Steven S. Gubser: Thunder and Lightning from Neutron Star mergers

As of late 2015, we have a new way of probing the cosmos: gravitational radiation. Thanks to LIGO (the Laser Interferometer Gravitational-wave Observatory) and its new sibling Virgo (a similar interferometer in Italy), we can now “hear” the thumps and chirps of colliding massive objects in the universe. Not for nothing has this soundtrack been described by LIGO scientists as “the music of the cosmos.” This music is at a frequency easily discerned by human hearing, from somewhat under a hundred hertz to several hundred hertz. Moreover, gravitational radiation, like sound, is wholly different from light. It is possible for heavy dark objects like black holes to produce mighty gravitational thumps without at the same time emitting any significant amount of light. Indeed, the first observations of gravitational waves came from black hole merger events whose total power briefly exceeded the light from all stars in the known universe. But we didn’t observe any light from these events at all, because almost all their power went into gravitational radiation.

In August 2017, LIGO and Virgo observed a collision of neutron stars which did produce observable light, notably in the form of gamma rays. Think of it as cosmic thunder and lightning, where the thunder is the gravitational waves and the lightning is the gamma rays. When we see a flash of ordinary lightning, we can count a few seconds until we hear the thunder. Knowing that sound travels one mile in about five seconds, we can reckon how distant the event is. The reason this method works is that light travels much faster than sound, so we can think of the transmission of light as instantaneous for purposes of our estimate.

Things are very different for the neutron star collision, in that the event took place about 130 million light years away, but the thunder and lightning arrived on earth pretty much simultaneously. To be precise, the thunder was first: LIGO and Virgo heard a basso rumble rising to a characteristic “whoop,” and just 1.7 seconds later, the Fermi and INTEGRAL experiments observed gamma ray bursts from a source whose location was consistent with the LIGO and Virgo observations. The production of gamma rays from merging neutron stars is not a simple process, so it’s not clear to me whether we can pin that 1.7 seconds down as a delay precisely due to the astrophysical production mechanisms; but at least we can say with some confidence that the propagation time of light and gravity waves are the same to within a few seconds over 130 million light years. From a certain point of view, that amounts to one of the most precise measurements in physics: the ratio of the speed of light to the speed of gravity equals 1, correct to about 14 decimal places or better.

The whole story adds up much more easily when we remember that gravitational waves are not sound at all. In fact, they’re nothing like ordinary sound, which is a longitudinal wave in air, where individual air molecules are swept forward and backward just a little as the sound waves pass them by. Gravitational waves instead involve transverse disturbances of spacetime, where space is stretched in one direction and squeezed in another—but both of those stretch-squeeze directions are at right angles to the direction of the wave. Light has a similar transverse quality: It is made up of electric and magnetic fields, again in directions that are at right angles to the direction in which the light travels. It turns out that a deep principle underlying both Maxwell’s electromagnetism and Einstein’s general relativity forces light and gravitational waves to be transverse. This principle is called gauge symmetry, and it also guarantees that photons and gravitons are massless, which implies in turn that they travel at the same speed regardless of wavelength.

It’s possible to have transverse sound waves: For instance, shearing waves in crystals are a form of sound. They typically travel at a different speed from longitudinal sound waves. No principle of gauge symmetry forbids longitudinal sound waves, and indeed they can be directly observed, along with their transverse cousins, in ordinary materials like metals. The gauge symmetries that forbid longitudinal light waves and longitudinal gravity waves are abstract, but a useful first cut at the idea is that there is extra information in electromagnetism and in gravity, kind of like an error-correcting code. A much more modest form of symmetry is enough to characterize the behavior of ordinary sound waves: It suffices to note that air (at macroscopic scales) is a uniform medium, so that nothing changes in a volume of air if we displace all of it by a constant distance.

In short, Maxwell’s and Einstein’s theories have a feeling of being overbuilt to guarantee a constant speed of propagation. And they cannot coexist peacefully as theories unless these speeds are identical. As we continue Einstein’s hunt for a unified theory combining electromagnetism and gravity, this highly symmetrical, overbuilt quality is one of our biggest clues.

The transverse nature of gravitational waves is immediately relevant to the latest LIGO / Virgo detection. It is responsible for the existence of blind spots in each of the three detectors (LIGO Hanford, LIGO Livingston, and Virgo). It seems like blind spots would be bad, but they actually turned out to be pretty convenient: The signal at Virgo was relatively weak, indicating that the direction of the source was close to one of its blind spots. This helped localize the event, and localizing the event helped astronomers home in on it with telescopes. Gamma rays were just the first non-gravitational signal observed: the subsequent light-show from the death throes of the merging neutron stars promises to challenge and improve our understanding of the complex astrophysical processes involved. And the combination of gravitational and electromagnetic observations will surely be a driver of new discoveries in years and decades to come.


BlackSteven S. Gubser is professor of physics at Princeton University and the author of The Little Book of String TheoryFrans Pretorius is professor of physics at Princeton. They both live in Princeton, New Jersey. They are the authors of The Little Book of Black Holes.

Announcing the trailer for The Seduction of Curves by Allan McRobie

CurvesCurves are seductive. These smooth, organic lines and surfaces—like those of the human body—appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world—from our bodies to Salvador Dalí’s paintings and the space-time fabric of the universe itself. A unique introduction to the language of beautiful curves, this book may change the way you see the world.

Allan McRobie is a Reader in the Engineering Department at the University of Cambridge, where he teaches stability theory and structural engineering. He previously worked as an engineer in Australia, designing bridges and towers.

