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→Research career 科研生涯
[[文件:Newton-lplane-Mandelbrot.jpg|缩略图|右|一个德布洛特集合]]
[[文件:Newton-lplane-Mandelbrot.jpg|缩略图|右|一个德布洛特集合]]
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke:
但是，曼德布洛特从未觉得他在发明一个新概念。在他与科学作家亚瑟·克拉克Arthur C. Clarke的纪录片中他描述了自己的感受：
Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.
Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science
在探索这个集合的时候我并未感觉在发明一个新概念。我也从没有感觉到我的想象力足以发现所有这些非凡的事物。其实他们就一直呈现在那里，即使过去没有人注意过他们。一个如此简单的公式就可以解释所有这些异常复杂的事物，太难以置信了。因此，科学的目标是从一团乱开始，再由一个简单的公式来解释它。我想这是研究科学的梦想。
According to Clarke, "the [[Mandelbrot set]] is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally ''infinite'' complexity?" Clarke also notes an "odd coincidence<blockquote>the name Mandelbrot, and the word "[[mandala]]"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.<ref name=Clarke /></blockquote>
According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence the name Mandelbrot, and the word "mandala"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.
克拉克Clarke说：“曼德布洛特集确实是整个数学史上最惊人的发现之一。谁能想到，如此难以置信的简单方程式就可以生成视觉上无限复杂的图像？“克拉克还注意到了一个奇怪的巧合”：我确信曼德布洛特的名称和“曼陀罗”（一个宗教象征）一词纯属巧合，但确实曼德布洛特集似乎包含了大量的曼陀罗。
Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.<ref name="wos44">{{cite web|url=http://www.webofstories.com/play/10483|title=Web of Stories • Benoît Mandelbrot • IBM: background and policies|last=Mandelbrot|first=Benoît|author2=Bernard Sapoval|author3=Daniel Zajdenweber|date=May 1998|publisher=[[Web of Stories]]|access-date=17 October 2010|archive-date=8 September 2011|archive-url=https://web.archive.org/web/20110908162215/http://www.webofstories.com/play/10483|url-status=live}}</ref> He joined the Department of Mathematics at [[Yale]], and obtained his first [[tenure]]d post in 1999, at the age of 75.<ref name="Tenner">{{cite news|url=https://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|title=Benoît Mandelbrot the Maverick, 1924–2010|last=Tenner|first=Edward|date=16 October 2010|work=[[The Atlantic]]|access-date=16 October 2010|archive-date=18 October 2010|archive-url=https://web.archive.org/web/20101018132145/http://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/|url-status=live}}</ref> At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.[25] He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75.[26] At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.
经过35年零12天的努力，曼德布洛特在1987年离开了IBM，当时IBM决定结束其部门的研究。之后他加入了耶鲁大学数学系，并于1999年以75岁的高龄获得了第一任终身职位。在2005年退休之时，他成为了斯特林数学科学教授。
=== Fractals and the "theory of roughness" 分形与“粗糙度理论” ===
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=Mandelbrot />{{rp|xi}} He began by asking himself various kinds of questions related to nature:
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.[8]:xi He began by asking himself various kinds of questions related to nature:
曼德布洛特创造了第一个“粗糙度理论”，他看到了山脉，海岸线和河流盆地形状的“粗糙度”。植物，血管和肺的结构的“粗糙度”；还有星系聚集的“粗糙度”。他个人的追求是创建一些数学公式来测量此类物体在自然界中的整体“粗糙度”。他首先问自己各种与自然有关的问题：
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=Mandelbrot>Mandelbrot, Benoit (2012). ''The Fractalist: Memoir of a Scientific Maverick'', Pantheon Books.
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?
几何图形能否传达其希腊词根[geo-]所蕴含的内容，即追求真实的测量数据？不仅能测量尼罗河沿岸的耕地，还能测量未开发的土地？
In his paper titled [[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>"Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?": Benoit Mandelbrot (1967). "[https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw Benoît Mandelbrot, Novel Mathematician, Dies at 85] {{Webarchive|url=https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw |date=31 December 2018 }}", ''The New York Times''.</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 | author=Mandelbrot, 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>
In his paper titled How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses 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.
曼德布洛特在1967年《科学》杂志上发表的论文《英国的海岸线有多长？统计自相似性和分数维》中讨论了'''<font color="#ff8000"> 豪斯多夫维数Hausdorff dimension</font>'''的自相似曲线。这些都是分形的例子，尽管曼德布洛特在论文中并没有使用这个术语，因为他直到1975年才创造这个名词。该论文是曼德布洛特关于分形主题的第一批出版物之一。
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=Mandelbrot />{{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:
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."[8]: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:
曼德布洛特特地强调可以使用分形作为描述现实世界中多数“粗糙”现象的模型，因其能真实且有效地展现出来。他还总结道：“实际粗糙度通常都是分形的，是可以测量出来的。” 不过，尽管他创造了“分形”一词，但他在《大自然的分形几何学》中提出的一些数学现象之前曾被其他数学家描述过。只是在曼德布洛特之前，这些现象被视为不自然和非直觉特性的特例存在。是曼德布洛特首次将这些现象或物体放在一起，并将它们变成了必要的工具，通过长期的努力，以科学的范畴去解释现实世界中这些非光滑的“粗糙”物体。
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.
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.
我越来越喜欢的几何形式是最古老，最具体，最包容的几何形式，特别是由眼睛，由手，甚至由当今计算机提供协助去赋予其力量……为认识和感知世界带来统一的元素……并且，在不经意间，作为创造美的目的，其实这也相当于是额外奖赏。
Fractals are also found in human pursuits, such as music, painting, architecture, and [[stock market]] prices. 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 /> —Mandelbrot, in his introduction to ''[[The Fractal Geometry of Nature]]''</blockquote>
Fractals are also found in human pursuits, such as music, painting, architecture, and stock market prices. 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:
分形也存在于人类的追求中，例如音乐，绘画，建筑和股票市场价格。曼德布洛特认为，分形超脱于自然，而且在许多方面比传统欧几里得几何形状的人工光滑物体更直观，更自然：
云不是球形，山不是圆锥形，海岸线不是圆形，树皮不是光滑的，闪电也不是直线传播的。
--曼德布洛特，《大自然的分形几何学》介绍
==Awards and honors==
==Awards and honors==