hand
our emotional responses to them.
And that is why I believe that there must be a form
of music inherent in nature, in natural objects, in the
patterns of natural processes. A music that would be as
deeply satisfying as any naturally occuring beauty
and our own deepest emotions are, after all, a form of
naturally occuring beauty...
The Belgian thought for a while. `For this kind of job, with all the work it entails, for the facilities available here and my own specialized knowledge, I must ask a fee of one thousand English pounds. I concede that it is above the rate for a simple rifle. It must be a work of art. I believe I am the only man in Europe capable of doing justice, of making a perfect job of it. Like yourself, monsieur, I am in my field the best. For the best one pays. Then on top there would be the purchasing price of the weapon, bullets, telescope and raw materials ... say, the equivalent of another two hundered pounds.'
`Done', replied the Englishman without argument. He reached into his breast pocket again and extracted a bundle of five-pound notes. They were bound in lots of twenty. He counted out five wads of twenty notes each.
`I would suggest', he went on evenly, `that in order to establish my bona fides I make you a down payment as an advance and to cover costs of five hundred pounds. I shall bring the remaining seven hundred pounds on my return in eleven days. Is that agreeable to you?'
`Monsieur', said the Belgian skilfully pocketing the notes, `it is a pleasure to do business both with a professional and a gentleman'.
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