Steven S. Gubser & Frans Pretorius: The Little Book of Black Holes

Black holes, predicted by Albert Einstein’s general theory of relativity more than a century ago, have long intrigued scientists and the public with their bizarre and fantastical properties. Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality—a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research—and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction. The Little Book of Black Holes by Steven S. Gubser and Frans Pretorius takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny. Read on to learn a bit more about black holes and what inspired the authors to write this book.

Your book tells the story of black holes from a physics perspective. What are black holes, really? What’s inside?

Black holes are regions of spacetime from which nothing can escape, not even light. In our book, we try to live up to our title by getting quickly to the heart of the subject, explaining in non-technical terms what black holes are and how we use Einstein’s theory of relativity to understand them. What’s inside black holes is a great mystery. Taken at face value, general relativity says spacetime inside a black hole collapses in on itself, so violently that singularities form. We need something more than Einstein’s theory of relativity to understand what these singularities mean. Hawking showed that quantum effects cause black holes to radiate very faintly. That radiation is linked with quantum fluctuations inside the black hole. But it’s a matter of ongoing debate whether these fluctuations are a key to resolving the puzzle of the singularity, or whether some more drastic theory is needed.

How sure are we that black holes exist?

A lot more certain than we were a few years ago. In September 2015, the LIGO experiment detected gravitational waves from the collision of two black holes, each one about thirty times the mass of the sun. Everything about that detection fit our expectations based on Einstein’s theories, so it’s hard to escape the conclusion that there really are black holes out there. In fact, before the LIGO detection we were already pretty sure that black holes exist. Matter swirling around gigantic black holes at the core of distant galaxies form the brightest objects in the Universe. They’re called quasars, and the only reason they’re dim in our sight is that they’re so far away, literally across the Universe. Similar effects around smaller black holes generate X-rays that we can detect relatively nearby, mere thousands of light years away from us. And we have good evidence that there is a large black hole at the center of the Milky Way.

Can you talk a bit about the formation of black holes?

Black holes with mass comparable to the sun can form when big stars run out of fuel and collapse in on themselves. Ordinarily, gravity is the weakest force, but when too much matter comes together, no force conceivable can hold it up against the pull of gravity. In a sense, even spacetime collapses when a black hole forms, and the result is a black hole geometry: an endless inward cascade of nothing into nothing. All the pyrotechnics that we see in distant quasars and some nearby X-ray sources comes from matter rubbing against itself as it follows this inward cascade.

How have black holes become so interesting to non-specialists? How have they been glorified in popular culture?

There’s so much poetry in black hole physics. Black hole horizons are where time stands still—literally! Black holes are the darkest things that exist in Nature, formed from the ultimate ashes of used-up stars. But they create brilliant light in the process of devouring yet more matter. The LIGO detection was based on a black hole collision that shook the Universe, with a peak power greater than all stars combined; yet we wouldn’t even have noticed it here on earth without the most exquisitely sensitive detector of spacetime distortions ever built. Strangest of all, when stripped of surrounding matter, black holes are nothing but empty space. Their emptiness is actually what makes them easy to understand mathematically. Only deep inside the horizon does the emptiness end in a terrible, singular core (we think). Horrendous as this sounds, black holes could also be doorways into wormholes connecting distant parts of the Universe. But before packing our bags for a trip from Deep Space Nine to the Gamma Quadrant, we’ve got to read the fine print: as far as we know, it’s impossible to make a traversable wormhole.

What inspired you to write this book? Was there a point in life where your interest in this topic was piqued?

We both feel extremely fortunate to have had great mentors, including Igor Klebanov, Curt Callan, Werner Israel, Matthew Choptuik, and Kip Thorne who gave us a lot of insight into black holes and general relativity. And we owe a big shout-out to our editor, Ingrid Gnerlich, who suggested that we write this book.

GubserSteven S. Gubser is professor of physics at Princeton University and the author of The Little Book of String Theory. Frans Pretorius is professor of physics at Princeton.

Kip Thorne & Roger Blandford on Modern Classical Physics

PhysicsThis first-year, graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn’t: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip S. Thorne, winner of the 2017 Nobel Prize in Physics, and Roger D. Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers.

This book emerged from a course you both began teaching nearly 4 decades ago. What drove you to create the course, and ultimately to write this book?

KST: We were unhappy with the narrowness of physics graduate education in the United States. We believed that every masters-level or PhD physicist should be familiar with the basic concepts of all the major branches of classical physics and should have some experience applying them to real world phenomena. But there was no obvious route to achieve this, so we created our course.

RDB: Of course we had much encouragement from colleagues who helped us teach it and students who gave us invaluable feedback on the content.

The title indicates that the book is a “modern” approach to classical physics (which emphasizes physical phenomena at macroscopic scales). What specifically is “modern” in your book’s approach to this subject?

KST: Classical-physics ideas and tools are used extensively today in research areas as diverse as astrophysics, high-precision experimental physics, optical physics, biophysics, controlled fusion, aerodynamics, computer simulations, etc. Our book draws applications from all these modern topics and many more. Also, these modern applications have led to powerful new viewpoints on the fundamental concepts of classical physics, viewpoints that we elucidate—for example, quantum mechanical viewpoints and language for purely classical mode-mode coupling in nonlinear optics and in nonlinear plasma physics.

Why do you feel that it is so important for readers to become more familiar with classical physics, beyond what they may have been introduced to already?

