The Fractal Geometry of Nature

„one must remember that a word’s common meaning is often so entrenched, that it is not erased by any amount of redefinition.”

„All pulchritude is relative.... We ought not ... to believe that the banks of the ocean are really deformed, because they have not the form of a regular bulwark; nor that the mountains are out of shape, because they are not exact pyramids or cones; nor that the stars are unskillfully placed, because they are not all situated at uniform distance. These are not natural irregularities, but with respect to our fancies only; nor are they incommodious to the true uses of life and the designs of man’s being on earth.”

„an interest in the history of ideas is good for the scientist’s soul.”

„prematurity, being too much ahead of one’s time, deserves nothing but compassionate oblivion. While excessive erudition in relation to the history of ideas is self-defeating. I do wish to assert the echoes from the past…”

„understanding of known concepts and the search for new concepts and conjectures are both helped by fine graphics. Rarely does contemporary scientific literature show such trust in the usefulness of graphics.”

„Graphics is wonderful for matching models with reality. When a chance mechanism agrees with the data from some analytic viewpoint but simulations of the model do not look at all “real,”

„One is reminded of William James writing in The Will to Believe that “The great field for new discoveries ... is always the unclassified residuum. Round about the accredited and orderly facts of every science there ever floats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to. The ideal of every science is that of a closed and completed system of truth ... Phenomena unclassifiable within the system are paradoxical absurdities, and must be held untrue ... —one neglects or denies them with the best of scientific consciences... Any one will renovate his science who will steadily look after the irregular phenomena. And when the science is renewed, its new formulas often have more of the voice of the exception in them than of what were supposed to be the rules.”

„. Rarely does contemporary scientific literature show such trust in the usefulness of graphics.”

„Graphics is wonderful for matching models with reality. . A formula can relate to only a small aspect of the relationship between model and reality, while the eye has enormous powers of integration and discrimination. True, the eye sometimes sees spurious relationships which statistical analysis later negates, but this problem arises mostly in areas of science where samples are very small.”

„One is reminded of William James writing in The Will to Believe that “The great field for new discoveries ... is always the unclassified residuum. Round about the accredited and orderly facts of every science there ever floats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to. The ideal of every science is that of a closed and completed system of truth ... Phenomena unclassifiable within the system are paradoxical absurdities, and must be held untrue ... —one neglects or denies them with the best of scientific consciences... Any one will renovate his science who will steadily look after the irregular phenomena. And”