150 years ago today, Alice in Wonderland was published

Alice's Adventures in WonderlandJuly 4, 2015 may be about Independence Day in the United States, but in Oxford, it’s about one of the great heroes of fiction, a young girl who followed a white rabbit, met a hookah-smoking caterpillar and asked, “Who are you?” 

In July 1865, 150 years ago, Charles Lutwidge Dodgson, a professor of mathematics and Anglican deacon, published Alice’s Adventures Underground, a story about a little girl who tumbles down a rabbit hole into a world of nonsense, but keeps her wits about her. With this the world was first introduced to Alice (who was inspired by a real child named Alice Liddell) and her pseudonymous creator, Lewis Carroll. To commemorate the anniversary, the rare first edition recently went on display in Oxford. Princeton University Press is honored to publish our own beautiful new edition of Alice’s Adventures in Wonderlandwith rarely seen illustrations by none other than Salvador Dalí.

Of course, Alice doesn’t just have a whimsical adventure full of anthropomorphic creatures. She falls into a world that is curiously logical and mathematical. Carroll expert Mark Burstein discusses Dalí’s connections with Carroll, his treatment of the symbolic figure of Alice, and the mathematical nature of Wonderland. In addition, mathematician Thomas Banchoff reflects on the friendship he shared with Dalí and the mathematical undercurrents in Dalí’s work.

Explore chapter one in full here, view the best illustrations over the years on Brain Pickings, or click here for a list of anniversary-related events. If you’re here in New Jersey, Washington Crossing’s Open Air Theater will be performing Alice in Wonderland in the park today at 11 and tomorrow at 4.

Happy birthday, Alice!

Q&A with Frank Farris, Author of Creating Symmetry: The Artful Mathematics of Wallpaper Patterns

Frank A. Farris teaches mathematics at Santa Clara University and is a former editor of Mathematics Magazine, a publication of the Mathematical Association of America. He is also the author of the new Princeton University Press book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. The book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry.

Frank Farris gave Princeton University Press a look at why he wrote Creating Symmetry, where he feels this book will have major contributions, and what comes next.

Before and After: A Peach and a Sierra Stream Become a Pattern, by Frank A Farris

Before and After: A Peach and a Sierra Stream Become a Pattern, by Frank A Farris

What inspired you to get into mathematical writing?
FF: After editing Mathematics Magazine for many years, I developed a passion for communicating mathematics: I didn’t want dry accounts written by anonymous authors; I wanted stories told by people. I wasn’t so interested in problems and puzzles, but in the stories that bring us face to face with the grand structures of mathematics.

Why did you write this book?
FF: Many years ago, I asked the innocent question: What is a wallpaper pattern, really? Creating Symmetry is the story of my dissatisfaction with standard answers and how it led me on a curious journey to a new kind of mathematical art. I took some risks and let my personality show through, while maintaining an honest, mathematically responsible approach. I hope readers enjoy the balance: real math told by a person.

What do you think is the book’s most important contribution?
FF: Most people who see my artwork say they’ve never seen anything like these images and that pleases me immensely. Of course, people have seen wallpaper patterns before, but the unusual construction method I use—wallpaper waves and photographs—gives my patterns an intricacy and rhythm that people wouldn’t create through the usual potato-stamp construction method, where the patterns is made from discrete blocks.

What is your next project?
FF: I am working on a “wallpaper lookbook,” a book for the simple joy of looking at patterns. Creating Symmetry tells people how to make the patterns, and there’s quite a lot of mathematical detail to process. Not everyone who likes my work wants to know all the details, but can still appreciate the “before and after” nature of the images.

Who do you see as the audience for this book?
FF: There are three audiences and they will read the book in different ways. The general reader, who knows some calculus but may be a little rusty, should find a refreshing and challenging way to reconnect with mathematics. Undergraduate mathematics majors will enjoy the book as a summer project or enrichment reading, as it makes surprising connections among topics they may have studied. The professional mathematician will find this light reading—a chance to enjoy the amazing interconnectedness of our field.

 

Tipping Point Math Tuesdays With Marc Chamberland: What’s the Best Paper Size?

Tipping Point Tuesday takes on a global debate!

The United States and Canada use paper that is 8.5 inches by 11 inches, called US letter. However, the rest of the world officially uses A4 paper, which has a different aspect ratio. Which paper size is better, US letter or A4? Find the mathematical answer with the help of Marc Chamberland in a video from his YouTube channel Tipping Point Math.

 

Marc Chamberland takes on more mathematical scenarios in his book Single Digits: In Praise of Small Numbers. Read the first chapter here.

Tipping Point Math Tuesdays with Marc Chamberland: How many guards are enough?

