Bird Fact Friday – All for one and one for all

From page 102 of The Crossley ID Guide: Raptors:

Harris Hawks, distinctive raptors of the arid Southwest, are the only type of hawk to hunt cooperatively. In fact, the hunting tactics of the Harris Hawk are among the most complex and unique of any bird. Groups usually consist of a pair of dominant adults assisted by several immature or adult birds, often offspring but occasionally other nesting pairs.

The Crossley ID Guide: Raptors
Richard Crossley, Jerry Liguori, Brian Sullivan

The Crossley ID GuidePart of the revolutionary Crossley ID Guide series, this is the first raptor guide with lifelike scenes composed from multiple photographs—scenes that allow you to identify raptors just as the experts do. Experienced birders use the most easily observed and consistent characteristics—size, shape, behavior, probability, and general color patterns. The book’s 101 scenes—including thirty-five double-page layouts—provide a complete picture of how these features are all related. Even the effects of lighting and other real-world conditions are illustrated and explained. Detailed and succinct accounts from two of North America’s foremost raptor experts, Jerry Liguori and Brian Sullivan, stress the key identification features. This complete picture allows everyone from beginner to expert to understand and enjoy what he or she sees in the field. The mystique of bird identification is eliminated, allowing even novice birders to identify raptors quickly and simply.

Comprehensive and authoritative, the book covers all thirty-four of North America’s diurnal raptor species (all species except owls). Each species is featured in stunning color plates that show males and females, in a full spectrum of ages and color variants, depicted near and far, in flight and at rest, and from multiple angles, all caught in their typical habitats. There are also comparative, multispecies scenes and mystery photographs that allow readers to test their identification skills, along with answers and full explanations in the back of the book. In addition, the book features an introduction, and thirty-four color maps accompany the plates.

Whether you are a novice or an expert, this one-of-a-kind guide will show you an entirely new way to look at these spectacular birds.

Gravitational waves making waves at Princeton

Today marks a new era in cosmology, astronomy, and astrophysics. The main page of the Einstein Papers Project website reports, “Gravitational waves do exist, as has been announced today with great joy by the scientists of the LIGO collaboration, after more than two decades of intensive experimental work.”

The cosmic breakthrough, which proves Einstein’s 100 year old prediction, has resulted in a tremendous response across the scientific community and social media. Scientific websites everywhere are already debating the meaning of the discovery, the #EinsteinWasRight hashtag has been bantered about on Twitter; You Tube featured a live announcement with over 80,000 people tuning in to watch (check it out at 27 minutes).

 

 

Princeton University Press authors Jeremiah Ostriker and Kip Thorne had a bet about gravitational wave detection in the 80s. Today when we contacted him, Ostriker, author of Heart of Darkness, was ebullient:

“The LIGO announcement today and the accompanying papers are totally persuasive. We all believed that Einstein had to be right in predicting gravitational waves, but to see them, so clean and so clear is marvelous. Two independent instruments saw the same signal from the same event, and it was just what had been predicted for the in-spiral and merger of two massive black holes.

A quarter of a century ago I had a bet with Kip Thorne that we would not see gravitational waves before the year 2000 – and I won that bet and a case of wine. But I did not doubt that, when the sensitivity of the instruments improved enough, gravitational waves would be found.  Now the skill and perseverance of the experimentalists and the support of NSF has paid off.

Hats off to all!!!”

But was Einstein always a believer in gravitational waves? Daniel Kennefick, co-author of The Einstein Encyclopedia says no:

“One hundred years ago in February 1916, Einstein mentioned gravitational waves for the first time in writing. Ironically it was to say that they did not exist. He said this in a letter to his colleague Karl Schwarzschild, who had just discovered the solution to Einstein’s equations which we now know describe black holes. Today brings a major confirmation of the existence both of gravitational waves and black holes. Yet Einstein was repeatedly skeptical about whether either of these ideas were really predictions of his theory. In the case of gravitational waves he soon changed his mind in 1916 and by 1918 had presented the first theory of these waves which still underpins our understanding of how the LIGO detectors work. But in 1936 he changed his mind again, submitting a paper to the Physical Review called “Do Gravitational Waves Exist?” in which he answered his own question in the negative. The editor of the journal responded by sending Einstein a critical referee’s report and Einstein angrily withdrew the paper and resubmitted it elsewhere. But by early the next year he had changed his mind again, completely revising the paper to present one of the first exact solutions for gravitational waves in his theory. So his relationship with gravitational waves was very far from the image of the cocksure, self-confident theorist which dominates so many stories about Einstein. Because of this, he would have been thrilled today, if he were still alive, to have this major confirmation of some of the most esoteric predictions of his theory.”

