5 Fascinating Physics Facts

NahinPaul J. Nahin shows that physics is all around us in his new book, In Praise of Simple Physics. Nahin takes the reader step by step through a variety of everyday examples, proving that you don’t need an advanced degree to appreciate the math behind a speeding car, a falling object, or the rotation of the planets. For instance:

1. The Sun’s gravitational force upon Earth is 180 times larger than the Moon’s gravitational force upon Earth (p. 45), but lunar tides are larger than solar tides because the Sun is so much further away than the Moon (p. 48).

2. Saturn’s rings are believed to have been caused by tidal forces due to gravitational variation. Long ago, a moon of Saturn got too close to the planet and was pulled apart—the fragments make up the rings (p. 49).

3. Gravity and centripetal acceleration caused by the Moon create two tidal bulges on Earth—one directly below the Moon and the other on the far side of the Earth opposite the first bulge. The Moon’s gravitational pull on the two tidal bulges produces a net counter-rotational torque that tends to reduce the Earth’s rotational speed. The result is that the length of a day on Earth is continually increasing by about 2 milliseconds per century. Assuming that this rate of increase has been in effect for the last 2,000 years, then the day Julius Caesar was assassinated in 44BC was shorter in duration, compared to yesterday, by about 40 milliseconds (p. 53).

4. Physics can be funny! What do you get when you cross a mosquito with a mountain climber? A biologist would say, “nothing, because that’s impossible to do,” and a mathematician would be able to prove why. In vector mathematics there are two different ways to multiply two vectors together: the dot product (which produces a scalar result), and the cross product (which produces another vector). Each starts with two vectors. While a mosquito is, in fact, a vector of disease, a mountain climber is a scalar and you cannot cross a vector with a scalar (p. 66).

5. The center of mass is the point at which we can imagine the entire mass of the object is concentrated as a point mass. If you stack books on top of each other with each staggered exactly halfway across the one beneath it (at the center of mass) and off the edge of the table, the stack will not fall (p. 97).

If any of these facts have you scratching your head and you want to know more, pick up a copy of In Praise of Simple Physics for detailed explanations of the math behind each of these—and many more!

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Carl Wunsch: Has oceanography grown too distanced from the ocean?

Wunsch jacketWith the advent of computers, novel instruments, satellite technology, and increasingly powerful modeling tools, we have vast knowledge about the ocean. Yet because of technological advances, a new generation of oceanographers have grown increasingly distanced from the object of their study. Physics Today recently published a Q&A with Carl Wunch, author of Modern Observational Physical Oceanography: Understanding the Global Ocean. According to Wunch, the field of oceanography cannot rely on theoretical truths alone. In this interview, he emphasizes the importance of the discipline’s observational roots:

Before Modern Observational Physical Oceanography: Understanding the Global Ocean (Princeton University Press, 2015) was published, Carl Wunsch had already made “an immense contribution” to the field, writes Stuart Cunningham in his January 2016 review of the book for Physics Today. Cunningham counts more than 250 papers and “an astonishing list of master’s and PhD students whose own merits are widely recognized.”

Modern Observational Physical Oceanography is Wunsch’s fifth book. Cunningham writes that it will be “of value to anyone wishing to know more about how to observe the ocean, interpret the data, and gain insights on ocean behavior and on how oceanographers reach their understanding of it.”

Carl Wunsch

Carl Wunsch

Wunsch was the Cecil and Ida Green Professor of Physical Oceanography at MIT before his retirement in 2013; he is now a visiting professor at Harvard University. He received his PhD at MIT under the tutelage of renowned oceanographer Henry Stommel. Among other things, Wunsch has studied the effects of ocean circulation on climate.

Physics Today recently caught up with Wunsch to discuss Modern Observational Physical Oceanography and his views on climate change issues.

PT: What motivated you to take up this book after retiring from MIT?

