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The Fourier Transform (or Listening to Whales)

May 16, 2011

A Rushed, but Unapologetic Essay

Math is my great white whale. Elusive and dangerous, I can only ever view it from a distance, catching a rare glimpse every couple of months, when computation and process momentarily give way to theory. My search, normally fruitless, most often degrades into me trying to keep afloat. I focus on swimming – on continuing to move – but that is never enough.

I meant to start talking about the Fourier transform, the backbone (whales are vertebrate mammals, after all) of autotuning and x-ray crystallography. The gift of a French mathemagician, it keeps creeping back into my life, begging me to look at it.

I meant to tell you that I can look at and even possibly reproduce the formula that makes the transform possible. I could locate the necessary parameters, or at least a program to do it for me. My knowledge is functional, or very nearly could be. And isn’t that enough?

The existence of this essay suggests not. Not when the Fourier Transform can turn into time what was once frequency, or splinter into fragments what was once whole. Not when using it makes the scatter of light diffracted by a crystal become a 3-D model of electrons no one can see.  Knowing enough to compute is not knowing enough at all. At the surface there is nothing to hold on to – thrash around blindly and I will fall, building a mathematical bridge to nowhere.

Which brings me to what I guess is my driving idea. I have a functional knowledge of the math I know, but no more. I have learned to apply what I cannot necessarily grasp and this has led me astray.

I used to think that math was the only perfect thing humanity created, a miracle untouched by our inconsistencies and shortcomings. It let us escape the immediate irrationality of our world view for a land of symmetric abstraction, of clean answers, of definitiveness.

But as I have looked, and seen fractals in the placement of tree branches, or sigmoid curves in leaves, or phi in snail shells, I am no longer convinced. Math is not ours and it is not perfect. But it is a secret language that runs through our world, something we can transcribe and translate to reveal the hidden architecture connecting ourselves and our surroundings.

Faced with evidence of this language, I can only circle the few words I recognize, accepting a fragmented picture of what I want to know but cannot hold. I can reproduce the useful phrases – “Comment ça va?” “Oui, ça va bien, merci. Et vous?” – and get to some expected result, but one that is no longer what I want.

So yes, indict me for mixing my metaphors, but math is a language I do not speak and a whale I will never catch. But, the dictionary-wielding, wizened Ahab-type character I am will not stop reading, or learning, or searching. My ship might always be slightly off course but at least moving makes me feel better.

If you made it all the way to the end, congrats. As a reward, check out spectral music (a quick Google will suffice). The Fourier Transform rears its fascinating head again, with chillingly interesting results.

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2 Comments leave one →
  1. May 16, 2011 10:34 pm

    This is fabulous. I enjoyed it thoroughly.

  2. May 22, 2011 5:24 am

    Wonderfully written.

    Math, even in its most abstract and pure, often winds up less perfect than we initially suspect. Gödel’s incompleteness theorems are a good example.

    My favourite, though, is Euclid’s first postulate. I remember when I first saw it, I was utterly thrilled with its elegance and simplicity (link!). Countless mathematicians have clamoured on about how this proof isn’t “rigorous enough”. It’s true, Euclid does a little handwaving, but it’s so minor, compared to the delightful simplicity of the construction.

    Anyways, that was my nerd-gush for the evening. Thanks for this! I really enjoyed it.

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