The Best Writing on Mathematics 2014
Editor Mercia Pitici’s intent is clear; “I want accessible but nontrivial content that presents for mathematicians and for the general public a wide assortment of informed and insightful perspective on pure and applied mathematics, on topics related to the learning and teaching of mathematics, on the practice and practicality of mathematics, on the social and institutional aspects in which the mathematics themes, or on other themes related to mathematics.”
And Mercia should be congratulated on his success in its execution. Of the many essays in The Best Writing on Mathematics 2014, there are several deserving of special mention.
For example in The Rise of Big Data” by Kenneth Cukier and Viktor Mayer-Schonberger point out the incredible growth of big data. “As recently as the year 2000 only one quarter of the world’s information was digital, now less than 2% of stored information is non-digital.” The reader is apprised of the three key implications for researchers in having access to big data. The first is that researchers can use large datasets instead of just sampling by statistics.
Second, instead of using “curated” data, researchers can directly apply messy data with statics to throw away non-bias errors. And third, messy data provides researchers a wide range of variability, patterns and correlations that can lead to interesting conclusions. The authors note that for example, that one could use “360 sensors in a car seat to identify a person by their bottom”, a comment that is followed by wry humor in that “[t]he research is not asinine.” To mix metaphors, the bottom is also a fingerprint.
Essays include math puzzles and games, different methods of multiplication, and paradoxes. A logic puzzle is offered by John H. Conway, inventor of the mathematical Game of Life. In “On Unsettleable Arithmetical Problems” that asks, “What are the simplest true assertions that are neither provable nor disprovable?”
An essay considers space filling curves, “Crinkly Curves” by Brian Hayes, is on the topic of Hilbert curves, Peano curves, how to calculate efficient rules for half toning in graphic arts, and improved algorithms for matrix multiplication.
In the essay, “Why Do We Perceive Logarithmically” by Lav R. Varshney and John Z. Sun, the reader learns that the biology of perception across animal species and sense modalities is non-linear in the manner of providing greater perceptual resolution for less intense stimuli, and less for greater stimuli. Animals do not notice absolute changes in the external world; they detect relative changes with statistical properties. The authors provide a theory in formal mathematical terms and in lay terms, explaining that perception is non-linear because it is efficient with respect to reducing errors.
However, “The Music of Math Games” by Keith Devlin seems a poor choice to include, reading as it does like a marketer’s advertisement. The essay’s topic is the use of video games to increase a student’s proficiency in math, and provides illustrations similar to the mathematics-game-as-work from the science fiction movie, The Zero Theorem.
In “The Arts—Digitized, Quantified, and Analyzed” by Nicole Lazar the reader discovers the intersection of statistics, big data, and the arts through the use of statistics, word counts and word distributions. Together these techniques are called “art analytics” and can be used to determine “true” authorship of books, or be applied to music to identify composers. Though art analytics has been applied mostly to literature, it can also be applied to social networks to uncover anonymity. Statistical sampling of an individuals selection of newspaper articles, and website topics can also be used as a predictor (or pusher) of the next hit pop song or the next hit book.
This is the first year that color plates are provided, and color definitively makes an impact compared to black and while. In the essay, “On the number of Klein Bottle Types”, by Carlos H. Sequin, ant though readers may be presented with more than they ever might want to know about the Klein bottle, the illustrations make the essay worthwhile. That essay ties to the next by Sarah-Marie Belcastro titled, “Adventures in Mathematical Knitting.” Here Sarah-Marie shows you how to knit a Klein bottle, also with illustrations in color.
There are a number of essays that focus on education. In “The Mathematics of Fountain Design” by Marshall Gordon, the reader will discover fountain design as practiced and experienced through STEM education. “Food for (Mathematical) Thought”, by Penelope Dunham addresses the use of food as a “manipulation model” for teaching mathematical concepts. Says Penelope, “One might ask, ‘Why teach math with food?’ . . . My simple reply is that everything goes better with food.” She suggests using carrots for canonical sections, goldfish crackers, M+Ms, Skittles, and hard-boiled eggs and an egg slicer for teaching geometry, volume, and statistics.
In “Wondering about Wonder”, the authors Dov Zazkis and Rina Zazkis explore the beauty of the Mandelbrot set but also ask an pointed question: “How can such a complicated pattern emerge from such a simple equation?” Their answer begins intriguingly but ends as a disappointment; their wordplay is no substitute for a simple answer.
There are essays on proofs and proving proofs, an essay that ties topology, the mathematics of shapes to real world physics. There are essays on real numbers and fractals, dynamic systems, and chaos theory. Readers will be impressed by the color plates that are provided with “Chaos at Fifty” by Adilson E. Motter and David K. Campbell. Their essay provides a short history of chaos theory that starts in the 1890s with Poincare and the 3-body problem, and moves on to the early 1960s with Edward Lorenz who discovered the “butterfly effect” while modeling weather with an early computer.
The mathematics of “College Admissions and the Stability of Marriage” by Dave Gale and LLoyd Shapely is an essay on the optimization of choice and prediction, which might be summarized as “be careful what you wish for.“
“The Lesson of Grace in Teaching” is a personal philosophy by Francis Edward Su, and in this humble reviewer’s opinion is the best essay in this collection, while this reviewer considers the second best to be “Twenty-five Analogies for Explaining Statistical Concepts” by Roberto Behar, Pere Grima, and Lluis Marco-Almagro, and meant for people who have trouble “getting” statistics," which might include most of us.
The contributors are a fascinating and diverse bunch, and readers may be interested in the their biographies at the back. Also at the back is a list of “notable writings” that didn’t make the cut, along with the editor’s acknowledgments, introduced with a personal note.
The Best Writing on Mathematics series should be lauded for Mercia Pitici‘s role as editor in not just selecting these essays but also their order and flow.