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Mike Breen and Annette Emerson
Public Awareness Officers
paoffice at ams.org
Tel: 401-455-4000
Fax: 401-331-3842 |
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Racism and mathematics
Taki's Magazine ("Our only ideology is to be against the junk culture foisted upon us and mirages of a new world order") posted, on April 5, 2012, "The Talk: Nonblack Version" by John Derbyshire, at that time a columnist affiliated with the National Review. A flippant and contrarian take on the news, engineered to be entertaining, is Taki's signature; only this time the flippancy went too far. Derbyshire, for example: "Thus, in those encounters with strangers that involve cognitive engagement, ceteris paribus the black stranger will be less intelligent than the white." Beneath the genteel erudition (ceteris paribus!) is a clearly racist opinion. Then: "There are, for example, no black Fields Medal winners. While this is civilizationally consequential, it will not likely ever be important to you personally. Most people live and die without ever meeting (or wishing to meet) a Fields Medal winner." One could analyze the cavalier attitude towards science that is part of Derbyshire's mid-Atlantic upper-class persona, but here he brings professional mathematics into his argument, and here he aroused the attention of Jonathan Farley, a black American mathematician. Farley answered with "Black mathematicians: the kind of problems they wish didn't need solving", on the website of The Guardian. "Derbyshire implies that the absence of a black winner means that black people are incapable of genius. In reality, black mathematicians face career-retarding racism that white Fields medallists never encounter." And he gives examples. Among them:
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"In 1951, [Saunders] Mac Lane was president of the Mathematical Association of America (MAA). Vanderbilt University hosted an MAA conference, and three black mathematicians wished to attend the conference's banquet. They were barred and Mac Lane refused to take a stand: Vanderbilt University was in racially segregated Tennessee, and he did not want to offend his hosts."
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David Blackwell (1919-2010) was a very distinguished American mathematician. "Blackwell obtained his PhD in mathematics when he was only 22. While he had a fellowship to work at the Institute for Advanced Study ... nearby Princeton University refused to allow Blackwell to attend lectures because he was black." At that time "the University of California at Berkeley's maths department would not hire Blackwell on account of his race ... ." Blackwell "later became the first black member of the National Academy of Sciences (with a colleague saying, "he would come into a field that had been well studied and find something really new that was remarkable")... ." [Blackwell was recruited by the Berkeley Department of Statistics in 1954, became Chair in 1956 and taught at Berkeley until his retirement in 1988.]
Farley ends with a quotation from Stephen Jay Gould: "Few tragedies can be more extensive than the stunting of life, few injustices deeper than the denial of an opportunity to strive or even to hope, by a limit imposed from without, but falsely identified as lying within."
Jonathan Farley was susbequently (April 18, 2012) interviewed on the topic by John Hockenberry on Public Radio International's "The Takeaway."
John Derbyshire is no longer affiliated with the National Review.
Frobenius on my mind
"The Geometric Structure of the Brain Fiber Pathways," by Van J. Wedeen (MGH) and seven collaborators, appeared in the March 30, 2012 Science. From the abstract: "We ... analyzed relationships of adjacency and crossing between cerebral fiber pathways in four nonhuman primate species and in humans by using diffusion magnetic resonance imaging." The result: with "strong cross-species homology, the cerebral fiber pathways formed a rectilinear three-dimensional grid continuous with the three principal axes of development."
This image, an annotated detail of a larger and higher resolution image (courtesy of Van Wedeen) of pathways of the sagittal stratum of the rhesus monkey occipital lobe, shows the most remarkable aspect of the team's discovery: the fibers are organized into three sets of orthogonal sheets that are interwoven into 2-dimensional strata just like the lines in a three-dimensional mathematical grid. The image shows a sample of 2 of the three sets: one, call it $X$, colored blue and purple, and another, $Y$, colored yellow and orange. "Interwoven" means that if an $X$-fiber $x_1$ intersects two $Y$-fibers $y_1$ and $y_2$, and $y_1$ intersects another $X$-fiber $x_2$, then $y_2$ and $x_2$ must also intersect. For example a blue fiber meets an yellow fiber at A and an orange fiber at B. The orange fiber meets another blue fiber at C. Then that second blue fiber and the original yellow fiber must meet: they do at D. As the authors note, this configuration is highly unlikely in nature. It can be destroyed by a small deformation of the direction fields generating the X and Y families. This mathematical fact, and the occurence of the phenomenon in the brains of all the species surveyed, underline the significance of the discovery. An image showing elements of all three families, as well as an explanation of how these images were obtained, are part of the Science report.
