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The signal-to-noise ratio and its relationship to information transfer and energy

One article in Julian Dibbell, ed., The Best Technology Writing 2010 (Yale Univ. 2010) at 65 (by Douglas Fox), explains clarity as essentially a thermodynamic relationship. If you double the signal-to-noise ratio in a message you quadruple the energy someone consumes to maintain the same level of accuracy of understanding. In terms of neurons firing in the brain, this principle tells us, the more crackle in the radio, the (many) more calories we burn to make sense of the message. The more jargon in the legal memo, the more footnotes and digressions, the more typos or long blocks of text, the more extraneous facts – clots of useless or low value noise – the harder the reader or listener has to work to make sense out of it.

Moreover, when noise increases, the increase consumes much more extra energy than a linear increase. The formula is S/N = 20 log10(Vs/Vn) where Vs is the signal strength and Vn is the noise level (expressed as Volts) and the result is in decibels. The natural log falls off quickly as noise increases (as you divide the voltage of the signal by a larger noise number). If my 20 slide PowerPoint presentation had one wasted noisy slide but then I lard it with 4 fluffy or off-point slides, the energy needed by those in the meeting to derive the same quality of information must increase significantly.

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