Everyone’s favorite genius takes the spotlight

Along with Einstein fans everywhere, we’re fairly excited to binge-watch National Geographic’s upcoming series, “Genius”, premiering Tuesday, April 25. The first episode shows a young Einstein (Johnny Flynn), poring over the nature of time, a concept well covered in our An Einstein Encyclopedia along with most any other topic that could interest an Einstein devotee, from fame, to family, to politics, to myths and misconceptions. In Genius, prepare to see a show-down between a feisty young Einstein and a particularly rigid teacher. Engrossing to watch—and bound to leave viewers wanting more. Not to worry: “Teachers, education and schools attended” are covered in depth in the Encyclopedia, as are “Rivals”.

Episode 2 of Genius promises to show Einstein embarking, after much head-butting, on a love affair with the determined Mileva Maric. Often remembered as the lone, eccentric, Princeton-based thinker, Einstein’s youthful relationship with Maric sometimes comes as a surprise even to Einstein fans. And yet in 1903, a young Albert Einstein married his confidante despite the objections of his parents. Her influence on his most creative years has given rise to much discussion—but theirs was only one of several romantic interests over the course of Einstein’s life that competed with his passion for physics. Einstein’s love life has been the subject of intense speculation over the years, but don’t believe everything you hear: “Romantic Interests: Actual, Probable, and Possible”, all included in the Encyclopedia, won’t leave you guessing.

Mileva Maric, first wife of Albert Einstein

 An Einstein Encyclopedia is the single most complete guide to Einstein’s life, perfect for browsing and research alike. Written by three leading Einstein scholars who draw on their combined wealth of expertise gained during their work on the Collected Papers of Albert Einstein, this accessible reference features more than one hundred entries and is divided into three parts covering the personal, scientific, and public spheres of Einstein’s life.

With science celebrated far and wide along with Earth Day this past weekend, what better time to get your dose of genius and #ReadUp.



Celebration of Science: A reading list

This Earth Day 2017, Princeton University Press is celebrating science in all its forms. From ecology to psychology, astronomy to earth sciences, we are proud to publish books at the highest standards of scholarship, bringing the best work of scientists to a global audience. We all benefit when scientists are given the space to conduct their research and push the boundaries of the human store of knowledge further. Read on for a list of essential reading from some of the esteemed scientists who have published with Princeton University Press.

The Usefulness of Useless Knowledge
Abraham Flexner and Robbert Dijkgraaf


The Serengeti Rules
Sean B. Carroll


Honeybee Democracy
Thomas D. Seeley


Silent Sparks
Sara Lewis


Where the River Flows
Sean W. Fleming


How to Clone a Mammoth
Beth Shapiro


The Future of the Brain
Gary Marcus & Jeremy Freeman


Searching for the Oldest Stars
Anna Frebel


Climate Shock
Gernot Wagner & Martin L. Weitzman


Welcome to the Universe
Neil DeGrasse Tyson, Michael A. Strauss, and J. Richard Gott


The New Ecology
Oswald J. Schmitz


J. Richard Gott: What’s the Value of Pi in Your Universe?

Carl Sagan’s sci-fi novel Contact famously introduced wormholes for rapid transit between the stars. Carl had asked his friend Kip Thorne to tell him if the physics of wormholes was tenable and this led Thorne and his colleagues to investigate their properties. They found that traversable wormholes required exotic matter to prop them open and that, by moving the wormhole mouths one could find general relativity solutions allowing time travel to the past. A quantum state called the Casimir vacuum whose effects have been observed experimentally, could provide the exotic matter. To learn whether such time machines could be constructible in principle, we may have to master the laws of quantum gravity, which govern how gravity behaves on microscopic scales. It’s one of the reasons physicists find these solutions so interesting.

But in Contact there is lurking yet another fantastic sci-fi idea, which gets less publicity because it was not included in the movie version. In the book, the protagonist finds out from the extraterrestrials that the system of wormholes throughout the galaxy was not built by them, but by the long gone “old ones” who could manipulate not only the laws of physics but also the laws of mathematics! And they left a secret message in the digits of pi. In his movie Pi, Darren Aronofsky showed a man driven crazy by his search for hidden meanings in the digits of pi.

This opens the question: could pi have been something else? And if so, does pi depend on the laws of physics? Galileo said: “Philosophy is written in this grand book…. I mean the universe … which stands continually open to our gaze…. It is written in the language of mathematics.” The universe is written in the language of mathematics. Nobel laureate Eugene Wigner famously spoke of the “unreasonable effectiveness of mathematics” in explaining physics. Many philosophers take the Platonic view that mathematics would exist even the universe did not. And cosmologist Max Tegmark goes so far as to say that the universe actually is mathematics.

