“As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.”

— James Joseph Sylvester

"A plea for the mathematician", Nature, Vol. 1, p. 261.

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James Joseph Sylvester 7

English mathematician 1814–1897

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“Now anarchy, on the other hand, is almost starting from the principle that “in diversity, there is strength,” which makes much more sense from the point of view of looking at the natural world.”

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Context: Fascism is a complete abdication of personal responsibility. You are surrendering all responsibility for your own actions to the state on the belief that in unity there is strength, which was the definition of fascism represented by the original roman symbol of the bundle of bound twigs. Yes, it is a very persuasive argument: “In unity there is strength.” But inevitably people tend to come to a conclusion that the bundle of bound twigs will be much stronger if all the twigs are of a uniform size and shape, that there aren’t any oddly shaped or bent twigs that are disturbing the bundle. So it goes from “in unity there is strength” to “in uniformity there is strength” and from there it proceeds to the excesses of fascism as we’ve seen them exercised throughout the 20th century and into the 21st.
Now anarchy, on the other hand, is almost starting from the principle that “in diversity, there is strength,” which makes much more sense from the point of view of looking at the natural world. Nature, and the forces of evolution — if you happen to be living in a country where they still believe in the forces of evolution, of course — did not really see fit to follow that “in unity and in uniformity there is strength” idea. If you want to talk about successful species, then you’re talking about bats and beetles; there are thousands of different varieties of different bat and beetle.

“I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for… science proper, especially of nature, requires a pure portion, lying at the foundation of the empirical, and based upon à priori knowledge of natural things. …the conception should be constructed. But the cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.”

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“The results of a scrutiny of the materials of chemical science from a mathematical standpoint are pronounced in two directions. In the first we observe crude, qualitative notions”

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