Here at Princeton University Press where we recently celebrated the 100th anniversary of Einstein’s theory of general relativity, the mood has been celebratory to say the least. If you’d like to read the Einstein Papers volumes that refer to his theory of gravitational waves, check out Document 32 in Volume 6, and Volume 7, which focuses on the theory. Or, kick off your own #EinsteinWasRight celebration by checking out some of our other relevant titles.

Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves
by Daniel Kennefick

j8387

Relativity: The Special and the General Theory, 100th Anniversary Edition
by Albert Einstein

relativity 100 years

The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field
by Albert Einstein

j484

Einstein Gravity in a Nutshell
by A. Zee

Zee_EinsteinGravityNutshell

The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” Featuring the Original Manuscript of Einstein’s Masterpiece
by Hanoch Gutfreund & Jürgen Renn.

The Road to Relativity

The Curious History of Relativity: How Einstein’s Theory of Gravity Was Lost and Found Again
by Jean Eisenstaedt

the curious history of relativity jacket

 An Einstein Encyclopedia
by Alice Calaprice, Daniel Kennfick, & Robert Sculmann

Calaprice_Einstein_Encyclopedia

Gravitation and Inertia
by Ignazio Ciufolini & John Archibald Wheeler

gravity and inertia jacket

Einstein’s Jury: The Race to Test Relativity
by Jeffrey Crelinsten

einstein's jury jacket

What Does a Black Hole Look Like?
by Charles D. Bailyn

black hole

Dynamics and Evolution of Galactic Nuclei
by David Merritt

dynamics and evolution of galactic nuclei

The Global Nonlinear Stability of the Minkowski Space (PMS-41)
by Demetrios Christodoulou & Sergiu Klainerman

the global nonlinear stability of the minkowski space

Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics
by Kip S. Thorne & Roger D. Blandford

modern classical physics

The Collected Papers of Albert Einstein, Volume 7: The Berling Years: Writings, 1918-1921
by Albert Einstein

albert einstein

Noah Wilson-Rich on city beekeeping

the bee jacketNoah Wilson-Rich is an unconventional beekeeper who spends most of his time building bee hives on hundreds of buildings, including major stadiums, in nine different cities. These urban settings now support live bee populations and the environmentally friendly trend is only growing. As author of The Bee: A Natural History, Wilson-Rich establishes himself as an authority not only on the species but on conservation as well. An article on his beekeeping and speaking tour appeared recently in The Wall Street Journal.

Wilson-Rich emphasizes the urgency of preserving the bees’ population, pointing out that his urban hives are just one step in the right direction. The Wall Street Journal reports:

Mr. Wilson-Rich is researching ways to improve bee health, so he also carries test tubes to collect samples. He believes urban beekeeping is part of the solution. “Anybody who eats fruits and veggies needs bees. We have to protect our pollinators!” he says.

Wilson-Rich goes on to speak about some little known facts about bees, their habits, and what exactly makes them so uniquely necessary to humans. Read the rest of the article here.

Noah Wilson-Rich is founder and chief scientific officer of The Best Bees Company, a Boston-based beekeeping service and research organization. He is author of the book The Bee: A Natural History.

Bird Fact Friday – 50 Shades of Grouse

From page 9 of The Birdwatcher’s Companion to North American Birdlife:

For many species of grouse during courtship rituals, the male will act aggressively towards the female and treat her as a rival before responding to the female’s attempts to gradually encourage a more benign approach by behaving in a way that defuses the male’s attack response.

 
The Birdwatcher’s Companion to North American Birdlife
Christopher W. Leahy
Illustrations by Gordon Morrison

LeahyThe quintessential A-Z guide, this is a book that anyone interested in birds will want to have close at hand. First published more than twenty years ago, this highly respected reference volume has been fully revised and updated. It captures the fundamental details as well as the immense fascination of North American bird life in a style that is authoritative, yet fresh, witty, and eminently readable.

Both a practical handbook for amateurs and a handy reference for seasoned birders, it provides accounts of the basic elements of birdlife, as well as a wealth of easy-to-access information on such subjects as bird physiology and anatomy, terms and jargon, name definitions and etymology, and ornithological groupings.

