Princeton University Press’s best-selling titles for the last week

These are the best-selling books for the past week.

 

GDP: A Brief but Affectionate History by Diane Coyle
Tesla: Inventor of the Electrical Age by W. Bernard Carlson Tesla: Inventor of the Electrical Age by W. Bernard Carlson
On Bullshit by Harry G. Frankfurt
The Limits of Partnership: U.S.-Russian Relations in the Twenty-First Century by Angela E. Stent
Fragile by Design: The Political Origins of Banking Crises and Scarce Credit by Charles W. Calomiris & Stephen H. Haber
1177 BC: The Year Civilization Collapsed by Eric H. Cline
Rare Birds of North America by Steve Howell, Ian Lewington, and Will Russell
Revolutionary Ideas: An Intellectual History of the French Revolution from The Rights of Man to Robespierre by Jonathan Israel
The Dollar Trap: How the U.S. Dollar Tightened Its Grip on Global Finance by Eswar S. Prasad
The Box: How the Shipping Container Made the World Smaller and the World Economy Bigger by Marc Levinson

Quick Questions for Tim Chartier, author of Math Bytes

Tim Chartier, Photo  courtesy Davidson CollegeTim Chartier is author of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing. He agreed to be our first victi… interview subject in what will become a regular series. We will ask our authors to answer a series of questions in hopes to uncover details about why they wrote their book, what they do in their day job, and what their writing process is. We hope you enjoy getting to know Tim!

PUP: Why did you write this book?

Tim Chartier: My hope is that readers simply delight in the book.  A friend told me the book is full of small mathematical treasures.  I have had folks who don’t like math say they want to read it.  For me, it is like extending my Davidson College classroom.  Come and let’s talk math together.  What might we discover and enjoy?  Don’t like math?  Maybe it is simply you haven’t taken a byte of a mathematical delight that fits your palate!

PUP: Who do you see as the audience for this book?

TC: I wanted this book, at least large segments of it, to read down to middle school.  I worked with public school teachers on many of the ideas in this book.  They adapted the ideas to their classrooms.  And yet, the other day, I was almost late taking my kids to school as I had to pull them from reading my book, a most satisfying reason.  In my mime training, Marcel Marceau often said, “Create your piece and let the genius of the audience teach you what you created.”  I see this book that way.  I wrote a book that I see my students and the many to whom I speak in broad public settings smiling at as they listen.  Who all will be in the audience of this book?  That’s for me to learn from the readers.  I look forward to it.


Don’t like math? Maybe it is simply you haven’t taken a byte of a mathematical delight that fits your palate!


PUP: What do you think is the book’s most important contribution?

TC: When I describe the book to people, many respond with surprise or even better a comment like, “I wish I had a teacher like you.”  My current and former students often note that the book is very much like class.  Let’s create and play with ideas and discover how far they can go and, of great interest to me, how fun and whimsical they can be.

PUP: What inspired you to get into your field?

TC: My journey into math came via my endeavors in performing arts.  I was performing in mime and puppetry at international levels in college.  Math was my “back-up” plan.  Originally, I was taking math classes as required courses in my studies in computer science.  I enjoyed the courses but tended to be fonder of ideas in computer science.  I like the creative edge to writing programming.  We don’t all program in the same way and I enjoyed the elegance of solutions that could be found.  This same idea attracted me to math — when I took mathematical proofs.  I remember studying infinity – a topic far from being entirely encompassed by my finite mind.  Yet, through a mathematical lens, I could examine the topic and prove aspects of it.  Much like when I studied mime with Marcel Marceau, the artistry and creativity of mathematical study is what drew me to the field and kept me hooked through doctoral studies.

PUP: What is the biggest misunderstanding people have about what you do?

TC: Many think mathematics is about numbers.  Much of mathematics is about ideas and concepts.  My work lies at the boundary of computer science and mathematics.  So, my work often models the real world so often mathematics is more about thinking how to use it to glean interesting or new information about our dynamic world.  Numbers are interesting and wonderful but so is taking a handful of M&Ms and creating a math-based mosaic of my son or sitting with my daughter and using chocolate chips to estimate the value of Pi.  And, just for the record, the ideas would be interesting even without the use of chocolate but that doesn’t hurt!