WUNSCH: In talking to students and postdocs, and in teaching, it became clear that we are in an era increasingly dominated by modelers and theoreticians, for many of whom observations are something downloaded from the Web and then taken as a “truth.” The field of physical oceanography and its climate components has become ever more remote from its observational roots.

In the past 25 years physical oceanography developed a number of highly useful, up-to-date, but theoretically based textbooks. There was no book known to me to which one could direct a colleague or student that emphasized the interesting complexities of the very diverse data types oceanographers now have available. The beautiful theories emphasized by the existing textbooks can produce the misperception of a laminar, essentially steady, ocean and in the extreme case, one reduced to a “conveyor belt.”

Read the full interview in Physics Today, here.

Business Insider calls Katherine Freese one of the “50 scientists who are changing the world”

The Cosmic CocktailBusiness Insider included Katherine Freese, author of The Cosmic Cocktail, in a list of the 50 scientists who are changing the world. Freese was recognized for her pioneering work in the study of dark matter. Other picks included Andrea Accomazo, the first person to land a probe on a comet, Alan Stern, the principal investigator for NASA’s New Horizons mission,  Cori Bargmann, autism and Alzheimer’s researcher, as well as an impressive lineup of other scientists whose “revolutionary research in human happiness, evolutionary biology, neutrino physics, biotechnology, archeology, and other fields is helping to advance our lives in more ways than we could ever imagine.”

You can read the full feature here, and watch Freese discuss the greatest mysteries of the universe here.

Congratulations, Katherine!

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.

Enter to win a copy of Alan Turing: The Enigma, the Book That Inspired the Film The Imitation Game

Hodges_AlanTuring movie tie inOn November 28, The Imitation Game will open in limited release. In the film, Benedict Cumberbatch stars as Alan Turing, the genius British mathematician, logician, cryptologist and computer scientist who led the charge to crack the German Enigma Code that helped the Allies win WWII. Turing went on to assist with the development of computers at the University of Manchester after the war, but was prosecuted by the UK government in 1952 for homosexual acts which the country deemed illegal. The film is inspired by the award-winning biography Alan Turing: The Enigma by Andrew Hodges.

To celebrate the release of the film, Princeton University Press is pleased to announce the publication of a new edition of the book with a movie still cover and new material from the author that brings the story current through Turing’s pardon by the Queen. Enter our giveaway below to win a copy of the new edition of the book AND a $25.00 Fandango gift certificate.

This giveaway will run from November 11 through November 24 and is open to residents of the U.S. and Canada, aged 18 and older. No purchase is necessary. If you prefer to enter via email, please send a note to blog@press.princeton.edu. Please see complete terms and conditions below.

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Quick Questions for Ian Roulstone and John Norbury, co-authors of Invisible in the Storm

Ian Roulstone (top) and John Norbury (bottom) are authors of Invisible in the Storm: The Role of Mathematics in Understanding Weather and experts on the application of mathematics in meteorology and weather prediction. As we head into hurricane season along the Eastern coast of the United States, we are still not fully recovered from Hurricane Sandy, empty lots still dot the stretch between Seaside and Point Pleasant and in countless other beach communities. But it could have been worse without the advance warning of meteorologists, so we had a few questions about the accuracy of weather prediction and how it can be further refined in the future.

Now, on to the questions!

Ian RoulstoneNorbury


What inspired you to get into this field?

Every day millions of clouds form, grow, and move above us, blown by the restless winds of our ever-changing atmosphere. Sometimes they bring rain and sometimes they bring snow – nearly always in an erratic, non-recurring way. Why should we ever be able to forecast weather three days or a week ahead? How can we possibly forecast climate ten years or more in the future? The secret behind successful forecasting involves a judicious mix of big weather-satellite data, information technology, and meteorology. What inspired us was that mathematics turns out to be crucial to bringing it all together.

Why did you write this book?