Yet maybe it is the other way around. The laws of physics are just the laws by which matter behaves. They determine the nature of our universe. Maybe humans have simply developed the mathematics appropriate for describing our universe, and so of course it fits with what we see. The mathematician Leopold Kronecker said, “God created the integers, all the rest is the work of man.” Are the laws of mathematics discovered by us in the same way as we discover the laws of physics? And are the laws of mathematics we discover just those which would have occurred to creatures living in a universe with physics like ours? In our universe, physics produces individual identical particles: all electrons are the same for example. We know about integers because there are things that look the same (like apples) for us to count. If you were some strange creature in a fractal universe containing only one object—yourself—and you thought only recursively, you might not ever think of counting anything and would never discover integers.

What about π = 3.14159265.…? Might it have a different value in a different universe? In our universe we have a fundamental physical dimensionless constant, the fine structure constant α which is related to the square of the value of the electric charge of the proton in natural geometrical Planck units (where the speed of light is 1 and the reduced Planck constant is 1 and Newton’s gravitational constant is 1). Now 1/α = 137.035999… Some physicists hope that one day we may have a mathematical formula for 1/α using mathematical constants such as π and e. If a theory for the fine structure constant could be developed giving a value in agreement with observations but allowing it to be calculated uniquely from pure mathematics, and if more and more digits of the constant were discovered experimentally fulfilling its prediction, it would certainly merit a Nobel Prize. But many physicists feel that no such magic formula will ever be discovered. Inflation may produce an infinite number of bubble universes, each with different laws of physics. Different universes bubbling out of an original inflating sea could have different values of 1/α. As Martin Rees has said, the laws of physics we know may be just local bylaws in an infinite multiverse of universes. String theory, if correct, may eventually give us a probability distribution for 1/α and we may find that our universe is just somewhere in the predicted middle 95% of the distribution, for example. Maybe there could be different universes with different values of π.

Let’s consider one possible example: taxicab geometry. This was invented by Hermann Minkowski. Now this brilliant mathematician also invented the geometrical interpretation of time as a fourth dimension based on Einstein’s theory of special relativity, so his taxicab geometry merits a serious look. Imagine a city with a checkerboard pattern of equal-sized square blocks. Suppose you wanted to take a taxicab to a location 3 blocks east, and 1 block north of your location, the shortest total distance you would have to travel to get there is 4 blocks. Your taxi has to travel along the streets, it does not get to travel as the crow flies. You could go 1 block east, then 1 block north then 2 blocks east, and still get to your destination, but the total distance you traveled would also be 4 blocks. The distance to your destination would be ds = |dx| + |dy|, where |dx| is the absolute value of the difference in x coordinates and |dy| is the absolute value of the difference in y coordinates. This is not the Euclidean formula. We are not in Kansas anymore! The set of points equidistant from the origin is a set of dots in a diamond shape. See diagram.


Image showing an intuitive explanation of why circles in taxicab geometry look like diamonds. Wikipedia.

Now if the blocks were smaller, there would be more dots, still in a diamond shape. In the limit where the size of the blocks had shrunk to zero, one would have a smooth diamond shape as shown in the bottom section of the diagram. The set of points equidistant from the origin has a name—a “circle!” If the circle has a radius of 1 unit, the distance along one side of its diamond shape is 2 units: going from the East vertex of the diamond to the North vertex of the diamond along the diagonal requires you to change the x coordinate by 1 unit and the y coordinate by 1 unit, making the distance along one side of the diagonal equal to 2 units (ds = |dx| + |dy| = 1 + 1 units = 2 units). The diamond shape has 4 sides so the circumference of the diamond is 8 units. The diameter of the circle is twice the radius, and therefore 2 units. In the taxicab universe π = C/d = C/2r = 8/2 = 4. If different laws of physics dictate different laws of geometry, you can change the value of π.

This taxicab geometry applies in the classic etch-a-sketch toy (Look it up on google, if you have never seen one). It has a white screen, and an internal stylus that draws a black line, directed by horizontal and vertical control knobs. If you want to draw a vertical line, you turn the vertical knob. If you want to draw a horizontal line you turn the horizontal knob. If you want to draw a diagonal line, you must simultaneously turn both knobs smoothly. If the distance between two points is defined by the minimal amount of total turning of the two knobs required to get from one point to the other, then that is the “taxicab” distance between the two points. In Euclidean geometry there is one shortest line between two points: a straight line between them. In taxicab geometry there can be many different, equally short, broken lines (taxicab routes) connecting two points. Taxicab geometry does not obey the axioms of Euclidean geometry and therefore does not have the same theorems as Euclidean geometry. And π is 4.

