On Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
This article discusses Claude Shannon, who has been called the father of the information age. April 30th was the 100th anniversary of Shannon's birth.
In the 1948 paper "A Mathematical Theory of Communication" Shannon introduced the concept of using zeroes and ones to measure data. He called these measurements "bits," a term he credited to John Turkey, his colleague at Bell Telephone Laboratories.
Shannon defined another important concept: channel capacity. Consider different materials that information can travel through, such as telephone wires and fiber optic cables. There is an upper bound to the rate at which information can travel through these channels and remain intact. This maximum rate is called the channel capacity or the Shannon limit.
James Gleik, who wrote "The Information," told the author of this article, "It's Shannon whose fingerprints are on every electronic device we own, every computer screen we gaze into, every means of digital communication. He's one of these people who so transform the world that, after the transformation, the old world is forgotten."
One of Shannon's hobbies was creating off-beat inventions, from rocket-powered frisbees to flame-throwing trumpets. Shannon died on February 24th, 2001 ("MIT Professor Claude Shannon dies; was founder of digital communications," MIT News, February 27, 2001). Each year since 1973, the IT Society has presented one Claude E. Shannon Award, "to honor consistent and profound contributions to the field of information theory." Shannon was the first recipient of the award. The 2016 recipient was Alexander S. Holevo of the Steklov Mathematical Institute of the Russian Academy of Sciences in Moscow. Photo: Oberwolfach Photo Collection (CC BY-SA 2.0 DE).
See "Claude Shannon, the Father of the Information Age, Turns 1100100," by Siobhan Roberts, The New Yorker, 30 April 2016.
--- Rachel Crowell
Tricia Serio, professor and head of molecular and cellular biology at the University of Arizona in Tucson, has personally experienced "microaggression" -- indirect, subtle or unintentional comments -- in the workplace. Her lead example is when she was early in her academic career she told her department head that she was pregnant and his response was "Was it planned?" Another was when she inquired about research opportunities at the institution and the response was "Why? Jeff [my significant other at the time] is doing a postdoc in another city." Serio believes that there are many untold stories of unconscious gender bias in academic science, and so she has set up Speak Your Story Survey, a website where women in mathematics and all sciences are invited to post their stories anonymously. "The purpose of this invitation is not to identify individual offenders. Rather, I hope to shine a light on the perception gap that I suspect leads to many microaggressions (and their subsequent impact), and to begin to quantify its scope by field, type of institution and location. My goal is to narrow or, ideally, to eliminate this gap. Let's inspire change by moving from unspoken anecdotes to awareness." She plans to share the stories periodically, though she doesn't indicate how she will do that.
See "Speak up about subtle sexism in science," by Tricia Serio, Nature, 26 April 2016 (print 28 April 2016).
--- Annette Emerson
In this article Jo Boaler explains why it is essential for children to use their fingers for counting in math class. Apparently, there is "a specific region in our brain that is dedicated to perception and representation of fingers known as the somatosensory finger area." When students learned ways to use their fingers to help their mathematical understanding it lead to greater math successes. Neuroscientists recommend that students learn 'finger discrimination' or distinguishing between their fingers. Unfortunately, conventional methods have warned students away from counting on their fingers but Boaler explains that new brain research shows that, "Stopping students from using their fingers when they count could be akin to halting their mathematical development." Teachers should encourage their students to use their fingers to "strengthen this brain capacity" and ask the students to visualize mathematical ideas and draw what they see.
See "Why Kids Should Use Their Fingers in Math Class," by Jo Boaler and Lang Chen, The Atlantic, April 13, 2016.
