Martin Rees: Stephen Hawking — An Appreciation

Soon after I enrolled as a graduate student at Cambridge University in 1964, I encountered a fellow student, two years ahead of me in his studies; he was unsteady on his feet and spoke with great difficulty. This was Stephen Hawking. He had recently been diagnosed with a degenerative disease, and it was thought that he might not survive long enough even to finish his PhD. But, amazingly, he lived on to the age of 76. Even mere survival would have been a medical marvel, but of course he didn’t just survive. He become one of the most famous scientists  in the world—acclaimed  as a world-leading researcher in mathematical physics, for his best-selling books about space, time, and the cosmos, and for his astonishing triumph over adversity.

Astronomers are used to large numbers. But few numbers could be as large as the odds I’d have given, back in 1964 when Stephen received his ‘death sentence,’ against witnessing this uniquely inspiring crescendo of achievement sustained for more than 50 years. Few, if any, of Einstein’s successors have done more to deepen our insights into gravity, space, and time.

Stephen went to school in St Albans, near London, and then to Oxford University. He was, by all accounts, a ‘laid back’ undergraduate, but his brilliance nonetheless earned him a first class degree in physics, and an ‘entry ticket’ to a research career in Cambridge. Within a few years of the onset of his disease he was wheelchair-bound, and his speech was an indistinct croak that could only be interpreted by those who knew him. But in other respects fortune had favored him. He married a family friend, Jane Wilde, who provided a supportive home life for him and their three children, Robert, Lucy, and Tim.

The 1960s were an exciting period in astronomy and cosmology: this was the decade when evidence began to emerge for black holes and the big bang. In Cambridge, Stephen  joined a lively research group. It was headed by Dennis Sciama, an enthusiastic and effective mentor who urged him to focus on the new mathematical concepts being developed by Roger Penrose, then at London University, which were initiating a renaissance in the study of Einstein’s theory of general relativity. Stephen mastered Penrose’s techniques and quickly came up with a succession of insights into the nature of black holes (then a very new idea),   along with new arguments that our universe had expanded from a ‘big bang.’ The latter work was done jointly with George Ellis, another of Sciama’s students, with whom Stephen wrote a monograph entitled The Large-Scale Structure of Space-Time. Especially important was the realization that the area of a black hole’s horizon (the ‘one-way membranes’ that shroud the interior of black holes, and from within which nothing can escape) could never decrease. The analogy with entropy (a measure of disorder, that likewise can never decrease) was developed further by the late Israeli theorist Jacob Bekenstein. In the subsequent decades, the observational support for these ideas  has strengthened—most spectacularly with the 2016 announcement of the detection of gravitational waves from colliding black holes.

Stephen was elected to the Royal Society, Britain’s main scientific academy, at the exceptionally early age of 32. He was by then so frail that most of us suspected that he could scale no further heights. But, for Stephen, this was still just the beginning. He worked in the same building as I did. I would often push his wheelchair into his office, and he would ask me to open an abstruse book on quantum theory—the science of atoms, not a subject that had hitherto much interested him. He would sit hunched motionless for hours—he couldn’t even to turn the pages without help. I wondered what was going through his mind, and if his powers were failing. But within a year he came up with his best-ever idea—encapsulated in an equation that he said he wanted on his memorial stone.

The great advances in science generally involve  discovering a link between phenomena that seemed hitherto conceptually unconnected: for instance, Isaac Newton famously realized that the force making an apple fall was the same as the force that held the moon and planets in their orbits. Stephen’s ‘eureka moment’ revealed a profound and unexpected  link between gravity and quantum theory: he predicted that black holes would not be completely black, but would radiate in a characteristic way. Bekenstein’s concept that black holes had ‘entropy’ was more than just an analogy. This radiation is only significant for black holes much less massive than stars—and none of these have been found. However, ‘Hawking radiation’ had very deep implications for mathematical physics—indeed one of the main achievements of string theory has been to corroborate his idea. It is still the focus of theoretical interest—a topic of debate and controversy more than 40 years after his discovery. Indeed the Harvard theorist, Andrew Strominger (with whom Stephen recently collaborated) said that this paper had caused ‘more sleepless nights among theoretical physicists than any paper in history.’ The key issue is whether information that is seemingly lost when objects fall into a black hole is in principle recoverable from the radiation when it evaporates. If it is not, this violates a deeply believed general physical principle. In 2013 he was one of the early winners of the Breakthrough Prize, worth 3 million dollars, which was intended to recognize theoretical work.

