Sunday, October 17, 2010
Saturday, October 16, 2010
Benoît B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85.
His death was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge.
Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.
“Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found,” said David Mumford, a professor of mathematics at Brown University. “He was one of the primary people who realized these were legitimate objects of study.”
In a seminal book, “The Fractal Geometry of Nature,”published in 1982, Dr. Mandelbrot defended mathematical objects that he said others had dismissed as “monstrous” and “pathological.” Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now “be approached in rigorous and vigorous quantitative fashion.”
For most of his career, Dr. Mandelbrot had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for I.B.M. in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns that other researchers may have overlooked in their own data, then often swooped in to collaborate.
“He knew everybody, with interests going off in every possible direction,” Professor Mumford said. “Every time he gave a talk, it was about something different.”
Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.
“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”
In the 1950s, Dr. Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a “fractal dimension,” an insight that has proved useful well beyond the field of cartography.
Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.
His influence has also been felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honor.
“I decided to go into fields where mathematicians would never go because the problems were badly stated,” Dr. Mandelbrot said. “I have played a strange role that none of my students dare to take.”
Benoît B. Mandelbrot (he added the middle initial himself, though it does not stand for a middle name) was born on Nov. 20, 1924, to a Lithuanian Jewish family in Warsaw. In 1936 his family fled the Nazis, first to Paris and then to the south of France, where he tended horses and fixed tools.
After the war he enrolled in the École Polytechnique in Paris, where his sharp eye compensated for a lack of conventional education. His career soon spanned the Atlantic. He earned a master’s degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, N.J., for a postdoctoral degree under the mathematician John von Neumann.
After several years spent largely at the Centre National de la Recherche Scientifique in Paris, Dr. Mandelbrot was hired by I.B.M. in 1958 to work at the Thomas J. Watson Research Center in Yorktown Heights, N.Y. Although he worked frequently with academic researchers and served as a visiting professor at Harvard and the Massachusetts Institute of Technology, it was not until 1987 that he began to teach at Yale, where he earned tenure in 1999.
Dr. Mandelbrot received more than 15 honorary doctorates and served on the board of many scientific journals, as well as the Mandelbrot Foundation for Fractals. Instead of rigorously proving his insights in each field, he said he preferred to “stimulate the field by making bold and crazy conjectures” — and then move on before his claims had been verified. This habit earned him some skepticism in mathematical circles.
“He doesn’t spend months or years proving what he has observed,” said Heinz-Otto Peitgen, a professor of mathematics and biomedical sciences at the University of Bremen. And for that, he said, Dr. Mandelbrot “has received quite a bit of criticism.”
“But if we talk about impact inside mathematics, and applications in the sciences,” Professor Peitgen said, “he is one of the most important figures of the last 50 years.”
Besides his wife, Dr. Mandelbrot is survived by two sons, Laurent, of Paris, and Didier, of Newton, Mass., and three grandchildren.
When asked to look back on his career, Dr. Mandelbrot compared his own trajectory to the rough outlines of clouds and coastlines that drew him into the study of fractals in the 1950s.
“If you take the beginning and the end, I have had a conventional career,” he said, referring to his prestigious appointments in Paris and at Yale. “But it was not a straight line between the beginning and the end. It was a very crooked line.”
Tuesday, October 12, 2010
Monday, October 4, 2010
An Ex-Resident’s Story
I was referred to Granada House in November 1989. “Referred” is a very
polite way to put it. I was a patient in a rehab attached to a well-known
mental hospital in Boston, and a psychiatrist in this rehab had established
some credibility with me, and he opined that (1) unless I signed up for
long-term treatment someplace, I wasn’t going to be able to stay off drugs
and alcohol; and that (2) if I couldn’t find a way to stay off drugs and
alcohol, I was going to be dead by 30. I was 27. This was not my first
in-patient rehab, nor was it my first mental hospital.
Because certain myths about both addiction and halfway houses die hard, I’ll
give you a little bio. I was raised in a solid, loving, two-parent family.
None of my close relatives have substance problems. I have never been in
jail or arrested–I’ve never even had a speeding ticket. In 1989, I already
had a BA and one graduate degree and was in Boston to get another. And I
was, at age 27, a late-stage alcoholic and drug addict. I had been in
detoxes and rehabs; I had been in locked wards in psych facilities; I had
had at least one serious suicide attempt, a course of ECT, and so on. The
diagnosis of my family, friends, and teachers was that I was bright and
talented but had “emotional problems.” I alone knew how deeply these
problems were connected to alcohol and drugs, which I’d been using heavily
since age fifteen. Every single one of my mental-health crises had followed
a period of heavy bingeing on marijuana, tranquilizers, and alcohol. I had
first vowed to quit at age nineteen; the longest I’d ever gone without any
sort of substance was three months. I was convinced that this was because I
was weak, or because I really did have intractable mental problems which
only drugs and alcohol gave me any relief from.