KST: In their undergraduate and graduate level education, most physicists have been exposed to classical mechanics, electromagnetic theory, elementary thermodynamics, and little classical physics beyond this. But in their subsequent careers, most physicists discover that they need an understanding of other areas of classical physics (and this book is a vehicle for that).

In many cases they may not even be aware of their need. They encounter problems in their research or in R&D where powerful solutions could be imported from other areas of classical physics, if only they were aware of those other areas. An example from my career: in the 1970s, when trying to understand recoil of a binary star as it emits gravitational waves, I, like many relativity physicists before me, got terribly confused. Then my graduate student, Bill Burke—who was more broadly educated than I—said “we can resolve the confusion by adopting techniques that are used to analyze boundary layers in fluid flows around bodies with complicated shapes.” Those techniques (matched asymptotic expansions), indeed, did the job, and through Bill, they were imported from fluid mechanics into relativity.

RDB: Yes. To give a second example, when I was thinking about ways to accelerate cosmic rays, I recalled graduate lectures on stellar dynamics and found just the tools I needed.

You also mention in the book that geometry is a deep theme and important connector of ideas. Could you explain your perspective, and how geometry is used thematically throughout the book?

KST: The essential point is that, although coordinates are a powerful, and sometimes essential, tool in many calculations, the fundamental laws of physics can be expressed without the aid of coordinates; and, indeed, their coordinate-free expressions are generally elegant and exceedingly powerful. By learning to think about the laws in coordinate-free (geometric) language, a physicist acquires great power. For example, when one searches for new physical laws, requiring that they be geometric (coordinate-free) constrains enormously the forms that they may take. And in many practical computations (for example, of the relativistic Doppler shift), a geometric route to the solution can be faster and much more insightful than one that uses coordinates. Our book is infused with this.

RDB: We are especially keen on presenting these fundamental laws in a manner which makes explicit the geometrically formulated conservation laws for mass, momentum, energy, etc. It turns out that this is often a good starting point when one wants to solve these equations numerically. But ultimately, a coordinate system must be introduced to execute the calculations and interpret the output.

One of the areas of application that you cover in the book is cosmology, an area of research that has undergone a revolution over the past few decades. What are some of the most transformative discoveries in the field’s recent history? How does classical physics serve to underpin our modern understanding of how the universe formed and is evolving? What are some of the mysteries that continue to challenge scientists in the field of cosmology?   

RDB: There have indeed been great strides in understanding the large scale structure and evolution of the universe, and there is good observational support for a comparatively simple description. Cosmologists have found that 26 percent of the energy density in the contemporary, smoothed-out universe is in the form of “dark matter,” which only seems to interact through its gravity. Meanwhile, 69 percent is associated with a “cosmological constant,” as first introduced by Einstein and which causes the universe to accelerate. The remaining five percent is the normal baryonic matter which we once thought accounted for essentially all of the universe. The actual structure that we observe appears to be derived from almost scale-free statistically simple, random fluctuations just as expected from an early time known as inflation. Fleshing out the details of this description is almost entirely an exercise in classical physics. Even if this description is validated by future observations, much remains to be understood, including the nature of dark matter and the cosmological constant, what fixes the normal matter density, and the great metaphysical question of what lies beyond the spacetime neighborhood that we can observe directly.

KST: Remarkably, in fleshing out the details in the last chapter of our book, we utilize classical-physics concepts and results from every one of the other chapters. ALL of classical physics feeds into cosmology!

The revolution in cosmology that you describe depends upon many very detailed observations using telescopes operating throughout the entire electromagnetic spectrum and beyond. How do you deal with this in the book?

RDB: We make no attempt to describe the rich observational and experimental evidence, referring the reader to many excellent texts on cosmology that describe these in detail. However, we do describe some of the principles that underlie the design and operation of the radio and optical telescopes that bring us cosmological data.

There is has also been a lot of excitement regarding the recent observation by LIGO of gravitational waves caused by merging black holes. How is this subject covered in the book, and how, briefly, are some of the concepts of classical physics elucidated in your description of this cutting-edge research area?   

KST: LIGO’s gravitational wave detectors rely on an amazingly wide range of classical physics concepts and tools, so time and again we draw on LIGO for illustrations. The theory of random processes, spectral densities, the fluctuation-dissipation theorem, the Fokker-Planck equation; shot noise, thermal noise, thermoelastic noise, optimal filters for extracting weak signals from noise; paraxial optics, Gaussian beams, the theory of coherence, squeezed light, interferometry, laser physics; the interaction of gravitational waves with light and with matter; the subtle issue of the conservation or non conservation of energy in general relativity—all these and more are illustrated by LIGO in our book.

What are some of the classical physics phenomena in every day life that you are surprised more people do not fully understand—whether they are lay people, students, or scientists?

KST: Does water going down a drain really have a strong preference for clockwise in the northern hemisphere and counterclockwise in the south? How strong? What happens as you cross the equator? How are ocean waves produced? Why do stars twinkle in the night sky, and why doesn’t Jupiter twinkle? How does a hologram work? How much can solid objects be stretched before they break, and why are there such huge differences from one type of solid (for example thin wire) to another (a rubber band)?

RDB: I agree and have to add that I am regularly humbled by some every day phenomenon that I cannot explain or for which I have carried around for years a fallacious explanation. There is, rightly, a lot of focus right now on climate change, energy, hurricanes, earthquakes, and so on. We hear about them every day. We physicists need to shore up our understanding and do a better job of communicating this.