Many books describe various types of weather for a general audience. Other books describe the physical science of forecasting for more specialist audiences. But no-one has explained, for a general readership, the ideas behind the successful algorithms of the latest weather and climate apps running on today’s supercomputers. Our book describes the achievements and the challenges of modern weather and climate prediction.

There’s quite a lot about the history and personalities involved in the development of weather forecasting in your book; why did you consider this aspect important?

When reviewing the historical development of weather science over the past three centuries, we found the role of individuals ploughing their own furrow to be at least as important as that of big government organisations. And those pioneers ranged from essentially self-taught, and often very lonely individuals, to charming and successful prodigies. Is there a lesson here for future research organisation?

“We can use mathematics to warn us of the potential for chaotic behaviour, and this enables us to assess the risks of extreme events.”

Weather forecasts are pretty good for the next day or two, but not infallible: can we hope for significant improvements in forecasting over the next few years? 

The successful forecasts of weather events such as the landfall of Hurricane Sandy in New Jersey in October 2012, and the St Jude Day storm over southern England in October 2013, both giving nearly a week’s warning of the oncoming disaster, give a taste of what is possible. Bigger computers, more satellites and radar observations, and even cleverer algorithms will separate the predictable weather from the unpredictable gust or individual thunderstorm. Further improvements will rely not only on advanced technology, but also, as we explain in our book, on capturing the natural variability of weather using mathematics.

But isn’t weather chaotic?

Wind, warmth and rain are all part of weather. But the very winds are themselves tumbling weather about. This feedback of cause and effect, where the “effects help cause the causes”, has its origins in both the winds and the rain. Clouds are carried by the wind, and rainfall condensing in clouds releases further heat, which changes the wind. So chaotic feedback can result in unexpected consequences, such as the ice-storm or cloudburst that wasn’t mentioned in the forecast. But we can use mathematics to warn us of the potential for chaotic behaviour, and this enables us to assess the risks of extreme events.

Are weather and climate predictions essentially “big data” problems?

We argue no. Weather agencies will continually upgrade their supercomputers, and have a never-ending thirst for weather data, mostly from satellites observing the land and sea. But if all we do is train computer programs by using data, then our forecasting will remain primitive. Scientific ideas formulated with mathematical insight give the edge to intelligent forecasting apps.

So computer prediction relies in various ways on clever mathematics: it gives a language to describe the problem on a machine; it extracts the predictable essence from the weather data; and it selects the predictable future from the surrounding cloud of random uncertainty. This latter point will come to dominate climate prediction, as we untangle the complex interactions of the atmosphere, oceans, ice-caps and life in its many varied forms.

Can climate models produce reliable scenarios for decision-makers?

The models currently used to predict climate change have proved invaluable in attributing trends in global warming to human activity. The physical principles that govern average global temperatures involve the conservation of energy, and these over-arching principles are represented very accurately by the numerical models. But we have to be sure how to validate the predictions: running a model does not, in itself, equate to understanding.

As we explain, although climate prediction is hugely complicated, mathematics helps us separate the predictable phenomena from the unpredictable. Discriminating between the two is important, and it is frequently overlooked when debating the reliability of climate models. Only when we take such factors into account can we – and that includes elected officials – gauge the risks we face from climate change.

What do you hope people will take away from this book?

From government policy and corporate strategy to personal lifestyle choices, we all need to understand the rational basis of weather and climate prediction. Answers to many urgent and pressing environmental questions are far from clear-cut. Predicting the future of our environment is a hugely challenging problem that will not be solved by number-crunching alone. Chaos and the butterfly effect were the buzzwords of the closing decades of the 20th Century. But incomplete and inaccurate data need not be insurmountable obstacles to scientific progress, and mathematics shows us the way forward.


bookjacket Invisible in the Storm
The Role of Mathematics in Understanding Weather
Ian Roulstone & John Norbury



What is the reality behind the race for scientific talent? Watch this EPI event with Michael Teitelbaum to find out

Also, in a related review of Michael Teitelbaum’s book Falling Behind? from Spectrum Magazine, published by the IEEE, they had this fun little quiz:

Okay, here are your choices: 1957, 1982, and 2014. Match each year to when the following statements were made:

a. “It is pretty generally realized that our country faces a serious scientific and engineering manpower shortage. We have at present about half the engineers which we need, and each year we are graduating only about half our annual needs.”

b. “Science, technology, engineering and math form the foundation of the global economy. Yet, … if educational trends continue, fewer qualified candidates will be available to support growth in these areas.”

c. “We appear to be raising a generation of Americans, many of whom lack the understanding and the skills necessary to participate fully in the technological world in which they live and work.”

To see the answers and to read their review, please visit http://spectrum.ieee.org/riskfactor/at-work/tech-careers/exposing-the-roots-of-the-perpetual-stem-crisis-

To learn more about the boom and bust cycles of STEM education, please read Falling Behind?

Wassim Haddad Wins the 2014 Pendray Aerospace Literature Award

Wassim Haddad, Winner of the 2014 Pendray Aerospace Literature Award, American Institute of Aeronautics and Astronautics

Professor Wassim Haddad of the School of Aerospace Engineering and chair of the Flight Mechanics and Control Discipline at Georgia Institute of Technology “has been selected to receive the 2014 Pendray Aerospace Literature Award. This is the highest honor in literature bestowed by the American Institute of Aeronautics and Astronautics (AIAA). The award is presented for an outstanding contribution or contributions to aeronautical and astronautical literature in the relatively recent past.”

The citation of Prof. Haddad’s award reads “Paramount and fundamental contributions to the literature of dynamical systems and control for large-scale aerospace systems.”

Prof. Haddad’s award is given in part for the research in his book, co-authored with Sergey G. Nersesov and published by PUP in 2011: Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

k9762Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures.

Wassim M. Haddad is a professor in the School of Aerospace Engineering and chair of the Flight Mechanics and Control Discipline at Georgia Institute of Technology.

Why You Hear What You Hear

Why You Hear What You Hear by Eric J. Heller Why You Hear What You Hear . . . has much to interest physicists and physics students. . . . This book contains a lot of physical insight, and I think it will be the rare acoustician who does not enjoy reading it. I particularly liked the use of color coding to introduce (with a minimum of math) a graphical algorithm to represent autocorrelation. Also interesting are the author’s diversions into history, including a story in which John William Strutt (Lord Rayleigh) and William Henry Bragg seem to have been mistaken about an echo transposed in pitch. . . . Acousticians will enjoy its interesting perspectives, and physicists and engineers outside of acoustics will find it an attractive introduction to some important parts of the discipline.”–Joe Wolfe, Physics Today

Why You Hear What You Hear:
An Experiential Approach to Sound, Music, and Psychoacoustics
by Eric J. Heller

Why You Hear What You Hear is the first book on the physics of sound for the nonspecialist to empower readers with a hands-on, ears-open approach that includes production, analysis, and perception of sound. The book makes possible a deep intuitive understanding of many aspects of sound, as opposed to the usual approach of mere description. This goal is aided by hundreds of original illustrations and examples, many of which the reader can reproduce and adjust using the same tools used by the author.

  • The first book on sound to offer interactive tools, building conceptual understanding via an experiential approach
  • Supplementary website (http://www.whyyouhearwhatyouhear.com) will provide Java, MAX, and other free, multiplatform, interactive graphical and sound applets
  • Extensive selection of original exercises available on the web with solutions
  • Nearly 400 full-color illustrations, many of simulations that students can do


Watch Prof. Eric Heller during “Alex Dalgarno Celebratory Symposium”, held at The Institute for Theoretical, Atomic and Molecular and Optical Physics (ITAMP), Harvard-Smithsonian Center for Astrophysics (CFA), Cambridge, Massachusetts. 

Table of Contents

Web resource for the book that provides Java, MAX, and other free, multiplatform, interactive graphical and sound applets

Sample this book:

Preface [PDF]

Request an examination copy.


