22 January 2020

On Simplicity X

"One should not be deceived by philosophical works that pretend to be mathematical, but are merely dubious and murky metaphysics. Just because a philosopher can recite the words lemma, theorem and corollary doesn't mean that his work has the certainty of mathematics. That certainty does not derive from big words, or even from the method used by geometers, but rather from the utter simplicity of the objects considered by mathematics." (Pierre L Maupertuis, "Les Loix du Mouvement et du Repos, déduites d'un Principe Métaphysique", 1746)

"The model of an object, process or phenomenon is some other object, process or phenomenon having certain features in common with the original. It is ordinarily assumed that the model is a simplified version of the object of study. However, it is not always easy to give precise meaning to the concept 'simpler than the original', for the simple reason that in reality all entities or phenomena are infinitely complicated and their study can be carried out with differing and constantly increasing degrees of accuracy." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"Certainty, simplicity, vividness originate in popular knowledge. That is where the expert obtains his faith in this triad as the ideal of knowledge. Therein lies the general epistemological significance of popular science." (Ludwik Fleck, "Genesis and Development of a Scientific Fact", 1979)

"Nature is capable of building complex structures by processes of self-organization; simplicity begets complexity." (Victor J Stenger, "God: The Failed Hypothesis", 2010)
 
"Simplicity in a system tends to increase that system's efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system's inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness." (Eric T Bell)
 
"[…] if one really understood the central point and its necessity in the construction of the world, one ought to be able to state it in one clear, simple sentence. Until we see the quantum principle with this simplicity we can well believe that we do not know the first thing about the universe, about ourselves, and about our place in the universe." (John A Wheeler)

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