--- Samantha Faria
"Scientists have long debated whether the basis of high-level mathematical thought is tied to the brain's language-processing centers—that thinking at such a level of abstraction requires linguistic representation and an understanding of syntax—or to independent regions associated with number and spatial reasoning," writes the author of this Scientific American article. According to a study that was recently published in Proceedings of the National Academy of Sciences by INSERM–CEA Cognitive Neuroimaging Unit director Stanislas Dehaene and graduate student Marie Amalric, that question has been answered: "Our results show that high-level mathematical reflection recycles brain regions associated with an evolutionarily ancient knowledge of number and space," Amalric states. In the study, Cepelewicz explains, functional magnetic resonance imaging (fMRI) was used "to scan the brains of 15 professional mathematicians and 15 non-mathematicians of the same academic standing. While in the scanner the subjects listened to a series of 72 high-level mathematical statements, divided evenly among algebra, analysis, geometry and topology, as well as 18 high-level nonmathematical (mostly historical) statements. They had four seconds to reflect on each proposition and determine whether it was true, false or meaningless." Previously, Dehaene, an experimental psychologist, "has studied how humans (and even some animal species) are born with an intuitive sense of numbers—of quantity and arithmetic manipulation—closely related to spatial representation," Cepelewicz notes. "How the connection between a hardwired 'number sense' and higher-level math is formed, however, remains unknown."
See "How Does a Mathematician's Brain Differ from That of a Mere Mortal?," by Jordana Cepelewicz, Scientific American, 12 April 2016, and "Math brains do differ from the rest of us," by Geoff Johnson, Times Colonist, 26 April 2016.
--- Claudia Clark
The only way to get to the meaty, higher-level science, technology, engineering and math college courses is by successfully passing the introductory course. Unfortunately, these courses can be "stultifying bores," reported a presidential council. This may leave students "with the impression that all STEM fields are dull and unimaginative." Transforming Post-Secondary Education in Mathematics, referred to as Tipsy, is addressing this issue. With support from large foundations, organizations, well-known mathematicians, colleges and universities, this group has already worked out four areas in which to focus. The first goal is to make the math relevant to the students by demonstrating how it is used in the subjects that already interest them. For example, political science students could take a course in mathematical modeling. Next, Tipsy recommends more experimentation in the classroom by trying out options that have already been shown to work, such as flipped classrooms. This method has the students watch lectures outside of class and then spend class time working on problems with the instructor. Often, mathematicians are trained in graduate school to research rather than learning how to effectively teach future students. One can be a brilliant mathematician yet an unsuccessful teacher. Tipsy urges that "future professors train in effective teaching methods." Lastly, the only way to accomplish these goals, Tipsy admits, is to create a higher-education network. Through partnerships with various organizations, such as the Association of Public and Land-Grant Universities and the National Association of System Heads, the network can reach out to large numbers of provosts, presidents, deans and department chairs.
See "4-Part Plan Seeks to Fix Mathematics Education," by Dan Berret, The Chronicle of Higher Education, April 10, 2016 (requires subscription).
--- Samantha Faria
According to this article, some scientists, such as Seth Shostak, director of the Search for Extra Terrestrial Intelligence (SETI), anticipate successfully contacting aliens within our lifetime. Without knowing their language, how will we communicate with extraterrestrials once we have achieved contact? Long before the invention of telephones and computers, scientists began pondering this question. Their answers have ranged from wacky and environmentally hazardous to specialized and tedious. In the early 1800’s, Joseph Johann Von Littrow, an Austrian astronomer, had a five step plan for alerting aliens to our presence: 1. Trek to the Sahara Desert. 2. Dig deep trenches. 3. Fill trenches with water. 4. Top water with kerosene. 5. Light kerosene on fire, catching extraterrestrial attention.
Littrow’s blazing idea was never tested. Hans Freudenthal, a German mathematician, proposed the next major idea in the field of extraterrestrial communication. If utilized, Freudenthal’s idea--a spoken, mathematically-based language called Lincos--wouldn’t produce quite the same spectacle as burning desert trenches. Lincos is a combination of lingua and cosmica. Freudenthal described Lincos in his 1960 book Lincos: Design of a Language for Cosmic Intercourse. Lincos shows promise as a basis for communicating with aliens who understand logic, mathematics and science. Scientists at SETI say these are the ETs we are likely to achieve communication with anyway. The reason? In order for an alien civilization to build receivers capable of understanding our messages, they would need to understand the mathematics and science behind constructing such devices.