Mathematician and computer scientist John von Neumann invented a cellular automaton universe that obeys taxicab geometry. It starts with an infinite checkerboard of pixels. Pixels can be either black or white. The state of a pixel at time step t = n + 1 depends only on the state of its 4 neighbors (with which it shares a side: north, south, east, west of it) on the previous time step t = n. Causal, physical effects move like a taxicab. If the pixels are microscopic, we get a taxicab geometry. Here is a simple law of physics for this universe: a pixel stays in the same state, unless it is surrounded by an odd number of black pixels, in which case it switches to the opposite state on the next time step. Start with a white universe with only 1 black pixel at the origin. In the next time step it remains black while its 4 neighbors also become black. There is now a black cross of 5 pixels at the center. It has given birth to 4 black pixels like itself. Come back later and there will be 25 black pixels in a cross-shaped pattern of 5 cross-shaped patterns.

Come back still later and you can find 125 black pixels in 5 cross-shaped patterns (of 5 cross-shaped patterns). All these new black pixels lie inside a diamond-shaped region whose radius grows larger by one pixel per time step. In our universe, drop a rock in a pond, and a circular ripple spreads out. In the von Neumann universe, causal effects spread out in a diamond-shaped pattern.

If by “life” you mean a pattern able to reproduce itself, then this universe is luxuriant with life. Draw any pattern (say a drawing of a bicycle) in black pixels and at a later time you will find 5 bicycles, and then 25 bicycles, and 125 bicycles, etc. The laws of physics in this universe cause any object to copy itself. If you object that this is just a video game, I must tell you that some physicists seriously entertain the idea that we are living in an elaborate video game right now with quantum fuzziness at small scales providing the proof of microscopic “pixelization” at small scales.

Mathematicians in the von Neumann universe would know π = 4 (Or, if we had a taxicab universe with triangular pixels filling the plane, causal effects could spread out along three axes instead of two and a circle would look like a hexagon, giving π = 3.). In 1932, Stanislaw Golab showed that if we were clever enough in the way distances were measured in different directions, we could design laws of physics so that π might be anything we wanted from a low of 3 to a high of 4.

Back to the inhabitants of the von Neumann universe who think π = 4. Might they be familiar with number we know and love, 3.14159265…? They might:

3.14159265… = 4 {(1/1) – (1/3) + (1/5) – (1/7) + (1/9) + …} (Leibnitz)

If they were familiar with integers, they might be able to discover 3.14159265… But maybe the only integers they know are 1, 5, 25, 125, … and 4 of course. They would know that 5 = SQRT(25), so they would know what a square root was. In this case they could still find a formula for

3.14159265. . . =
SQRT(4) {SQRT(4)/SQRT(SQRT(4))}{SQRT(4)/SQRT(SQRT(4) + SQRT(SQRT(4)))}{SQRT(4)/ SQRT(SQRT(4) + SQRT(SQRT(4) + SQRT(SQRT(4))))} …

This infinite product involving only the integer 4 derives from one found by Vieta in 1594.

There are indeed many formulas equal to our old friend 3.14159265… including a spectacular one found by the renowned mathematician Ramanujan. Though every real number can be represented by such infinite series, products and continued fractions, these are particularly simple. So 3.14159265… does seem to have a special intimate relationship with integers, independent of geometry. If physics creates individual objects that can be counted, it seems difficult to avoid learning about 3.14159265… eventually—“If God made the integers,” as Kronecker suggested. So 3.14159265… appears not to be a random real number and we are still left with the mystery of the unreasonable effectiveness of mathematics in explaining the physics we see in our universe. We are also left with the mystery of why the universe is as comprehensible as it is. Why should we lowly carbon life forms be capable of finding out as much about how the universe works as we have done? Having the ability as intelligent observers to ask questions about the universe seems to come with the ability to actually answer some of them. That’s remarkable.

UniverseGottJ. Richard Gott is professor of astrophysics at Princeton University. His books include The Cosmic Web: Mysterious Architecture of the Universe. He is the coauthor of Welcome to the Universe: An Astrophysical Tour with Neil DeGrasse Tyson and Michael A. Strauss.