Happy Birthday, Tesla!! Enter to win a copy of Tesla: Inventor of the Electric Age

Celebrate with us by entering our giveaway to win a copy of Tesla: Inventor of the Electric Age by W. Bernard Carlson.

“Carlson sheds light on the man and plenty of his inventions. . . . [An] electric portrait.”

–Publishers Weekly

“Superb. . . . Carlson brings to life Tesla’s extravagant self-promotion, as well as his eccentricity and innate talents, revealing him as a celebrity-inventor of the ‘second industrial revolution’ to rival Thomas Alva Edison.”

–W. Patrick McCray, Nature

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FACT: “No sooner did the Tacoma Narrows Bridge—the world’s third longest suspension bridge, and the pride of Washington State—open in July 1940 than it earned its epitaphic nickname, “Galloping Gertie.” The 4,000-foot structure, its main span reaching 2,800 feet, twisted and bucked in the wind. The pronounced heave, or more technically speaking the longitudinal undulation, caused some automobile passengers to complain of seasickness during crossings. Others observed oncoming cars disappearing from sight as if traveling a hilly country road. By November 7, amid 39-mile-an-hour winds, the $6,400,000 bridge wobbled and flailed, then rippled and rolled, then twisted like a roller coaster, until in its final throes it plunged, with a beastly roar, 190 feet into the waters of Puget Sound.” -Siobhan Roberts, from chapter 1 of Wind Wizard

We invite you to read the full chapter online at:

Wind Wizard:
Alan G. Davenport and the Art of Wind Engineering

by Siobhan Roberts

With Wind Wizard, Siobhan Roberts brings us the story of Alan Davenport (1932-2009), the father of modern wind engineering, who investigated how wind navigates the obstacle course of the earth’s natural and built environments–and how, when not properly heeded, wind causes buildings and bridges to teeter unduly, sway with abandon, and even collapse.

In 1964, Davenport received a confidential telephone call from two engineers requesting tests on a pair of towers that promised to be the tallest in the world. His resulting wind studies on New York’s World Trade Center advanced the art and science of wind engineering with one pioneering innovation after another. Establishing the first dedicated “boundary layer” wind tunnel laboratory for civil engineering structures, Davenport enabled the study of the atmospheric region from the earth’s surface to three thousand feet, where the air churns with turbulent eddies, the average wind speed increasing with height. The boundary layer wind tunnel mimics these windy marbled striations in order to test models of buildings and bridges that inevitably face the wind when built. Over the years, Davenport’s revolutionary lab investigated and improved the wind-worthiness of the world’s greatest structures, including the Sears Tower, the John Hancock Tower, Shanghai’s World Financial Center, the CN Tower, the iconic Golden Gate Bridge, the Bronx-Whitestone Bridge, the Sunshine Skyway, and the proposed crossing for the Strait of Messina, linking Sicily with mainland Italy.

Chronicling Davenport’s innovations by analyzing select projects, this popular-science book gives an illuminating behind-the-scenes view into the practice of wind engineering, and insight into Davenport’s steadfast belief that there is neither a structure too tall nor too long, as long as it is supported by sound wind science.

This Week’s Book Giveaway

We’re back with another giveaway! This week we’re giving our Twitter followers a chance to win 1 of 4 great books from our new Princeton Puzzlers series. The lucky winner will get to choose from Across the Board: The Mathematics of Chessboard Problems by John J. Watkins, Duelling Idiots and Other Probability Puzzlers by Paul J. Nahin, Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics by Robert B. Banks, and Chases and Escapes: The Mathematics of Pursuit and Evasion by Paul J. Nahin.

All you have to do to win is follow Princeton University Press on Twitter and retweet one of our tweets beginning today until 10am EST Friday 7/20. We’ll select our random winner on Friday at 11am EST.

For more information on Princeton Puzzlers, please visit: