What is Calculus?: The Two Pillars

By Oscar Fernandez

This is the third in a series of short articles exploring calculus. The first article explored the origins of calculus, including the three “big problems” that drove calculus’ development. The second article explored limits, the foundation of calculus. This article discusses how limits help us solve the three “big problems” and introduces two of calculus’ pillars: derivatives and integrals.

In the first article in this series I discussed three Big Problems that drove the development of calculus: the instantaneous speed problem, the tangent line problem, and the area problem. I illustrated these via the figure below.

Reprinted, with permission, from Calculus Simplified (Princeton University Press). Click to expand.

These problems stumped mathematicians for millennia. (We briefly talked about why in the first article.) But their inability to solve these problems—echoing Morpheus in the movie The Matrix—was not due to the techniques they were using; it was due to their mindset.

How a Dynamics Mindset Solves the Three Big Problems

If you’ve read the second article in this series, you’ll remember my first characterization of calculus: calculus is a dynamics mindset. Yet nothing about the figure above says “dynamics.” Every image is a static snapshot of something (e.g., an area). So let’s calculus the figure. (Yep, I’m encouraging you to think of calculus as a verb.)

The figure below takes each Big Problem from the figure above and adds in the dynamics.

Reprinted, with permission, from Calculus Simplified (Princeton University Press). Click to expand.

These images show apples falling, gray lines approaching a blue tangent line, and areas being swept out. Lots of movement (dynamics)! Moreover, notice that as the central change in each row of the figure gets closer to zero —the quantity ∆t in the first row and ∆x in the second and third rows—the resulting diagram approaches the respective diagram in the first figure in this article. We’ve met this “as ∆t  approaches zero” language before—it’s the language of limits we discussed in the second article! Adding this new revelation to the figure above produces…

 

Reprinted, with permission, from Calculus Simplified (Princeton University Press. Click to expand.

Finally, expressing our result in terms of equations involving limits yields the final piece of the puzzle…

Notice how each row employs a dynamics mindset to recast the Big Problem (contained in the “limiting picture” column) as the limit of a sequence of similar quantities (e.g., speeds) involving finite changes, changes which pre-calculus mathematics can handle. Specifically:

  • Row #1: The instantaneous speed of the falling apple is realized as the limit of its average speeds  ∆d / ∆t (ratios of changes in distance to changes in time) as ∆t —> 0.
  • Row #2: The slope of the tangent line is realized as the limit of the secant line slopes ∆y / ∆x (the gray lines in the figure) as ∆x —> 0.
  • Row #3: The area under the curve is realized as the limit as ∆x —> 0 of the area swept out from x = a up to ∆x  past b.

Introducing…Derivatives and Integrals

The limit obtained in the second row of the last figure is called the derivative of f(x) at x = a, the x-value of point P. The limit obtained in the third row of the Figure is called the definite integral of f(x) between x = a and x = b. Derivatives and integrals round out the three most important concepts in calculus (limits are the third).

You now have a working understanding of what derivatives and definite integrals are, what they measure, and how they arise from the application of a dynamics mindset to pre-calculus mathematics. The next post in this series will explore the derivative in greater details. We’ll discover that it has a nice geometric interpretation and a powerful real-world interpretation. (The last figure above hints to what these are.) Near the end of this series we will return to these interpretations to illustrate the power of derivatives, using them to help us understand phenomena as diverse as the fate of the Universe and, more pragmatically, how to find the best seat in a movie theater. Stay tuned!

 

Calculus Simplified
By Oscar E. Fernandez

Calculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a “Goldilocks approach” to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure.

Fernandez begins by offering an intuitive introduction to the three key ideas in calculus—limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources—including video tutorials and interactive graphs—are available on the book’s website.

Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions—these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics—chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus.

Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.

  • An accessible, intuitive introduction to first-semester calculus
  • Nearly 200 solved problems and more than 300 exercises (all with answers)
  • No prior knowledge of exponential, logarithmic, or trigonometric functions required
  • Additional online resources—video tutorials and supplementary exercises—provided

Editor Ben Tate on his trip to Hay Festival

It’s the mother of all literary festivals, and since its establishment in the late 1980s virtually every living writer of consequence has attended. It was here that the late Christopher Hitchens promoted, in turn, both his atheist manifesto as well as his memoir, and it was here that Margaret Atwood appeared just last year for an extended discussion of A Handmaid’s Tale. In 2004 John Updike, before presenting one of his last novels, insisted upon arriving by train ‘because they don’t have trains in Massachusetts’, and famously, and rather awkwardly, Paul Theroux and V.S. Naipaul were reunited here in 2011 after their long estrangement. It was in 2000 that Gore Vidal made one of his last truly robust public appearances, amusing audiences with his impressions of Ronald Reagan and Spiro Agnew; and Bill Clinton, after peddling his own book here in 2001, referred to it as ‘the Woodstock of the Mind’, though he was thinking more of upstate New York than of West Oxfordshire. This is, of course, the Hay Festival, staged every May in the Welsh market town of Hay-on-Wye, which is perched along the River Wye, and not too far from the southern extension of Offa’s Dyke, the Anglo-Saxon earth wall which more or less demarcates England from Wales. But it’s not for the stunning countryside that the festival is held here. For many bibliophiles, Hay-on-Wye is the very centre of the known universe: it’s the ‘town of books’ for a reason, as there are more than 30 used bookshops tucked into its narrow streets. And it’s such a relatively small place that one could conclude a ratio of one bookshop for every resident.

I had made pilgrimages to the town in the past, primarily to buy books I never intended to read with money I never really had. Last month, however, I visited the actual festival for the first time. And what a spectacle. Although until a few years ago the festival was held literally in the town, it is now of such a magnitude that it’s staged in an open field on the outskirts, in what is really a self-contained city of tents and marquees, with two bookshops on the site and a food hall of overwhelming variety and quality. I was there with a purpose, specifically to see our author Marion Turner, whose new book, Chaucer: A European Life, has been acclaimed as nothing less than a literary milestone. It’s a biography which situates Chaucer within the broadest cultural, political, social, and intellectual context, and by predicating the narrative upon the places in which Chaucer is known to have lived and travelled the author has rendered the subject’s life and work into a tangibly concrete and complicated reality. With helpful instruction from our publicist Katie Lewis, herself an expert hand at Hay, my wife Ginny and I made our way to the festival green room, where we found Katie and author in mid-conversation, and mid-prosecco, just about an hour or so before the early afternoon event. The green room was exactly what one would want it to be. Cake, bubbly and coffee were in generous and complimentary supply, as were various British cultural celebrities: Jeanette Winterson was there chatting with friends before her event; Bettany Hughes, the popular ancient historian, breezed through on her way to a panel on reconciliation in time of conflict; BBC lion Melvyn Bragg was holding court, because he’s Melvyn Bragg and this is the sort of thing he does; and finally there was Stephen Fry, whose presence exerted a kind of gravitational pull on the rest of the room. I had to remind myself that I first knew him as Jeeves more than twenty-five years ago.

Marion was whisked away by a festival official for a debriefing, and then after a quick lunch Katie, my wife and I walked over to Llwyfan Cymru (Wales Stage) for the sold-out event. 800 people crammed under the marquee to hear Marion discuss the book with Jerry Brotton, a professor of Renaissance studies Queen Mary. Brotton was the perfect interlocutor: he never imposed himself upon the proceedings, and his questions were posed just frequently enough to move the conversation naturally from one subject to the next.  Marion, not surprisingly, was effortlessly lucid and engaging, distilling her considerable learning with a youthful and noticeably infectious enthusiasm.  Audience questions, including one from the former manager of Tower Bridge, carried on until the very last minute of the hour-and-a-half event before a throng queued up in the main festival bookshop to buy signed copies.