Readers will discover everything from the color of a dipper’s eggs (glossy, white, and unmarked) to the number of species of woodpeckers in the world (216). They will also find more than one hundred of the best-known and most colorful colloquial names for birds, alphabetized and briefly defined. Collective nouns relating to birdlife–for example, “an exaltation of larks”–are included in the “Nouns of Assemblage” section. Biographical sketches of persons responsible for describing or naming a significant number of North American species are also included, as well as handsome and accurate illustrations by Gordon Morrison. And for those who want to go beyond reading about their favorite birds and take to the great outdoors, the book offers still more useful information: descriptive entries on a selection of the best-known birdwatching spots of North America.

Interview with Sean B. Carroll, author of The Serengeti Rules

CarrollIn the fields of biological and environmental studies, Sean B. Carroll has made a name for himself not only as a scientist, writer, and educator, but as a storyteller. In his newest book, The Serengeti Rules: The Quest to Discover How Life Works and Why It Matters, Carroll argues that the most critical thing we have learned about human life at the molecular level is that everything is regulated.

Carrol uses medical analogies, comparing the current blight on nature to a disease that ravages the body. The book will leave readers considering life on several scales, both personal and global. Recently he took the time to answer some questions about the book:

One of the central themes of your book is that “everything is regulated” in life. What does that mean?

SC: What it means is that at all scales of life the numbers of things are controlled. For example, in our bodies, the concentration of every kind of chemical – hormones, salts, enzymes and fats, and the numbers of every kind of cell –red cells, white cells and so on, are maintained within certain ranges by regulation. Similarly, in nature, the numbers and kinds of animal and plants in a given place are regulated.

Why is all of this regulation important?

SC: Regulation is very important because diseases (heart disease, cancer and so on) are generally abnormalities of regulation, when too little or too much of something is made. Likewise, in nature, when key species are lost or removed, too many or too few individuals of other species persist, and that habitat becomes unhealthy and may collapse. So learning the “rules of regulation” is very important to both medicine and conservation.

What have we learned about those rules?

SC: A century-long quest of biology has been to discover how life works, and that entails the deciphering of the “rules of regulation” in the body and in nature at large. The stories that make up the book are about those pioneers who tackled the mysteries of regulation and discovered important rules that have had huge impacts in medicine, ecology and conservation.

The scientists portrayed in The Serengeti Rules are admirable, sometimes heroic figures. Why did you choose to organize the book around their stories?

SC: I am a firm believer in the power of stories. Science is far more enjoyable, understandable, and memorable when we follow scientists all over the world and share in their struggles and triumphs.

You use an analogy from sports to explain how scientists have figured out how to treat many diseases. How does that analogy apply to medicine?

SC: In the body, the key “players” are molecules that regulate a process. To intervene in a disease, we need to know what players are injured or missing or what rules of regulation have been broken. The task for biologists is to identify the important players in a process, figure out the rules that regulate their action, and then design medicines that target the key players. In the book, I tell the stories of just how that was done to make such dramatic progress against heart disease and cancer.

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CC Image courtesy of Celso Flores on flickr

Your book is called The Serengeti Rules. What are those rules?

SC: Just as there are rules that regulate the numbers of different kinds of molecules and cells in the body, there are ecological rules that regulate the numbers and kinds of animals and plants in a given place. I have called these the “Serengeti Rules” because that is one place where they have been worked out and they determine, for example, how many lions, or buffalo, or elephants live on an African savanna.

But these rules apply all over the globe, in oceans, rivers, and lakes, as well as on land.

Do these rules apply then to conserving and restoring species?

SC: Absolutely. But in contrast to the considerable care and expense we gladly undertake in applying molecular rules to human medicine, we have done a very poor job in considering and applying these Serengeti Rules to human affairs. For centuries we have hunted, fished, farmed, forested, and settled wherever we could, with no or very little grasp of altering other species. For a long time, we did not know any better, but now we do. So minding these Serengeti Rules may have as much or more to do with our future welfare than all of the molecular rules we may ever discover.

But as you describe in several chapters, there have been some encouraging successes in restoring species and habitats

SC: Yes, and I thought it was very important to tell those stories, to show that even war-torn and devastated places like Gorongosa National park in Mozambique could rebound given time, protection, and the efforts of just a small band of extraordinarily dedicated people.

You visited Gorongosa in the course of writing this book. What was that experience like?