PUP: What would you have been if not a mathematician?

TC: Many people think I would have been a full-time performer.  I actually intentionally walked away from that field.  I want to be home, have a home, walk through a neighborhood where I know my neighbors.  To me, I would have found a field, of some kind, where I could teach.  Then, again, I always wanted to be a creative member of the Muppet team – either creating ideas or performing!


I pick projects that I believe aren’t just exciting now, but will be exciting in retrospect.


PUP: What was the best piece of advice you ever received?

TC: At one time, I was quite ill.  It was a scary time with many unknowns.  I remember resting in a dark room and wondering if I could improve and get better.  I reflected on my life and felt good about where I was, even if I was heading into my final stretch.  I remember promising myself that if I ever got better that I would live a life that later — whether it be a decade later or decades and decades later — that I would try to live a life that I could again feel good about whenever I might again be in such a state.  I did improve but I pick projects that I believe aren’t just exciting now, but will be exciting in retrospect.  This book is easily an example of such a decision.

PUP: Describe your writing process. How long did it take you to finish your book? Where do you write?

TC: The early core of the book happened at 2 points.  First, I was on sabbatical from Davidson College working at the University of Washington where I taught Mathematical Modeling.  Some of the ideas of the book drew from my teaching at Davidson and were integrated into that course taught in Seattle.  At the end of the term, my wife Tanya said, “You can see your students and hear them responding.  Sit now and write a draft. Write quickly and let it flow.  Talk to them and get the class to smile.”  It was great advice to me.  The second stage came with my first reader, my sister Melody.  She is not a math lover and is a critical reader of any manuscript. She has a good eye.  I asked her to be my first reader.  She was stunned.  I wanted her to read it as I knew if she enjoyed it, even though there would be parts she wouldn’t understand fully, then I had a draft of the book I wanted to write.  She loved it and soon after I dove into the second draft.

PUP: Do you have advice for other authors?

TC: My main advice came from award-winning author Alan Michael Parker from Davidson College.  As I was finishing, what at the time I saw as close to my final draft, Alan said, “Tim, you are the one who will live with this book for a lifetime.  Many will read it only once.  You have it for the rest of your life.  Write your book. Make sure it is your voice.  Take your time and know it is you.”  His words echoed in me for months.  I put the book down for several months and then did a revision in which I saw my reflection in the book’s pages — I had seen my reflection before but never as clearly.


Tim is the author of:

bookjacket

Math Bytes
Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing
Tim Chartier

“A magnificent and curious romp through a wonderful array of mathematical topics and applications: maze creation, Google’s PageRank algorithm, doodling, the traveling salesman problem, math on The Simpsons, Fermat’s Last Theorem, viral tweets, fractals, and so much more. Buy this book and feed your brain.”–Clifford A. Pickover, author of The Math Book

Math Bytes is a playful and inviting collection of interesting mathematical examples and applications, sometimes in surprising places. Many of these applications are unique or put a new spin on things. The link to computing helps make many of the topics tangible to a general audience.”–Matt Lane, creator of the Math Goes Pop! Blog

 

5, 4, 3, 2, 1…. Blast off! Announcing University Presses in Space

header_upinspace_1200
A collaborative web site, University Presses in Space, launched this week in an effort to bring together space exploration and astronomy/astrophysics titles from across the university press universe. “University presses have explored the known universe and beyond, producing a galaxy of intriguing and informative books about outer space and space exploration,” notes the introductory page.

The web site is created with readers in mind. As Ellen W. Faran, director of The MIT Press, wrote in her announcement of the launch, “The hypothesis here is that space readers don’t stop at one book and that they appreciate quality.”

We are delighted to see Princeton University Press titles like The Cosmic Cocktail: Three Parts Dark Matter by Katherine Freese and Heart of Darkness: Unraveling the Mysteries of the Invisible Universe by Jeremiah P. Ostriker and Simon Mitton included in the mix.

Maybe we can get an endorsement from others who have boldly gone into space before us?