Princeton’s Hay experience this year extended well beyond Chaucer. Martin Rees, Astronomer Royal, talked about the future, and more specifically his wonderful On the Future, and later in the week Jonathan Bate attracted a crowd of 1500 for his talk on How the Classics Made Shakespeare. It’s difficult to get one’s head round a festival like Hay. For more than a week, thousands of readers converge on muddy farmland to see authors both prominent and obscure and to listen, learn, eat, drink, talk and buy books. The scale of it overwhelms and reassures at the same time. We’re fortunate to publish authors who are invited to engage with the public at such an annual gathering, and more literally we’re fortunate to be positioned in such proximity to the ‘town of books’.

What is Calculus?: Limits

This is the second in a series of short articles exploring calculus. The first article explored the origins of calculus. The next few articles explore the mathematics of calculus. This article focuses on the foundation of calculus: limits.

The first article in this series asked the question: What is calculus? I promised then that the second article in the series would explore the substance of calculus, the mathematics of calculus. So let’s dive right in.

Here’s my two-part answer to the “what is calculus?” question:

Calculus is a mindset—a dynamics mindset.
Contentwise, calculus is the
mathematics of infinitesimal change.

The second sentence describes the mathematics of calculus. But I don’t expect you to understand that sentence just yet. That’s where the first sentence comes in. If you ask me, all of calculus flows from a more fundamental—and intuitive—principle, articulated in the first sentence: the notion that calculus is a dynamics mindset. Let me explain.

Calculus: A New Way of Thinking

The mathematics that precedes calculus—often called “pre-calculus,” which includes algebra and geometry—largely focuses on static problems: problems devoid of change. By contrast, change is central to calculus. Calculus is all about dynamics. Example:

  • What’s the perimeter of a square of side length 2 feet? ← Pre-calculus problem.
  • How fast is the square’s perimeter changing if its side length is increasing at the constant rate of 2 feet per second? ← Calculus problem.

Now that I’ve sensitized you to thinking “calculus!” whenever you read about or infer the presence of change, take a quick look at the second sentence in my two-part answer above. What’s the last word? Change. But it’s a new type of change—infinitesimal change—and this requires some explaining. That’s our next stop.

A Philosopher Walks Into a Starbucks

First, a rough definition of “infinitesimal change”:

“Infinitesimal change” means: as close to zero change as you can imagine, but not zero change.

“What?!” I hear you saying. So let me illustrate this definition via my friend, Zeno of Elea (c. 490-430 BC). This ancient Greek philosopher thought up a set of paradoxes arguing that motion is not possible. One such paradox—the Dichotomy Paradox—can be stated as follows:

To travel a certain distance you must first traverse half of it.

Makes perfect sense. Two is one plus one. And one is one-half plus one-half. But don’t be fooled by this seemingly innocent reasoning; it’s a trap! (Admiral Ackbar!) 

To appreciate what’s going on—and connect Zeno’s paradox back to calculus—let’s pretend Zeno is in line at Starbucks, two feet away from the cash register. He’s almost done scanning the menu when the barista yells out “next!” And that’s when poor Zeno panics. He must now walk two feet, but because of his mindset, he walks only half that distance with his first step. He then walks half of the remaining distance with his second step. (Can you imagine how annoying those in line behind him are getting?) The figure below keeps track of the total distance d Zeno has walked and the change in distance Δd after each of his steps.

Fig. 1.2: Zeno trying to walk a distance of 2 feet by traversing half the remaining distance with each step. (Reprinted, with permission, from Calculus Simplified.)

Here’s a tabular representation of the action:

Table 1.1: The distance d and change in distance Δd after each of Zeno’s steps. (Reprinted, with permission, from Calculus Simplified.)

Each change d in Zeno’s distance is half the previous one. So as Zeno continues his walk, d gets closer to zero but never becomes zero.[1] If we checked back in with Zeno after he’s taken an infinite

amount of steps—what a patient barista!—the change d resulting from his next step would be . . . drum roll please . . . an infinitesimal change—as close to zero as you can imagine but not equal to zero.

This example, in addition to illustrating what an infinitesimal change is, also does two more things. First, it illustrates the dynamics mindset of calculus. We discussed Zeno walking; we thought about the change in the distance he traveled; we visualized the situation with a figure and a table that each conveyed movement. (Calculus is full of action verbs!) Second, the example challenges us. Clearly, one can walk 2 feet. But as Table 1.1 suggests, that doesn’t happen during Zeno’s walk—he approaches the 2-foot mark with each step yet never arrives. How do we describe this fact with an equation? (That’s the challenge.) No pre-calculus equation will do. We need a new concept that quantifies our very dynamic conclusion. That new concept is the mathematical foundation of calculus: limits.

Limits: The Foundation of Calculus

In modern calculus speak we paraphrase the main takeaway of Table 1.1 this way: the distance d traveled by Zeno approaches 2 as Δd approaches zero. It’s important to note that d never equals 2 and Δd never equals 0. Today we express these conclusions more compactly by writing

read “the limit of d as Δd approaches zero (but is never equal to zero) is 2.” This new equation—and what we take it to mean—remind us that d is always approaching 2 yet never arrives at 2. (Oh, the dynamics!) The same idea holds for Δd: it is always approaching 0 yet never arrives at 0. Said more succinctly:

Limits approach indefinitely (and thus never arrive).

You’ve now met the foundational concept of calculus—limit. You’ve also gotten a glimpse of what infinitesimal change means and how a limit encodes that notion. Finally, you’ve seen many times how a dynamics mindset is at the core of calculus’ new way of thinking about mathematics. In the next article in this series we’ll employ a dynamics mindset and limits to solve the three Big Problems that drove the development of calculus—instantaneous speed, the tangent line problem, and the area problem (discussed in the first post in this series). See you then!

Footnote: [1] Because each d is always half of a positive number.

 

Calculus Simplified
By Oscar E. Fernandez

Calculus is a beautiful subject that most of us learn from professors, textbooks, or supplementary texts. Each of these resources has strengths but also weaknesses. In Calculus Simplified, Oscar Fernandez combines the strengths and omits the weaknesses, resulting in a “Goldilocks approach” to learning calculus: just the right level of detail, the right depth of insights, and the flexibility to customize your calculus adventure.

Fernandez begins by offering an intuitive introduction to the three key ideas in calculus—limits, derivatives, and integrals. The mathematical details of each of these pillars of calculus are then covered in subsequent chapters, which are organized into mini-lessons on topics found in a college-level calculus course. Each mini-lesson focuses first on developing the intuition behind calculus and then on conceptual and computational mastery. Nearly 200 solved examples and more than 300 exercises allow for ample opportunities to practice calculus. And additional resources—including video tutorials and interactive graphs—are available on the book’s website.

Calculus Simplified also gives you the option of personalizing your calculus journey. For example, you can learn all of calculus with zero knowledge of exponential, logarithmic, and trigonometric functions—these are discussed at the end of each mini-lesson. You can also opt for a more in-depth understanding of topics—chapter appendices provide additional insights and detail. Finally, an additional appendix explores more in-depth real-world applications of calculus.

Learning calculus should be an exciting voyage, not a daunting task. Calculus Simplified gives you the freedom to choose your calculus experience, and the right support to help you conquer the subject with confidence.

