Humanity had to learn about measuring roughness.

Benoit Mandelbrot Fractals and the art of roughness

To the right, I took a higher roughness.

So on the left, I took the roughness copied from many landscapes.

So these numbers are the numbers which denote the roughness of these surfaces.

So Brownian motion, which happens to have a roughness number of two, goes around.

Roughness is part of human life forever and forever, and ancient authors have written about it.

Regularity is the contrary of roughness because the basic aspect of the world is very rough.

That one can measure roughness by a number, a number, 2.3, 1.2 and sometimes much more.

It adds roughness to the dune's surface, to the texture of the dune's surface, binding the grains.

They were done on a computer, and the only input is a number, and that number is roughness.

And the only part which is natural is a number, the roughness of the cloud, which is taken from nature.

One day, a friend of mine, to bug me, brought a picture and said, What is the roughness of this curve?

Materials of varying roughness a factor which is dependent on the particular radar wavelength being used reflect the radar signal in different ways.

I prefer the word roughness to the word irregularity because irregularity to someone who had Latin in my long past youth means the contrary of regularity.

Well, a man named Hausdorff in 1919 introduced a number which was just a mathematical joke, and I found that this number was a good measurement of roughness.

At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.

Now, in fact, by a complete fluke, I got involved many years ago in a study of this form of complexity, and to my utter amazement, I found traces very strong traces, I must say of order in that roughness.

But they're necessary they're necessary to make that mathematics work.

Necessary Migrants

19. In general, through a knowledge of the interdependence of the factors which have a major influence on radar response (e.g. incidence angle, moisture content, surface roughness, geometry and slope orientation), ERS imagery corresponding to a single date can be interpreted for a variety of terrestrial applications.

Europe s Necessary Union

What's not necessary?

That is not necessary.

Is it really necessary?

That's all that's necessary.

I've done everything necessary.

I happen to believe that Libya was necessary and that military intervention in Afghanistan was also necessary.

You did what was necessary.

Why should it be necessary?

The necessary transition period periods?

Interviews are given whenever necessary.

(c) The Spaceguard Integrated System for Potentially Hazardous Objects Survey (SISYPHOS) was proposed by the Alenia Spazio company, Surrey Satellite Technology Ltd. and Osservatorio Astronomico di Torino. A space based observatory would detect and carry out remote sensing and the physical characterization of NEOs their size, composition, surface roughness, and so forth

And sometimes military intervention is necessary.

It's hard, but it is necessary.

These are necessary but insufficient questions.

I've talked about what's desperately necessary.

Food is always necessary for life.

I don't think that it's necessary.

For that, time will be necessary.

And as I say, energy was necessary.

But it's a necessary thing to do.

They just talked about it being necessary.

You can keep this dictionary if necessary.

I will go with you if necessary.