The Extreme Life of the Sea at the Commonwealth Club/WonderFest, San Francisco

Steve Palumbi, one of today’s leading marine scientists, takes us to the absolute limits of the aquatic world—into the icy arctic, toward boiling hydrothermal vents, and into the deepest undersea trenches—to show how marine life thrives against the odds. He helps us appreciate and understand the fastest and deepest, the hottest and oldest creatures of the oceans.

But such fragile ecosystems face new challenges: climate change and overfishing could pose the greatest threats yet to our planet’s tenacious marine life. Prof. Palumbi shares unforgettable stories of some of the most marvelous life forms on Earth, and reveals surprising lessons of how we humans can learn to adapt to climate change.

This lecture was recorded at the Commonwealth Club earlier this year. Steve and Tony’s book is The Extreme Life of the Sea. You can sample the prologue here: http://press.princeton.edu/chapters/s10178.pdf

These Two Numbers Make Spring Possible (and the other seasons too)

Happy first day of spring! Princeton University Press is celebrating the coming of the crocuses and daffodils with this mathematical post by Oscar Fernandez, author of Everyday Calculus: Discovering the Hidden Math All around Us.


March 20th. Don’t recognize that date? You should, it’s the official start of spring! I won’t blame you for not knowing, because after the unusually cold winter we’ve had it’s easy to forget that higher temperatures are coming. But why March 20th, and not the 21st or the 19th? And while we’re at it, why are there even seasons at all?

The answer has to do with 2 numbers. Don’t worry, they’re simple numbers (not like pi [1]). Stick around and I’ll show you some neat graphs to help you understand where they come from, and hopefully entertain you in the process too.

The first star of this show is the number 92 million. No, it’s not the current Powerball jackpot; it’s also not the number of times a teenager texts per day. To appreciate its significance, have a look at our first chart:

 fernandez 1

Figure 1: The average surface temperature (on the vertical axis) of the planets in our solar system sorted by their distance from our sun (the horizontal axis). From left to right: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto (technically, Pluto lost its planet status in 2006).

That first planet on the left is Mercury. It’s about 36 million miles away from the sun and has an average surface temperature of 333o. (Bring LOTS of sunscreen.) Fourth down the line is the red planet, Mars. At a distance of about 141 million miles from the sun, Mars’ average temperature is -85o. (Bring LOTS of hot chocolate.) We could keep going, but the general trend is clear: planets farther away from the sun have lower average temperatures.[2]

If neither 333o nor -85o sound inviting, I’ve got just the place for you: Earth! At a cool 59o this planet is … drumroll please … 92 million miles from the sun.

We actually got lucky here. You see, it turns out that a planet’s temperature T is related to its distance r from the sun by the formula , where k is a number that depends on certain properties of the planet. I’ve graphed this curve in Figure 1. Notice that all the planets (except for the pesky Venus) closely follow the curve. But there’s more here than meets the eye. Specifically, the T formula predicts that a 1% change in distance will result in a 0.5% change in temperature.[3] For example, were Earth just 3% closer to the sun—about 89 million miles away instead of 92 million—the average temperature would be about 1.5o higher. To put that in perspective, note that at the end of the last ice age average temperatures were only 5o to 9o cooler than today.[4]

So our distance from the sun gets us more reasonable temperatures than Mercury and Mars have, but where do the seasons come from? That’s where our second number comes in: 23.4.

Imagine yourself in a park sitting in front of a bonfire. You’re standing close enough to feel the heat but not close enough to feel the burn. Now lean in. Your head is now hotter than your toes; this tilt has produced a temperature difference between your “northern hemisphere” and your “southern hemisphere.” This “tilt effect” is exactly what happens as Earth orbits the sun. More specifically, our planet is tilted about 23.4o from its vertical axis (Figure 2).

 fernandez 2

Figure 2. Earth is tilted about 23.4o from the plane of orbit with the sun (called the ecliptic plane).

Because of its tilt, as the Earth orbits the sun sometimes the Northern Hemisphere tilts toward the sun—roughly March-September—and other times it tilts away from the sun—roughly September-March (Figure 3).[5]

  f3

Figure 3. Earth’s tilt points toward the sun between mid-March and mid-September, and points away from it the remaining months of the year. The four marked dates describe how this “tilt effect” changes the number of daylight hours throughout the year. Assuming you live in the Northern Hemisphere, days are longest during the summer solstice (shorter nights) and shortest during the winter solstice (longer nights). During the equinoxes, daytime and nighttime are about the same length.

Now that you know how two numbers—92 million and 23.4—explain the seasons, let’s get back to spring in particular. As Figure 3 shows, there are two days each year when Earth’s tilt neither points toward nor away from the sun. Those two days, called the equinoxes, divide the warmer months from the colder ones. And that’s exactly what happened on March 20th: we passed the spring equinox.

Before you go, I have a little confession to make. It’s not entirely true that just two numbers explain the seasons. Distance to the sun and Earth’s tilt are arguably the most important factors, but other factors—like our atmosphere—are also important. But that would’ve made the title a lot longer. And anyway, I would’ve ended up explaining those factors using more numbers. The takeaway: math is powerful, and the more you learn the better you’ll understand just about anything.[6]

 


[1] The ratio of a circle’s circumference to its diameter, pi is a never-ending, never repeating number. It is approximately 3.14.

[2] Venus is the exception. Its thick atmosphere prevents the planet from cooling.

[3] Here’s the explanation for the mathematically inclined. In calculus, changes in a function are described by the function’s derivative; the derivative of T is . This tells us that for a small change dr in r the temperature change dT is . Relative changes are ratios of small changes in a quantity to its original value. Thus, the relative change in temperature, dT/T, is

which is minus 0.5 times the relative change in distance, dr/r. The minus sign says that the temperature decreases as r increases, confirming the results of Figure 1.

[5] Just like in our thought experiment, the Southern Hemisphere’s seasons are swapped with our own; when one is cold the other is warm and vice versa.

Gary Marcus to give public lecture: Towards a Theory of How the Brain Works

Marcus_Future_jktYou’re invited to a public lecture by Gary Marcus, co-editor of the forthcoming The Future of the Brain: Essays by the World’s Leading Neuroscientists, on Monday, March 31, 2014 at 6:00 p.m. in McCosh 50 at Princeton University.

The basic parts list of the brain is relatively well understood, but the logic of its operation remains almost entirely elusive, despite enormous technical advances. Even as our tools for understanding the brain become finer and finer grained, our theoretical apparatus for characterizing what we observe remains weak. In this talk, Professor Marcus will focus what we know about the six-layered sheet known as the neocortex, and will argue that two of the most dominant paradigms in theoretical neuroscience are inadequate. He will outline an alternative framework that aims to better bridge neuroscience with behavior, computation, development and evolutionary biology.

Gary Marcus, Professor of Psychology at NYU and Visiting Cognitive Scientist at the Allen Institute for Brain Science, is the author of four books including the NYTimes Bestseller Guitar Zero and frequently blogs for the The New Yorker. His research on language, evolution, computation and cognitive development has been published widely, in leading journals such as Science and Nature.

This event, sponsored by the Vanuxem Lecture Series, is free and open to the public. For more information, please visit http://lectures.princeton.edu/2013/gary-marcus-nyu-professor-of-psychology/.

Need help filling out your brackets? Watch these free videos from Tim Chartier

Chartier_MathStill rushing to fill out your brackets for the NCAA tournament? This free online course from mathematician Tim Chartier, author of Math Bytes, might help.

In this course, you will learn three popular rating methods two of which are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The first method is simple winning percentage. The other two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. We also learn how to adapt the methods to take late season momentum into account. This allows you to create your very own mathematically-produced brackets for March Madness by writing your own code or using the software provided with this course.

From this course, you will learn math driven methods that have led Dr. Chartier and his students to place in the top 97% of 4.6 million brackets submitted to ESPN!

Explore Tim Chartier’s March MATHness lectures:

Pi Day: Where did π come from anyway?