  • An accessible, intuitive introduction to first-semester calculus
  • Nearly 200 solved problems and more than 300 exercises (all with answers)
  • No prior knowledge of exponential, logarithmic, or trigonometric functions required
  • Additional online resources—video tutorials and supplementary exercises—provided

Tanya Bub: Things My Father Taught Me (quantum edition)

Totally Random is a comic for the serious reader who wants to really understand the central mystery of quantum mechanics–entanglement: what it is, what it means, and what you can do with it.  In honor of father’s day, we asked author Tanya Bub to reflect on some “totally random” memories with her dad, theoretical physicist and co-author Jeffrey Bub. 

BubOne of the earliest memories I have of my father is of playing “the limerick game”. I think we came up with it when I was about six or seven years old. We’d play in the car. One of us would throw down an opening line like a gauntlet. Then the other had to repeat it back and follow up with the next invented line of the poem. For example:

Quoin landings are totally random.
They nevertheless land in tandem.

Then the ball is back in the opener’s court for the third and fourth lines, ideally punchy five to six syllable zingers. Bonus points for gratuitous rhyming, double meanings and clever silliness.

Quoin landings are totally random.
They nevertheless land in tandem.
What gives us pause,
is the laws have no cause.

The last line, always the hardest, had to rhyme with the first two and tie everything together. The best would add something new or surprising to the theme.

Quoin landings are totally random
they nevertheless land in tandem.
What gives us pause,
is the laws have no cause.

Einstein for one couldn’t stand ’em.

We might be driving down some icy Ontario road as we played, but really we were somewhere else. Traffic lights, snow drifts and pedestrians had to be respected of course, but only in the most perfunctory way. Because all the action was elsewhere. We were together in a far more exciting place playing with words, extending their meanings. I always had the feeling that that world, the one outside the world we see, smell, touch and taste was more important and maybe even more real to my Dad than the one in which you tie your shoes, take out the garbage and walk the dog. That was where all the really fantastic and important stuff happened.

And in fact my Dad, a theoretical physicist, has spent the better part of a lifetime thinking about things that can’t be seen or touched or even easily imagined. He has “lived” much of his life in the quantum world, exploring the reality that underlies the everyday one we perceive.  Growing up with a father like that makes an impression.

So this father’s day, I decided to reflect on the ways my Dad’s unusual relationship with reality has influenced me, by creating a Things My Father Taught Me (quantum edition) list.

Here are my top three.

1. The world is stranger than you can possibly imagine.
Be willing to change your ideas if the evidence demands it. But not without a fight.

2.  Follow the Rabbit.
Should you be so lucky to be invited down a conceptual rabbit hole, go! You may be in for the adventure of a lifetime.

3. Don’t be afraid to think.
You have just as much of a right as anyone to wrestle with life’s mysteries. Do it well! The rewards are incalculable.

Now, as a fully-fledged adult and mother, I find myself a steward of two fresh, bright and curious minds, passing on these very same values and ideas.

And we also play the limerick game.

Curious about the meaning of the limerick in this article? Then pick up a copy of Totally Random, the book my Dad and I wrote together. It’s a graphic interpretation of my Dad’s life work and an extension of our lifelong collaborative exploration of reality in all it’s delightfully impossible and sometimes hilarious presentations.

Tanya Bub is founder of 48th Ave Productions, a web development company. She lives in Victoria, British Columbia. Jeffrey Bub is Distinguished University Professor in the Department of Philosophy and the Institute for Physical Science and Technology at the University of Maryland, where he is also a fellow of the Joint Center for Quantum Information and Computer Science. His books include Bananaworld: Quantum Mechanics for Primates. He lives in Washington, DC.

Producing non-fiction audiobooks

Jennifer Howard is Director at Sound Understanding. She was previously Head of BBC Audio Production and also Director of Talking Issues.

Once upon a time, an audiobook was something your grandmother borrowed from the library. The shoebox-sized case contained hundreds of cassettes, and the cover generally featured a woman in a shawl looking tragic as she gazed wistfully out to sea…

Of course, audio publishers have always published more than romantic fiction, and listeners have always been made up of more than the elderly or partially sighted.

Yet, Audiobooks have finally come of age. Their popularity has been driven by technology; the device that we now carry around in our pocket can store hundreds of hours of audio. We can listen to whatever we want, wherever we are and whatever we’re doing.

Sound Understanding has recently been appointed audio partner to Princeton University Press; a publisher that has recognised the prolific growth of audiobooks and has been very forward thinking in becoming the first academic publisher to launch an audio list. Princeton’s authors are the thought leaders of our generation. From “On the Future” by Lord Martin Rees and read by Samuel West, to “Gods and Robots” written and read by Professor Adrienne Mayor; these authors offer historical context and in-depth analysis borne out of years of thorough research.

Producing academic or non-fiction books in audio is a challenge, albeit a rewarding one, and preparation is key. 

We begin with casting. Non-fiction is difficult to voice; possibly more difficult than fiction. As the style is generally 1st or 3rd person, there is rarely opportunity for the narrator to mix things up or vary their delivery.  They really need to be engaged with the material and understand what they’re reading; comprehension can’t be disguised with vocal tricks and the light and shade of characterisation.  Voicing non-fiction also requires a tremendous amount of concentration and perseverance to sustain these complex ideas. Coming out of a recording session can sometimes feel like one has just run a marathon!

Getting the right voice goes beyond the usual criteria of region, age, tone, gender. This is always done in partnership with the publisher and with full permission of the author. I personally very much favour author-own readings; no one knows their books better than the authors themselves and the passion they hold for their subject carries a unique authenticity in their voice.

Our narrators are fully supported in studio by a Producer who has sourced pronunciations and—in conjunction with publisher/author—made decisions about where to incorporate footnotes and how to handle graphs and diagrams. Behind our producers are our Editors and Proof Listeners; we aim to marry the subject matter with the education and broadcast experience of our production staff – be that Economics, Natural Science, Maths, History, Classics etc. 

Sometimes the author’s premise can spark controversy if, for example, the narrator disagrees with the author’s point of view. However, in academic publishing, we have found there is respect for these opinions because challenging convention is the lifeblood of learning.

Overall, it is a collegiate and very fulfilling area of audio production.

—Jennifer Howard

 

 

Insect of the Week: Pipiza

Adapted from page 308 of Field Guide to the Flower Flies of Northeastern North America:

Pipiza are small black syrphids that vary from having all black abdomens to having paired yellow spots on tergite 2 and sometimes also tergite 3. They can be mistaken for Heringia and Trichopsomyia and so should be checked for a bare anterior anepisternum and katepimeron. Th ere are 52 world species; 11 in the Nearctic and seven from the northeast.

A recent revision in Europe (Vujić et al. 2013) turned much of the original taxonomy on its head and illustrated how difficult this group is. Despite recent work by Coovert (1996) in the Nearctic, taxonomic concepts need to be reevaluated incorporating genetic data. Many problems with current concepts exist but cannot be solved without complete revision. We thus follow Coovert here with the caveat that changes are needed.

Pipiza species are often found flying through herbaceous vegetation or around shrubs. Known larvae are predators of aphids and phylloxera (mostly gall-making or leaf-rolling aphids that create waxy secretions). Characters illustrated below generally work, but male genitalia should be checked for confirmation.

