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Electronic copy available at: http://ssrn.com/abstract=1693217
BENOIT MANDELBROT 1924 – 1910
A Greek among Romans
Fernando Estrada
Nassim Nicholas Taleb yields the best posthumous tribute to Benoit Mandelbrot to call
it: “A Greek among Romans”. In the second half of the twentieth century few
mathematicians
achieved
universal
influence
as
remarkable
as
Mandelbrot. The
international scientific community will not cease to mourn the death of one of its finest
sons.
In this brief note describes the trajectory of the fractal models / multifractal F / M by
Benoit Mandelbrot. The promise was discovered by the geometry of Mandelbrot covers
a broad area of research fields, from meteorology and mathematical physics to the
individual and collective behavior in society, besides his contributions to the analysis of
the financial crisis in his wonderful essay on
The (mis) Behavior of Markets. A fractal
view
of
Risk,
Ruin
and
Reward
(2004). Mandelbrot's
arguments
have
revealed
significant anomalies in the prevailing paradigms. Is this a new paradigm in Kuhn's
sense as stated by the same Mandelbrot?
Mandelbrot's hypothesis has been extended creatively to the field of financial modeling,
the mathematical approach to the markets since the fractals geometric structures of
various levels of size, each of which repeats a small scale the overall structure. The
hypothesis suggests that Mandelbrot fractal rough measures reflect the nature and allow
an approach nonEuclidean: geometric structures such as clouds, coast, wind gusts and
conferences in the bags. To Mandelbrot the main feature in a market price, as in various
phenomena of culture and nature, is the fractal geometry.
Summarizing his argument is as follows:
The fractal geometry of roughness measured intrinsically. Thus marking the beginning
of a specific quantity theory: the roughness in all its manifestations [Mand05]
The roughness behavior translates ubiquitous in nature and in culture (including
financial markets). Fractality is scattered everywhere as fractal geometry objects are
multiform. An overview of fractals and multifractal is described by Mandelbrot in a
long chapter [Mand02]. Despite its unquestionable antiquity, the study of roughness has
been quite behind when compared with older concepts of physics as a slope (of a road
or trend), weight, tone, warmth, color and similar categories. The problem, as
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emphasized by Mandelbrot is that the density of roughness was not measured. Work in
this direction had to wait until the author.
A brief explanation of the author can see the contrast between the implications of fractal
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This note was uploaded on 10/24/2011 for the course SCIENCE PHY 453 taught by Professor Barnard during the Winter '11 term at BYU.
 Winter '11
 BARNARD
 Physics, RNA, pH

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