This article is extracted from Joseph Mazur’s fascinating history of mathematical notation, Enlightening Symbols. For more Pi Day features from Princeton University Press, please click here.

 


 

k10204[1]When one sees π in an equation, the savvy reader automatically knows that something circular is lurking behind. So the symbol (a relatively modern one, of course) does not fool the mathematician who is familiar with its many disguises that unintentionally drag along in the mind to play into imagination long after the symbol was read.

Here is another disguise of π: Consider a river flowing in uniformly erodible sand under the influence of a gentle slope. Theory predicts that over time the river’s actual length divided by the straight-line distance between its beginning and end will tend toward π. If you guessed that the circle might be a cause, you would be right.

The physicist Eugene Wigner gives an apt story in his celebrated essay, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” A statistician tries to explain the meaning of the symbols in a reprint about population trends that used the Gaussian distribution. “And what is this symbol here?” the friend asked.

“Oh,” said the statistician. “This is pi.”

“What is that?”

“The ratio of the circumference of the circle to its diameter.”

“Well, now, surely the population has nothing to do with the circumference of the circle.”

Wigner’s point in telling this story is to show us that mathematical concepts turn up in surprisingly unexpected circumstances such as river lengths and population trends. Of course, he was more concerned with understanding the reasons for the unexpected connections between mathematics and the physical world, but his story also points to the question of why such concepts turn up in unexpected ways within pure mathematics itself.

 

The Good Symbol

The first appearance of the symbol π came in 1706. William Jones (how many of us have ever heard of him?) used the Greek letter π to denote the ratio of the circumference to the diameter of a circle. How simple. “No lengthy introduction prepares the reader for the bringing upon the stage of mathematical history this distinguished visitor from the field of Greek letters. It simply came, unheralded.” But for the next thirty years, it was not used again until Euler used it in his correspondence with Stirling.

We could accuse π of not being a real symbol. It is, after all, just the first letter of the word “periphery.” True, but like i, it evokes notions that might not surface with symbols carrying too much baggage. Certain questions such as “what is ii?” might pass our thoughts without a contemplating pause. Pure mathematics asks such questions because it is not just engaged with symbolic definitions and rules, but with how far the boundaries can be pushed by asking questions that everyday words could ignore. You might think that ii makes no sense, that it’s nothing at all, or maybe a complex number. Surprise: it turns out to be a real number!

It seems that number has a far broader meaning than it once had when we first started counting sheep in the meadow. We have extended the idea to include collections of conceptual things that include the usual members of the number family that still obey the rules of numerical operations. Like many of the words we use, number has a far broader meaning than it once had.

Ernst Mach mused:

Think only of the so-called imaginary quantities with which mathematicians long operated, and from which they even obtained important results ere they were in a position to assign to them a perfectly determinate and withal visualizable meaning.

It is not the job of mathematics to stick with earthly relevance. Yet the world seems to eventually pick up on mathematics abstractions and generalizations and apply them to something relevant to Earth’s existence. Almost a whole century passed with mathematicians using imaginary exponents while a new concept germinated. And then, from the symbol i that once stood for that one-time peculiar abhorrence √−1, there emerged a new notion: that magnitude, direction, rotation may be embodied in the symbol itself. It is as if symbols have some intelligence of their own.

What is good mathematical notation? As it is with most excellent questions, the answer is not so simple. Whatever a symbol is, it must function as a revealer of patterns, a pointer to generalizations. It must have an intelligence of its own, or at least it must support our own intelligence and help us think for ourselves. It must be an indicator of things to come, a signaler of fresh thoughts, a clarifier of puzzling concepts, a help to overcome the mental fatigues of confusion that would otherwise come from rhetoric or shorthand. It must be a guide to our own intelligence. Here is Mach again:

In algebra we perform, as far as possible, all numerical operations which are identical in form once for all, so that only a remnant of work is left for the individual case. The use of the signs of algebra and analysis, which are merely symbols of operations to be performed, is due to the observation that we can materially disburden the mind in this way and spare its powers for more important and more difficult duties, by imposing all mechanical operations upon the hand.