Cambridge was Stephen’s base throughout his career, and he became a familiar figure navigating his wheelchair around the city’s streets. By the end of the 1970s, he had advanced to one of the most distinguished posts in the University—the Lucasian Professorship of Mathematics, once held by Newton himself. He held this chair with distinction for 30 years; but reached the retiring age in 2009 and thereafter held a special research professorship. He travelled widely: he was an especially frequent visitor at Caltech, in Pasadena, California; and at Texas A&M University. He continued to seek new links between the very large (the cosmos) and the very small (atoms and quantum theory) and to gain deeper insights into the very beginning of our universe—addressing questions like ‘was our big bang the only one?’ He had a remarkable ability to figure things out in his head. But latterly he worked with students and colleagues who would write a formula on a blackboard; he would stare at it, and say whether he agreed with it, and perhaps what should come next.

In 1987, Stephen contracted pneumonia. He had to undergo a tracheotomy, which removed even the limited powers of speech he then possessed. It had been more than 10 years since he could write, or even  use a keyboard. Without speech, the only way he could communicate was by directing his eye towards  one of the letters of the alphabet on a big board in front of him.

But he was saved by technology. He still had the use of one hand; and a computer, controlled by a single lever, allowed him to spell out sentences. These were then declaimed by a speech synthesizer, with the androidal American accent that has since become his trademark. His lectures were, of course, pre-prepared, but conversation remained a struggle. Each word involved several presses of the lever, so even a sentence took several minutes. He learnt to economize with words. His comments were aphoristic or oracular, but often infused with wit. In his later years, he became too weak to control this machine effectively, even via facial muscles or eye movements, and his communication—to his immense frustration—became even slower.

At the time of his tracheotomy operation, he had a rough draft of a book, which he’d hoped would describe his ideas to a wide readership and earn something for his two eldest children, who were then of college age. On his recovery from pneumonia, he resumed work with the help of an editor. When the US edition of   A Brief History of Time appeared, the printers made some errors (a picture was upside down), and the publishers tried to recall the stock. To their amazement, all copies had already been sold. This was the first inkling that the book was destined for runaway success—four years on bestseller lists around the world.

The feature film The Theory of Everything (where he was superbly impersonated by Eddie Redmayne, in an Oscar-winning performance) portrayed  the human story behind his struggle. It surpassed most biopics in  representing the main characters so well that they themselves were happy with the portrayal (even though it understandably omitted and conflated key episodes in his scientific life). Even before this film, his life and work had featured in movies. In  an excellent TV docudrama made in 2004, he was played by Benedict Cumberbatch (In 2012 Cumberbatch spoke his words in a 4-part documentary The Grand Design made for the Discovery TV  Channel).

Why did he become such a ‘cult figure?’ The concept of an imprisoned mind roaming the cosmos plainly grabbed people’s imagination. If he had achieved equal distinction in (say) genetics rather than cosmology, his triumph of intellect against adversity probably wouldn’t have achieved the same resonance with a worldwide public.

The Theory of Everything conveyed with sensitivity how the need for support (first from a succession of students, but later requiring a team of nurses) strained his marriage to breaking point, especially when augmented by the pressure of his growing celebrity. Jane’s book, on which the film is based chronicles the 25 years during which, with amazing dedication, she underpinned his family life and his career.

This is where the film ends. But it left us only half way through Stephen’s adult life. After the split with Jane, Stephen married, in 1995, Elaine Mason, who had been one of his nurses, and whose former husband had designed Stephen’s speech synthesizer. But this partnership broke up within a decade. He was sustained, then and thereafter, by a team of helpers and personal assistants, as well as his family. His daughter Lucy has written books for children with her father as coauthor. His later theories were described, and beautifully illustrated, in other books such as Our Universe in a Nutshell and The Grand Design. These weren’t  bought by quite as many people as his first book—but probably more readers got to the end of them.

