A Quote by Benoit Mandelbrot
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.
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Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.
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.
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 have yet to see any problem, however complicated, which, when looked at in the right way did not become still more complicated.
I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.
Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.
This film [Teknolust] in particular, showing the way in which having a sexual dialogue with someone can be something developing and changeable and maybe uncomfortable and complicated. Just complicated and human, no more and no less.
The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found.
Immigration policy is a complicated issue. Or perhaps one should say immigration policies are complicated, since we have many different immigration laws and practices which interact in complex ways.
The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.
I believe strongly that characters are five-dimensional, and they're complicated, and life is complicated, and people are complicated.
Puerto Rico is complicated. The people are complicated. The history is complicated. The story of the United States' relationship to Puerto Rico is complicated.
You see this incredible capacity for replication in nature, survival, development, all of these things that are around us all the time in nature that just happen. By comparison, human life is really, really complicated. We're gifted animals, but we are so complicated. Nothing is easy for us, except maybe eating too much.
The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.
But violence is news, to a certain extent, and people don't want complicated news. Because as soon as you realize things are complicated, your life becomes more complicated.
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