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I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."
--
As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594

 

Benoit Mandelbrot

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"Your mind has been conditioned to Euclid," Holloway said. "So this — thing — bores us, and seems pointless. But a child knows nothing of Euclid. A different sort of geometry from ours wouldn't impress him as being illogical. He believe what he sees."
"Are you trying to tell me that this gadget's got a fourth dimensional extension?" Paradine demanded.
"Not visually, anyway," Holloway denied. "All I say is that our minds, conditioned to Euclid, can see nothing in this but an illogical tangle of wires. But a child  especially a baby  might see more. Not at first. It'd be a puzzle, of course. Only a child wouldn't be handicapped by too many preconceived ideas."
"Hardening of the thought-arteries," Jane interjected.

 

Lewis Padgett

 

Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur.

 

Euclid

 

Professor Klein then speaks of "that artistic finish that we admire in Euclid's Elements," and mentions Allman's important historical work. I heartily concur in this estimate of Euclid, and desire to contrast it with the error of Charles S. Peirce, in the Nation, where he speaks of "Euclid's proof (Elements Bk. I., props. 16 and 17)" as "really quite fallacious, because it uses no premises not as true in the case of spherics." Our bright American seems to have forgotten Euclid's Postulate 6 (Axiom 12 in Gregory, Axiom 9 in Heiberg), "Two straight lines cannot enclose a space;" that is, two straights having crossed never recur.

 

Charles Sanders Peirce

 

A few men, philosophers or lovers of wisdom-or truth- may by study learn at least in outline the proper patterns of true existence. If a powerful ruler should form a state after these patterns, then its regulations could be preserved. An education could be given which would sift individuals, discovering what they were good for, and supplying a method of assigning each to the work in life for which his nature fits him. Each doing his own part, and never transgressing, the order and unity of the whole would be maintained.

 

John Dewey

 

Like Freud and Jung and Rudolf Otto, all of whom contributed deep strands to his work, Eliade argued boldly for universals where he might more safely have argued for widely prevalent patterns. Yet many of the patterns that he identified in religions that spanned the entire globe and the whole of human history — a span that no one has ever known as well as he did — inspired an entire generation of both scholars and amateurs of the study of religion, and they still prove useful as starting points for the comparative study of religion and still hold water even after the challenges posed by new data to which Eliade did not have access. His concept of hierophany, the sudden irruption of the sacred in the profane world, sacred time opening to the transcendent, resulting in radical discontinuities, has proved a far more widely applicable and heuristic term than the older, narrower term "theophany," denoting the manifestation of a god. And his argument that religious forms, particularly myths, are usefully studied in popular culture as well as in the great scriptures is a postmodern idea that he formulated long before postmodernism. He taught us that myths (and, to a great extent, rituals) retold and reenacted in the present transport the worshipper back to the world of origins, the world of events that took place in illo tempore, "in that time"; this basic idea of what he called (after Nietzsche) "the eternal return" has become a truism in the study of religion and does, I think, apply to many mythologies, though not, as Eliade claimed, to all. His ideas about the alternation and interaction of cosmos and chaos, and cyclical/mythical time and linear/historical time, the sacred and the profane, are similarly fruitful starting points for many, if not all, cultures. Above all, his insistence that it is possible to find meaningful synchronic patterns of symbolism in addition to the phenomena that are unique to each time and place--this is the foundation on which the entire field of comparative religion still stands, and Eliade laid the cornerstone.

 

Mircea Eliade