Noise IS Information

A Discussion by Data Integrity Engineer Matt LaMantia

Thermodynamically, information content or entropy is a measure of the unpredictability of a signal. Unpredictable signals contain more information because based on what we have already of the signal, we can say less about an unpredictable signal than we can about a predictable signal. For example, a signal that just says "1... 1... 1... 1... 1... 1... 1... 1... 1... 1... 1... 1..." forever tells you a lot less than a signal that says "1... 0... 1... 1... 0... 1... 0... 0... 0... 0...1..." Note that information content is a purely symbolic rather than a semantic characteristic of the signal: It is a property of the encoding and decoding of the signal (and therefore its division into symbols or parameters) rather than what is being encoded itself. A signal that is pure "noise" is thermodynamically indistiguishable from a perfectly encoded and compressed semantic message: They both look like a varying signal in which you could not predict one bit of the signal based on the previous ones.

Semantically, we think of information as a useful thing because a signal tells us something useful about its source. Radio waves are an encoding of an acoustic wave performed at the broadcast source, and we have a device that decodes them into a form that we can listen to. Thermodynamically, an ongoing radio sine wave contains very little information (which we could probably represent just by saying, "10 kHz for 5 minutes at 1000 watts") compared to a symphony (which could arguably be represented by its score), which contains less information than white noise (a totally unpredictable signal which can't be compressed to anything less compact than itself).

Notice that I say the white noise is unpredictable but I don't say random. It is the result of some process at its source. We think of noise as what we throw away. It's the static in your phone line, the snow on your television screen. Most often we only want to have to pay attention to the important stuff, the stuff with a ready-made "useful" interpretation. But the snow on your television screen is not a random garble; it is encoded information about the thermal and electromagnetic processes going on in the atmosphere and in your power lines. Decoding it into a description of its source(s) may result only in a statistical or probablistic description of what created it, and maybe the decoding isn't even computable in any conventional sense. But a signal is always to some extent a description of a source process, and noise is a signal, so noise is information.

I think of Noise Laboratories as providing creative decoding schemes for information from our enviroment that is normally classified as noise.

Send E-mail to the Laboratory
Return to the Lab Directory

Updated 30 December 1996
Steve Hoey, Chief Safety Inspector