SC: Life-changing. The people behind the Gorongosa Restoration Project are so inspiring, and the magnitude of the recovery in just ten years is astounding and so encouraging. If Gorongosa can be rescued from utter disaster, we should all take heart that we can restore other places and species.

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CC image courtesy of F Mira on Flickr

When readers close The Serengeti Rules after finishing it, what do you hope they will be feeling?

First of all, I hope that they feel inspired by the stories of some exceptional people who tackled and solved great mysteries. Second, that they feel enriched with fresh insights into the wonders of life at different scales. Third, that they feel more hope for the future — that there is time to change the road we’re on. And finally, that they can’t wait to tell their friends to read the book!

You have had a very distinguished career as a molecular biologist. What inspired you to delve into ecology and conservation and write this book?

First, a desire to explore the bigger picture of life. When I gazed upon the Serengeti for the first time, I was as enchanted as any tourist, but I did not understand what I was looking at. For someone who has spent decades figuring out how complex, invisible things worked, that was a bit unsettling and embarrassing. So I dove into what was known and realized that the rules of ecology and even how they were discovered had some parallels to what we understood about life at the molecular level. These parallels had never been drawn; this book is an attempt to do that in the context of explaining why understand all of the rules matters.

And second, a sense of urgency. The disappearance of nature is an existential crisis for biology and humanity. As much as I love the world of DNA and cells, it felt a contradiction – to care so much about life at one level and to ignore what was happening to life at large. It is time to look up from the microscope.

Sean B. Carroll is an award-winning scientist, writer, educator, and executive producer. He is vice president for science education at the Howard Hughes Medical Institute and the Allan Wilson Professor of Molecular Biology and Genetics at the University of Wisconsin–Madison. His books include Endless Forms Most Beautiful, Brave Genius, and Remarkable Creatures, which was a finalist for the National Book Award for nonfiction. His most recent book is The Serengeti Rules. He lives in Chevy Chase, Maryland.

Congratulations to Sean B. Carroll on an outstanding achievement

Carroll

Sean B. Carroll has earned The Rockefeller University’s Lewis Thomas Prize for Writing about Science. He joins the ranks of such esteemed authors as Atul Gawande, E.O. Wilson, and many others. The much-deserved award honors him for an impressive body of work, including Brave Genius: A Scientist, A Philosopher and their Daring Adventures from the French Resistance to the Nobel Prize and Endless Forms Most Beautiful: The New Science of Evo Devo. We are proud to be publishing his next book, The Serengeti Rules: The Quest to Discover How Life Works and Why It Matters. Read on for a snippet from the book.

If you travel through the Serengeti, you’ll notice something odd. As you zip along in a dusty old Land Rover, your guide helpfully pointing out key elements of the surrounding flora and fauna, you’ll see vast herds of wildebeests existing in peaceful abundance. There’s nothing so very strange about that, but what is peculiar is that spotting a buffalo is a much rarer occurrence. Indeed, there are about 1,000,000 wildebeest populating the Serengeti, and only 60,000 buffalo. Why should that be?, you might wonder. At 450 kg, the buffalo is much less vulnerable to predation than the 170 kg wildebeest, after all. The answer can be found in The Serengeti Rules.

Wildebeest

Serengeti Rule 6
Migration increases animal numbers

Migration increases animal numbers by increasing access to food (reducing bottom-up regulation) and decreasing susceptibility to predation (reducing top-down regulation).

Why are there about 50 wildebeest for every 3 buffalo in the Serengeti? Because wildebeests are constantly on the move and the buffalo stays put.

The two major ways to regulate population are predation and food limitation. The wildebeest is on a constant 600-mile path moving during the wet season toward the green, nutritious, short-grass plains and then, as the plains dry out, toward the tall-grass savanna and woodlands, which receive more rainfall than the open plains. This is how they feed themselves. How the effects of predation are mitigated is a bit more complicated. There are actually two types of wildebeest in the Serengeti. These include the vast migratory herds and the smaller pockets of “resident” populations. The hyenas and lions that prey on wildebeests cannot follow the herds because they are restricted to their territories as they raise their young. They find their food mostly in the smaller sedentary populations of wildebeests while the active ones roam free. The buffalo, meanwhile, are restricted by their sedentary lifestyle in procuring enough food to flourish quite as spectacularly as the smaller wildebeest.

Migration, then, is … [an] ecological rule, or more aptly a rule-breaker, a way of exceeding the limits imposed by density-dependent regulation.

