"By sampling we can learn only about collective properties of populations, not about properties of individuals. We can study the average height, the percentage who wear hats, or the variability in weight of college juniors [...]. The population we study may be small or large, but there must be a population - and what we are studying must be a population characteristic. By sampling, we cannot study individuals as particular entities with unique idiosyncrasies; we can study regularities (including typical variabilities as well as typical levels) in a population as exemplified by the individuals in the sample." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)
"Theories are usually introduced when previous study of a class of phenomena has revealed a system of uniformities. […] Theories then seek to explain those regularities and, generally, to afford a deeper and more accurate understanding of the phenomena in question. To this end, a theory construes those phenomena as manifestations of entities and processes that lie behind or beneath them, as it were." (Carl G Hempel, "Philosophy of Natural Science", 1966)
"System' is the concept that refers both to a complex of interdependencies between parts, components, and processes, that involves discernible regularities of relationships, and to a similar type of interdependency between such a complex and its surrounding environment." (Talcott Parsons, "Systems Analysis: Social Systems", 1968)
"The dynamics of any system can be explained by showing the relations between its parts and the regularities of their interactions so as to reveal its organization. For us to fully understand it, however, we need not only to see it as a unity operating in its internal dynamics, but also to see it in its circumstances, i.e., in the context to which its operation connects it. This understanding requires that we adopt a certain distance for observation, a perspective that in the case of historical systems implies a reference to their origin. This can be easy, for instance, in the case of man-made machines, for we have access to every detail of their manufacture. The situation is not that easy, however, as regards living beings: their genesis and their history are never directly visible and can be reconstructed only by fragments." (Humberto Maturana, "The Tree of Knowledge", 1987)
"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)
"A measure that corresponds much better to what is usually meant by complexity in ordinary conversation, as well as in scientific discourse, refers not to the length of the most concise description of an entity (which is roughly what AIC [algorithmic information content] is), but to the length of a concise description of a set of the entity’s regularities. Thus something almost entirely random, with practically no regularities, would have effective complexity near zero. So would something completely regular, such as a bit string consisting entirely of zeroes. Effective complexity can be high only a region intermediate between total order and complete." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)
"The second law of thermodynamics, which requires average entropy (or disorder) to increase, does not in any way forbid local order from arising through various mechanisms of self-organization, which can turn accidents into frozen ones producing extensive regularities. Again, such mechanisms are not restricted to complex adaptive systems." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)
"A form of machine learning in which the goal is to identify regularities in the data. These regularities may include clusters of similar instances within the data or regularities between attributes. In contrast to supervised learning, in unsupervised learning no target attribute is defined in the data set." (John D Kelleher & Brendan Tierney, "Data science", 2018)
"The idea behind deeper architectures is that they can better leverage repeated regularities in the data patterns in order to reduce the number of computational units and therefore generalize the learning even to areas of the data space where one does not have examples. Often these repeated regularities are learned by the neural network within the weights as the basis vectors of hierarchical features." (Charu C Aggarwal, "Neural Networks and Deep Learning: A Textbook", 2018)
"Unexpected phenomena appearing (and often having a regularity or pattern) from a collection of apparently unrelated elements and where the elements themselves do not have the characteristics of the phenomena and that phenomena itself is not contained deductively within the elements." (Jeremy Horne, "Visualizing Big Data From a Philosophical Perspective", Handbook of Research on Big Data Storage and Visualization Techniques, 2018)
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