Do you believe that some of your intended readers might be surprised to discover the deep relevance of classical physics to certain subject areas?

KST: In subjects that physicists think of as purely quantum, classical ideas and classical computational techniques can often be powerful. Condensed matter physics is an excellent example—and accordingly, our book includes a huge number of condensed-matter topics. Examples are Bose-Einstein condensates, the van der Waals gas, and the Ising model for ferromagnetism.

RDB: Conversely, quantum mechanical techniques are often used to simplify purely classical problems, for example in optics.

Writing a book is always an intellectual journey. In the preparation of this tremendously wide-ranging book, what were some of the most interesting things you learned along the way?

KST: How very rich and fascinating is the world of classical physics—far more so than we thought in 1980 when we embarked on this venture. And then there are the new inventions, discoveries, and phenomena that did not exist in 1980 but were so important or mind-boggling that we could not resist including them in our book. For example, optical-frequency combs and the phase-locked lasers that underlie them, Bose-Einstein condensates, the collapse of the World Trade Center buildings on 9/11/01, the discovery of gravitational waves and the techniques that made it possible, laser fusion, and our view of the universe at large.

Kip S. Thorne is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation and Black Holes and Time Warps. Roger D. Blandford is the Luke Blossom Professor of Physics and the founding director of the Kavli Institute of Particle Astrophysics and Cosmology at Stanford University. Both are members of the National Academy of Sciences.


Global Math Week: The Universal Language

by Oscar Fernandez

FernandezFill in the blank: Some people speak English, some speak French, and some speak ____. I doubt you said “math.” Yet, as I will argue, the thought should have crossed your mind. And moreover, the fact that mathematics being a language likely never has, speaks volumes about how we think of math, and why we should start thinking of it—and teaching it—as a language.

To make my point, consider the following fundamental characteristics shared by most languages:

  •  A set of words or symbols (the language’s vocabulary)
  •  A set of rules for how to use these words or symbols (the language’s rules of grammar)
  •  A set of rules for combining these words or symbols to make statements (the language’s syntax)

Now think back to the math classes you have taken. I bet you will soon remember each of these characteristics present throughout your courses. (For instance, when you learned that 𝑎2 means 𝑎 × 𝑎, you were learning how to combine some of the symbols used in mathematics to make a statement—that the square of a number is the number multiplied by itself.) Indeed, viewed this way, every mathematics lesson can be thought of as a language lesson: new vocabulary, rules of grammar, or syntax is introduced; everyone then practices the new content; and the cycle repeats. By extension, every mathematics course can be thought of as a language course.

Now that I have you thinking of mathematics as a language, let me point out the many benefits of this new viewpoint. For one, this viewpoint helps dispel many myths about the subject. For instance, travel to any country and you will find a diverse set of people speaking that country’s language. Some are smarter than others; some are men and some women; perhaps some are Latino and some Asian. Group them as you wish, they will all share the capacity to speak the same language. The same is true of mathematics. It is not a subject accessible only to people of certain intelligence, sex, or races; we all have the capacity to speak mathematics. And once we start thinking of the subject as a language, we will recognize that learning mathematics is like learning any other language: all you need are good teachers, and lots of practice. And while mastering a language is often the endpoint of the learning process, mastering the language that is mathematics will yield much larger dividends, including the ability to express yourself precisely, and the capacity to understand the Universe. As Alfred Adler put it: “

Mathematics is pure language – the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms.” Galileo—widely regarded the father of modern science—once wrote that Nature is a great book “written in the language of mathematics” (The Assayer, 1623). Centuries later, Einstein, after having discovered the equation for gravity using mathematics, echoed Galileo’s sentiment, writing: “pure mathematics is, in its way, the poetry of logical ideas” (Obituary for Emmy Noether, 1935). Most of us today wouldn’t use words like “language” and “poetry” to describe mathematics. Yet, as I will argue, we should. And moreover, we should start thinking of—and teaching—math as a language.

Oscar E. Fernandez is assistant professor of mathematics at Wellesley College and the author of The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love. He also writes about mathematics for the Huffington Post and on his website,

Global Math Week: Counting on Math

by Tim Chartier

The Global Math Project has a goal of sharing the joys of mathematics to 1 million students around the world from October 10th through the 17th. As we watch the ever-increasing number of lives that will share in math’s wonders, let’s talk about counting, which is fundamental to reaching this goal.

Let’s count. Suppose we have five objects, like the plus signs below. We easily enough count five of them.




You could put them in a hat and mix them up.








If you take them out, they might be jumbled but you’d still have five.











Easy enough! Jumbling can induce subtle complexities, even to something as basic as counting.

Counting to 14 isn’t much more complicated than counting to five. Be careful as it depends what you are counting and how you jumble things! Verify there are 14 of Empire State Buildings in the picture below.








If you cut out the image along the straight black lines, you will have three pieces to a puzzle. If you interchange the left and right pieces on the top row, then you get the configuration below. How many buildings do you count now? Look at the puzzle carefully and see if you can determine how your count changed.








Can you spot any changes in the buildings in the first versus the second pictures? How we pick up an additional image is more easily seen if we reorder the buildings. So, let’s take the 14 buildings and reorder them as seen below.








Swapping the pieces on the top row of the original puzzle has the same effect as shifting the top piece in the picture above. Such a shift creates the picture below. Notice how we pick up that additional building. Further, each image loses 1/14th of its total height.








