"In short, the rule that no more dimensions or axes should be used in the chart than the data calls for, is fundamental. Violate this rule and you bring down upon your head a host of penalties. In the first place, you complicate your computing processes, or else achieve a grossly deceptive chart. If your chart becomes deceptive, it has defeated its purpose, which was to represent accurately. Unless, of course, you intended to deceive, in which case we are through with you and leave you to Mark Twain’s mercies. If you make your chart accurate, at the cost of considerable square or cube root calculating, you still have no hope, for the chart is not clear; your reader is more than likely to misunderstand it. Confusion, inaccuracy and deception always lie in wait for you down the path departing from the principle we have discussed - and one of them is sure to catch you." (Karl G Karsten, "Charts and Graphs", 1925)
"All the events in a man's life would accordingly stand in two fundamentally different kinds of connection: firstly, in the objective, causal connection of the natural process; secondly, in a subjective connection which exists only in relation to the individual who experiences it, and which is thus as subjective as his own dreams [...]" (Arthur Schopenhauer, "Parerga and Paralipomena", 1851)
"Graphs [for time series] can be misleading, however, and we need to subject our first impression to a closer scrutiny. We must develop more precise methods of analysis of time series. The variations of a time series are of many kinds which can be grouped under three heads. There is, first, the general direction of movement or the trend of the variable over the long period. Then there are oscillations of various types, of greater or less regularity, superimposed on the trend. Finally, there are residual or irregular variations which may arise from isolated events such as a war or general strike, or which may be due to the operation of random influences." (Roy D G Allen, "Statistics for Economists", 1951)
"The economists, of course, have great fun - and show remarkable skill - in inventing more refined index numbers. Sometimes they use geometric averages instead of arithmetic averages" (the advantage here being that the geometric average is less upset by extreme oscillations in individual items), sometimes they use the harmonic average. But these are all refinements of the basic idea of the index number [...]" (Michael J Moroney, "Facts from Figures", 1951)
“Synchronistic phenomena prove the simultaneous occurrence
of meaningful equivalences in heterogeneous, causally unrelated processes; in
other words, they prove that a content perceived by an observer can, at the
same time, be represented by an outside event, without any causal connection.
From this it follows either that the psyche cannot be localized in space, or
that space is relative to the psyche. The same applies to the temporal
determination of the psyche and the psychic relativity of time. I do not need
to emphasize that the verification of these findings must have far-reaching
consequences.” (Carl G Jung, Synchronicity: An Acausal Connecting Principle, 1952)
"Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions. They consist of a lattice of sites, each with a finite set of possible values. The value of the sites evolve synchronously in discrete time steps according to identical rules. The value of a particular site is determined by the previous values of a neighbourhood of sites around it." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)
"A depressing corollary of the butterfly effect (or so it was widely believed) was that two chaotic systems could never synchronize with each other. Even if you took great pains to start them the same way, there would always be some infinitesimal difference in their initial states. Normally that small discrepancy would remain small for a long time, but in a chaotic system, the error cascades and feeds on itself so swiftly that the systems diverge almost immediately, destroying the synchronization. Unfortunately, it seemed, two of the most vibrant branches of nonlinear science - chaos and sync - could never be married. They were fundamentally incompatible."
"The best case that can be made for human sync to the environment (outside of circadian entrainment) has to do with the possibility that electrical rhythms in our brains can be influenced by external signals."
"This synergistic character of nonlinear systems is precisely what makes them so difficult to analyze. They can't be taken apart. The whole system has to be examined all at once, as a coherent entity. As we've seen earlier, this necessity for global thinking is the greatest challenge in understanding how large systems of oscillators can spontaneously synchronize themselves. More generally, all problems about self-organization are fundamentally nonlinear. So the study of sync has always been entwined with the study of nonlinearity."
"There is no linear additive process that, if all the parts are taken together, can be understood to create the total system that occurs at the moment of self-organization; it is not a quantity that comes into being. It is not predictable in its shape or subsequent behavior or its subsequent qualities. There is a nonlinear quality that comes into being at the moment of synchronicity." (Stephen H Buhner, "Plant Intelligence and the Imaginal Realm: Beyond the Doors of Perception into the Dreaming of Earth", 2014)
"The most amazing thing about social insect colonies is that there's no individual in charge. If you look at a single ant, you may have the impression that it is behaving, if not randomly, at least not in synchrony with the rest of the colony. You feel that it is doing its own things without paying too much attention to what the others are doing." (Eric Bonabeau)
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