Field Guide to the Flower Flies of Northeastern North America
By Jeffrey H. Skevington, Michelle M. Locke, Andrew D. Young, Kevin Moran, William J. Crins, and Stephen A. Marshall

This is the first comprehensive field guide to the flower flies (also known as hover flies) of northeastern North America. Flower flies are, along with bees, our most important pollinators. Found in a varied range of habitats, from backyard gardens to aquatic ecosystems, these flies are often overlooked because many of their species mimic bees or wasps. Despite this, many species are distinctive and even subtly differentiated species can be accurately identified. This handy and informative guide teaches you how.

With more than 3,000 color photographs and 400 maps, this guide covers all 416 species of flower flies that occur north of Tennessee and east of the Dakotas, including the high Arctic and Greenland. Each species account provides information on size, identification, abundance, and flight time, along with notes on behavior, classification, hybridization, habitats, larvae, and more.

Summarizing the current scientific understanding of our flower fly fauna, this is an indispensable resource for anyone, amateur naturalist or scientist, interested in discovering the beauty of these insect.

InDialogue with Marcia Bjornerud and Mark Serreze: Why long-term thinking on the natural world matters

The dangers of a colonial attitude toward the Earth

Marcia Bjornerud

Anthropologist Clifford Geertz famously defined culture as the constellation of stories that groups of humans tell themselves about their place and purpose in the world.  In western culture, with its Judeo-Christian underpinnings grafted to principles of social democracy and capitalism, the stories we share about who we are largely exclude the Natural World.  Nature is at most a passive backdrop – the scenery against which the ‘real’ stories unfold, not a central protagonist in the narrative.

As a result, most of us believe we can simply opt out of Nature’s own long-term plans for the future.  We tend to confuse technological prowess with wisdom.  The people we call “visionaries” base their conceptions of the future on the notion that we should do everything in our power to circumvent the bothersome constraints of the natural world.  We love the stories these great and powerful wizards tell us of how they will make life ‘frictionless’ and reality virtual.  Bedazzled by their shiny gadgets and habituated to the constant streams of novelty they feed us, we in the audience can¹t be bothered to look up and think for ourselves about where exactly we might be going.

And so we behave like bad tourists, entitled conquerors, on Earth, enjoying its amenities and ransacking its bounty without ever having noticed that it has its own ancient language and customs.

This colonial attitude toward the Earth leads to insanities like our continued collective inaction on climate change, or the idea that it could be solved by a silver bullet solution like injecting sulfate aerosols in the stratosphere — and that this will have no unintended consequences.  Or in the extreme case, the delusion that we could create a livable space for ourselves on another planet (once we wreck this one).  Engineering the climate or terraforming Mars sound easy if you are completely unaware of the intrinsic timescales of geological and biological phenomena, the deep evolutionary pathways that gave rise to the world we live in, the intricately choreographed, behind-the-scenes biogeochemical cycles – the housekeeping crew — that make Earth habitable.

We are naïve and impetuous. Earth is old and patient. It has seen good times and bad, hosted biospheres through mass extinctions and evolutionary radiations, reshuffled its continents in countless configurations, constructed and dismantled mountains many times over.  Whether we like it or not, our long-term plans must conform to its long-established practices.  We can alter and accelerate some of these, temporarily, but nature will take notice and take action.  That is, the scenery is going to start directing the play.

We imperil ourselves both physically and psychologically if we don’t bring our conceptions of time in line with nature’s rhythms.  Environmental malefactions and existential malaise are both rooted in a distorted view of humanity’s place in the history of the natural world. 

The solution is to tell different stories about who we are as Earthlings.  That’s all it will take – nothing more than a simple cultural revolution.

Marcia Bjornerud is professor of geology and environmental studies at Lawrence University. She is the author of Timefulness: How Thinking Like a Geologist Can Help Change the World,  Reading the Rocks: The Autobiography of the Earth, and a contributing writer for Elements, the New Yorker’s science and technology blog. She lives in Appleton, Wisconsin.

Beating climate change: Taking action and accepting hard realities

Mark Serreze

Mitigating climate change promises to be a defining battle of the 21st century.  Climate change has already taken hold across the planet. In the Arctic, it is already leading to a radically new environment, with the impacts of rapid warming and shrinking sea ice cascading through the food chain. As a climate scientist who has spent 35 years studying the north, I’ve had a front row seat to watch it all unfold.  Can we beat climate change and maintain a livable planet?   We can, but we must take a long-term view, and accept some hard realities.    

SerrezeCarbon dioxide has a long residence time in the atmosphere, so even if emissions were quickly reduced, much of what we’ve added still will be up there for the foreseeable future.  We are making strong inroads in transitioning to renewable energy sources, notably solar and wind, and have become more efficient in how we use energy.  But for many years to come, we will still be largely dependent on fossil fuels, and greenhouse gas levels will continue to rise.   

It also takes quite a while for the climate to adjust to a change in greenhouse gas levels, mostly because of the immense thermal inertia of the oceans.  The planet has yet to come into balance with the greenhouse gases we’ve already put in the atmosphere – there is heat “in the pipeline”.  Similarly, it will take time for the planet to cool in response to a reduction in carbon dioxide levels.  Simply put, we can’t simply stop climate change in its tracks.

Where does this leave us?  First, stop the blame game and accept where we are.  We have built a modern global society around the immense amount of energy in a lump of coal and a barrel of crude oil.   What we didn’t realize, or perhaps chose not to realize, is that it was a trap.  We need to move on.   Second, prepare to adapt to a warmer world.  It promises to be a rough road, and climate change will have the biggest impacts on those in less developed parts of the world that are least responsible for causing it (and are justified in pointing fingers).  I believe that the planet will manage, provided that we can get a handle on limiting the amount of warming but we have to act quickly – the window of opportunity is closing.

We need to further develop renewables and increase efficiency but also be pragmatic as we transition.  We must to be willing to make honest assessments of the risks and benefits of all energy sources.  As we mobilize against climate change, we must be prepared to be in it for the long haul, and understand that when it comes to powering our future, nothing comes for free. 

Mark C. Serreze is director of the National Snow and Ice Data Center, professor of geography, and a fellow of the Cooperative Institute for Research in Environmental Sciences at the University of Colorado at Boulder. He is the coauthor of Brave New Arctic and The Arctic Climate System. He lives in Boulder, Colorado.

      

InDialogue with Thomas Seeley and Nick Haddad: Why is insect conservation important?

The PUP Ideas blog is pleased to announce our new InDialogue series. In keeping with our mission to provide a range of perspectives and voices, each month we’ll be posing a big question to a pair of authors. With Earth Day fast approaching, we’ve asked a series of questions to our natural history authors on issues from the central role of oceans to climate science. Today we asked PUP authors Thomas Seeley and Nick Haddad to sound off on why insect conservation is important, and to reflect on the magnitude of the loss of key populations. Watch this space for more Earth Day posts in the coming days.

Being stewards to the bees

Thomas D. Seeley

There is no doubt that humans are now the primary movers and shakers of the natural world.   We are busy tearing down the planet’s forests and, in one way or another, we are appropriating some 40 percent of the solar energy captured by plants.  But we are not self-sufficient.  We depend on what Edward O. Wilson has called “the little things that run the world”:  the insects and other invertebrates, which together form most of the biomass in terrestrial habitats.  If humans were to disappear from the planet, then life on Earth would certainly go on.  Indeed, it would begin to heal itself.  But if insects were to disappear, then our species and countless others would go extinct, because most of the flowering plants—including those that produce the fruits and vegetables we eat—would die out for lack of pollination.   

There is one insect whose pollination services are especially important to us:  the honey bee, Apis mellifera.  This bees’ paramount value to humans was recently quantified in an authoritative, 59-author paper on the contributions of various bee species to crop pollination.  It reports that honey bees provide nearly half of all crop pollination services worldwide.  Remarkably, this one species’ contribution to humanity’s food production nearly equals the combined contributions of the many thousands of other bee species.  Clearly, the conservation of honey bees merits special attention. 

One way we can support Apis mellifera is by conserving forests.  They provide habitat for wild colonies of honey bees, and these colonies are important to their species’ long-term survival.  Recent studies of the population genetics of honey bees in the southern and western states of the U.S. have found that wild colonies—those living on their own in hollow trees and the walls of buildings—have far higher genetic diversity than the managed colonies in these states.  This is because commercial beekeepers typically replace the queens in their colonies every year or so using queens purchased from large-scale queen producers, and these replacement queens are the daughters of a small number of “breeder queens” (ca. 600 for the entire U.S.).  These practices create a genetic bottleneck in the population of managed honey bee colonies within the U.S. 

Other studies have revealed recently that the wild colonies of honey bees—those not living in beekeepers’ hives—possess effective mechanisms of resistance to a species of parasitic mite (Varroa destructor) introduced from east Asia.  The females of this species feed on the adult and immature honey bees.  They also spread a virus that deforms the bees’ wings and destroys their health.   Approximately 40% of the managed colonies in the U.S. die each year from infections of the deformed wing virus.  The wild colonies are also infested with these mites, but they have better survival because they have experienced strong natural selection for mechanisms of resistance to Varroa destructor.   These include chewing the legs off adult mites and destroying cells of bee brood infested with mites.

Besides conserving forests that support populations of wild colonies, we can help Apis mellifera by revising the practices of beekeeping, to find a better balance between the needs of bees and the desires of beekeepers.  Most of the practices of conventional beekeeping—such as encouraging colonies to grow extremely large, and packing them close together in apiaries—boost the productivity of colonies as honey makers and crop pollinators, but also increase their vulnerability to parasites and pathogens, including deadly Varroa destructor.   To conserve Apis mellifera, we must build a new relationship between human beings and honey bees.  We must revise our methods of beekeeping to bring them more in harmony with the honey bee’s natural way of life.  Only then will we be truly responsible stewards of Apis mellifera, our greatest friend among the insects.

Thomas D. Seeley is author of The Lives of Bees. He is the Horace White Professor in Biology at Cornell University. He is the author of Following the Wild BeesHoneybee Democracy, and Honeybee Ecology (all Princeton) as well as The Wisdom of the Hive. He lives in Ithaca, New York.

 

The value of the rarest butterflies

Nick Haddad

When I began writing The Last Butterflies in 2013, I worried that the title was over the top. After all, I was writing about just a handful of the rarest butterflies in the world. The five rarest butterflies number from a few hundred to a few tens of thousands of individuals. Could these be in any way representative of the last butterflies on the earth?

One way they are not representative is in their “value”. Their value might be to ecological systems. However, the earth’s thirty thousand individual Fender’s Blue butterflies might weigh as much as a basketball. These simply cannot be of consequence to interactions with other plants or animals as parts of functioning foodwebs. They are not effective pollinators or herbivores of, or food sources for, other species in their environments. Perhaps their value is in the bigger lessons the understanding of their declines holds for the declines of other butterflies. If so, then knowledge accrued during their decline can provide guidance to avert catastrophic declines of other insects.

Also when I started writing this book, I did not imagine broad implications to other insects that have economic value that can be measured. Data had not yet amassed to support the “insect apocalypse,” a phrase used to refer to catastrophic loss of abundance and diversity of insects. Then in 2014, reports surfaced that Monarchs reached epic low numbers, 97% below their peak two decades earlier. Later that year, a more general survey found declines across butterfly and insect species at the rate of 10% or more per decade. Such broad losses across insects must have substantial cost.

In this context, the rarest butterflies have higher value. Most of what we know about the insect apocalypse is what we know about butterflies. Are the rarest butterflies and Monarchs representative? A chilling picture has emerged. My former student Tyson Wepprich just completed an analysis of butterfly abundances using data collected across Ohio in surveys conducted every week for two decades. He found that butterfly abundances are declining by 2%  / year; abundances are now a third lower than twenty years ago. This is not an isolated case. Tyson reviewed other, decades-long studies in the UK, the Netherlands, and Spain. All of them have found 2%/ year decline in butterfly abundances. It appears that, after all, The Last Butterflies is an appropriate book title.

This rate and magnitude of loss is perhaps the best indicator of the cost of insect decline. Considered together, butterflies are the best known group of the earth’s 5.5 million insects. The less substantial evidence that exists for other insects points in the same downward direction. Like butterflies, those insects are herbivores, prey, and pollinators (and, of course, many are predators). They are exposed to the same levels of habitat loss, pesticides, and climate change. The scale of loss of butterflies, even if it is only partially representative of loss of other insects, will cause catastrophic loss of functioning ecosystems on which we all depend.

Circling back around to the rarest butterflies in the world: what is their value? It is certainly not in their importance within their ecosystem, at least not now. Their decline has generated some value in the sense that is provides some guidance for conservation of other insects, animals, and plants. Their true value, however, is intrinsic; when driven to extinction by global environmental changes, loss of value will be to people, and to the earth.

Nick Haddad is author of The Last Butterflies. He is a professor and senior terrestrial ecologist in the Department of Integrative Biology and the W. K. Kellogg Biological Station at Michigan State University. He lives in Kalamazoo, Michigan. Twitter @nickmhaddad

Clifford Bob on Rights as Weapons

Bob_Rights as WeaponsRights are usually viewed as defensive concepts representing mankind’s highest aspirations to protect the vulnerable and uplift the downtrodden. But since the Enlightenment, political combatants have also used rights belligerently, to batter despised communities, demolish existing institutions, and smash opposing ideas. Delving into a range of historical and contemporary conflicts from all areas of the globe, Rights as Weapons focuses on the underexamined ways in which the powerful wield rights as aggressive weapons against the weak. Clifford Bob looks at how political forces use rights as rallying cries: naturalizing novel claims as rights inherent in humanity, absolutizing them as trumps over rival interests or community concerns, universalizing them as transcultural and transhistorical, and depoliticizing them as concepts beyond debate.

How exactly are rights weaponized?

Rights become weapons when political forces use them aggressively to advance their goals and attack other groups, institutions, and customs. Of course, rights do not literally become material weapons, but politically they have similar effects. For instance, powerful or majority groups often claim their own cultural rights as a way of attacking minority and immigrant groups by forcing them to assimilate or by keeping them out of the society completely. This use of majority rights seems to be increasingly common, and I analogize it to the use of dynamite because it is often intended to undermine or destroy the minority culture itself (at least in its adopted home). In other chapters, I show how rights are used in other weapon-like ways, as rallying cries to mobilize political forces and as camouflage to cover up sometimes questionable political goals.

Overall, one of the key points I make in the book is that rights are tools or weapons that political groups of any ideology can pick up and use to advance their goals. Why can rights be used on multiple sides of conflicts? It is chiefly because they are a means of achieving political or economic goals, rather than ends in themselves. A right, even a human right, is a right to something. It is that thing, whether abstract such as privacy or concrete such as food, rather than the right to the thing, that is the ultimate focus of conflict. It is true that the right and its underlying content are often discussed interchangeably, but analyzing them in isolation from one another, as I do, makes it possible to see how rights can be used in multiple ways, as various types of political tools or weapons.

What are some historical examples of the biggest culprits in the use of rights to further nefarious ends?

As I’ve said, my view of rights as weapons does not apply only to what we might call the misuses of rights by the nefarious. But let’s talk about them first! One of the most important examples in the U.S. has been states’ rights, in effect a form of majority rights used by powerful interests along with outright violence to block the political advance of African Americans. That sordid story is well known. Less known, at least to me  as a political scientist before I began this book, was the way in which major voting rights movements in nineteenth-century America competed against one another. There were three major suffrage movements, among those without property, African-Americans, and women. Although there was no necessary bar to their working together for universal suffrage, and although some forward thinking activists proposed such unity, for the most part the three movements sought suffrage for their own group alone. Even more interesting, at times each movement used its own rights claims as a blockade against the similar claims of the other groups. White men without property urged that a grant of the vote for them would help ensure the continuing power of white males. For their part, although women such as Elizabeth Cady Stanton and Susan B. Anthony began their careers in the abolitionist movement, they frequently argued against the vote for freed slaves or argued that women should receive the vote first. When the opposite happened after the Civil War, suffrage leaders continually proposed that women should receive the vote as a way of blocking black power, because white women would vote with white men against African-Americans. I used this and other cases to develop a systematic conceptual account of when and how rights are used as blockades.

Is this phenomenon of rights as weapons an inevitable aspect of democracy, or are there strategies that can be employed to prevent it?

I do see the use of rights as weapons as an inevitable part of modern politics—and not necessarily a bad part. For one thing, it is usually better than the use of real weapons to achieve political goals, although at times political forces combine the two sets of tactics, with rights arguments serving to legitimate violence. Trying to prevent political groups from using rights aggressively would be futile. What I hope to have contributed, however, is a way that observers can cut through the righteous rhetoric in which most conflicts are clouded—to uncover what is truly driving the rivals and to understand the tactics they are using to promote themselves and attack their foes. Recent American wars have frequently been draped in rights talk. The war in Afghanistan, for instance, began as a response to 9/11, but within weeks the Bush administration justified it as a means of improving women’s rights. Clearly, women were treated terribly by the Taliban, and some Afghan women welcomed the invasion as a means of advancing their rights. But others, even Afghan women who fought for their rights before 2001, opposed the invasion and saw it as a greater threat to the lives of Afghan women than the Taliban’s laws. They also argued that women’s rights could never succeed in Afghanistan if they were imposed by foreigners at the tip of a drone, rather than growing indigenously through the efforts of Afghan women themselves. In the U.S., however, this complex reality was obscured by the appealing nature of women’s rights (which I of course fully support). This may be one reason we are still fighting there, whatever the Afghan people really want.

When rights are used in this way, is it always a negative? Are there examples of groups weaponizing rights for positive aims?

Many! For centuries, political movements have used rights to advance human progress, as in the abolitionist, suffrage, and civil rights movements in the U.S. and similar movements worldwide. In the book, I discuss the American Revolution and the reasons that in the 1770s the colonists transformed their prior claims to the rights of British subjects into demands for their “natural right” to independence. I would call that a positive example of using rights as a rallying cry, with the express purpose of advancing the revolt and attracting foreign fighters and support. But of course the British saw things rather differently—as illegitimate claims put forth, in Samuel Johnson’s words, by “dictators of sedition” who had strategically “put in motion the engine of political electricity, to attract, by the sounds of liberty and property.”

In the modern era, we have many examples of minority groups in democratic countries using rights as what I call spears. Because of such groups’ political weakness, majoritarian political institutions may not offer promising fields for their operation. One way they can achieve their goals of equality and nondiscrimination is to mount narrowly targeted attacks on a single key law, with the hope that a court will support their cause as a matter of right. There are many such cases, including Brown v. Board of Education and the recent Obergefell v. Hodges same-sex marriage decision. In the book, I examine a more ambiguous and less successful case in Italy. In the mid-2000s, a small group of atheists unhappy at the power of the Catholic Church in Italian society brought a lawsuit challenging one small but important policy, mandating crucifixes in public school classrooms. The group had no chance of ejecting the crucifix through legislation. So instead they opted for a spear-like thrust in the courts, based on Italian and European human rights law. And they won at the European Court of Human Rights! But only for a brief time, because a transnational coalition of religiously conservative countries fought back and reversed the judgment on appeal. In the end the court found that the crucifix symbolized Italian culture and history, as much as Catholicism, and held that the majority had a right to maintain its culture, even if in other countries with other traditions, a crucifix would be illegal in a public school classroom.

What should vulnerable groups know about the use of rights as weapons as they work to further their goal of equality?

Vulnerable and minority groups have often used rights claims to advance their agendas and improve their lives. Many have been experts at using rights to mobilize their constituencies and appeal for outside support. In many cases, they have succeeded in establishing their rights claims as laws and have been able to move toward achievement of the underlying social, economic, and political goals they seek.

But what the vulnerable may not always be prepared for is the way in which contrary rights claims may be used by their opponents to mobilize their constituencies and counter-attack. Moreover, they may be caught by surprise that opponents they thought they had defeated long ago have risen again, in new guises promoting novel rights. This has been the case with the radical feminists discussed previously, many of whom say that they have been shocked by the possibility that the advances for women they thought they had won long ago may now be threatened by people they consider to be men. Long-running conflicts over voting rights in the U.S. take the same form, with current voter suppression efforts in many ways an echo of rights-based battles fought in decades and centuries past. Vulnerable groups need to remain constantly on guard and adept at defending what they have previously achieved—as in fact most of them are.

Was there anything that surprised you as you were researching for this book?

Lots of things! One of the most interesting parts of the research focused on the use of rights as camouflage for ulterior goals. This is hard to study because political forces that use rights in this way typically cover up their real purposes. I examined the use of animal rights to mask nationalist aims in Spain, specifically how Catalan nationalists implemented a ban on bullfighting in the region, ostensibly to protect the bulls but in fact as a means of attacking a key symbol of Castilian nationalism. The bullfighting ban was the brainchild of a transnational animal rights movement that interacted strategically with the Catalan nationalists—and fought against Spanish nationalists and the bullfighting lobby. I learned a great deal about how multiple social movements make use of one another in complex political struggles (and far more than I intended about bullfighting). In the end, I was able to find very good proof of camouflaging in this case, and on that basis I developed a framework for understanding how rights are used as camouflage in many other conflicts.

What do you hope readers will take away from reading this book?

In addition to reading about fascinating rights conflicts from around the world and learning how to analyze them systematically, I hope that readers take away a fuller idea of how political groups view and use rights. Rights are not only shields to protect the powerless or hoists to uplift the downtrodden. Although that is one aspect of rights, they can also be offensive weapons, that the powerful can use to oppress the weak. Ultimately, this means that although rights claims can be helpful to political movements, it is political power, amassed through any number of means, including the use of righteous rallying cries to galvanize support for one’s cause, that is crucial to allowing a movement to achieve and maintain its goals.

Clifford Bob is professor and chair of political science at Duquesne University. His previous books include The Marketing of Rebellion, The Global Right Wing and the Clash of World Politics, and The International Struggle for New Human Rights. Twitter @cliffordbob

 

Myronn Hardy on Origin: “Birches”

It began with that set of Encyclopedia Britannicas on the tall family room shelves.  Those maroon and navy bound books that had everything in them.  The volumes I often used to lookup random things: cities, countries, animals, historical figures and events.  Those were the books we had in my Michigan childhood home.  Those books and a random one I hadn’t touched until I was six or seven, the thick book with a black dust cover photograph of blurry sun beams passing through heavy boughs of nondescript trees. 

I remember having to hoist myself onto the counter and stretch my arm to its limit just to pull that one book from the high shelf.  Once safe, down from the counter with the book in hand, safe on the gray carpeted floor, I read its cover, The Poetry of Robert Frost: The Collected Poems, Complete and Unabridged.  I opened the book erratically to the poem, “Birches.”  I read it intensely.  I knew what the world “birch” meant because there was a birch in the front yard.  And whenever my parents and I walked through the yard, or other yards or forests, they’d named the trees in it.  Perhaps they wanted me to know their names, to know they had names, histories even.  They wanted me to be aware.

In that poem, Frost refers to ice storms and that ice breaking from those birches as glass.  After a storm, I remembered making the same assertion in my very young mind.  The language in the poem was thrilling.  The way it worked on the page both charmed and perplexed me.  I got up from the floor to ask my mom what was the difference between this form of writing and what I’d seen in those encyclopedias or the newspaper.  She said, “This” she pointed to the poem, “is concentrated.”  She when on to compare it to the pulpy-concentrated orange juice she mixed with water each morning. 

            “So this is pure?” I asked.

            “I don’t know about pure but that’s kind of it,” she said.  I didn’t tell her then, but I felt I’d found something to make, something to attempt to make.  I found myself staring at that birch in the front yard and noticing the strange beauty in its pealing skin.  Somewhere in the process of staring at this tree, and once swinging in its boughs, I realized that that poem and other poems I’d read in Frost’s book, were prompting me to notice or see more profoundly: to notice the small, or what I’d later be told, the “insignificant.”  And that my task, perhaps, was to make that “insignificant” thing momentous, to make it the center.

            This one poem, this one book of poems, that almost fresh awareness of the birch in our front yard, began my seeing, my imagination, my seeing-imagination in poetry.  It began my writing of poetry.  I had no idea but now pondering it, sifting through it, there is the birch.  There are birches. 

            In high school, one of the large boughs of the birch had becoming infected.  The leaves became yellow and dropped in the summer.  Eventually, it had to be removed from the tree to potentially save the whole of it.  Of course, this large bough seemed to be almost half the tree.  I watched that large part being sawed off and helped with its later chopping up and removal from the yard.  I later wrote something about this.  A poem that began with yellow dust billowing from an electric saw as yellow leaves blew about the speaker in August. 

            That image became nightmarish.  It kept repeating itself in dream and I kept writing that poem, kept changing it.  The poem never worked but it marked a moment:  the birch’s almost death, that title of the first poem I remembered reading, and my first real attempting at writing poetry.

            In 2009, a year after my second book, The Headless Saints was published, I received the Robert Frost Poetry Fellowship to attended the Bread Loaf Writers’ Conference.  A month after that conference, I moved to Morocco where I lived and taught at a university there for nine years.  I didn’t see any birches there. But there were sycamores and cedars.  And I wrote several poems with those trees in them.

             I’ve lived now in Maine for eight months.  Here there are birches everywhere.  And I’ve seen their branches covered with ice.  I’ve been carrying around Frost’s “Birches.” 

            I keep thinking about this idea of return, the space of return.  These groves of birches I walk though almost every day is a return I hadn’t expected.   Perhaps this is the next poem. 

Myronn Hardy is the author of four previous books of poems: Approaching the Center, winner of the PEN/Oakland Josephine Miles Prize; The Headless Saints, winner of the Hurston/Wright Legacy Award; Catastrophic Bliss, winner of the Griot-Stadler Award for Poetry; and, most recently, Kingdom. He divides his time between Morocco and New York City.

A Celebration of Mathematics Editor Vickie Kearn

This month, across the world, we have celebrated the enduring contributions of all women. For those of us at PUP, it is a chance as well to focus on a particularly generous, intelligent, and dynamic publisher, Vickie Kearn. In April, Vickie will retire from the Press after 18 years of synergistic and inspiring collaborations in math and computer science publishing, leaving us with a library of books that have educated and entertained millions, billions, and zillions of readers (borrowing from the title of one of her recent acquisitions).

Vickie has also been a powerful role model for women in STEM publishing, and one who empowered a population of publishers, myself included, and our new math editor Susannah Shoemaker as another. Vickie’s strength as a competitive publisher set the bar dauntingly high, but in that competition was also always an admirable collaboration, knowing that a cohort of us were changing the face of scholarly STEM publishing. It has been such a great privilege to be a colleague of Vickie’s since 2017, to travel to a math meeting with her, to meet incredibly creative authors with whom she has worked, and to learn from her at weekly project meetings. The PUP math list, particularly the popular math list, has grown exponentially and in multiple dimensions under Vickie’s leadership. If there are theorems or rules in math publishing, I would attribute these to Vickie’s rule: be smart, be curious, be generous, and be strong.

–Christie Henry

CH: Some say math is its own language. How did you learn to speak it?

I grew up in Venezuela and the English school only went through the 9th grade, so when I was 15, I went away to boarding school in North Carolina. There were only 125 girls in the whole school and there were two math teachers. One taught the girls who liked math and another taught those who did not like math. My class was very small since fewer of us liked math. Elsie Nunn was my teacher for three years and she made me fall in love with math. Before she taught anything new, she taught us about the person responsible for what we were about to learn. There was always a face behind the numbers, a person who had a family and hobbies. I found I could connect with these people. We had math club every day after school and she always had wonderful stories to tell. When I went to the University of Richmond, I knew I was going to major in math. This led to an unexpected benefit and a bit of a surprise. In the late 1960’s, University of Richmond was a Baptist school, and the classes for the men and women were held on separate sides of a lake. The one exception was that the upper level math classes were on the men’s side. Men and women were only allowed to talk with one another on Wednesday, Saturday, and Sunday, but I was able to talk with them every day because we had math class together. The surprise for me was that I was the only female math major. This felt strange at times, but Ms. Nunn had prepared me well and I got along fine with my classmates. The classes were small and we stuck together because unlike many people at UR we were more interested in math and less interested in parties.

CH: How can we continue to empower girls and women in STEM- as authors and publishers?

Based on conversations I have had with other women my age, I have had a very easy time in my career. This could be because I only have an undergraduate degree and did not experience the problems that arise in graduate school and a career as a mathematician. However, I would advise young women to join an organization that focuses on confidence building, like the Girl Scouts. I would also recommend finding a mentor—someone to look up to who can advise about a field that has long been male dominated. After I got my undergraduate degree, I taught school for 8 years, five of them in elementary school and 3 teaching math in junior high school. Most of the elementary teachers were female and the math teachers were both men and women. Although all of my college classmates in my math courses were male, it wasn’t until I went into publishing and attended my first mathematics meeting that I realized how gender specific math was.  I believe that as more women with math PhD degrees publish books and give plenary talks at conferences, the more visible they will be, and in turn, young women majoring in math will feel more a part of the mathematics community. It is critical for publishers to encourage female mathematicians to write scholarly books and ask them to review books under consideration for publication. We need more women who are advising publishers on the decisions we are making about the books we are publishing and not rely only on male scholars to help us make these decisions. Publishers need to ask female scholars to blurb books and endorse scholarly publications. There are many terrific female mathematicians and we need to increase their visibility in the book publishing community.

CH: You have published textbooks, popular math books, graphic works, works of magic, and monographs, all successful. What are the 5 essentials of a great math book?