I therefore spent most of the 1980s on the horns of a dilemma that many
addicts and alcoholics understand very well. On the one hand, I knew that
drugs and alcohol controlled me, ran my life, and were killing me. On the
other, I loved them–I mean really loved them, as in the sort of love where
you’ll do anything, tell yourself any sort of lie to keep from having to let
the beloved go. For most of the late 80s, my method for “quitting” drugs was
to switch for a period from just drugs to just alcohol. Then I’d switch back
to drugs in order to “quit” drinking. The idea of months or* *years without
any chemicals at all was unimaginable. This was my basic situation. I both
wanted help and didn’t. And I made it hard for anyone to help me: I could go
to a psychiatrist one day in tears and desperation and then two days later
be fencing with her over the fine points of Jungian theory; I could argue
with drug counselors over the difference between a crass pragmatic lie and
an “aesthetic” lie told for its beauty alone; I could flummox 12-Step
sponsors over certain obvious paradoxes inherent in the concept of denial.
And so forth.
Six months in Granada House helped me immeasurably. I still wince at some of
the hyperbole and melodrama that are used in recovery-speak, but the fact of
the matter is that my experience at Granada House helped me, starting with
the fact that the staff admitted me despite the obnoxious condescension with
which I spoke of them, the House, and the l2-Step programs of recovery they
tried to enable. They were patient, but they were not pushovers. They
enforced a structure and discipline about recovery that I was not capable of
on my own: mandatory counseling, mandatory AA or NA meetings, mandatory
employment, curfew, chores, etc. Not to mention required reading of AA/NA
literature whether I found it literarily distinguished or not. Granada House
also provided my first experience of an actual recovering community: there
were over twenty newly recovering residents, and the paid staff–almost all
of whom were in recovery–and the unpaid volunteers, and the dozens of House
alumni who seemed always to be around in the kitchen and living room and
offices. I made friends, and enemies, and enemies who then became friends. I
was, for six months, literally immersed in recovery. At the time, it seemed
crowded and claustrophobic and loud, and I resented the lack of “privacy,”
just as I resented the radical simplicity of l2-Step programs’ advice to
newcomers: go to a l2-Step meeting every day, make one such meeting your
home group, get a sponsor and tell him the truth, get active with some kind
of job in your home group, pray for help whether you believe in God or not,
etc. The whole thing seemed uncomfortable and undignified and dumb. Now,
from the perspective of almost fourteen years sober, it looks like precisely
what I needed. In Granada House, I was surrounded by recovering human beings
in all their variety and sameness and neurosis and compassion, and I was
kept busy, and I was made bluntly and continually aware of the fact that I
had a potentially fatal disease that could be arrested only by doing some
very simple, strange-looking things. I was denied the chance to sit
chain-smoking in private and drive myself crazy with abstract questions
about stuff that didn’t matter nearly as much as simply not putting
chemicals into my body.
This is not to say that the staff and volunteers at Granada House didn’t
listen. The House was structured and disciplined, but it was not
authoritarian. One of the kindest and most helpful things the House staff
did for me was to sit down and listen–to complaints, cravings, questions,
confessions, rants, resentments, terrors, and insights both real and
imagined–because a lot of my early recovery consisted of learning to say
aloud the stuff about drugs and alcohol and recovery I was thinking, instead
of keeping it twisting and writhing around inside my head. People at Granada
House listened to me for hours, and did so with neither the clinical
disinterest of doctors nor the hand-wringing credulity of relatives. They
listened because, in the last analysis, they really understood me: they had
been on the fence of both wanting to get sober and not, of loving the very
thing that was killing you, of being able to imagine life neither with drugs
and alcohol nor without them. They also recognized bullshit, and
manipulation, and meaningless intellectualization as a way of evading
terrible truths–and on many days the most helpful thing they did was to
laugh at me and make fun of my dodges (which were, I realize now,
pathetically easy for a fellow addict to spot), and to advise me just not to
use chemicals today because tomorrow might very well look different. Advice
like this sounds too simplistic to be helpful, but it was crucial: I had
gotten through a great many days sober before I realized that one day is all
I really had to get through.
Finally, because all the staff and ex-residents were members of AA and NA,
my relationships with them helped ease me into active membership in l2-Step
fellowships, which is pretty much the only proven method for maintaining
long-term sobriety. Now, in 2003, I no longer live in Boston, but I am an
active, committed member of AA in my new community.