The Standing Invitation

Archive for October 9th, 2011

Quieten Down

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I dislike noise. When I go to a pub I go there to listen to people, and there is nothing I hate more in a night out than not being able to hear what they are saying.

When you listen to someone speak, you are trying to detect with your ears the audible signals they produce with their mouths; noise is everything you hear that is not a signal. How well you can hear a person depends on how clearly their words stand out against the background: the signal-to-noise ratio.

Signal-to-noise ratios appear everywhere in science where a precise measurement must be taken. In order to understand measurement ­– in order to comment on what it is we can ever hope to know about the world – we have to have a working knowledge of the properties of noise.

Now noise from a Shannon-information perspective is anything that disrupts a flow of information, but generally speaking it is useful to separate noise into two different types: intrinsic noise (or thermal noise), and extrinsic noise (or interference).

Let’s say you want to use a microphone to measure some very faint sound – the sound of an ant chewing a leaf, say. Plug in your headphones and the first thing you’ll hear will be a your neighbour’s washing machine, or traffic on the street outside. This is extrinsic noise and can be reduced by shielding. People build anechoic chambers to reduce extrinsic noise: carefully insulated and coated with foam pads to deaden echoes, they offer some of the quietest places on Earth. According to John Cage, his piece 4’33” was inspired by his experience in an anechoic chamber. Expecting to hear nothing but peaceful silence, he was surprised to hear

two sounds, one high and one low. Afterward I asked the engineer in charge why, if the room was so silent, I had heard two sounds. He said, ‘Describe them.’ I did. He said, ‘The high one was your nervous system in operation. The low one was your blood in circulation.’

What Cage experienced was intrinsic noise, noise that no soundproofing can remove because it originates inside the thing doing the measurement. In his case, the noise came from inside his body, but even an electronic microphone will hiss and crackle from the random motion of electrons in its wiring.

No analytical tool is safe from intrinsic noise, not even a simple ruler, whose length fluctuates randomly on a scale too small for us to notice, but is sufficient to preclude its use for measuring things on the molecular scale. This is all because everything, ultimately, is made of particles that are always in motion ­– tiny, incessant, random movement caused by the ambient temperature.

So that background hiss interfering with your measurement will never go away. It is also totally random ­– and yet, as a consequence of this randomness, it is in some ways completely predictable. Some maths shows, for example, you can increase the accuracy of your measurement simply by taking lots of measurements and averaging them out: the more measurements you take, the more your signal stands out against the background noise. More exactly, if you take four times as many measurements, your signal-to-noise ratio doubles.

But measurements can be costly; noise can never be removed completely; and there is a law of diminishing returns. If a measurement with precision x costs you £10, twice as much precision would cost £40; twice as much again would cost £160. Sometimes the size of the error bars depends on how much you can afford.

REFERENCES

http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf

http://www.physics.utoronto.ca/~phy225h/experiments/thermal-noise/Thermal-Noise.pdf

http://www.lichtensteiger.de/anechoic.html

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Written by The S I

October 9, 2011 at 11:59 pm