Today’s Tipping Point Tuesday gives us a behind the scenes look at how mathematics can be used in unique ways in the workplace.

Here’s the scenario: In busy museums, guards keep an eye on the priceless works of art. Suppose a museum wants to schedule the fewest number of guards per museum shift without leaving any art display unmonitored. Marc Chamberland explains how a museum manager could use mathematics to calculate the ideal number of guards per shift.

Continue exploring numbers with Chamberland in his book, Single Digits: In Praise of Small Numbers. Start by reading the first chapter here.

Q&A with Marc Chamberland, author of Single Digits: In Praise of Small Numbers

Marc Chamberland is the Myra Steele Professor of Natural Science and Mathematics at Grinnell College. He is also the creator of the popular YouTube channel Tipping Point Math, which strives to make mathematics accessible to everyone. Continuing on his mathematics mission, Marc Chamberland has authored Single Digits: In Praise of Small Numbers, a book that looks at the vast numerical possibilities that can come from the single digits. j10437Over the course of the coming weeks, we will be exploring the single digits in real life math situations with the author himself by featuring a series of original videos from Tipping Point Math.

Recently Chamberland gave the press a look at the inspiration behind the book, along with some personal insights on being a mathematician, and more:

What was the motivation behind your Tipping Point Math website?

MC: I have long felt that many people are sour on math because they think it is all technical stuff that leads to nowhere. I felt that if they could be exposed to the rich ideas and beauty of mathematics presented in an interesting way, their negative opinion could change.

I had wondered for a while how YouTube could be used since it is such a popular medium. In 2013, I reconnected with Henry Reich, a former student of mine, who created the highly successful channels MinutePhysics and MinuteEarth. With his inspiration and advice, I was convinced that a similar channel for mathematics was possible. Thus the concept of Tipping Point Math was born.

What is the biggest misunderstanding people have about your mathematics profession?

MC: Besides my remarks about people thinking that math is only about technical stuff, there is also the misconception that all of mathematics is known. This is not the case at all. New mathematics is being developed every day. This ranges from very abstract ideas to applications such as signal processing, medical imaging, population modeling, and computer algorithms.

What would you have been if not a mathematician?

MC: In my last year of high school, I developed an unquenchable thirst to explore two academic areas: mathematics and music. Since I eventually became a mathematics professor, I suppose one could say that mathematics “won”. But music was also consuming. I would ask myself, “Why does that piece of music sound so good? Why does it produce particular emotional states? How can I compose music that affects people in different ways?” To this day I still ask some of these questions, I occasionally compose short pieces, and I play the piano, guitar, and sing. Would I have been a musician? Is it too late to change?

What are you reading right now?

MC: I’m reading “The Alchemist” (by Paulo Coelho) out loud to my wife. The simple language and overflowing spirituality is stunning.

Who do you see as the audience for your book, Single Digits?

MC: My audience: those who love beauty. I did not choose topics for their depth or their technical superiority. I principally chose vignettes that I thought are beautiful.

In Memory of John and Alicia Nash

NashGradThe staff and community of Princeton University Press mourns the tragic loss of John and Alicia Nash. In 2001 we had the great privilege of publishing The Essential John Nash, a collection of Professor Nash’s scholarly articles edited by his biographer, Sylvia Nasar, and his longtime colleague and friend, Princeton mathematician Harold Kuhn, (now deceased). The Essential John Nash received impressive public exposure largely because it was published during the release of the Academy Award-winning movie version of Nash’s biography, A Beautiful Mind. Critics and readers admired The Essential John Nash as a faithful representation of Nash’s most important work, made available for a broadly intellectual audience of mathematicians and social scientists. Gratifying as this recognition was for us, during the course of publication, the staff members at PUP who worked on Professor Nash’s book had the great good fortune to get to know him and Alicia, two gentle and wonderful people. Our thoughts and prayers are with their family.

Peter J. Dougherty
Director

Book Fact Friday – #8 Single Digits

From chapter eight of Marc Chamberland’s Single Digits:

How many times should you shuffle a deck of cards so that they’re well-mixed? Gamblers know that three or four times is not sufficient and take advantage of this fact. In 1992, researchers did computer simulations and estimated that seven rough riffle shuffles is a good amount. They took their research further and figured out that further shuffling does not significantly improve the mixing. If the shuffler does a perfect riffle shuffle (a Faro shuffle), in which s/he perfectly cuts the deck and shuffles so that each card from one side alternates with each card from the other side, then a standard 52-card deck will end in the same order that it started in after it is done 8 times.

Single Digits: In Praise of Small Numbers by Marc Chamberland
Read chapter one or peruse the table of contents.