The success of A Brief History of Time catapulted Stephen to international stardom. He  featured in numerous TV programs; his lectures filled the Albert Hall, and similar venues in the US and Japan. He  featured in Star Trek and The Simpsons, and in numerous TV documentaries, as well as advertisements. He lectured at Clinton’s White House; he was back there more recently when President Obama presented him with the US Medal of Freedom, a very rare honor for any foreigner—and of course just one of the many awards he accumulated over his career (including Companion of Honor from the UK). In the summer of 2012, he reached perhaps his largest-ever audience when he had a star role at the opening ceremony of the London Paralympics.

His 60th birthday celebrations, in January 2002 , were a memorable occasion for all of us. Hundreds of leading scientists came from all over the world to honor and celebrate Stephen’s discoveries, and to spend a week discussing the latest theories on space, time, and the cosmos. But the celebrations weren’t just scientific—that wouldn’t have been Stephen’s style. Stephen was surrounded by his children and grandchildren; there was music and singing; there were ‘celebrities’ in attendance. And when the week’s events were all over, he celebrated with a trip in a hot air balloon.

It was amazing enough that Stephen reached the age of 60; few of us then thought that he would survive 16 more years. His 70th birthday was again marked by an international gathering of scientists in Cambridge, and also with some razzmatazz. So was his 75th birthday, though now shared by several million people via a livestream on the internet. He was in these last years plainly weakening. But he was still able to ‘deliver’ entertaining (and sometimes rather moving) lectures via his speech synthesizer and with the aid of skillfully prepared visuals.

Stephen continued, right until his last decade, to coauthor technical papers, and speak at premier international conferences—doubly remarkable in a subject where even healthy researchers tend to peak at an early age. Specially influential were his contributions to ‘cosmic inflation’—a theory that many believe describes the ultra-early phases of our expanding universe. A key issue is to understand the primordial seeds which eventually develop into galaxies. He proposed (as, independently, did the Russian theorist Viatcheslav Mukhanov) that these were quantum fluctuations—somewhat analogous to those involved in ‘Hawking radiation’ from black holes. He hosted an important meeting in 1982 where such ideas were thoroughly discussed. Subsequently, particularly with James Hartle and Thomas Hertog, he made further steps towards linking the two great theories of 20th century physics: the quantum theory of the microworld and Einstein’s theory of gravity and space-time.

He continued  to be an inveterate traveller—despite attempts to curb this as his respiration weakened. This wasn’t just to lecture. For instance, on a visit to Canada he was undeterred by having to go two miles down a mine-shaft to visit an underground laboratory where famous and delicate experiments had been done. And on a later trip, only a last-minute health setback prevented him from going to the Galapagos. All these travels—and indeed his everyday working life—involved an entourage of assistants and nurses. His fame, and the allure of his public appearances, gave him the resources for  nursing care, and protected him against the ‘does he take sugar?’ type of indignity that the disabled often suffer.

Stephen was far from being the archetype unworldly or nerdish scientist—his personality remained amazingly unwarped by his frustrations and handicaps. As well as his extensive travels, he enjoyed  trips to theatre or opera. He had robust common sense, and was ready to express forceful political opinions. However, a downside of his iconic status was that that his comments attracted exaggerated attention even on topics where he had  no special expertise—for instance philosophy, or the dangers from aliens or from intelligent machines. And he was sometimes involved in media events where his ‘script’ was written by the promoters of causes about which he may have been ambivalent.

But there was absolutely no gainsaying his lifelong commitment to campaigns for the disabled, and (just in the last few months) in support of the NHS—to which he acknowledged he owed so much. He was always, at the personal level, sensitive to the misfortunes of others. He recorded  that, when in hospital soon after his illness was first diagnosed, his depression was lifted when he compared his lot with a boy in the next bed who was dying of leukemia. And he was firmly aligned with other political campaigns and causes. When he visited Israel, he insisted on going also to the West Bank. Newspapers in 2006 showed remarkable pictures of him, in his wheelchair, surrounded  by fascinated and curious crowds in Ramallah.

Even more astonishing are the pictures of him ‘floating’ in the NASA aircraft  (the ‘vomit comet’) that allows passengers to experience weightlessness—he was manifestly overjoyed at escaping, albeit briefly, the clutches of the gravitational force he’d studied for decades and which had so cruelly imprisoned his body.