Let’s look at the original puzzle before and after the swap.














This type of puzzle is called a Dissection Puzzle. Our eyes can play tricks on us. We know 14 doesn’t equal 15 so something else must be happening when a puzzle indicates that 14 = 15. Mathematics allows us to push through assumptions that can lead to illogical conclusions. Math can also take something that seems quite magical and turn it into something very logical — even something as fundamental as counting to 14.

Want to look at counting through another mathematical lens? A main topic of the Global Math Project will be exploding dots. Use a search engine to find videos of James Tanton introducing exploding dots. James is a main force behind the Global Math Project and quite simply oozes joy of mathematics. You’ll also find resources at the Global Math Project web page. Take the time to look through the Global Math Project resources and watch James explain exploding dots, as the topic can be suitable from elementary to high school levels. You’ll enjoy your time with James. You can count on it!

ChartierTim Chartier is associate professor of mathematics at Davidson College. He is the coauthor of Numerical Methods and the author of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing.

Global Math Week: Around the World from Unsolved to Solved

by Craig Bauer

BauerWhat hope do we have of solving ciphers that go back decades, centuries, or even all the way back to the ancient world? Well, we have a lot more hope than we did in the days before the Internet. Today’s mathematicians form a global community that poses a much greater threat to unsolved problems, of every imaginable sort, than they have every faced before.

In my Princeton University Press book, Unsolved! The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies, I collected scores of the most intriguing unsolved ciphers. It’s a big book, in proper proportion to its title, and I believe many of the ciphers in it will fall to the onslaught the book welcomes from the world’s codebreakers, both professionals and amateurs. Why am I making this prediction with such confidence? Well, I gave a few lectures based on material from the book, while I was still writing it, and the results bode well for the ciphers falling.

Here’s what happened.

Early in the writing process, I was invited to give a lecture on unsolved ciphers at the United States Naval Academy. I was surprised, when I got there, by the presence of a video camera. I was asked if I was okay with the lecture being filmed and placed on YouTube. I said yes, but inside I was cursing myself for not having gotten a much needed haircut before the talk. Oh well. Despite my rough appearance, the lecture went well.[1] I surveyed some of the unsolved ciphers that I was aware of at the time, including one that had been put forth by a German colleague and friend of mine, Klaus Schmeh. It was a double transposition cipher that he had created himself to show how difficult it is to solve such ciphers. He had placed it in a book he had written on unsolved ciphers, a book which is unfortunately only available in German.[2] But to make the cipher as accessible as possible, he assured everyone that that particular bit of writing was in English.
















Figure 1. Klaus Schmeh’s double transposition cipher challenge.

When the YouTube video went online, it was seen by an Israeli computer scientist, George Lasry, who became obsessed with it. He was not employed at the time, so he was able to devote a massive amount of time to seeking the solution to this cipher. As is natural for George, he attacked it with computer programs of his own design. He eventually found himself doing almost nothing other than working on the cipher. His persistence paid off and he found himself reading the solution.

I ended up being among the very first to see George’s solution, not because I’m the one who introduced him to the challenge via the YouTube video, but because I’m the editor-in-chief of the international journal (it’s owned by the British company Taylor and Francis) Cryptologia. This journal covers everything having to do with codes and ciphers, from cutting edge cryptosystems and attacks on them, to history, pedagogy, and more. Most of the papers that appear in it are written by men and women who live somewhere other than America and it was to this journal that George submitted a paper describing how he obtained his solution to Klaus’s challenge.

George’s solution looked great to me, but I sent it to Klaus to review, just to be sure. As expected, he was impressed by the paper and I queued it up to see print. The solution generated some media attention for George, which led to him being noticed by people at Google (an American company, of course). They approached him and, after he cleared the interviewing hurdles, offered him a position, which he accepted. I was very happy that George found the solution, but of course that left me with one less unsolved cipher to write about in my forthcoming book. Not a problem. As it turns out there are far more intriguing unsolved ciphers than can be fit in a single volume. One less won’t make any difference.

Later on, but still before the book saw print, I delivered a similar lecture at the Charlotte International Cryptologic Symposium held in Charlotte, North Carolina. This time, unlike at the Naval Academy, Klaus Schmeh was in the audience.

One of the ciphers that I shared was fairly new to me. I had not spoken about it publicly prior to this event. It appeared on a tombstone in Ohio and seemed to be a Masonic cipher. It didn’t look to be sophisticated, but it was very short and shorter ciphers are harder to break. Brent Morris, a 33rd degree Mason with whom I had discussed it, thought that it might be a listing of initials of offices, such as PM, PHP, PIM (Past Master, Past High Priest, Past Illustrious Master), that the deceased had held. This cipher was new to Klaus and he made note of it and later blogged about it. Some of his followers collaborated in an attempt to solve it and succeeded. Because I hadn’t even devoted a full page to this cipher in my book, I left it in as a challenge for readers, but also added a link to the solution for those who want to see the solution right away.


Figure 2. A once mysterious tombstone just south of Metamora, Ohio.

So, what was my role in all of this? Getting the ball rolling, that’s all. The work was done by Germans and an Israeli, but America and England benefited as well, as Google gained yet another highly intelligent and creative employee and a British owned journal received another great paper.

I look forward to hearing from other people from around the globe, as they dive into the challenges I’ve brought forth. The puzzles of the past don’t stand a chance against the globally networked geniuses of today!