For the first five Serengeti Rules and much more information on their ramifications both large and small, pick up a copy of The Serengeti Rules by Sean B. Carroll, coming in March 2016.

Bird Fact Friday – City Birds

From page 132 of The Crossley ID Guide: Raptors:

The Taiga Merlin, the most common type of Merlin, generally makes its home in the boreal forest out of earshot of the Bald Eagle. Recently, like a number of other raptors, it has begun adapting to humans and making its home in urban areas.

The Crossley ID Guide: Raptors
Richard Crossley, Jerry Liguori, Brian Sullivan
Introduction

RaptorsPart of the revolutionary Crossley ID Guide series, this is the first raptor guide with lifelike scenes composed from multiple photographs—scenes that allow you to identify raptors just as the experts do. Experienced birders use the most easily observed and consistent characteristics—size, shape, behavior, probability, and general color patterns. The book’s 101 scenes—including thirty-five double-page layouts—provide a complete picture of how these features are all related. Even the effects of lighting and other real-world conditions are illustrated and explained. Detailed and succinct accounts from two of North America’s foremost raptor experts, Jerry Liguori and Brian Sullivan, stress the key identification features. This complete picture allows everyone from beginner to expert to understand and enjoy what he or she sees in the field. The mystique of bird identification is eliminated, allowing even novice birders to identify raptors quickly and simply.

Comprehensive and authoritative, the book covers all thirty-four of North America’s diurnal raptor species (all species except owls). Each species is featured in stunning color plates that show males and females, in a full spectrum of ages and color variants, depicted near and far, in flight and at rest, and from multiple angles, all caught in their typical habitats. There are also comparative, multispecies scenes and mystery photographs that allow readers to test their identification skills, along with answers and full explanations in the back of the book. In addition, the book features an introduction, and thirty-four color maps accompany the plates.

Whether you are a novice or an expert, this one-of-a-kind guide will show you an entirely new way to look at these spectacular birds.

Bird Fact Friday – Identifying males and females

From page 21 of Waterfowl of North America, Europe & Asia:

In family groups of geese and swans, you can easily differentiate between the father and mother. The father will stand slightly apart, staying alert for potential threats. The young stay close to the mother, frequently following her. When occasional conflicts break out, the males are more aggressive.

Waterfowl of North America, Europe & Asia
Sébastien Reeber

waterfowlThis is the ultimate guide for anyone who wants to identify the ducks, geese, and swans of North America, Europe, and Asia. With 72 stunning color plates (that include more than 920 drawings), over 650 superb photos, and in-depth descriptions, this book brings together the most current information on 84 species of Eurasian and North American waterfowl, and on more than 100 hybrids. The guide delves into taxonomy, identification features, determination of age and sex, geographic variations, measurements, voice, molt, and hybridization. In addition, the status of each species is treated with up-to-date details on distribution, population size, habitats, and life cycle. Color plates and photos are accompanied by informative captions and 85 distribution maps are also provided. Taken together, this is an unrivaled, must-have reference for any birder with an interest in the world’s waterfowl.

Upcoming event with Oliver Morton and Future Tense

Planet

On Monday, February 1 Oliver Morton, author of The Planet Remade, will partner with Katherine Mangu-Ward at a lunch hosted by Future Tense to discuss the potential role of geoengineering in climate change in Washington D.C.. If you would like to attend, RSVP here. In the meantime, learn more about the topic on the Future Tense blog, excerpted here:

Geoengineering, the deliberate hacking of Earth’s climate, might be one of the most promising potential responses to climate change, especially in the absence of significant carbon emission reductions. It’s also one of the most controversial. We engineered our planet into our environmental crisis, but can we engineer our way out with a stratospheric veil against the sun, the cultivation of photosynthetic plankton, or fleets of unmanned ships seeding the clouds?

Nick Higham on beautiful equations

The Most Beautiful Equations in Applied Mathematics

By Nick Higham

pcam-p171-wave.jpg

From p. 171 of PCAM,
typeset in all its splendour in the Lucida Bright font.

The BBC Earth website has just published a selection of short articles on beautiful mathematical equations and is asking readers to vote for their favourite.

I wondered if we had included these equations in The Princeton Companion to
Applied Mathematics
(PCAM), specifically in Part III: Equations, Laws, and Functions of Applied Mathematics. We had indeed included the ones most
relevant to applied mathematics. Here are those equations, with links to the
BBC articles.

