On Noise VI

"In a white-noise process, every value of the process (e.g., the successive frequencies of a melody) is completely independent of its past - it is a total surprise. By contrast, in 'brown music' (a term derived from Brownian motion), only the increments are independent of the past, giving rise to a rather boring tune." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"In contrast to gravitation, interatomic forces are typically modeled as inhomogeneous power laws with at least two different exponents. Such laws (and exponential laws, too) are not scale-free; they necessarily introduce a characteristic length, related to the size of the atoms. Power laws also govern the power spectra of all kinds of noises, most intriguing among them the ubiquitous (but sometimes difficult to explain)." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"We might expect that the noise will 'smear out' each data point and make it difficult for the network to fit individual data points precisely and hence will reduce over-fitting. In practice it has been demonstrated that training with noise can indeed lead to improvements in network generalization." (Christopher M Bishop, "Neural Networks for Pattern Recognition", 1995)

"A moderate amount of noise leads to enhanced order in excitable systems, manifesting itself in a nearly periodic spiking of single excitable systems, enhancement of synchronized oscillations in coupled systems, and noise-induced stability of spatial pattens in reaction-diffusion systems." (Benjamin Lindner et al, "Effects of Noise in Excitable Systems", Physical Reports. vol. 392, 2004)

"Linear systems do not benefit from noise because the output of a linear system is just a simple scaled version of the input [...] Put noise in a linear system and you get out noise. Sometimes you get out a lot more noise than you put in. This can produce explosive effects in feedback systems that take their own outputs as inputs." (Bart Kosko, "Noise", 2006)

"One person’s signal is another person’s noise and vice versa. We call this relative role reversal the noise-signal duality." (Bart Kosko, "Noise", 2006)

"Many scientists who work not just with noise but with probability make a common mistake: They assume that a bell curve is automatically Gauss's bell curve. Empirical tests with real data can often show that such an assumption is false. The result can be a noise model that grossly misrepresents the real noise pattern. It also favors a limited view of what counts as normal versus non-normal or abnormal behavior. This assumption is especially troubling when applied to human behavior. It can also lead one to dismiss extreme data as error when in fact the data is part of a pattern." (Bart Kosko, "Noise", 2006)

"Noise is an unwanted signal. A signal is anything that conveys information or ultimately anything that has energy. The universe consists of a great deal of energy. Indeed a working definition of the universe is all energy anywhere ever. So the answer turns on how one defines what it means to be wanted and by whom." (Bart Kosko, "Noise", 2006)

"The noise takes its toll on the message as it randomly turns some of the 1 bits into 0 bits and randomly turns some of the 0 bits into 1 bits: Noise randomly flips bits. [...] But noise can be subtler in a digital system. Noise can disturb the timing of when a bit value arrives at a receiver as well as randomly flipping that bit value." (Bart Kosko, "Noise", 2006)

"[...] in the statistical world, what we see and measure around us can be considered as the sum of a systematic mathematical idealized form plus some random contribution that cannot yet be explained. This is the classic idea of the signal and the noise." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)