Tragedy struck Stephen Hawking when he was only 22. He was diagnosed with a deadly disease, and his  expectations dropped to zero. He himself said that everything that happened since then was a bonus. And what a triumph his life has been. His name will live in the annals of science; millions have had their cosmic horizons widened by his best-selling books; and even more, around the world, have been inspired by a unique example of achievement against all the odds—a manifestation of amazing will-power and determination.

Martin Rees is Astronomer Royal of Great Britain, a Fellow of Trinity College, Cambridge, a former director of the Cambridge Institute of Astronomy and author, most recently, of the bestselling Just Six Numbers: The Deep Forces That Shape the Universe. His forthcoming book, On the Future, will be available in October 2018.

Celebrate Pi Day with Books about Einstein

Pi Day is coming up! Mathematicians around the world celebrate on March 14th because the date represents the first three digits of π: 3.14.

In Princeton, Pi Day is a huge event even for the non-mathematicians among us, given that March 14 is also Albert Einstein’s birthday. Einstein was born on March 14, 1879, in Ulm, in the German Empire. He turns 139 this year! If you’re in the Princeton area and want to celebrate, check out some of the festivities happening around town:

Saturday, 3/10/18

  • Apple Pie Eating Contest, 9:00 a.m., McCaffrey’s (301 North Harrison Street). Arrive by 8:45 a.m. to participate.
  • Einstein in Princeton Guided Walking Tour, 10:00 a.m. Call Princeton Tour Company at (855) 743-1415 for details.
  • Einstein Look-A-Like Contest, 12:00 p.m., Nassau Inn. Arrive early to get a spot to watch this standing-room-only event!
  • Pi Recitation Contest, 1:30 p.m., Prince William Ballroom, Nassau Inn. Children ages 12 and younger may compete. Register by 1:15 p.m.
  • Pie Throwing Event, 3:14 p.m., Palmer Square. Proceeds to benefit the Princeton Educational Fund Teacher Mini-Grant Program.
  • Cupcake Decorating Competition, 4:00 p.m., House of Cupcakes (34 Witherspoon Street). The winner receives one free cupcake each month for the rest of the year.

Wednesday, 3/14/18

  • Princeton School Gardens Cooperative Fundraiser, 12:00 p.m. to 6:00 p.m., The Bent Spoon (35 Palmer Square West) and Lillipies (301 North Harrison Street). All proceeds from your afternoon treat will be donated to the Princeton School Gardens Cooperative.
  • Pi Day Pop Up Wedding/Vow Renewal Ceremonies, 3:14 p.m. to 6:00 p.m., Princeton Pi (84 Nassau Street). You must pre-register by contacting the Princeton Tour Company.

Not into crowds, or pie? You can also celebrate this multifaceted holiday by picking up one of PUP’s many books about Albert Einstein! In 1922, Princeton University Press published Einstein’s The Meaning of Relativity, his first book produced by an American publisher. Since then, we’ve published numerous works by and about Einstein.

The books and collections highlighted here celebrate not only his scientific accomplishments but also his personal reflections and his impact on present-day scholarship and technology. Check them out and learn about Einstein’s interpersonal relationships, his musings on travel, his theories of time, and his legacy for the 21st century.

Volume 15 of the Collected Papers of Albert Einstein, forthcoming in April 2018, covers one of the most thrilling two-year periods in twentieth-century physics, as matrix mechanics—developed chiefly by W. Heisenberg, M. Born, and P. Jordan—and wave mechanics—developed by E. Schrödinger—supplanted the earlier quantum theory. The almost one hundred writings by Einstein, of which a third have never been published, and the more than thirteen hundred letters show Einstein’s immense productivity and hectic pace of life.

Einstein quickly grasps the conceptual peculiarities involved in the new quantum mechanics, such as the difference between Schrödinger’s wave function and a field defined in spacetime, or the emerging statistical interpretation of both matrix and wave mechanics. Inspired by correspondence with G. Y. Rainich, he investigates with Jakob Grommer the problem of motion in general relativity, hoping for a hint at a new avenue to unified field theory.

Readers can access Volumes 1-14 of the Collected Papers of Albert Einstein online at The Digital Einstein Papers, an exciting new free, open-access website that brings the writings of the twentieth century’s most influential scientist to a wider audience than ever before. This unique, authoritative resource provides full public access to the complete transcribed, annotated, and translated contents of each print volume of the Collected Papers. The volumes are published by Princeton University Press, sponsored by the Hebrew University of Jerusalem, and supported by the California Institute of Technology. Volumes 1-14 of The Collected Papers cover the first forty-six years of Einstein’s life, up to and including the years immediately before the final formulation of new quantum mechanics. The contents of each new volume will be added to the website approximately eighteen months after print publication. Eventually, the website will provide access to all of Einstein’s writings and correspondence accompanied by scholarly annotation and apparatus, which are expected to fill thirty volumes.

The Travel Diaries of Albert Einstein is the first publication of Albert Einstein’s 1922 travel diary to the Far East and Middle East, regions that the renowned physicist had never visited before. Einstein’s lengthy itinerary consisted of stops in Hong Kong and Singapore, two brief stays in China, a six-week whirlwind lecture tour of Japan, a twelve-day tour of Palestine, and a three-week visit to Spain. This handsome edition makes available, for the first time, the complete journal that Einstein kept on this momentous journey.

The telegraphic-style diary entries—quirky, succinct, and at times irreverent—record Einstein’s musings on science, philosophy, art, and politics, as well as his immediate impressions and broader thoughts on such events as his inaugural lecture at the future site of the Hebrew University in Jerusalem, a garden party hosted by the Japanese Empress, an audience with the King of Spain, and meetings with other prominent colleagues and statesmen. Entries also contain passages that reveal Einstein’s stereotyping of members of various nations and raise questions about his attitudes on race. This beautiful edition features stunning facsimiles of the diary’s pages, accompanied by an English translation, an extensive historical introduction, numerous illustrations, and annotations. Supplementary materials include letters, postcards, speeches, and articles, a map of the voyage, a chronology, a bibliography, and an index.

Einstein would go on to keep a journal for all succeeding trips abroad, and this first volume of his travel diaries offers an initial, intimate glimpse into a brilliant mind encountering the great, wide world. 

More than fifty years after his death, Albert Einstein’s vital engagement with the world continues to inspire others, spurring conversations, projects, and research, in the sciences as well as the humanities. Einstein for the 21st Century shows us why he remains a figure of fascination.

In this wide-ranging collection, eminent artists, historians, scientists, and social scientists describe Einstein’s influence on their work, and consider his relevance for the future. Scientists discuss how Einstein’s vision continues to motivate them, whether in their quest for a fundamental description of nature or in their investigations in chaos theory; art scholars and artists explore his ties to modern aesthetics; a music historian probes Einstein’s musical tastes and relates them to his outlook in science; historians explore the interconnections between Einstein’s politics, physics, and philosophy; and other contributors examine his impact on the innovations of our time. Uniquely cross-disciplinary, Einstein for the 21st Century serves as a testament to his legacy and speaks to everyone with an interest in his work. 

The contributors are Leon Botstein, Lorraine Daston, E. L. Doctorow, Yehuda Elkana, Yaron Ezrahi, Michael L. Friedman, Jürg Fröhlich, Peter L. Galison, David Gross, Hanoch Gutfreund, Linda D. Henderson, Dudley Herschbach, Gerald Holton, Caroline Jones, Susan Neiman, Lisa Randall, Jürgen Renn, Matthew Ritchie, Silvan S. Schweber, and A. Douglas Stone.

On April 6, 1922, in Paris, Albert Einstein and Henri Bergson publicly debated the nature of time. Einstein considered Bergson’s theory of time to be a soft, psychological notion, irreconcilable with the quantitative realities of physics. Bergson, who gained fame as a philosopher by arguing that time should not be understood exclusively through the lens of science, criticized Einstein’s theory of time for being a metaphysics grafted on to science, one that ignored the intuitive aspects of time. Jimena Canales tells the remarkable story of how this explosive debate transformed our understanding of time and drove a rift between science and the humanities that persists today.

The Physicist and the Philosopher is a magisterial and revealing account that shows how scientific truth was placed on trial in a divided century marked by a new sense of time.

 

After completing the final version of his general theory of relativity in November 1915, Albert Einstein wrote a book about relativity for a popular audience. His intention was “to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.” The book remains one of the most lucid explanations of the special and general theories ever written.