  • The wave equation (which quotes PCAM author Ian Stewart). PCAM has a short
    article by Paul Martin of the same title (III.31), and the wave equation
    appears throughout the book.
  • Einstein’s field equation. PCAM has a 2-page article Einstein’s Field
    Equations
    (note the plural), by Malcolm MacCallum (article III.10).
  • The Euler-Lagrange equation. PCAM article III.12 by Paul Glendinning is about
    these equations, and more appears in other articles, especially The
    Calculus of Variations
    (IV.6), by Irene Fonseca and Giovanni Leoni.
  • The Dirac equation. A 3-page PCAM article by Mark Dennis (III.9) describes
    this equation and its quantum mechanics roots.
  • The logistic map. PCAM article The logistic equation (III.19), by Paul
    Glendinning treats this equation, in both differential and difference forms.
    It occurs in several places in the book.
  • Bayes’ theorem. This theorem appears in the PCAM article Bayesian Inference in Applied Mathematics (V.11), by Des Higham, and in other articles employing
    Bayesian methods.

A natural equation is: Are there other worthy equations that are the
subject of articles in Part III of PCAM that have not been included in the BBC
list? Yes! Here are some examples (assuming that only single equations are
allowed, which rules out the Cauchy-Riemann equations, for example).

  • The Black-Scholes equation.
  • The diffusion (or heat) equation.
  • Laplace’s equation.
  • The Riccati equation.
  • Schrödinger’s equation.

Higham jacketThis article is cross posted to Nick Higham’s blog.

Check out the Princeton Companion to Applied Math here.

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

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

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

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

Carl Wunsch

Carl Wunsch

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

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

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

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

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

Read the full interview in Physics Today, here.

Solving last week’s L.A. Math challenge

LA MathWe’re back with the conclusion to last week’s LA Math challenge, The Case of the Vanishing Greenbacks, (taken from chapter 2 of the book). After the conclusion of the story, we’ll talk a little more with the author, Jim Stein. Don’t forget to check out the fantastic trailer for LA Math here.

Forty‑eight hours later I was bleary‑eyed from lack of sleep. I had made no discernible progress. As far as I could tell, both Stevens and Blaisdell were completely on the up‑and‑up.   Either I was losing my touch, or one (or both) of them were wasting their talents, doctoring books for penny‑ante amounts.   Then I remembered the envelope Pete had sealed. Maybe he’d actually seen something that I hadn’t.

I went over to the main house, to find Pete hunkered down happily watching a baseball game. I waited for a commercial break, and then managed to get his attention.

“I’m ready to take a look in the envelope, Pete.”

“Have you figured out who the guilty party is?”

“Frankly, no. To be honest, it’s got me stumped.” I moved to the mantel and unsealed the envelope. The writing was on the other side of the piece of paper. I turned it over. The name Pete had written on it was “Garrett Ryan and the City Council”!

I nearly dropped the piece of paper. Whatever I had been expecting, it certainly wasn’t this. “What in heaven’s name makes you think Ryan and the City Council embezzled the money, Pete?”

“I didn’t say I thought they did. I just think they’re responsible for the missing funds.”

I shook my head. “I don’t get it. How can they be responsible for the missing funds if they didn’t embezzle them?”

“They’re probably just guilty of innumeracy. It’s pretty common.”

“I give up. What’s innumeracy?”

“Innumeracy is the arithmetical equivalent of illiteracy. In this instance, it consists of failing to realize how percentages behave.” A pitching change was taking place, so Pete turned back to me. “An increase in 20% of the tax base will not compensate for a reduction of 20% in each individual’s taxes.   Percentages involve multiplication and division, not addition and subtraction. A gain of 20 dollars will compensate for a loss of 20 dollars, but that’s because you’re dealing with adding and subtracting. It’s not the same with percentages, because the base upon which you figure the percentages varies from calculation to calculation.”

“You may be right, Pete, but how can we tell?”

Pete grabbed a calculator. “Didn’t you say that each faction was out $198,000?”

I checked my figures. “Yeah, that’s the amount.”

Pete punched a few numbers into the calculator. “Call Ryan and see if there were 99,000 taxpayers in the last census. If there were, I’ll show you where the money went.”

I got on the phone to Ryan the next morning. He confirmed that the tax base in the previous census was indeed 99,000. I told Pete that it looked like he had been right, but I wanted to see the numbers to prove it.

