Life by the Numbers is the overall title for a series of TV programs on mathematics produced by WQED Pittsburgh with support from a number of foundations and corporations. The first program in the series was shown on PBS on April 8. Subsequent programs were transmitted to affiliate stations which were free to schedule them at any time; many have delayed showing them until June. The series has a supporting web page, and an accompanying book by Keith Devlin. The set of video tapes is for sale; call 1-800-274-2307 for more information.
Our reviewer is Colm Mulcahy, from the mathematics department at Spelman College in Atlanta, Georgia.
Keith Devlin, who was a consultant for the Life by the Numbers series, has some wise words for those who fear complexity in mathematics: "To most people, mathematics makes the world more complicated, it doesn't do that! Math makes the world more simple! Mathematicians are simplistic creatures. We look at the world in the simplest possible way. We look at it in such a simple way that the only way of capturing the simplicity is with symbols, lines, nodes, edges of graphs. We strip away the complexity!" Unfortunately, this wonderful observation is tucked away at the end of the sixth program of this seven part PBS series.
The subtitle of this series, "math like you've never seen it before", is a good one, because it applies just as much to those of us in the profession as it does to the average non-specialist viewer. These TV programs are about how mathematics is used all around us, often in conjunction with physics and engineering, in science, medicine, industry, commerce, sports, art and entertainment. The approach taken is fresh, and not all of these manifestations of applied mathematics will be familiar to the very people who are entrusted with getting students to learn mathematics - those of us who teach. That's a good enough reason for us to watch the series: too often we lose sight of the fact that we are an exclusive minority, the few survivors of a long, difficult and often unnatural process of learning (in graduate school) and training (on the job), which leaves many talented but bewildered people in its wake, and inevitably has the rest of us convinced that that if anybody knows what mathematics is and what it's good for, we do. Don't be so sure!
While an increased appreciation for the beauty of mathematics does come with advanced learning, and may serve as a primary motivation for why we do what we do, that subtlety is usually lost on the rest of the population. Here, the relevant question is: Do we have a real appreciation of the range of application of mathematics in the world around us today? Do some of us feel that such applications are suspect because they are lacking in "purity", or are not founded on firm theoretical bases? Such reservations would certainly color our reactions to the content and slant of this series.
An informal email survey suggests that some mathematicians' responses to early episodes of Life By The Numbers were lukewarm: could this be because there is very little overlap between the series and what goes on it our classrooms? And very few mathematicians in evidence? Perhaps, but it would be a mistake to view the absence of calculus, vector spaces and groups from these innovative programs as evidence of a lack of depth or relevance. We get our chance to convert people to mathematics every time we enter a classroom, with the usual mixed results. As a general rule, Mathematics is the last topic to which the medium of television gravitates, and now that PBS is trying to get the masses hooked, stressing the role of mathematics as a tool, the least we can do is give the series a fair hearing and try to judge it on its own merits.
One of the principal messages of Life By The Numbers is that mathematics permeates virtually all of our lives, and that people can be motivated to learn mathematics via things they find interesting, be that special effects in movies and educational films, the miracle of the internet, the history of art, the wonders of cosmology, the pitfalls of gambling, sports analysis, building better boats, map making, flight simulation, national surveys, wearable computers, modelling international economies, DNA, life insurance, playing chess on the surface of a doughnut, or the chances of being attacked by giant locusts!
The inescapable conclusion, which is so obvious to those with training in the field but still surprises most otherwise well educated people in the world, is that mathematics is not dead! For instance, it is the invisible fuel that drives much of this information age: without recent advances in the application of mathematics, there would be no fast cheap phone network encircling the globe, no fax, television, email, no MAA Online.
The seven parts are titled: "Seeing Is Believing" (special effects), "The Numbers Game" (sports), "Patterns Of Nature" (biology), "Chances Of A Lifetime" (probability), "Shape Of The World" (exploration), "A New Age" (information age) and "Making A Difference" (education). The last, which this writer has not yet seen, is the only one to consider the teaching of mathematics. Unfortunately, many PBS affiliates have chosen to air only the first program, and others haven't aired any. A PBS station in Georgia defended their decision not to bring this series to the state whose students standardized mathematics scores are ranked among the lowest in the nation by claiming that the programs were "too esoteric". So much for education and trying to make a difference.
The series is presented by actor Danny Glover, who puts his dramatic skills to good use, introducing each program with an inviting tease, and narrating most of what follows. Almost no formulas are presented, none are dwelled on, and intuitive understanding, especially with visual cues, is emphasized throughout. Typically, each show highlights a half dozen related topics, with key practitioners profiled in an engaging fashion.
