"Either all things proceed from one intelligent source and come together as in one body, and the part ought not to find fault with what is done for the benefit of the whole; or there are only atoms, and nothing else than a mixture and dispersion. Why, then, art thou disturbed? Say to this ruling faculty, Art thou dead, art thou corrupted, art thou playing the hypocrite, art thou become a beast, dost thou herd and feed with the rest?" (Marcus Aurelius, "Meditations". cca. 121–180 AD)
"Look at everything that exists, and observe that it is already in dissolution and change, and as it were putrefaction or dispersion, or that everything is so constituted in nature as to die." (Marcus Aurelius, "Meditations". cca. 121–180 AD)
"To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements. It seems interesting to ask if this statistical element be thought of as arising, as in classical statistical mechanics, because the states in question are averages over better defined states for which individually the results would be quite determined. These hypothetical 'dispersion free' states would be specified not only by the quantum mechanical state vector but also by additional 'hidden variables' - 'hidden' because if states with prescribed values of these variables could actually be prepared, quantum mechanics would be observably inadequate." (John S Bell, "On the problem of hidden variables in quantum mechanics" [in "Reviews of Modern Physics"], 1966)
"[...] the influence of a single butterfly is not only a fine detail-it is confined to a small volume. Some of the numerical methods which seem to be well adapted for examining the intensification of errors are not suitable for studying the dispersion of errors from restricted to unrestricted regions. One hypothesis, unconfirmed, is that the influence of a butterfly's wings will spread in turbulent air, but not in calm air." (Edward N Lorenz, [talk] 1972)
"Determinism was eroded during the nineteenth century and a space was cleared for autonomous laws of chance. The idea of human nature was displaced by a model of normal people with laws of dispersion. These two transformations were parallel and fed into each other. Chance made the world seem less capricious; it was legitimated because it brought order out of chaos. The greater the level of indeterminism in our conception of the world and of people, the higher the expected level of control." (Ian Hacking, "The Taming of Chance", 1990)
"The flaw in the classical thinking is the assumption that variance equals dispersion. Variance tends to exaggerate outlying data because it squares the distance between the data and their mean. This mathematical artifact gives too much weight to rotten apples. It can also result in an infinite value in the face of impulsive data or noise. [...] Yet dispersion remains an elusive concept. It refers to the width of a probability bell curve in the special but important case of a bell curve. But most probability curves don't have a bell shape. And its relation to a bell curve's width is not exact in general. We know in general only that the dispersion increases as the bell gets wider. A single number controls the dispersion for stable bell curves and indeed for all stable probability curves - but not all bell curves are stable curves." (Bart Kosko, "Noise", 2006)
"We can simplify the relationships between fragility, errors, and antifragility as follows. When you are fragile, you depend on things following the exact planned course, with as little deviation as possible - for deviations are more harmful than helpful. This is why the fragile needs to be very predictive in its approach, and, conversely, predictive systems cause fragility. When you want deviations, and you don’t care about the possible dispersion of outcomes that the future can bring, since most will be helpful, you are antifragile. Further, the random element in trial and error is not quite random, if it is carried out rationally, using error as a source of information. If every trial provides you with information about what does not work, you start zooming in on a solution - so every attempt becomes more valuable, more like an expense than an error. And of course you make discoveries along the way." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)
"Two clouds of uncertainty may have the same center, but one may be much more dispersed than the other. We need a way of looking at the scatter about the center. We need a measure of the scatter. One such measure is the variance. We take each of the possible values of error and calculate the squared difference between that value and the center of the distribution. The mean of those squared differences is the variance." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)
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