Pete got out a piece of paper. “I think you can see where the money went if you simply do a little multiplication. The taxes collected in the previous census were $100 for each of 99,000 individuals, or $9,900,000. An increase of 20% in the population results in 118,800 individuals. If each pays $80 (that’s the 20% reduction from $100), the total taxes collected will be $9,504,000, or $396,000 less than was collected after the previous census. Half of $396,000 is $198,000.”

I was convinced. “There are going to be some awfully red faces down in Linda Vista. I’d like to see the press conference when they finally announce it.” I went back to the guesthouse, called Allen, and filled him in. He was delighted, and said that the check would be in the mail.   As I’ve said before, when Allen says it, he means it. Another advantage of having Allen make the arrangements is that I didn’t have to worry about collecting the fee, which is something I’ve never been very good at.

I wondered exactly how they were going to break the news to the citizens of Linda Vista that they had to pony up another $396,000, but as it was only about $3.34 per taxpayer I didn’t think they’d have too much trouble. Thanks to a combination of Ryan’s frugality and population increase, the tax assessment would still be lower than it was after the previous census, and how many government agencies do you know that actually reduce taxes? I quickly calculated that if they assessed everyone $3.42 they could not only cover the shortage, but Allen’s fee as well. I considered suggesting it to Ryan, but then I thought that Ryan probably wasn’t real interested in hearing from someone who had made him look like a bungler.

My conscience was bothering me, and I don’t like that. I thought about it, and finally came up with a compromise I found acceptable. I went back to the main house.

Pete was watching another baseball game. The Dodgers fouled up an attempted squeeze into an inning‑ending double play. Pete groaned. “It could be a long season,” he sighed.

“It’s early in the year.” I handed him a piece of paper. “Maybe this will console you.”

“What’s this?” He was examining my check for $1,750. “Your rent’s paid up.”

“It’s not for the rent, Pete. It’s your share of my fee.”

“Fee? What fee?”

“That embezzling case in Orange County. It was worth $3,500 to me to come up with the correct answer. I feel you’re entitled to half of it. You crunched the numbers, but I had the contacts and did the legwork.”

Pete looked at the check. “It seems like a lot of money for very little work. Tell you what. I’ll take $250, and credit the rest towards your rent.”

A landlord with a conscience! Maybe I should notify the Guinness Book of Records. “Seems more than fair to me.”

Pete tucked the check in the pocket of his shirt. “Tell me, Freddy, is it always this easy, doing investigations?”

I summoned up a wry laugh. “You’ve got to be kidding. So far, I’ve asked you two questions that just turned out to be right down your alley. I’ve sometimes spent months on a case, and come up dry. That can make the bottom line look pretty sick. What’s it like in your line of work?”

“I don’t really have a line of work. I have this house and some money in the bank. I can rent out the guesthouse and make enough to live on. People know I’m pretty good at certain problems, and sometimes they hire me. If it looks like it might be interesting, I’ll work on it.” He paused. “Of course, if they offer me a ridiculous amount of money, I’ll work on it even if it’s not interesting. Hey, we’re in a recession.”

“I’ll keep that in mind.”   I turned to leave the room. Pete’s voice stopped me.

“Haven’t you forgotten something?”

I turned around. “I give up. What?”

“We had a bet. You owe me five bucks.”

I fished a five out of my wallet and handed it over. He nodded with satisfaction as he stuffed it in the same pocket as the check, and then turned his attention back to the game.

What made you include this particular idea in the book?

JS: The story features one of the most common misunderstandings about percentages.  There are innumerable mistakes made because people assume that percentages work the same way as regular quantities.  But they don’t — if a store lowers the cost of an item by 30% and then by another 20%, the cost of the item hasn’t been lowered by 50% — although many people make the mistake of assuming that it has.  I’m hoping that the story is sufficiently memorable that if a reader is confronted by a 30% discount followed by a 20% discount, they’ll think “Wasn’t there something like that in The Case of the Vanishing Greenbacks?

There are 14 stories in the book, and each features a mathematical point, injected into the story in a similar fashion as the one above.  I think the stories are fun to read, and if someone reads the book and remembers just a few of the points, well, I’ve done a whole lot better than when I was teaching liberal arts math the way it is usually done.

James D. Stein is emeritus professor in the Department of Mathematics at California State University, Long Beach. His books include LA Math, Cosmic Numbers (Basic) and How Math Explains the World (Smithsonian).