This new edition features an authoritative English translation of the text along with an introduction and a reading companion by Hanoch Gutfreund and Jürgen Renn that examines the evolution of Einstein’s thinking and casts his ideas in a broader present-day context.

Published on the hundredth anniversary of general relativity, this handsome edition of Einstein’s famous book places the work in historical and intellectual context while providing invaluable insight into one of the greatest scientific minds of all time.

 

Browse Our 2018 Physics & Astrophysics Catalog

Our new Physics & Astrophysics catalog includes two new graduate-level textbooks from Kip S. Thorne, Co-Winner of the 2017 Noble Prize in Physics, as well as a look into the physics behind black holes.

If you plan on attending AAS 2018 in National Harbor, MD this weekend, please stop by Booth 1003 to see our full range of Physics and Astrophysics titles and more.

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 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.

Modern Classical Physics is a long-awaited, 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 Thorne and Roger 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.

First published in 1973, Gravitation is a landmark graduate-level textbook that presents Einstein’s general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This authoritative text has shaped the research of generations of physicists and astronomers, and the book continues to influence the way experts think about the subject.

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.

 

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.

Thorne

For more information, please contact:

Julia Haav, Assistant Publicity Director

Julia_Haav@press.princeton.edu, 609.258.2831

 

Welcome to the Universe microsite receives a Webby

We’re pleased to announce that the accompanying microsite to Welcome to the Universe by Neil DeGrasse Tyson, Michael A. Strauss, and J. Richard Gott has won a People’s Choice Webby in the Best Use of Animation or Motion Graphics category. Congratulations to Eastern Standard, the web designer, on a beautifully designed site.

Winning a Webby is especially gratifying because it honors how much fun we had making the site. We knew we wanted an unconventional approach that would mirror both the complexity and accessibility of the book it was meant to promote. Our wonderful in-house team and creative partners, Eastern Standard took on this challenge, and we are so happy with the results.
—Maria Lindenfeldar, Creative Director, Princeton University Press 

Creating this microsite was a wonderful experiment for us at Princeton University Press.  We wanted to explore how we, as a publisher, could present one of our major books to the public in a compelling way in the digital environment.  Ideally, we had a vision of creating a simple site with intuitive navigation that would give readers an inviting mini-tour through the topics of the book, Welcome to the Universe, by Neil deGrasse Tyson, Michael Strauss, and Richard Gott.  The animation was meant to be subtle, but meaningful, and to gently encourage user interaction, so that the focus would always remain immersing the reader in the content of the book – what we feel is the most interesting part!  We were very happy with how it turned out and now all the more thrilled and honored that the site was chosen for a Webby!
—Ingrid Gnerlich, Science Publisher, Princeton University Press

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.

 

 

Welcome to the Universe microsite nominated for a Webby

We’re thrilled to announce that the microsite for Welcome to the Universe by Neil DeGrasse Tyson, Michael A. Strauss, and J. Richard Gott, designed by Eastern Standard, has been nominated for a Webby in the Best Use of Animation or Motion Graphics category. Be sure to check it out and vote for the best of the internet!

webby

 

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.

Gott

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.

Michael Strauss: Our universe is too vast for even the most imaginative sci-fi

As an astrophysicist, I am always struck by the fact that even the wildest science-fiction stories tend to be distinctly human in character. No matter how exotic the locale or how unusual the scientific concepts, most science fiction ends up being about quintessentially human (or human-like) interactions, problems, foibles and challenges. This is what we respond to; it is what we can best understand. In practice, this means that most science fiction takes place in relatively relatable settings, on a planet or spacecraft. The real challenge is to tie the story to human emotions, and human sizes and timescales, while still capturing the enormous scales of the Universe itself.

Just how large the Universe actually is never fails to boggle the mind. We say that the observable Universe extends for tens of billions of light years, but the only way to really comprehend this, as humans, is to break matters down into a series of steps, starting with our visceral understanding of the size of the Earth. A non-stop flight from Dubai to San Francisco covers a distance of about 8,000 miles – roughly equal to the diameter of the Earth. The Sun is much bigger; its diameter is just over 100 times Earth’s. And the distance between the Earth and the Sun is about 100 times larger than that, close to 100 million miles. This distance, the radius of the Earth’s orbit around the Sun, is a fundamental measure in astronomy; the Astronomical Unit, or AU. The spacecraft Voyager 1, for example, launched in 1977 and, travelling at 11 miles per second, is now 137 AU from the Sun.

