“The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.”

If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.

Beautiful, damn hard, increasingly useful. That’s fractals.

It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.

The techniques I developed for studying turbulence, like weather, also apply to the stock market

I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.

The Mandelbrot set is the most complex mathematical object known to mankind.

If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.

Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.

Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.

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.

A fractal is a way of seeing infinity.

The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.

Order doesn’t come by itself.

My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.

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.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

The reason I make art is because I get to make a choice about who I am, what I do, and what I put out into the world, the footsteps I leave behind.

I feel, having the choices I had, I felt I had more control over my own medium than I did over photography.

We don’t need to set this up as we either take a bunch of refugees who will be infiltrated with terrorists, I guarantee you. For them not to be would be terrorist malpractice. And we need to – to choose the right choice, not these false choices.

If the director wishes to print it, then you have a series of choices, maybe millions of choices within that minute-and-a-half, or 80 seconds, or 2 minutes or however long or short the take is, you have all those choices committed to celluloid. I find that absolutely thrilling.

Hopefully, as I get older in the business, I make my choices more accurately, and I perhaps know from either the script or the first meeting that it isn’t going to work.

Every time you have to make a choice about anything, think Does this go toward or away from what I want? Always choose what goes toward what you want.

The number of choices you make in the event that you see on stage, those choices are sometimes largely determined by the rehearsal process and the experiments that you go through and the choices that you make in the rehearsal room, not in front of an audience.

Economics is a highly sophisticated field of thought that is superb at explaining to policymakers precisely why the choices they made in the past were wrong. About the future, not so much.