The student of mathematics often finds it hard to throw off the uncomfortable feeling that his science, in the person of his pencil, surpasses him in intelligence—an impression which the great Euler confessed he often could not get rid of.

A single symbol can tell a whole story.

There was no single moment when xn was first used to indicate the nth power of x. A half century separated Bombelli’s , from Descartes’s xn. It may seem like a clear-cut idea to us, but the idea of symbolically labeling the number of copies of x in the product was a huge step forward. The reader no longer had to count the number of x’s, which paused contemplation, interrupted the smoothness of reading, and hindered any broad insights of associations and similarities that could extend ideas. The laws xnxm = xn+m and (xn)m = xnm, where n and m are integers, were almost immediately suggested from the indexing symbol. Not far behind was the idea to let x½ denote √x, inspired by extending the law xnxm = xn+m to include fractions, so x½ x½  = x1.

Further speculation on what nx might be would surely have inspired questions such as what x might be for a given y in an equation such as y = 10x. Answer that and we would have a way of performing multiplication by addition. But Napier, the inventor of logarithms, already knew the answer long before mathematics had any symbols at all!

Symbols acquire meanings that they originally didn’t have. But symbolic representation has, likewise, the disadvantage that the object represented is very easily lost sight of, and that operations are continued with the symbols to which frequently no object whatever corresponds.

Ernst Mach once again:

A symbolical representation of a method of calculation has the same significance for a mathematician as a model or a visualisable working hypothesis has for a physicist. The symbol, the model, the hypothesis runs parallel with the thing to be represented. But the parallelism may extend farther, or be extended farther, than was originally intended on the adoption of the symbol. Since the thing represented and the device representing are after all different, what would be concealed in the one is apparent in the other.

Top Tips for 2014 March Madness Brackets from Tim Chartier

Chartier_MathWith a $1 billion dollar payday on the line, we predict there will be more people filling out March Madness brackets this year than ever before, so it isn’t surprising that everyone is looking to mathematician Tim Chartier for tips and tricks on how to pick the winners. Tim has been using math to fill out March Madness brackets with his students for years and his new book Math Bytes will have an entire section devoted to best tips and tricks. In the meantime, we invite you to check out these tips from an interview at iCrunchData News.

ICrunchData: What are a few variables that are used that are out of the ordinary?

Chartier: “In terms of past years, it helps if you look at scores in buckets. For instance, you decide close games are within 3 points and count those as ties. Medium wins are 4 to 10 points and could as 6 points and anything bigger is an 11 point win. That’s worked really well in some cases and reduces some of the noise of scores.”

“Here is another that comes out of our most current research. This year’s tournament will enable us to test it in brackets. We tried it on conference tournaments and it had good success. We use statistics (specifically Dean Oliver’s 4 Factors) and look at that as a point, in this case in 4D space. Then we find another team that has a point in the fourth dimension closest to that team’s point. This means they play similarly. Suddenly, we can begin to look at who similar teams win and lose against.”

Pi Day Recipe: Brandy Alexander Pie from Cooking for Crowds

This recipe is presented as part of our Pi Day celebration. For more Pi Day features from Princeton University Press, please click here.


Brandy Alexander Pie

This pie is as sweet and delicious as the drink for which it is named, and a great deal less alcoholic. It is light and fluffy, but very filling.

6 12 20 50
unflavored gelatin envelopes 1 2 4 8
cold water ½ c 1 c 2 c 4 c
granulated sugar ⅔ c 1⅓ c 2⅔ c 2 lbs
salt ⅛ tsp ¼ tsp ½ tsp 1 tsp
eggs, separated 3 6 12 24
Cognac ¼ c ½ c 1 c 2 c
Grand Marnieror ¼ c ½ c 1 c 2 c
creme de cacao ¼ c ½ c 1 c 2 c
heavy cream 2 c 4 c 4 pts 8 pts
graham cracker crust 1 2 4 8
Garnish
4-ounce bars semisweet chocolate 1 2 3
heavy cream 1 c 2 c 3½ c 6 c

Sprinkle the gelatin over the cold water in a saucepan. Add ⅓ cup [⅔ cup, 1⅓ cups, 2⅔ cups] of the sugar, the salt, and egg yolks. Stir to blend, then heat over low heat, stirring, until the gelatin dissolves and the mixture thickens. Do not boil. Remove from the heat and stir in the Cognac and Grand Marnier (or creme de cacao). Chill in the refrigerator until the mixture mounds slightly and is thick.