But the stars are far more distant than this. The nearest, Proxima Centauri, is about 270,000 AU, or 4.25 light years away. You would have to line up 30 million Suns to span the gap between the Sun and Proxima Centauri. The Vogons in Douglas Adams’s The Hitchhiker’s Guide to the Galaxy (1979) are shocked that humans have not travelled to the Proxima Centauri system to see the Earth’s demolition notice; the joke is just how impossibly large the distance is.

Four light years turns out to be about the average distance between stars in the Milky Way Galaxy, of which the Sun is a member. That is a lot of empty space! The Milky Way contains about 300 billion stars, in a vast structure roughly 100,000 light years in diameter. One of the truly exciting discoveries of the past two decades is that our Sun is far from unique in hosting a retinue of planets: evidence shows that the majority of Sun-like stars in the Milky Way have planets orbiting them, many with a size and distance from their parent star allowing them to host life as we know it.

Yet getting to these planets is another matter entirely: Voyager 1 would arrive at Proxima Centauri in 75,000 years if it were travelling in the right direction – which it isn’t. Science-fiction writers use a variety of tricks to span these interstellar distances: putting their passengers into states of suspended animation during the long voyages, or travelling close to the speed of light (to take advantage of the time dilation predicted in Albert Einstein’s theory of special relativity). Or they invoke warp drives, wormholes or other as-yet undiscovered phenomena.

When astronomers made the first definitive measurements of the scale of our Galaxy a century ago, they were overwhelmed by the size of the Universe they had mapped. Initially, there was great skepticism that the so-called ‘spiral nebulae’ seen in deep photographs of the sky were in fact ‘island universes’ – structures as large as the Milky Way, but at much larger distances still. While the vast majority of science-fiction stories stay within our Milky Way, much of the story of the past 100 years of astronomy has been the discovery of just how much larger than that the Universe is. Our nearest galactic neighbour is about 2 million light years away, while the light from the most distant galaxies our telescopes can see has been travelling to us for most of the age of the Universe, about 13 billion years.

We discovered in the 1920s that the Universe has been expanding since the Big Bang. But about 20 years ago, astronomers found that this expansion was speeding up, driven by a force whose physical nature we do not understand, but to which we give the stop-gap name of ‘dark energy’. Dark energy operates on length- and time-scales of the Universe as a whole: how could we capture such a concept in a piece of fiction?

The story doesn’t stop there. We can’t see galaxies from those parts of the Universe for which there hasn’t been enough time since the Big Bang for the light to reach us. What lies beyond the observable bounds of the Universe? Our simplest cosmological models suggest that the Universe is uniform in its properties on the largest scales, and extends forever. A variant idea says that the Big Bang that birthed our Universe is only one of a (possibly infinite) number of such explosions, and that the resulting ‘multiverse’ has an extent utterly beyond our comprehension.

The US astronomer Neil deGrasse Tyson once said: ‘The Universe is under no obligation to make sense to you.’ Similarly, the wonders of the Universe are under no obligation to make it easy for science-fiction writers to tell stories about them. The Universe is mostly empty space, and the distances between stars in galaxies, and between galaxies in the Universe, are incomprehensibly vast on human scales. Capturing the true scale of the Universe, while somehow tying it to human endeavours and emotions, is a daunting challenge for any science-fiction writer. Olaf Stapledon took up that challenge in his novel Star Maker (1937), in which the stars and nebulae, and cosmos as a whole, are conscious. While we are humbled by our tiny size relative to the cosmos, our brains can none the less comprehend, to some extent, just how large the Universe we inhabit is. This is hopeful, since, as the astrobiologist Caleb Scharf of Columbia University has said: ‘In a finite world, a cosmic perspective isn’t a luxury, it is a necessity.’ Conveying this to the public is the real challenge faced by astronomers and science-fiction writers alike. Aeon counter – do not remove

UniverseMichael A. Strauss is professor of astrophysics at Princeton University and coauthor with Richard Gott and Neil DeGrasse Tyson of Welcome to The Universe: An Astrophysical Tour.

This article was originally published at Aeon and has been republished under Creative Commons.

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.