Mircea Pitici on the best mathematics writing of 2016

PiticiThe Best Writing on Mathematics 2016 brings together the year’s finest mathematics writing from around the world. In the 2016 edition, Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein’s proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York’s Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. And there’s much, much more. Read on to learn about how the essays are chosen, what is meant by the ‘best’ mathematics writing, and why Mircea Pitici, the volume editor, enjoys putting this collection together year after year:

What is new in the new volume of The Best Writing on Mathematics series?

The content is entirely new, as you expect! The format is the same as in the previous volumes—with some novelties. Notably, this volume has figures in full color, in line with the text (not just an insert section of color figures). Also, the reference section at the end of the book is considerably more copious than ever before; besides a long list of notable writings and a list of special journal issues on mathematical topics, I offer two other resources: references for outstanding book reviews on mathematics and references for interviews with mathematical people. I included these additional lists to compensate for the rule we adopted from the start of the series, namely that we will not include in the selection pieces from these categories. Yet book reviews and interviews are important to the mathematical community. I hope that the additional bibliographic research required to do these lists is worth the effort; these references can guide the interested readers if they want to find materials of this sort on their own. The volume is not only an anthology to read and enjoy but also a research tool for the more sophisticated readers.

What do you mean by “the best” writings—and are the pieces you include in this volume really the best?

The superlative “best” in the title caused some controversy at the beginning. By now, perhaps most readers understand (and accept, I hope) that “best” denotes the result of a comparative, selective, and subjective procedure involving several people, including pre-selection reviewers who remain anonymous to me. Every year we leave out exceptional writings on mathematics, due to the multiple constraints we face when preparing these anthologies. With this caveat disclosed, I am confident that the content satisfies the most exigent of readers.

Where do you find the texts you select for these anthologies?

I survey an immense body of literature on mathematics published mainly in academic journals, specialized magazines, and mass media. I have done such searches for many years, even before I found a publisher for the series. I like to read what people write about mathematics. A comprehensive survey is not possible but I aspire to it; I do both systematic and random searches of publications and databases. A small proportion of the pieces we consider are suggested to me either by their authors or by other people. I always consider such pieces; some of them made it into the books, most did not.

Who are the readers you have in mind, for the volumes in this series?

The books are addressed to the public, in the sense that a curious reader with interest toward mathematics can understand most of the content even if their mathematical training is not sophisticated. And yet, at the same time, the series may also interest mathematical people who want to place mathematics in broad social, cultural, and historical contexts. I am glad that we struck a good balance, making this series accessible to these very different audiences.

Why should people read about mathematics, in addition to (or instead of) learning and doing mathematics?

Mathematics is to a high degree self-contained and self-explanatory, in no need for outside validation. One can do mathematics over a lifetime and not care about “the context.” From a broader intellectual perspective though, interpreting mathematics in social-historical contexts opens up the mind to grasping the rich contribution made by mathematics and mathematicians to ubiquitous aspects of our daily lives, to events, trends, and developments, and to imagining future possibilities. Writing about mathematics achieves such a contextual placement, unattainable by doing mathematics.

What drives you to edit the volumes in this series?

Curiosity, interest in ideas, joy in discovering talented people who show me different perspectives on mathematics; foremost, fear of dogmatism. This last point might sound strange; I readily admit that it is rooted in my life experience, growing up in Romania and emigrating to the U.S. (now I am a naturalized citizen here). Editing this series comes down to a simple recipe: I edit books I will enjoy reading; that sets a high bar by default, since I am a demanding reader. Editing this series allows me to have a personal rapport with mathematics, different from the rapport everyone else has with it. It’s my thing, my placement in relationship with this complicated human phenomenon we call ‘mathematics.’ Or, rather, it is one facet of my rapport to mathematics, one that transpired to the public and gained acceptance. I relate to mathematics in other ways, also important to me—but those facets remain unacknowledged yet, despite my (past) efforts to explain them. Most dramatically, once I went to a business school full of ideas about mathematics and how it relates to the world. At that well-known business school, a handful of faculty dressed down my enthusiasm so efficiently that I learned to be guarded in what I say. After that misadventure of ideas in a place that supposedly encouraged creative thinking, I lost confidence in my persuasive abilities and, disappointed, I gave up on expressing my views on mathematics. Instead, I now rejoice in accomplishing the next best thing: finding and promoting other people’s originality, not mine!

Are you working on the next volume in the series?

The content of the next volume is already selected. We are close to approaching the production stage.

Mircea Pitici holds a PhD in mathematics education from Cornell University and is working on a master’s degree in library and information science at Syracuse University. He has edited The Best Writing on Mathematics since 2010.

