“When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone.”

— Benoît Mandelbrot

A Theory of Roughness (2004)
Context: When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achi…" by Benoît Mandelbrot?

Benoît Mandelbrot 56

Polish-born, French and American mathematician 1924–2010

J. G. Ballard (1930–2009) British writer

As quoted in "some ideas for free from time recording" by Emit Records (1995) https://archive.is/20130628060534/www.emit.cc/img/catalog-page9.jpg

“You and I want our lives to matter. We want our lives to make a real difference — to be of genuine consequence in the world. We know that there is no satisfaction in merely going through the motions in life, even if those motions make us successful or even if we have arranged to make those motions pleasant. We want to know we have had some impact on the world. In fact, you and I want to contribute to the quality of life. We want to make the world work.”

Werner Erhard (1935) Critical Thinker and Author

Source: The End of Starvation : Creating an Idea Whose Time Has Come, Werner Erhard, 1977, 3 http://www.wernererhard.net/thpsource.html,
Source: Also published in — The end of starvation: creating an idea whose time has come, 3, 1982, Werner Erhard http://books.google.com/books?id=4o4wAAAAMAAJ&q=%22be+of+genuine+consequence+in+the+world%22&dq=%22be+of+genuine+consequence+in+the+world%22&hl=en&sa=X&ei=rpyFUvTMB6_MsQT0sYCwDQ&ved=0CDQQ6AEwAQ,
Source: Also quoted in — [The Answer : What do you mean I have to figure it out for myself?, 2001, Quila H. Creig] and — [The Spartan Life 2, Scott Westerman, ‎2012]

“My memoirs "On the Mechanical Theory of Heat" are of different kinds. Some are devoted to the development of the general theory and to the application thereof to those properties of bodies which are usually treated of in the doctrine of heat. Others have reference to the application of the mechanical theory of heat to electricity. …Other memoirs… have reference to the conceptions I have formed of the molecular motions which we call heat. These conceptions, however, have no necessary connexion with the general theory, the latter being based solely on certain principles which may be accepted without adopting any particular view as to the nature of molecular motions. I have therefore kept the consideration of molecular motions quite distinct from the exposition of the general theory.”

Rudolf Clausius (1822–1888) German mathematical physicist

Preface (August, 1864)
The Mechanical Theory of Heat (1867)

“Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion.”

Gerald James Whitrow (1912–2000) British mathematician

The Structure of the Universe: An Introduction to Cosmology (1949)
Context: Galileo had raised the concepts of space and time to the status of fundamental categories by directing attention to the mathematical description of motion. The midiaevel qualitative method had made these concepts relatively unimportant, but in the new mathematical philosophy the external world became a world of bodies moving in space and time. In the Timaeus Plato had expounded a theory that outside the universe, which he regarded as bounded and spherical, there was an infinite empty space. The ideas of Plato were much discussed in the middle of the seventeenth century by the Cambridge Platonists, and Newton's views were greatly influenced thereby. He regarded space as the 'sensorium of God' and hence endowed it with objective existence, although he confessed that it could not be observed. Similarly, he believed that time had an objective existence independent of the particular processes which can be used for measuring it.<!--p.46

“Why would we do this? she asked, watching smoke trickle towards the ceiling. A whole world of rigid rules covering temperature, convection and Brownian motion all busily pretending to be truly chaotic.”

Jon Courtenay Grimwood (1953) British writer

Source: Stamping Butterflies (2004), Chapter 39 (pp. 246-247)

“Proposition I. Theorem I: When a projectile is carried in motion compounded from equable horizontal and from naturally accelerated downward [motions], it describes a semiparabolic line in its movement.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Author, Day Four, Stillman Drake translation (1974) p. 269
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

“It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.”

Hermann Weyl (1885–1955) German mathematician

Introduction
Space—Time—Matter (1952)
Context: Space and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of time. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.

“Among these Ways, or any other whatever, of generating Magnitudes, the Primary and Chief is, that perform'd by local Motion, which all of them must in some Sort suppose, because without Motion, nothing can be generated or produced and therefore this must first be considered. The following Axiom of Aristotle concerning Motion is famous… He that is ignorant of Motion, must necessarily know nothing of Nature… in Nature every Thing created is produc'd by Motion, or certainly not without Motion.”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

p, 125
Geometrical Lectures (1735)

“Already at the very beginning of the productive act, shortly after the initial motion to create, occurs the first counter motion, the initial movement of receptivity. This means:
the creator controls whether what he has produced so far is good.”

Paul Klee (1879–1940) German Swiss painter

I.13 Productive | Receptive, p. 33
1921 - 1930, Pedagogical Sketch Book, (1925)

“I don't want to hold you and feel so helpless
I don't want to smell you and lose my senses
And smile in slow motion
With eyes in love.”

Rufus Wainwright (1973) American-Canadian singer-songwriter and composer

Foolish Love
Song lyrics, Rufus Wainwright (1998)

Help us to complete the source, original and additional information

Benoît Mandelbrot 56

Related quotes

Related topics