Editing Benoit Mandelbrot (section)

===Fractals and the "theory of roughness"===
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, [[coastline]]s and [[river basin]]s; the structures of plants, [[blood vessel]]s and [[lung]]s; the clustering of [[galaxy|galaxies]]. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.<ref name= maverick />{{rp|xi}} He began by asking himself various kinds of questions related to nature:
{{blockquote|Can [[geometry]] deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?<ref name= maverick>{{cite book| last= Mandelbrot| first= Benoit |year= 2012| title= The Fractalist: Memoir of a Scientific Maverick| publisher= Pantheon Books |isbn= 978-0-307-38991-6}}</ref>{{rp|xii}}}}

In his paper "[[How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension]]", published in [[Science (journal)|''Science'']] in 1967, Mandelbrot discusses [[self-similarity|self-similar]] curves that have [[Hausdorff dimension]] that are examples of ''fractals'', although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.<ref>{{cite news| quote= Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?"| url= https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw |title= Benoît Mandelbrot, Novel Mathematician, Dies at 85| archiveurl= https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw |archivedate=31 December 2018 | work= The New York Times| date= 17 October 2010| access-date= }}</ref><ref name="Mandelbrot_Science_1967">{{cite journal | title=How long is the coast of Britain? Statistical self-similarity and fractional dimension | journal=Science | date=5 May 1967 | last= Mandelbrot| first= Benoit B. | pages=636–638 | volume=156 | issue=3775 | doi=10.1126/science.156.3775.636 | pmid=17837158 | url= http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf | bibcode=1967Sci...156..636M | s2cid=15662830 | access-date=11 January 2016 | archive-date=13 July 2015 | archive-url=https://web.archive.org/web/20150713023120/http://www.sciencemag.org/content/156/3775/636 | url-status=live }}</ref>

Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured."<ref name= maverick />{{rp|296}} Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in ''[[The Fractal Geometry of Nature]]'' had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new:
{{blockquote|The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.<ref name= maverick />{{rp|292}}}}

Fractals are also found in human pursuits, such as music, painting, architecture, and in the financial field. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional [[Euclidean geometry]]: <blockquote>Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.<br />&nbsp;&nbsp;—Mandelbrot, in his introduction to ''The Fractal Geometry of Nature''</blockquote>
[[File:Mandel zoom 08 satellite antenna.jpg|thumb|right|Section of a Mandelbrot set]]

Mandelbrot has been called an artist, and a visionary<ref name="RLD">{{cite journal| last= Devaney| first= Robert L.|author-link= Robert L. Devaney |title= Mandelbrot's Vision for Mathematics| journal= Proceedings of Symposia in Pure Mathematics| volume= 72| number= 1 |publisher=American Mathematical Society |year=2004 |url=http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |access-date=5 January 2007 |url-status=dead |archive-url= https://web.archive.org/web/20061209093734/http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf |archive-date=9 December 2006 }}</ref> and a maverick.<ref>{{cite web| url= https://www.pbs.org/wgbh/nova/fractals/mandelbrot.html| title=A Radical Mind| last=Jersey| first=Bill |date=24 April 2005|work=Hunting the Hidden Dimension, NOVA|publisher= PBS|access-date=20 August 2009 |archive-date= 22 August 2009|archive-url=https://web.archive.org/web/20090822022402/http://www.pbs.org/wgbh/nova/fractals/mandelbrot.html|url-status=live}}</ref> His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made ''The Fractal Geometry of Nature'' accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of [[Olbers' paradox]] (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a [[Necessity and sufficiency|sufficient, but not necessary]], resolution of the paradox. He postulated that if the [[star]]s in the universe were fractally distributed (for example, like [[Cantor dust]]), it would not be necessary to rely on the [[Big Bang]] theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.<ref>{{cite journal| title= Galaxy Map Hints at Fractal Universe| first= Amanda |last= Gefter| journal= New Scientist| date= 25 June 2008| url= | access-date= }}</ref>