Craig P. Bauer is professor of mathematics at York College of Pennsylvania. He is editor in chief of the journal Cryptologia, has served as a scholar in residence at the NSA’s Center for Cryptologic History, and is the author of Unsolved!: The History and Mystery of the World’s Greatest Ciphers from Ancient Egypt to Online Secret Societies. He lives in York, Pennsylvania.


[1] It was split into two parts for the YouTube channel. You can see them at (Part 1) and (Part 2). A few years later, I got cleaned up and delivered an updated version of the talk at the International Spy Museum. That talk, aimed at a wider audience, may be seen at

[2] Schmeh, Klaus, Nicht zu Knacken, Carl Hanser Verlag, Munich, 2012.

Vickie Kearn kicks off Global Math Week

October 10 – 17 marks the first ever Global Math Week. This is exciting for many reasons and if you go to the official website, you’ll find that there are already 736,546—and counting— reasons there. One more: PUP will be celebrating with a series of posts from some of our most fascinating math authors, so check this space tomorrow for the first, on ciphers, by Craig Bauer. Global Math Week provides a purposeful opportunity to have a global math conversation with your friends, colleagues, students, and family.

Mathematics is for everyone, as evidenced in the launch of Exploding Dots, which James Tanton brilliantly demonstrates at the link above. It is a mathematical story that looks at math in a new way, from grade school arithmetic, all the way to infinite sums and on to unsolved problems that are still stumping our brightest mathematicians. Best of all, you can ace this and no longer say “math is hard”, “math is boring”, or “I hate math”.

Vickie Kearn visits the Great Wall during her trip to our new office in Beijing

I personally started celebrating early as I traveled to Beijing in August to attend the Beijing International Book Fair. I met with the mathematics editors at a dozen different publishers to discuss Chinese editions of our math books. Although we did not speak the same language, we had no trouble communicating. We all knew what a differential equation is and a picture in a book of a driverless car caused lots of hand clapping. I was thrilled to be presented with the first Chinese editions of two books written by Elias Stein (Real Analysis and Complex Analysis) from the editor at China Machine Press. Although I love getting announcements from our rights department that one of our math books is being translated into Chinese, Japanese, German, French, etc., there is nothing like the thrill I had of meeting the people who love math as much as I do and who actually make our books come to life for people all over the world.

Because Princeton University Press now has offices in Oxford and Beijing, in addition to Princeton, and because I go to many conferences each year, I am fortunate to travel internationally and experience global math firsthand. No matter where you live, it is possible to share experiences through doing math. I urge you to visit the Global Math Project website and learn how to do math(s) in a global way.

Check back tomorrow for the start of our PUP blog series on what doing math globally means to our authors. Find someone who says they don’t like math and tell them your global math story.

Read like a Nobel Prize-winning physicist

This morning Princeton University Press was thrilled to congratulate PUP author and celebrated physicist Kip Thorne on being a co-winner of the Nobel Prize in Physics for 2017. Dr. Thorne’s research has focused on Einstein’s general theory of relativity and astrophysics, with emphasis on relativistic stars, black holes, and especially gravitational waves. The latter observation, made in September 2015, validated a key prediction of Einstein’s general theory of relativity. Princeton University Press is honored to be the publisher of Dr. Thorne’s Modern Classical Physics, co-authored with Roger Blandford, and the new hardback edition of the renowned classic, Gravitation, co-authored with Charles Misner and the late John Wheeler, forthcoming this fall.

Over the years, we’ve published several Nobel winners, including:

  • Einstein
  • Richard Feynman (QED)
  • P.W. Anderson (the classic and controversial Theory of Superconductivity in the High-Tc Cuprates)
  • Paul Dirac (General Theory of Relativity)
  • Werner Heisenberg (Encounters with Einstein)

Interested in learning more about physics yourself? We put together the ultimate Nobel reading list. Click the graphic for links to each book.

PUP congratulates Kip S. Thorne, joint winner of the Nobel Prize in Physics

New Books Gravitation and Modern Classical Physics Publishing in October 2017

Princeton, NJ, October 3, 2017—Upon today’s announcement that Dr. Kip S. Thorne is the joint winner of the Nobel Prize in Physics for 2017, Princeton University Press would like to extend hearty congratulations to the celebrated physicist.

The Royal Swedish Academy recognizes Dr. Thorne, along with Rainer Weiss and Barry C. Barish, for decisive contributions to the LIGO detector and the observation of gravitational waves”.

Feynman Professor of Theoretical Physics, Emeritus at the California Institute of Technology, Dr. Thorne has focused his research on Einstein’s general theory of relativity and on astrophysics, with emphasis on relativistic stars, black holes, and especially gravitational waves. The latter observation, made in September 2015, validated a key prediction of Einstein’s general theory of relativity.

Princeton University Press is honored to be the publisher of Dr. Thorne’s Modern Classical Physics, co-authored with Roger Blandford, and the new hardback edition of the renowned classic, Gravitation, co-authored with Charles Misner and the late John Wheeler, publishing in October 2017.

According to Christie Henry, director of Princeton University Press, “Dr. Thorne’s creativity and brilliance have been as grounding to Princeton University Press’s publishing program in the physical sciences as gravitation is to the human experience.  His recently released Princeton University Press contributions, Gravitation and Modern Classical Physics, are vital to our mission of illuminating spheres of knowledge to advance and enrich the human conversation, and today we celebrate his commitment to science with the Nobel committee and readers across the universe.”