Beat the egg whites until stiff (use a portable electric mixer in a large kettle). Gradually beat in the remaining sugar and fold into the thickened mixture. Whip half of the cream until it holds peaks. Fold in the whipped cream, and turn into the crusts. Chill several hours, or overnight. To serve, garnish with the remaining cream, whipped. Using a vegetable peeler, make chocolate curls from the chocolate bars and let drop onto the cream.


cookingFor additional recipes for feeding the masses, please check out Cooking for Crowds by Merry “Corky” White.

Princeton authors speaking at Oxford Literary Festival 2014

We are delighted that the following Princeton authors will be speaking at the Oxford Literary Festival in Oxford, UK, in the last week of March. Details of all events can be found at the links below:images5L8V7T97

Jacqueline and Simon Mitton, husband and wife popular astronomy writers and authors of From Dust to Life: The Origin and Evolution of Our Solar System and Heart of Darkness: Unraveling the Mysteries of the Invisible Universe respectively, will be speaking  on Monday 24 March at 4:00pm  http://oxfordliteraryfestival.org/literature-events/2014/Monday-24/in-search-of-our-cosmic-origins-from-the-big-bang-to-a-habitable-planet

David Edmonds, author of Would You Kill the Fat Man? The Trolley Problem and What Your Answer Tells Us  about Right and Wrong will be speaking on Monday 24 March at 6:00pm http://oxfordliteraryfestival.org/literature-events/2014/Monday-24/morality-puzzles-would-you-kill-the-fat-man

Robert Bartlett, author of Why Can the Dead Do Such Great Things? Saints and Worshippers from the Martyrs to the Reformation will be speaking on Tuesday 25 March at 2:00pm http://oxfordliteraryfestival.org/literature-events/2014/Tuesday-25/why-can-the-dead-do-such-great-things

Michael Scott, author of Delphi: A History of the Center of the Ancient World will be speaking on Wednesday 26 March at 10:00am http://oxfordliteraryfestival.org/literature-events/2014/Wednesday-26/delphi-a-history-of-the-centre-of-the-ancient-world

Simon Blackburn, author of Mirror, Mirror: The Uses and Abuses of Self-Love will be speaking on Wednesday 26 March at 4:00pm http://oxfordliteraryfestival.org/literature-events/2014/Wednesday-26/mirror-mirror-the-uses-and-abuses-of-self-love

Roger Scruton author of the forthcoming The Soul of the World will be speaking Thursday 27 March 12:00pm http://oxfordliteraryfestival.org/literature-events/2014/Thursday-27/the-soul-of-the-world

Alexander McCall Smith, author of What W. H. Auden Can Do for You will be speaking about how this poet has enriched his life and can enrich yours too on Friday 28 March at 12:00pm http://oxfordliteraryfestival.org/literature-events/2014/Friday-28/what-w-h-auden-can-do-for-youMcCallSmith_Auden

Averil Cameron, author of Byzantine Matters will be speaking on Friday 28 March at 2:00pm  http://oxfordliteraryfestival.org/literature-events/2014/Friday-28/byzantine-matters

Edmund Fawcett, author of Liberalism: The Life of an Idea will be speaking on Saturday 29 March at 10:00am http://oxfordliteraryfestival.org/literature-events/2014/Saturday-29/liberalism-the-life-of-an-idea

In addition, Ian Goldin will be giving the inaugural “Princeton Lecture” at The Oxford Literary Festival, on the themes within his forthcoming book, The Butterfly Defect: How Globalization Creates Systemic Risks, and What to Do about It on Thursday 27 March at 6:00pm  http://oxfordliteraryfestival.org/literature-events/2014/Thursday-27/the-princeton-lecture-the-butterfly-defect-how-globalisation-creates-system

 

#PiDay Art from Beautiful Geometry – “Squaring the Circle”

This article has been extracted from Beautiful Geometry by Eli Maor and Eugen Jost. For more Pi Day features from Princeton University Press, please click here.