In 1999, astrophysicists Yvan Dutil and Stéphane Dumas used a Ukrainian radio telescope to send messages intended for an extraterrestrial audience. Their transmissions, known as the Evaptoria Messages, were the third set of messages ever directed at potential ET civilizations. Unlike the two previous sets of messages sent out by other scientists, the Evaptoria Messages were created based on protocols outlined in Freudenthal’s Lincos. Dutil and Dumas’s 1999 messages were sent to cosmic addresses between 50 and 70 light years away. The first message is expected to reach cosmic address Hip4872 in Cassiopeia in approximately 19 years.
Researchers continue to refine their methods for communicating with possible ETs. CosmicOS, a computer program that aliens could run if they receive it, was developed by Paul Fitzpatrick, a former postdoctoral lecturer at MIT and co-founder of Robot Rebuilt, a U.S. robotics company. Alexander Ollongren, a Dutch mathematician, created a second-generation lingua cosmica. Messages in Ollongren’s language are created using constructive logic. Scientists have even considered combining Fitzpatrick and Ollongren’s approaches.
Scientists agree that mathematics is central to our pursuit of meaningful communication with ETs. (Image: Allan Telescope Array, Colby Gutierrez-Kraybill/Wikimedia.)
See "Building a Language to Communicate With Extraterrestrials," by Daniel Oberhaus, The Atlantic, 6 April 2016.
--- Rachel Crowell
Looking for some worthwhile cinematic entertainment? Check out the film The Man Who Knew Infinity, based on a biography of Indian mathematician Srinivasa Ramanujan, written by Robert Kanigel. Director Matthew Brown "dramatizes the purest of mathematics for a general audience, and explores the strange personal life of Ramanujan, who died at 32, at the height of his powers, probably from tuberculosis," writes Robinson in a review in Nature.
Ramanujan is played by actor Dev Patel while Jeremy Irons plays Ramanujan's colleague and champion, G. H. Hardy. Their performances benefited from the careful advising of mathematician and Ramanujan scholar, Ken Ono (who has just published an autobiography entitled My Search for Ramanujan) and Fileds Medalist Manjul Bhargava. Much of the film—and the mathematics—takes place at Trinity College in Cambridge, England, where Ramanujan and Hardy collaborated intensely between 1914 and 1919. While praising the film, Robinson notes that it "struggles to shed light on the origins of Ramanujan's prodigious gift. Biographers have had the same problem with Gauss and many other mathematicians. As India's great film director Satyajit Ray put it: 'This whole business of creation, of the ideas that come in a flash, cannot be explained by science.'" Hardy was awed and mystified as well, writing of Ramanujan "All his results, new or old, right or wrong, had been arrived at by a process of mingled argument, intuition and induction, of which he was entirely unable to give any coherent account."
(Photo: Ken Ono, associate producer and math consultant on the film; Jeremy Irons, who plays G.H. Hardy; Devika Bhise, who plays Ramanujan's wife, Janaki; Dev Patel, who plays Ramanujan; and Manjul Bhargava, associate producer and math consultant on the film.) Photo courtesy of Manjul Bhargava. Ono has recently co-authored a book with Amir Aczel, My Search for Ramanujan: How I Learned to Count.)
See "In search of Ramanujan," by Andrew Robinson, Nature, 31 March 2016, "Ramanujan biopic "The Man Who Knew Infinity" tells mathematician's journey," Reuters/Daily Mail, 7 April 2016, and "Genius by numbers: why Hollywood maths movies don't add up," by Stuart Jeffries, The Guardian, 6 April 2016; "The Man Who Knew Infinity fails to break the mathematical mould," by Jacob Aron, New Scientist, 8 April 2016; "A Math Biopic, With Dev Patel, Applies a Different Calculus," by Kathryn Shattuck, New York Times, 20 April 2016; "Jeremy Irons on how prejudice blinds us to genius," Q interview with Shadrach Kabango, CBC Radio, 19 May 2016.
--- Claudia Clark
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