Since the publication of Albert Einstein’s The Meaning of Relativity in 1922, Princeton University Press has remained committed to publishing global thought leaders in the sciences and beyond. We are honored to count Dr. Thorne’s work as part of this legacy.


For more information, please contact:

Julia Haav, Assistant Publicity Director, 609.258.2831


Emmet Gowin: Mariposas Nocturnas

American photographer Emmet Gowin is best known for his portraits of his wife, Edith, and their family, as well as for his images documenting the impact of human activity upon landscapes around the world. For the past fifteen years, he has been engaged in an equally profound project on a different scale, capturing the exquisite beauty of more than one thousand species of nocturnal moths in Bolivia, Brazil, Ecuador, French Guiana, and Panama. The result is Mariposas Nocturnas. These stunning color portraits present the insects—many of which may never have been photographed as living specimens before, and some of which may not be seen again—arrayed in typologies of twenty-five per sheet. The moths are photographed alive, in natural positions and postures, and set against a variety of backgrounds taken from the natural world and images from art history. Essential reading for audiences both in photography and natural history, this lavishly illustrated volume reminds readers that, as Terry Tempest Williams writes in her foreword, “The world is saturated with loveliness, inhabited by others far more adept at living with uncertainty than we are.” Read on to learn more about Gowin’s evolution as a photographer, the underlying philosophy that he brought to this project, and his biggest influences.

As a photographer you’ve long been known for intimate photos of your family, and later, aerial landscapes of the American West. Can you explain your evolution from these projects to work on these stunning portraits of more than one thousand species of nocturnal moths?

There are two main factors in my evolution from images of family and landscape to this long term study of moths. Even as a child I seemed to have an interest in small things, and if the small thing was alive all the better. If I drew, the drawing was usually small. Later I came to a deep reverence for insects even if I didn’t photograph them yet. In the 1970s I used a child’s small collection of insects, found dead in the windowsill, to enliven a nineteenth century book on rhetoricThat became an important image for me, though it was a singular event at the time. Later, I worked with some neighborhood boy scouts on their insect merit badgethus learning the basics of how a collection was built. So a respect for insects has been a part of my makeup, my curiosity, for as long as I can remember.

More particularly, my experience photographing the Nevada Test Site in 1996-97 left me at a turning point. Later I came to realize that one cannot study industrial scale agriculture, excessive water usage, and the building and testing of the atomic bomb without being changed. Three visits to the Nevada Test Site were all I could endure.

Its an important story but the next step will need to be taken by others. And all this exactly as my wife Edith and I made our first trip to Ecuador. Initially, I could not have told you what I was doing there, only that it was where I wanted to spend more time.

Can you talk a bit about the philosophy that underlies your work on this project? Was it your intention at the outset to raise awareness of the need for biodiversity?

Not so much a philosophy, although one must have one, I suppose, but the desire to turn a corner and begin to educate myself to the concerns of a working tropical biologist.  Even as a beginner this seemed a critical subject and also a key time in Earth’s history. And I was about to publish Changing the Earth, in 2002. For me, a respect for and admiration for insects was already in place, but I was also interested in learning something about field biology and in getting into the field myself. Alfred Wallace’s Malay Archipelago and Darwin’s Voyage of the Beagle were already important books for me.

Also, in our time even children understand the importance of loss of habitat and that the destruction of the Amazonian forest, any forest, concerns us all. At the Nevada Test Site I was stunned by just how many tests had been conducted, mostly to little real gain. I understood the history but I still felt a great shock in witnessing this destruction, mostly hidden from our view, and with such grave consequences to Americans downwind. That America had in fact bombed itself breaks one’s heart. I’ll just say that at this point I felt I had learned enough about the human willingness to destroy ourselves. Then, an almost chance visit to Ecuador opened my eyes to how I felt about the tropical forest. At first I imagined that the forest itself would be my subject, but the introduction to a research cabin in Panama in 1999 changed all that. There I recognized that the symbiotic relationship between the insects and the forest would be my way of discovery.

A nice story: After a few years in Panama I had made my first moth portrait grid. We took it to a store for framing. When our poster was collected there was an interest in selling them. “Where did you find these?” “Panama”, we said.  To which the shop owner said, “No, you can’t fool me, I’m from Panama, and none of these live here. I would know.” We didn’t argue, but leaving we conferred, “I guess we are on to something here.”

What photographers have been your biggest influencers in terms of style and aesthetics?

Let me just say that it was a very small photograph that first brought me to a feeling of transcendence. I later learned it was by Ansel Adams. That photograph and that feeling I never forgot. However, the artists I really loved were a mixed lot. Of course, Henri Cartier Bresson and Robert Frank were among the practical examples, and of course they were spiritual examples too.  Walker Evans and Harry Callahan were especially dear to me, and Callahan was my graduate advisor in Rhode Island. At the same time I was introduced to the history of art and film. Both felt very important to me, but perhaps painting and drawing felt the most accessible to me then, at least until photography arrived with its particular capacity for transcendence, which was closely followed by the introduction to the miracle of the silver image and its process. I still love the process of photography.

After Callahan, Frederick Sommer was perhaps the clearest example of the possibility of combining all these interests. Sommer would say, “you have to make it to find it or you have to find it to make it,” indicating that photography in a sly way combined everything that was of interest to me. That in our search for discovery and revelation, chance and purpose were intertwined, and both could and should serve the imagination.

How (if at all) has your early interest in drawing impacted your work as a photographer?