At first glance, the circle may seem to be the simplest of all geometric shapes and the easiest to draw: take a string, hold down one end on a sheet of paper, tie a pencil to the other end, and swing it around—a simplified version of the compass. But first impressions can be misleading: the circle has proved to be one of the most intriguing shapes in all of geometry, if not the most intriguing of them all.

How do you find the area of a circle, when its radius is given? You instantly think of the formula A = πr2. But what exactly is that mysterious symbol π? We learn in school that it is approximately 3.14, but its exact value calls for an endless string of digits that never repeat in the same order. So it is impossible to find the exact area of a circle numerically. But perhaps we can do the next best thing—construct, using only straightedge and compass, a square equal in area to that of a circle?

This problem became known as squaring the circle— or simply the quadrature problem—and its solution eluded mathematicians for well over two thousand years. The ancient Egyptians came pretty close: In the Rhind Papyrus, a collection of 84 mathematical problems dating back to around 1800 BCE, there is a statement that the area of a circle is equal to the area of a square of side  of the circle’s diameter. Taking the diameter to be 1 and equating the circle’s area to that of the square, we get π(½)2 = ( )2, from which we derive a value of π equal to ≈ 3.16049—within 0.6 percent of the true value. However, as remarkable as this achievement is, it was based on “eyeballing,” not on an exact geometric construction.

Numerous attempts have been made over the centuries to solve the quadrature problem. Many careers were spent on this task—all in vain. The definitive solution—a negative one—came only in 1882, when Carl Louis Ferdinand von Lindemann (1852– 1939) proved that the task cannot be done—it is impossible to square a circle with Euclidean tools. Actually, Lindemann proved something different: that the number π, the constant at the heart of the quadrature problem, is transcendental. A transcendental number is a number that is not the solution of a polynomial equation with integer coefficients. A number that is not transcendental is called algebraic. All rational numbers are algebraic; for example,  is the solution of the equation 5x − 3 = 0. So are all square roots, cubic roots, and so on; for example,  is the positive solution of x2 − 2 = 0, and  is one solution of x6 − 4x3 − 1 = 0. The name transcendental has nothing mysterious about it; it simply implies that such numbers transcend the realm of algebraic (polynomial) equations.

Now it had already been known that if π turned out to be transcendental, this would at once establish that the quadrature problem cannot be solved. Lindemann’s proof of the transcendence of π therefore settled the issue once and for all. But settling the issue is not the same as putting it to rest; being the most famous of the three classical problems, we can rest assured that the “circle squarers” will pursue their pipe dream with unabated zeal, ensuring that the subject will be kept alive forever.

 pi maor

Metamorphosis of a Circle

Metamorphosis of a Circle, shows four large panels. The panel on the upper left contains nine smaller frames, each with a square (in blue) and a circular disk (in red) centered on it. As the squares decrease in size, the circles expand, yet the sum of their areas remains constant. In the central frame, the square and circle have the same area, thus offering a computer-generated “solution” to the quadrature problem. In the panel on the lower right, the squares and circles reverse their roles, but the sum of their areas is still constant. The entire sequence is thus a metamorphosis from square to circle and back.

Of course, Euclid would not have approved of such a solution to the quadrature problem, because it does not employ the Euclidean tools—a straightedge and compass. It does, instead, employ a tool of far greater power—the computer. But this power comes at a price: the circles, being generated pixel by pixel like a pointillist painting, are in reality not true circles, only simulations of circles.1 As the old saying goes, “there’s no free lunch”—not even in geometry.


Note:

1. The very first of the 23 definitions that open Euclid’s Elements defines a point as “that which has no part.” And since all objects of classical geometry—lines, circles, and so on—are made of points, they rest on the subtle assumption that Euclidean space is continuous. This, of course, is not the case with computer space, where Euclid’s dimensionless point is replaced by a pixel—small, yet of finite size—and space between adjacent pixels is empty, containing no points.