"Seeing Is Believing" kicks the series off, with state-of-the-art immersive theme park movies and the 15th century Italian breakthroughs in perspective drawing and art. It makes the point that the ability to copy precise pictures of mechanical devices changed the way the previously oral tradition of the European master/apprentice guild system worked, making technology available to a much wider audience and paving the way for the industrial revolution. Donna Cox (of the University of Illinois) shows how the National Center for Supercomputing
Applications generates simulations of colliding galaxies and how artists' sketches are turned into flashy and hopefully accurate IMAX films. Cox also works with George Francis (University of Illinois) to help animate complicated topological shapes on computer screens, which leads into a segment on "invisible realities". Tom Banchoff (Brown University) discusses the challenge of trying to visualize 4-dimensional space, in particular the hypercube. He makes the excellent point that even 3-dimensional objects, such as his office building, can never be taken in all at once by the human eye, we piece it together in our minds from many different 2-dimensional experiences of it. (One might add that there is a further reduction here: we've just explained this in a linear, 1-dimensional sentence!). Unfortunately, this first program in the series loses focus towards at the end, with some overly long segments featuring guests who make portentous (and usually meaningless) statements about mathematics.
The topics in "The Numbers Game" include: the competitive edge that can be gained in American football by statistically analyzing playback videos, how tennis has changed in the last 50 years through engineering analysis, how computer aided geometric design modeling is involved in building winning boats for the America's Cup, the role of biomechanics in enabling American ice-skaters to master the once undreamed of triple axle jump, and how to fine-tune training for the extraordinarily challenging triathalon.
"Patterns of Nature" gets off on a good footing by explaining how giant locusts and other staples of horror movies are simply not possible, as the weight/size ratios would not be sustainable, then moves on to consider how leopards get their spots, the relationship between DNA and knots (featuring De Witt Sumners of Florida State University), the ever-popular fractals, and the challenges of designing artificial life in computers.
"Chances Of A Lifetime" brings to the screen some more familiar material related to probability and statistics, often using a historical perspective: the origins of the subject in gambling, casino gambling today, the use of statistics in health issues (the Salk vaccine trail), baseball statistics, insurance and actuarial concerns. Did you know you can insure all (well, most) aspects of your wedding?!
The "Shape Of The World" episode starts with the ancient role of geometry in navigation and mapmaking, and proceeds to flight simulators, the mapping of 5000 sq. miles of the mountainous Yukon terrain for the first time in the 1930s (using photogrammetry), the work of the National Image and Mapping Agency (which now has accurate maps of 90% of the earth's land surface), the ongoing project of mapping the earth's ocean's floors, and the recent triumph of the Global Positioning System, which uses satellite distances rather than angles to tell us exactly where we are. But there's more! Robert Osserman (MSRI/Stanford) introduces the idea of a curved universe, and Jeff Weeks takes up the tale with a charming and highly effective segment (featuring his young son Adam) on the possible shapes of space. Geometry Center video excerpts and torus chess demonstrations help to make the point.
"A New Age" concerns the information revolution, and hooks the viewer early on with discussion of software agents (aka digital butlers), wearable computers, the role of Boolean algebra in the design of computers, Bill Massey (Lucent Technology) on queueing theory, and Nate Dean (Bell Labs) on data mining - with the amusing conclusion that if you want to run a grocery store, put bananas on display everywhere! Graciela Chichilninsky (Columbia University) models economies, and argues convincingly that mathematics is to the information age what fossil fuels were to the industrial revolution. Danny Glover wraps things up by pointing out that: "Far from being a dry and boring subject, mathematics is a powerful tool we can use to create a new era, a new world that begins with our ability to imagine and dream."
Throughout the series there is a conscious effort to downplay "the geek factor" and stress the human element and the excitement quotient. Fancy graphics are used, in moderation. Clever production tricks keep the series lively, such as occasional glimpses of personal lives or amusing clips from old movies, and overall the editing is seamless. While some might question the real value of some of the applications of mathematics presented here, it's a small price to pay for the overall good to our profession these shows could do. If anything, there is too much material per show, it's hard to absorb it all in one sitting. That's not such a bad complaint, however, and all the more reason to order this series on videotape for your library. This is a series that deserves to be widely seen. If your local PBS station has been slow to bring it to your TV screen, there is still time to try to twist their arm.
MAA Online is edited by Fernando Q. GouvÃÂªa
***************************************************************** Jerry P. Becker Dept. of Curriculum & Instruction Southern Illinois University Carbondale, IL 62901-4610 USA Fax: (618)453-4244 Phone: (618)453-4241 (office) E-mail: JBECKER@SIU.EDU