Browse Our Physics & Astrophysics 2017 Catalog

We invite you to explore our Physics & Astrophysics 2017 Catalog:

PUP will be at the 229th Meeting of the American Astronomical Society in Grapevine, Texas from January 3 to January 7. Come and visit us at booth #200! Also, follow #AAS229 and @PrincetonUnivPress on Twitter for updates and information on our new and forthcoming titles throughout the meeting.

Welcome to the Universe is a personal guided tour of the cosmos by three of today’s leading astrophysicists: Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott. Breathtaking in scope and stunningly illustrated throughout, this book is for those who hunger for insights into our evolving universe that only world-class astrophysicists can provide.

Tyson et al Welcome to the Universe

In Fashion, Faith, and Fantasy in the New Physics of the Universe, acclaimed physicist and bestselling author Roger Penrose argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today’s researchers astray in three of the field’s most important areas—string theory, quantum mechanics, and cosmology.

Penrose Fashion

An accessible blend of narrative history and science, Strange Glow describes mankind’s extraordinary, thorny relationship with radiation, including the hard-won lessons of how radiation helps and harms our health. Timothy Jorgensen explores how our knowledge of and experiences with radiation in the last century can lead us to smarter personal decisions about radiation exposures today.

Jorgensen Strange Glow

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Exclusive interview with Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott on their NYT bestseller, Welcome to the Universe

UniverseWe’re thrilled to announce that Welcome to the Universe, a guided tour of the cosmos by three of today’s leading astrophysicists, recently made the New York Times extended bestseller list in science. Inspired by the enormously popular introductory astronomy course that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton, this book covers it all—from planets, stars, and galaxies to black holes, wormholes, and time travel. The authors introduce some of the hot topics in astrophysics in today’s Q&A:

What is the Cosmic Perspective?

NDT: A view bigger than your own that offers a humbling, yet enlightening, and occasionally empowering outlook on our place as humans in time, space, on Earth and in the Universe. We devote many pages of Welcome to the Universe to establishing our place in the cosmos – not only declarations of that place, but also the reasons and the foundations for how we have come to learn how we fit in that place. When armed with a cosmic perspective, many earthly problems seem small, yet you cultivate a new sense of belonging to the universe. You are, in fact, a participant in the great unfolding of cosmic events.

What are some of the takeaways from the book?

NDT: If you read the entire book, and if we have succeeded as authors, then you should walk away with a deep sense of the operations of nature, and an appreciation for the size and scale of the universe; how and why planets form; how and why we search for planets orbiting around other stars, and alien life that may thrive upon them; how and why stars are born, live out their lives and die; what galaxies are and why they are the largest organizations of stars in the universe; the large scale structure of galaxies and space-time; the origins and future of the universe, Einstein’s relativity, black holes, and gravitational waves; and time travel. If that’s not enough, you will also learn about some of the continued unsolved mysteries in our field, such as dark matter, dark energy, and multiverses.

This book has more equations than do most popular books about astrophysics.  Was that a deliberate decision?

MAS: Yes.  The book’s subtitle is “An Astrophysical Tour,” and one of our goals in writing it was to show how observations, the laws of physics, and some high school mathematics can combine to yield the amazing discoveries of modern astrophysics: A Big Bang that happened 13.8 billion years ago (we show you how that number is determined), the dominant role dark matter has in the properties of galaxies (we tell you how we came to that conclusion), even the fact that some planets orbiting other stars have conditions conducive for liquid water to exist on their surface, thought to be a necessary prerequisite for life. Our goal is not just to present the wonders of the universe to the reader, but to have the reader understand how we have determined what we know, and where the remaining uncertainties (and there are plenty of them!) lie.

So your emphasis is on astrophysics as a quantitative science, a branch of physics?

MAS:  Yes.  We introduce the necessary physics concepts as we go: we do not expect the reader to know this physics before they read the book.  But astrophysicists are famous (perhaps notorious!) for rough calculations, “to astrophysical accuracy.”  We also lead the reader through some examples of such rough calculations, where we aim to get an answer to “an order of magnitude.”  That is, we’re delighted if we get an estimate that’s correct to within a factor of 2, or so.  Such calculations are useful in everyday life, helping us discriminate the nonsensical from the factual in the numerical world in which we live.

Can you give an example?

MAS: Most people in everyday discourse don’t think much about the distinction between “million,” “billion,” “trillion,” and so on, hearing them all as “a really big number,” with not much difference between them.  It is actually a real problem, and the difference between Federal budget items causing millions vs. billions of dollars is of course huge.  Our politicians and the media are confusing these all the time.  We hope that the readers of this book will come away with a renewed sense of how to think about numbers, big and small, and see whether the numbers they read about in the media make sense.

