A Quote by Benoit Mandelbrot
I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
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."
The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.
There are only patterns, patterns on top of patterns, patterns that affect other patterns. Patterns hidden by patterns. Patterns within patterns. If you watch close, history does nothing but repeat itself. What we call chaos is just patterns we haven't recognized. What we call random is just patterns we can't decipher. what we can't understand we call nonsense. What we can't read we call gibberish. There is no free will. There are no variables.
Abstraction didn't have to be limited to a kind of rectilinear geometry or even a simple curve geometry. It could have a geometry that had a narrative impact. In other words, you could tell a story with the shapes. It wouldn't be a literal story, but the shapes and the interaction of the shapes and colors would give you a narrative sense. You could have a sense of an abstract piece flowing along and being part of an action or activity. That sort of turned me on.
Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.
Burma is not yet a full-fledged democracy. We have started working on the road to full democracy. We have a lot of things to do in order to build a democratic structure and to be become a full-fledged democracy.
The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?
I just toured around looking for fractals, and when I found something that had a scaling geometry, I would ask the folks what was going on - why they had made it that way.
The tribalizing power of the new electronic media, the way in which they return to us to the unified fields of the old oral cultures, to tribal cohesion and pre-individualist patterns of thought, is little understood. Tribalism is the sense of the deep bond of family, the closed society as the norm of community.
Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
Real shapes and real patterns are things you would observe in nature, like the marks on the back of a cobra's hood or the markings on a fish or a lizard. Imaginary shapes are just that, symbols that come to a person in dreams or reveries and are charged with meaning.
If you look at the soap bubbles in the sink when you're doing dishes, you'll see the incredible diversity of shapes in there. There are cubes in there; there are decahedrons and tetrahedrons; there are odd, irregular shapes without names, you know.
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
Kamal Haasan got inspired by his brief appearance in a role similar to Charlie Chaplin in 'Punnagai Mannan' and developed that into a full-fledged character in 'Apoorva Sagodharargal.'
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
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