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I'm writing about the history of the concept of noise and am having trouble tracking down references from when the term "noise" started being associated with statistical noise such as Gaussian Noise and not just things like people talking in the background and RF noise that prevents the interception of radio signals.

An article in Science describing a new telephone device invented by Tuft’s College professor A. E. Dolbear noted that the words sounded “clear without the sputtering and confused noises” of Alexander Bell’s system. By the 1920s, engineers at AT&T are measuring and comparing the noise between trans-Atlantic radio links and cables.

But I can't find references that go from these early uses of the term "noise" to "Gaussian Noise." The earliest reference I've found so far is Technical Report 189 from the Cruft Laboratory, June 1, 1954.

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    $\begingroup$ Claude Shannon's paper Communication in the Presence of Noise , written in 1940 but not widely disseminated until 1949, uses both Gaussian Noise and signal-to-noise ratio. $\endgroup$
    – nwr
    Oct 8, 2023 at 17:27
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    $\begingroup$ @nwr please consider turning your comment into an answer. I am not an expert on this, but I think Shannon's works were pioneering w.r.t. mathematical modeling of information/communication. $\endgroup$ Oct 9, 2023 at 6:56
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    $\begingroup$ You don't repeat the title's question in the question text, but: Isn't "when did statisticians start using the term "noise" to describe randomness" backwards? "Noise" seems the intuitive, perception-based word while randomness hints at a more rigorous, mathematical approach which formally described things formerly known as noise ;-). $\endgroup$ Oct 9, 2023 at 12:47

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You are looking at relatively recent references. Noise originally comes from telecommunication analysis in early 1900s well before Shannon; basically, the electrical noise was heard as audible noise- hence the term

"Signal to Noise" can be traced to 1923 article, by Arnold, H. D., & Espenschied, L. (1923). Transatlantic Radio Telephony 1. Bell System Technical Journal, 2(4), 116-144.

Ratio of Signal to Noise Strength; Words Received. The noise curve of Fig. 9 and that of Fig. 10 can, therefore, be read as "The strength of the signal tone which can just be heard through the noise." It can, therefore, be directly compared with the signal curve itself and the difference between the two curves is a measure of the level of the actual signal strength above that which would just permit of the signals being heard. Actually, the difference between the two curves, as shown in the figures, is proportional to the ratio of the signal to the noise strength, because the curves are plotted to a logarithmic scale.

Figure 10

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    $\begingroup$ Really nice. Do you know when they started modeling the noise with random numbers drawn from a Gaussian distribution? I'm trying to figure out if the term "Gaussian Noise" went from communications to statistics or vice-versa. $\endgroup$
    – vy32
    Oct 9, 2023 at 0:17
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    $\begingroup$ @vy32, I tried but I could not find it except in Shannon's paper-1940s. $\endgroup$
    – AChem
    Oct 9, 2023 at 0:57
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    $\begingroup$ Thanks. I also came up empty. It's my thought that the statisticians picked up the term in the 1950s from people in telecom, but I have no evidence of that. However, I have found multiple papers from the 1950s that used the term outside of the telecom context. $\endgroup$
    – vy32
    Oct 9, 2023 at 1:31
  • $\begingroup$ The main problem could be the fact that Gaussian and noise were not written together, we can have so many alternatives like noise with Gaussian distribution, or Gaussian distributed noise and many more variations. $\endgroup$
    – AChem
    Oct 9, 2023 at 2:32
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    $\begingroup$ I don't have anything to back this up, but I have thought that the earlier analyses of "noise" used simpler models, leading to randomness that does not follow a normal distribution. Only when multiple sources of noise are present at the same time, can we see the gaussian distribution. The central limit theorem and all that. I am only familiar with telcomm models. Undoubtedly something similar can be found in all measurements, where an experiment is repeated multiple times, and the distribution of the measure values is recorded. Typically only the average (may be with an error bar) is reported. $\endgroup$ Oct 9, 2023 at 6:46
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The article "The history of noise [on the 100th anniversary of its birth]" in Volume 22, Issue 6, November 2005 of the IEEE Signal Processing Magazine seems to go in the same direction. https://ieeexplore.ieee.org/document/1550188

Looking at one of the older papers referenced in that article, W. Schottky "Über spontane Stromschwankungen in verschiedenen elektrizitätsleitern" I see he uses the term "Schroteffekt" so I guess the German term "Rauschen" had not yet been established in 1918...

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