Is time travel possible?

JRG: In 1905 Einstein proved that time travel to the future is possible. Get on a rocket and travel out to the star Betelgeuse 500 light-years away and return at a speed of 99.995 % the speed of light and you will age only 10 years, but when you get back it will be the year 3016 on Earth. Even though we have not gone that fast or far, we still have time travelers among us today. Our greatest time traveler to date is the Russian cosmonaut Gennady Padalka, who by virtue of traveling at high speed in low Earth orbit for 879 days aged 1/44 of a second less than if he had stayed home. Thus, when he returned, he found Earth to be 1/44 of a second to the future of where he expected it to be. He has time traveled 1/44 of a second to the future. An astronaut traveling to the planet Mercury, living there for 30 years, and returning to Earth, would time travel into the future by 22 seconds. Einstein’s equations of general relativity, his theory of curved spacetime to explain gravity, have solutions that are sufficiently twisted to allow time travel to the past. Wormholes and moving cosmic strings are two examples. The time traveler can loop back to visit an event in his own past. Such a time machine cannot be used to journey back in time before it was created. Thus, if some supercivilization were to create one by twisting spacetime in the year 3000, they might use it to go from 3002 back to 3001, but they couldn’t use it go back to 2016, because that is before the time loop was created. To understand whether such time machines can be realized, we may need to understand how gravity works on microscopic scales, which will require us to develop a theory of quantum gravity. Places to look for naturally occurring time machines would be in the interiors of rotating black holes and at the very beginning of the universe, where spacetime is strongly curved.

Do we live in a multiverse?

JRG: A multiverse seems to be a natural consequence of the theory of inflation. Inflation explains beautifully the pattern of slightly hotter and colder spots we see in the Cosmic Microwave Background Radiation. It explains why the universe is so large and why it is as smooth as it is and still has enough variations in density to allow gravity to grow these into galaxies and clusters of galaxies by the present epoch. It also explains why the geometry of the universe at the present epoch is approximately Euclidean. Inflation is a period of hyperactive accelerated expansion occurring at the beginning of our universe. It is powered by a large vacuum energy density and negative pressure permeating empty space that is gravitationally repulsive. The universe doubles in size about every 3 10-38 seconds. With this rate of doubling, it very quickly grows to enormous size: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024… That explains why the universe is so large. When the high density vacuum state decays, it doesn’t do so all at once. Like water boiling in a pot, it does not turn into steam all at once, but should form bubbles. Each expanding bubble makes a universe. The inflationary sea should expand forever, creating an infinite number of bubble universes, ours being one of them. Other distant bubble universes are so far away, and the space between us and them is expanding so fast, that light from them may never reach us. Nevertheless, multiple universes seem a nearly inevitable consequence of inflation.

What discovery about the universe surprises or inspires you the most?

JRG: Perhaps the most amazing thing about the universe is that it is comprehensible to intelligent, carbon-based life forms like ourselves. We have been able to discover how old the universe is (13.8 billion years) and figure out many of the laws by which it operates. The object of this book is to make the universe comprehensible to our readers.

Don’t miss this C-Span video on the book, in which the authors answer questions about the universe, including how it began and the likelihood of intelligent life elsewhere.

Neil deGrasse Tyson is director of the Hayden Planetarium at the American Museum of Natural History. He is the author of many books, including Space Chronicles: Facing the Ultimate Frontier, and the host of the Emmy Award–winning documentary Cosmos: A Spacetime Odyssey. Michael A. Strauss is professor of astrophysics at Princeton University. J. Richard Gott is professor of astrophysics at Princeton University. His books include The Cosmic Web: Mysterious Architecture of the Universe (Princeton).

Neil DeGrasse Tyson & Stephen Colbert: Make America Smart Again

On November 9, Neil DeGrasse Tyson joined Stephen Colbert on The Late Show to talk about Welcome to the Universe and to blow his own mind. Watch the clip here:


The companion website to Welcome to the Universe launches today

Welcome to the UniverseWe’re thrilled to launch this beautiful companion website to the highly anticipated new book, Welcome to the Universe by Neil DeGrasse Tyson, Michael Strauss, and Richard Gott.

If you’ve ever wondered about the universe and our place in it, then this elegant mini-tour of the cosmos is for you. Divided into three parts called ‘Stars, Planets and Life,’ ‘Galaxies,’ and ‘Einstein and the Universe,’ the site is designed to take you on a journey through the major ideas in Welcome to the Universe. We hope you learn something new and exciting about outer space. If you find something interesting and would like to share, please do! The site is set up to make sharing interesting tidbits on social media easy. Want to learn more? The site also includes information on where to learn more about each topic. Keep an eye out for the book in October 2016.