This finding has a mathematical consequence, described towards the end of the report: "By the Frobenius theorem [they reference the Meisner-Thorn-Wheeler Gravitation and William Thurston's Three Dimensional Topology and Geometry] any three families of curves in 3D mutually cross in sheets if and only if they represent the gradients of three corresponding scalar functions. Accordingly, we hypothesize that the pathways of the brain follow a base-plan established by the three chemotactic gradients of early embryogenesis. Thus, the pathways of the mature brain [present] an image of these three primordial gradients, plastically deformed by development."
Topics in computational biology
The April 13, 2012 issue of Science has a Special Section on Computational Biology. A couple of the reviews describe the various mathematical approaches that have been and can be useful.
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"Cell Polarity: Quantitative Modeling as a Tool in Cell Biology," by Alex Mogliner, Jun Allard (U.C. Davis) and Roy Woolman (Stanford) itemizes and describes the modeling tools available.
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Ordinary differential equations
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Partial differential equations
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Stochastic simulations
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Agent-based simulations ("... rely on explicitly tracking all essential molecules")
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Boolean networks
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Baysian models
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Network analysis
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"Computational Approaches to Developmental Patterning," by Luis Morelli (Max-Plank Institute, Dresden), Koiciro Uriu, Saúl Ares and Andrew C. Oates, outlines various mathematical approaches to the problem: morphogen gradient, activator-inhibitor system (can be analyzed deterministically with differential equations or stochastically with cellular automata), genetic oscillators and the geometric study of mechanical deformation.
Tony Phillips
Stony Brook University
tony at math.sunysb.edu
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Math Digest Summaries posted May 2012:
Mobile App of IBM's Math History Timeline, Turing and the Fibonacci sequence in nature, the Liar Paradox ...
"Now that's calculated! Physicist writes four-page math paper to beat $400 traffic ticket," Daily Mail, 16 April 2012, and "Victory of science over traffic ticket debunked," by Pat Flynn. U-T San Diego, 23 April 2012.
Did the traffic cop really see Dmitri Krioukov run a stop sign? Although it may have appeared to be so, Krioukov convinced a California judge that a passing vehicle and the difference between linear and angular velocity had obscured the police officer’s view of reality. Using graphs and a four-page paper, Krioukov showed that from the vantage point of a patrol car parked on a perpendicular side street, the movement of a vehicle that quickly stopped and then accelerated would appear nearly identical to that of a vehicle that maintained a constant speed (and skipped the stop sign) if the officer’s view was briefly blocked at the exact time of the stop—which Krioukov's car was. End result of Krioukov’s mathematical handiwork: the judge bought the argument, and Krioukov avoided a $400 ticket.
The AP news release was picked up widely in the media (by San Francisco Chronicle, Washington Post, Boston Globe, San Jose Mercury News, among others), and covered by this blog: "Research paper saves UCSD scientist from $400 traffic fine," by Matt Stevens, Los Angeles Times Blog, 18 April 2012.
Krioukov's paper, "The Proof of Innocence," is posted on the ArXiv.
A week after this story broke, another news item was posted in which the traffic court judge offered a different, and more mundane, explanation of her decision. Superior Court Commissioner Karen Riley told U-T San Diego that she listened to the physics argument but much of it went over her head. Riley says she found Krioukov not guilty because the officer who cited him wasn't close enough to the intersection to have a good view.
--- Lisa DeKeukelaere
Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996.
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