The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really “six degrees of separation” between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics.
Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan’s conjecture, and so much more. The book’s short sections can be read independently and digested in bite-sized chunks—especially good for learning about the Ham Sandwich Theorem and the Pizza Theorem.
Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.

#MammothMonday: PUP’s pups sound off on How to Clone a Mammoth

The idea of cloning a mammoth, the science of which is explored in evolutionary biologist and “ancient DNA expert” Beth Shapiro’s new book, How to Clone a Mammoth, is the subject of considerable debate. One can only imagine what the animal kingdom would think of such an undertaking, but wonder no more. PUP staffers were feeling “punny” enough to ask their best friends:

 

Chester reads shapiro

Chester can’t get past “ice age bones”.

 

Buddy reads shapiro

Buddy thinks passenger pigeons would be so much more civilized… and fun to chase.

 

Tux reads shapiro

Tux always wanted to be an evolutionary biologist…

 

Stella reads Shapiro

Stella thinks 240 pages on a glorified elephant is a little excessive. Take her for a walk.

 

Murphy reads shapiro

A mammoth weighs how much?! Don’t worry, Murphy. The tundra is a long way from New Jersey.

 

Glad we got that out of our systems. Check out a series of original videos on cloning from How to Clone a Mammoth author Beth Shapiro here.

Win a copy of Relativity: 100th Anniversary Edition by Albert Einstein through Corbis!

We are teaming with Corbis Entertainment to offer this terrific giveaway through their official Albert Einstein Facebook page. Contest details below, but please head over to the “official Facebook page of the world’s favorite genius” to enter!

Enter for a chance to win a FREE COPY of “Relativity: 100th Anniversary Edition” by Albert Einstein!

Math Drives Careers: Paul Nahin on Electrical Engineering and √-1

Paul Nahin is the author of many books we’ve proudly published over the years, including An Imaginary Tale, Dr. Euler’s Fabulous Formula, and Number Crunching. For today’s installment in our Math Awareness Month series, he writes about his first encounter with √-1.

Electrical Engineering and √-1

It won’t come as a surprise to very many to learn that mathematics is central to electrical engineering. Probably more surprising is that the cornerstone of that mathematical foundation is the mysterious (some even think mystical) square-root of minus one. Every electrical engineer almost surely has a story to tell about their first encounter with √-1, and in this essay I’ll tell you mine.

Lots of different kinds of mathematics have been important in my personal career at different times; in particular, Boolean algebra (when I worked as a digital logic designer), and probability theory (when I wore the label of radar system engineer). But it’s the mathematics of √-1 that has been the most important. My introduction to √-1 came when I was still in high school. In my freshman year (1954) my father gave me the gift of a subscription to a new magazine called Popular Electronics. From it I learned how to read electrical schematics from the projects that appeared in each issue, but my most important lesson came when I opened the April 1955 issue.

It had an article in it about something called contra-polar power: a desk lamp plugged into a contra-polar outlet plug would emit not a cone of light, but a cone of darkness! There was even a photograph of this, and my eyes bugged-out when I saw that: What wondrous science was at work here?, I gasped to myself —I really was a naive 14-year old kid! It was, of course, all a huge editorial joke, along with some nifty photo-retouching, but the lead sentence had me hooked: “One of the reasons why atomic energy has not yet become popular among home experimenters is that an understanding of its production requires knowledge of very advanced mathematics.” Just algebra, however, was all that was required to understand contra-polar power.

contra power scan

Contra-polar power ‘worked’ by simply using the negative square root (instead of the positive root) in calculating the resonant frequency in a circuit containing both inductance and capacitance. The idea of negative frequency was intriguing to me (and electrical engineers have actually made sense of it when combined with √-1, but then the editors played a few more clever math tricks and came up with negative resistance. Now, there really is such a thing as negative resistance, and it has long been known by electrical engineers to occur in the operation of electric arcs. Such arcs were used, in the very early, pre-electronic days of radio, to build powerful AM transmitters that could broadcast music and human speech, and not just the on-off telegraph code signals that were all the Marconi transmitters could send. I eventually came to appreciate that the operation of AM/FM radio is impossible to understand, at a deep, theoretical level, without √-1.

When, in my high school algebra classes, I was introduced to complex numbers as the solutions to certain quadratic equations, I knew (unlike my mostly perplexed classmates) that they were not just part of a sterile intellectual game, but that √-1 was important to electrical engineers, and to their ability to construct truly amazing devices. That early, teenage fascination with mathematics in general, and √-1 in particular, was the start of my entire professional life. I wish my dad was still alive, so I could once again thank him for that long-ago subscription.