Welcome to the Universe: An Astrophysical Tour by Neil deGrasse Tyson, Michael A. Strauss & J. Richard Gott from Princeton University Press on Vimeo.

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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Stephen Heard: Write like a scientist

the scientist's guide to writing heardScientific writing should be as clear and impactful as other styles, but the process of producing such writing has its own unique challenges. Stephen Heard, scientist, graduate advisor, and editor speaks from personal experience in his book The Scientist’s Guide to Writing: How to Write More Easily and Effectively Throughout Your Scientific Career. Heard’s focus on the writing process emphasizes the pursuit of clarity, and his tips on submissions, coauthorship, citations, and peer reviews are crucial for those starting to seek publication. Recently, Heard agreed to answer a few questions about his book.

What made you decide to write a book about scientific writing?

SH: I think the first spark was when I realized I give the same writing advice to all my students, over and over, and caught myself thinking it would be easier to just write it all down once. That was foolish, of course: writing the book wasn’t easy at all! But before long, my rationale shifted. The book became less about stuff I wanted to tell everyone else, and more about stuff I wished somebody had told me. A lot of us get into science without much writing experience, and without thinking much about how important a role scientific writing plays – and when we start doing it, we discover that doing it well isn’t easy. It took me many years to become a reasonably competent scientific writer, and the book includes a lot of the things I discovered along the way. I was surprised to discover that writing the book made me a better writer. I think reading it can help too.

Surely there a bunch of other scientific-writing books out there? What do you do differently?

SH: Yes – and some of them are quite good! But I wanted to write something different. I’m not sure my book says anything that no one else knows about outlining or paragraph structure or citation formatting (for example). But I thought there was a lot of value in a book that pays attention to the writer as much as the writing: to the way writers behave as they write, and to ways in which some deliberate and scientific attention to our behavior might help us write faster and better. I’ve also discovered that knowing a bit about the history and culture of scientific writing can help us understand the way we write (and why). Just as one example: knowing something about the history of the Methods section, and how it’s changed over the last 350 years as scientists have struggled with the question of how scientific studies gain authority, can help us decide how to write our own Methods sections. I also tackle the question of whether there’s a place in scientific writing for beauty or for humor – something that gets discussed so rarely that it seems almost like a taboo.

Finally, I wanted to write a book that was really engaging: to show that thinking about writing (as we all need to) needn’t be dry and pedantic. So readers might be surprised, in a book about scientific writing, to find mentions of Voltaire’s lover, SpongeBob SquarePants, and the etymology of the word fart. But I hope they’ll also find that there are lessons in all those things – and more – for scientists who want to write better and more quickly.

You also go into a lot of depth about the review and publication process. Why are these things important to cover alongside the writing process?

SH: Well, maybe that isn’t “writing”, strictly speaking – but it’s an essential part of getting one’s scientific writing in the hands of readers. All of us want our scientific writing to be read, and to be cited, and to help move our fields forward. So it’s not enough to write a good manuscript; we have to be able to shepherd it through the process of submission, review, revision, and eventual acceptance. Early in my own career I found this process especially mysterious. Since then, I’ve learned a lot about it – by publishing quite a few papers myself, but also by reviewing hundreds of manuscripts and acting as an Associate Editor for hundreds more. So I have a pretty good overview of the publishing process, from both the writer’s and the journal’s perspective. There’s no particular reason that process has to be mysterious, and I thought it would be helpful to draw back the curtain.

Is scientific writing really that different from other kinds of writing?

SH: Both yes and no! Of course, there are technical issues that matter in scientific writing, like ways of handling text dense with numbers, or ways we handle citations. There are also more cultural ways in which scientific writing is its own thing. One of them is that we’ve developed a writing form that efficiently conveys material to other people who are familiar with that form. Our conventional division of papers into Abstract, Introduction, Methods, Results, and Discussion is a piece of that. Our writing (and our publication process) have evolved in many other ways that aren’t quite the same as you’d find in the humanities, or in writing about science for the public. That’s why there are books about scientific writing, not just about writing. But on another level, good scientific writing is like most other good writing: clear, concise, engaging whenever possible, and did I mention clear? Nothing is more important than clarity! As a result of this similarity, people who learn good scientific writing are well positioned for any career that involves writing – which is to say, pretty much any career.

Do you think of yourself as a good writer?