Drawing was the first art which opened for me. I drew often as a child and loved projects in which I could add a drawing. Like all dreamy and inattentive children I drew in school when I should have been paying attention. It was an impulse which seemed to come out of nowhere, which felt so real; I knew I could trust it. I saw very little art until art school, but when I was shown the great works I knew this is what I wanted, where I belonged. When photography came along I could see that I would need to serve all the same problems and concerns of painting an drawing; the distribution of weights, configuration of space, tonality and edge, the bounding line.  Within drawing and painting, it felt to me, that everything matters. By the end of my first year in art school I realized and I could serve these concerns with photography too, and it seemed to fit my nature and quickly became my constant joy.

Let me end this thought by calling attention to the kind of materials I began to carry into the tropics; most of them were copies of drawings and paintings—and the long history of graphic arts: Degas, Matisse, Picasso, Redon among the moderns and the old masters like Gruenwald, Bellini, Blake and Segurs. A small pantheon of great love and wisdom.

I’ve read you grew up in Chincoteague Island, surrounded by marshes and nature. Has that experience had a lasting impact on your work and your choice of subject matter?

Actuallyour family moved to Chincoteague when I was 13 and we only lived there two years.  I think I have given the mistaken impression of growing up there as that experience, beguiled as I was by the riches of the natural world, has always felt to me that it was there that I found my self, my identity, and the desire to be either a naturalist or an artist in those two short years.

How do you capture such photographs of moths, which are all, it should be noted, photographed alive? How do you keep them still?

The question of keeping them still is a bit misleading. Rarely do they stay still except for small periods when they settle themselves under a light onto the white collecting sheet. and then only until disturbed by another insect, which is quite often. Any moth I am seeing for the first time I attempt to photograph there on the white sheet to at least have a record of the species. But as my feelings were being educated by the moths I learned which I could touch, which could be nudged, which would fly with the first flash of the strobe. Some were, of course, photographed where I found them. but as I learned my way, I found I could transfer a moth to another surface with some success. Then I might have a minute to get a decent photograph. I was always aware that my chance to make a photograph could end in an instant. In Ecuador we sometimes collected moths in small plastic bags at night for photography the next day. Its a bit risky but on its leaf and with plenty of air inside, most remain calm. Sometimes these could be photographed in our motel room the next day. They could, of course, take flight, but at least we were in the same room.

Terry Tempest Williams writes in her foreword to this book, “The world is saturated with loveliness, inhabited by others far more adept at living with uncertainty than we are.” How does this idea of uncertainty play out in your work?

That “the world is saturated with loveliness” I have never doubted, but I rejoice in her finding just these words. In the late 60s and early 70s, our corner of Virginia felt something like the passage from St. Matthew—let me say it as I remember it—”unless you become as a little child, you can never enter the kingdom of heaven.” That is how I felt. At the same time we were visited each evening by images from the Vietnam war, and yet in our daily lives there were just the opposite. There was an intuitive sense that both the war and the “Kingdom or Heaven” saturated the same world, and in many ways it was chance which had placed us there, in Virginia. “Its what you do every day in the most simple way that counts,” my friend Frederick Sommer reminds us. This may sound too simple but if we could only live like this; treat everyone we meet as, just perhaps, the most important person in the world. And if you live that way, some of this feeling will embrace the butterfly, the ant, the moth.


GowinEmmet Gowin is emeritus professor of photography at Princeton University. His many books include Emmet Gowin and Changing the Earth. His photographs are in collections around the world, including at the Art Institute of Chicago, the Cleveland Museum of Art, the J. Paul Getty Museum, the Metropolitan Museum of Art, the Museum of Modern Art, and the Tokyo Museum of Art. Terry Tempest Williams is an author, conservationist, and activist. Her books include The Hour of Land: A Personal Topography of America’s National Parks and Refuge: An Unnatural History of Family and Place.

Essential Reading in Natural History

Princeton University Press is excited to have a wide variety of excellent titles in natural history. From the Pacific Ocean, to horses, to moths, our books cover a range of topics both large and small. As summer winds down, take advantage of the last weeks of warm weather by bringing one of our handy guides out into the field to see if you can spot a rare butterfly or spider. To find your next read, check out this list of some of our favorite titles in natural history, and be sure to visit our website for further reading.

Britain’s Mammals by Dominic Couzens, Andy Swash, Robert Still, and Jon Dun is a comprehensive and beautifully designed photographic field guide to all the mammals recorded in the wild in Britain and Ireland in recent times.


Horses of the World by Élise Rousseau, with illustrations by Yann Le Bris, is a beautifully illustrated and detailed guide to the world’s horses.


A Swift Guide to the Butterflies of North America, Second Edition, by Jeffrey Glassberg is a thoroughly revised edition of the most comprehensive and authoritative photographic field guide to North American butterflies.


Big Pacific by Rebecca Tansley is the companion book to PBS’s five-part mini series that breaks the boundaries between land and sea to present the Pacific Ocean and its inhabitants as you have never seen them before.


Britain’s Spiders by Lawrence Bee, Geoff Oxford, and Helen Smith is a photographic guide to all 37 of the British families.


The second edition of Garden Insects of North America by Whitney Cranshaw and David Shetlar is a revised and updated edition of the most comprehensive guide to common insects, mites, and other “bugs” found in the backyards and gardens of the United States and Canada.


Last but not least, Mariposas Nocturnas is a stunning portrait of the nocturnal moths of Central and South America by famed American photographer Emmet Gowin.