Math Drives Careers: Author Louis Gross

Gross jacketLouis Gross, distinguished professor in the departments of ecology, evolutionary biology, and mathematics at the University of Tennessee, is the author, along with Erin Bodine and Suzanne Lenhart, of Mathematics for the Life Sciences. For our third installment in the Math Awareness Month series, Gross writes on the role mathematics and rational consideration have played in his career, and in his relationship with his wife, a poet.

Math as a Career-builder and Relationship-broker

My wife is a poet. We approach most any issue with very different perspectives. In an art gallery, she sees a painting from an emotional level, while I focus on the methods the artist used to create the piece. As with any long-term relationship, after many years together we have learned to appreciate the other’s viewpoint and while I would never claim to be a poet, I have helped her on occasion to try out different phrasings of lines to bring out the music. In the reverse situation, the searching questions she asks me about the natural world (do deer really lose their antlers every year – isn’t this horribly wasteful?) force me to consider ways to explain complex scientific ideas in metaphor. As the way I approach science is heavily quantitative, with much of my formal education being in mathematics, this is particularly difficult without resorting to ways of thought that to me are second nature.

The challenges in explaining how quantitative approaches are critical to science, and that science advances in part through better and better ways to apply mathematics to the responses of systems we observe around us, arise throughout education, but are particularly difficult for those without a strong quantitative bent. An example may be helpful. One of the central approaches in science is building and using models – these can be physical ones such as model airplanes, they can be model systems such as an aquarium or they can be phrased in mathematics or computer code. The process of building models and the theories that ultimately arise from collections of models, is painstaking and iterative. Yet each of us build and apply models all the time. Think of the last time you entered a supermarket or a large store with multiple checkout-lines. How did you decide what line to choose? Was it based on how many customers were in each line, how many items they had to purchase, or whether they were paying with a check or credit card? Did you take account of your previous experience with that check-out clerk if you had it, or your experience with using self-checkout at that store? Was the criterion you used some aspect of ease of use, or how quickly you would get through the line? Or was it something else such as how cute the clerk was?

As the check-out line example illustrates, your decision about what is “best” for you depends on many factors, some of which might be quite personal. Yet somehow, store managers need to decide how many clerks are needed at each time and how to allocate their effort between check-out lines and their other possible responsibilities such as stocking shelves. Managers who are better able to meet the needs of customers, so they don’t get disgusted with long lines and decide not to return to that store, while restraining the costs of operation, will likely be rewarded. There is an entire field, heavily mathematical, that has been developed to better manage this situation. The jargon term is “queuing models” after the more typically British term for a waiting line. There is even a formal mathematical way of thinking about “bad luck” in this situation, e.g. choosing a line that results in a much longer time to be checked out than a different line would have.

While knowing that the math exists to help decide on optimal allocation of employee effort in a store will not help you in your decision, the approach of considering options, deciding upon your criteria and taking data (e.g. observations of the length of each line) to guide your decision is one that might serve you well independent of your career. This is one reason why many “self-help” methods involve making lists. Such lists assist you in deciding what factors (in math we call these variables) matter to you, how to weight the importance of each factor (we call these parameters in modeling) and what your objective might be (costs and benefits in an economic sense). This process of rational consideration of alternative options may assist you in many aspects of everyday life, including not just minor decisions of what check-out line to go into, but major ones such as what kind of car or home to purchase, what field to major in and even who to marry! While I can’t claim to have followed a formal mathematical approach in deciding on the latter, I have found it helpful throughout my marriage to use an informal approach to decision making. I encourage you to do so as well.

Check out Chapter 1 of Mathematics for the Life Sciences here.

Alan Turing’s handwritten notebook brings $1 million at auction

turing jacket

Alan Turing: The Enigma

Old journals can be fascinating no matter who they belong to, but imagine looking over the old notebook of the mathematician credited with breaking German codes during WWII.

The Associated Press and other venues reported that a handwritten notebook by British code-breaker Alan Turing, subject of the 2014 Oscar-winning film “The Imitation Game,” a movie based on our book, Alan Turing: The Enigma, brought more than $1 million at auction from an anonymous buyer on Monday. Originally given to Turing’s mathematician-friend Robin Gandy, the notebooks are thought to be the only ones of their kind, and contain Turing’s early attempts to chart a universal language, a precursor to computer code. (In an interesting personal wrinkle, Gandy had used the blank pages for notes on his dreams, noting that, “It seems a suitable disguise to write in between these notes of Alan’s on notation, but possibly a little sinister; a dead father figure, some of whose thoughts I most completely inherited.”)

Andrew Hodges, author of Alan Turing: The Enigma, commented that “the notebook sheds more light on how Turing ‘remained committed to free-thinking work in pure mathematics.'” To learn more about the life of Turing, check out the book here.