SH: No! And to loop back to the first question, that’s a big part of why I wrote the book. There are a very few natural writers out there – geniuses – for whom good writing just seems to come naturally. But these are rare. I’m like nearly everyone else: writing is hard work for me. It’s a craft I’ve learned over the years by practicing, by thinking deliberately about how I do it, and by reading advice from books that have gone before mine. It’s still hard work, but that’s OK: I’m willing to put in the effort for my writing product to seem pretty good, even if my writing process is laborious. If I’d understood earlier in my career that most writers are just like me, I would have been less crushed by the discovery that my papers didn’t just write themselves! Every scientific writer can do what I’ve done: practice the craft and improve at it. I hope my book can help.

Stephen B. Heard is professor of biology at the University of New Brunswick in Canada and associate editor of the journal American Naturalist. His most recent book is The Scientist’s Guide to Writing: How to Write More Easily and Effectively Throughout Your Scientific Career.

Even celebrities misquote Albert Einstein

Calaprice_QuotableEinstein_pb_cvrAlice Calaprice is the editor of The Ultimate Quotable Einstein, a tome mentioned time and again in the media because famous folks continue to attribute words to Einstein that, realistically, he never actually said. Presidential candidates, reality stars, and more have used social media make erroneous references to Einstein’s words, perhaps hoping to give their own a bit more credibility. From the Grapevine recently compiled the most recent misquotes of Albert Einstein by public figures and demonstrated how easy it is to use The Ultimate Quotable Einstein to refute those citations:

Albert Einstein was a wise man, even outside the science laboratory. He has inspired painters, young students and comic book creators. Even budding romantics take advice from him.

So it should come as no surprise, then, that so many people today quote Einstein. Or, to be more precise, misquote Einstein.

“I believe they quote Einstein because of his iconic image as a genius,” Alice Calaprice, an Einstein expert, tells From The Grapevine. “Who would know better and be a better authority than the alleged smartest person in the world?”

Read more here.


Where would we be without Pi?

Pi Day, the annual celebration of the mathematical constant π (pi), is always an excuse for mathematical and culinary revelry in Princeton. Since 3, 1, and 4 are the first three significant digits of π, the day is typically celebrated on 3/14, which in a stroke of serendipity, also happens to be Albert Einstein’s birthday. Pi Day falls on Monday this year, but Princeton has been celebrating all weekend with many more festivities still to come, from a Nerd Herd smart phone pub crawl, to an Einstein inspired running event sponsored by the Princeton Running Company, to a cocktail making class inside Einstein’s first residence. We imagine the former Princeton resident would be duly impressed.

Einstein enjoying a birthday/ Pi Day cupcake

Einstein enjoying a birthday/ Pi Day cupcake

Pi Day in Princeton always includes plenty of activities for children, and tends to be heavy on, you guessed it, actual pie (throwing it, eating it, and everything in between). To author Paul Nahin, this is fitting. At age 10, his first “scientific” revelation was,  If pi wasn’t around, there would be no round pies! Which it turns out, is all too true. Nahin explains:

Everybody “knows’’ that pi is a number a bit larger than 3 (pretty close to 22/7, as Archimedes showed more than 2,000 years ago) and, more accurately, is 3.14159265… But how do we know the value of pi? It’s the ratio of the circumference of a circle to a diameter, yes, but how does that explain how we know pi to hundreds of millions, even trillions, of decimal digits? We can’t measure lengths with that precision. Well then, just how do we calculate the value of pi? The symbol π (for pi) occurs in countless formulas used by physicists and other scientists and engineers, and so this is an important question. The short answer is, through the use of an infinite series expansion.

NahinIn his book In Praise of Simple Physics, Nahin shows you how to derive such a series that converges very quickly; the sum of just the first 10 terms correctly gives the first five digits. The English astronomer Abraham Sharp (1651–1699) used the first 150 terms of the series (in 1699) to calculate the first 72 digits of pi. That’s more than enough for physicists (and for anybody making round pies)!

While celebrating Pi Day has become popular—some would even say fashionable in nerdy circles— PUP author Marc Chamberland points out that it’s good to remember Pi, the number. With a basic scientific calculator, Chamberland’s recent video “The Easiest Way to Calculate Pi” details a straightforward approach to getting accurate approximations for Pi without tables or a prodigious digital memory. Want even more Pi? Marc’s book Single Digits has more than enough Pi to gorge on.

Now that’s a sweet dessert.

If you’re looking for more information on the origin of Pi, this post gives an explanation extracted from Joseph Mazur’s fascinating history of mathematical notation, Enlightening Symbols.

You can find a complete list of Pi Day activities from the Princeton Tour Company here.