Benoit Mandelbrot Quotes

If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals.

All human knowledge thus begins with intuitions, proceeds thence to concepts, and ends with ideas.

Anybody can find infinite Mandelbrot figures in his navel.

You existed. You existed now as a fractal. Definition: A fractal is generally a rough or fragmented geometric shape that can be broken into parts, each of which is (at least approximately) a reduced-size copy of the whole. Maybe I was a fractal. Maybe the photographer was a fractal. Maybe we were all fractals.

An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.

What interests me about thoughts is not the moment when it crystallises into formal ideas but its earlier stages.

The math helps you have better understanding and helps you have more creative ideas, but you can't replace the creative ideas

Old ideas are continually being slain by new facts. There is nothing stable in the conclusions of the mind, and it is impossible that there ever should be unless we hold that the universe is made to the measure of the human mind, an assumption for which nothing in the past gives any warrant.

Values, both those that we approve and those that we don't, have roots as deep as creosote rings, and live as long and grow as slowly

Some ideas, like dandelions in lawns, strike tenaciously: you may pull off the top but the root remains, drives down suckers and may even sprout again.

I am more of a sponge than an inventor. I absorb ideas from every source. I take half-matured schemes for mechanical development and make them practical. I am a sort of a middleman between the long-haired and impractical inventor and the hard-headed business man who measures all things in terms of dollars and cents. My principal business is giving commercial value to the brilliant but misdirected ideas of others.

There are things which seem incredible to most men who have not studied Mathematics.

Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.

I believe that we are a story-driven species and that we understand how things are put together, in the context of narrative. It's a shame that science hasn't been taught that way, in a long time. It's usually the fact completely devoid of any human experience or any idea of how the scientist came to that conclusion.

Sometimes it takes a germ of an idea, which takes a long time to digest.

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.

I don't start with an idea or concept in the sense that I flesh out an idea or concept and set it at the center of something.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our thoughts.

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

If you don't generalize you don't philosophize.

Images also help me find and realise ideas. I look at hundreds of very different, contrasting images and I pinch details from them, rather like people who eat from other people's plates.

More than most, I believe I'm highly attuned to how heresies eventually become mainstream belief systems and how the vast majority of people who consider themselves 'edgy' are those who only embraced radical ideas LONG after it became safe for them to do so.

Time is but the measure of the difficulty of a conception. Pure thought has scarcely any need of time, since it perceives the two ends of an idea almost at the same moment.

When an idea is not robust enough to stand expression in simple terms, it is a sign that it should be rejected.