A great book is not always measured by the number of copies it sells. It is sometimes measured by the impact it makes on a small community of scholars. Did it provide that one missing piece of information that led to the solution of an unsolved problem? Did it inspire a high school student to major in math? Did it turn a “math hater” into someone curious about math? Nevertheless, they all can benefit from some essential advice.

First, I feel that the most essential thing is that the author writes on something that she or he is passionate about. If this is the case, the reader will be engaged and love reading the book. Second, the author needs to clearly define the audience. No book can be for everyone. If the author defines the audience that way, then the book will be for no one. Third, the author needs to write for the audience and keep the mathematical level consistent throughout the book. One problem I have had with authors writing for audiences without an advanced math degree is over and under explaining math concepts. Fourth on my list is authors often introduce terms without defining them or define them by introducing other terms that need elaboration but instead lead to further confusion. Always provide examples that clarify definitions. Finally, if you have included any jokes or explanation marks in your manuscript, please delete them before sending the manuscript to your editor.

CH: What are the 5 math books you would gift to every aspiring female mathematician to learn about the art and science of math? 

Before I reveal my suggestions, I would like to say that I think that the books I have suggested would make anyone want to learn about the art and science of math. They are particularly important to me because they point out the personal relationships that can develop out of the love of a subject. It is so hard for me to select only five because each book one selects to publish is special. Each one has a backstory. Most of my choices are, OF COURSE, Princeton University Press books because they are the ones I know the best and ones I have the time to read. 

My first suggestion is not a book but a wonderful website, MacTutor History of Mathematics. I have spent many hours there and there is a link to Female Mathematicians, which is updated regularly.

The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math by Steven Strogatz (Princeton University Press) is a book about a teacher and a student and their love of calculus as chronicled over thirty years through their letters. As you know by now, my love of math came from my high school math teacher. This author tried to help me find her. Unfortunately, we were unsuccessful. Later, at my 50th high school reunion I found out that she had passed away but it was the act of trying to find her that is illustrative of how tightly knit and wonderful I find the math community to be.

The Housekeeper and the Professor by Yoko Ogawa (Picador) was translated from Japanese. This is a novel about a math professor whose memory, due to an accident, is reset every 80 minutes, his housekeeper, and her young son. It is a wonderful story about how mathematics can bind three very different people.

Mathematics and Art: A Cultural History by Lynn Gamwell (Princeton University Press) covers the history of mathematics through exquisite works of art from antiquity to the present. I believe that learning about the history of mathematics is as important as the mathematics itself because you understand the time and place in which it is set and the math takes on more meaning.

The Seduction of Curves: The Lines of Beauty that Connect Mathematics, Art and the Nude by Allan McRobie (Princeton University Press) connects mathematics with art and engineering. This book focuses on the seven curves that are the basis of the catastrophe theory of mathematician René Thom. It is an accessible discussion of their role in nature, science, engineering, architecture, art, and other areas. Also included are their use in the work of David Hockney, Henry Moore, Anish Kapoor, and the delicate sculptures of Naum Gabo. The final two chapters focus on the collaborative work and friendship of Thom and Salvador Dalí. I searched for a book that could explain the work of René Thom for over twenty years before I found this one so it is pretty special.

CH: If you could invite five historic women mathematicians to join you at a dinner, who would they be, and why?

There are so many wonderful women mathematicians, historical and modern, that it is hard to choose just five. There are also many women who have made terrific contributions to mathematics who do not have advanced math degrees. See the references at the end of this post for additional resources.

At the top of my list would be Olga Taussky-Todd. Early in my career, I had the privilege of working with her on a book and got to know her a bit. I would love to spend more time with her. Not only was she smart, she had a great sense of humor. She made many contributions to the field of linear algebra, as did her husband, John, and we spent many hours talking about results in which, at the time, was one of my favorite topics in math. After Olga died, John gave me the poster from which the photo here was taken.

Emmy Noether is very important to me as I published a biography of her in my first position as an acquiring editor. I learned a lot about her work and would like to know more about her as a person. She has been described by many as the most important woman in the history of math. She developed the theories of rings, fields, and algebras.

Sophie Germain and I share a birthday, so of course I have to have dinner with her. Due to the great opposition against women in mathematics Sophie was not able to have a career in mathematics. Even her parents opposed her. She learned from books in her father’s library, often secretly after everyone was asleep. In spite of this she made many contributions to math such as her work on Fermat’s Last Theorem.

CH: What are five of your favorite mathematical puzzles?

Instead of listing single puzzles, I’ve chosen my favorite puzzles as types or groups. The following are some illustrations.

Word logic puzzles are fascinating and can also drive you crazy. Here is an example from Brain Food:

At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many were there, and who were they? Go to Rinkworks.com for more excellent puzzles and the answer to this one. However, you should try to solve it first.

Kakuro is like a crossword puzzle with numbers. Each word” must add up to the number provided in the clue above it or to the left. Words can only use the numbers 1 through 9, and a given number can only be used once in a word. Every kakuro puzzle has one and only one solution and can be solved through logic alone.

Martin Gardner was a master puzzler. If you don’t know who he is, or his puzzles (like cutting the pie, twiddled bolts, and the mutilated chessboard) head over to martin-gardner.org You will be glad you did.

I love playing Yahtzee which is more a game of logic, luck, and chance but always a lot of fun.
Jenga also does not strictly fall into the category of math but a lot of my math friends love playing it and it often appears at math meetings.

CH: how should we best compute the impact of mathematical publishing on the world?

From teaching in rural and inner-city schools for 8 years, I learned that there were so many students and adults who knew nothing about surviving in an increasingly complicated world that depends on a mastery of basic math skills. Over the past 42 years, I have seen the publication of numerous wonderful books for this very audience. These are books coming from university presses, commercial presses and society presses. These are books that have been published for the “math haters” and those who think math is hard. They present math through music and art and in graphic novels, detective stories, and puzzle books. There are ancillary materials posted on websites where readers can manipulate equations and discover new math of their own invention. As the number of books being published continues to increase, more people are clearly reading them. I am finding that there is much more enthusiasm for mathematics than there was four decades ago. There has been an increase in math clubs, math circles are very active, and the Girl Scouts announce many new STEM badges each year. I believe that publishers will continue to produce high quality books from mathematical writers around the world. This includes books that are being translated from one language into another, fostering an understanding of cultural differences through books about mathematics. I take every opportunity I can to tell people about the cool factor of math. If you are reading this post and have not discovered the wonder and empowerment of math, I’d advise you to go find a mathematician or anyone who has and ask them to let you in on the secret.

Additional Resources for inspiring information on women in STEM
MacTutor
Grandma Got STEM
A Mighty Girl

Bird Fact Friday: The Evolution of Avian Intelligence

Adapted from pages 14-15 of Bird Brain:

Despite there being almost 10,000 species of birds, only a few have yet to be studied for their cognitive abilities. Some, based on their lifestyles and relative brain size, such as this woodpecker (left), hornbill, and falcon (right), are likely to also demonstrate smart behavior in intelligence tests.

The species lived in splendid isolation on the island of Mauritius in the Indian Ocean until contact with European sailors in the seventeenth century led to its extinction in just a few decades. Although the relatives of dodos (pigeons and doves) are not thought of as the smartest of birds, can we put the dodo’s demise down to its own stupidity? Certainly, having no natural predators and not having had much contact with humans before the seventeenth century, they had little or no reason to fear us. If dodos had had the capacity for rapid learning, perhaps they might have adapted quickly and learned to escape their human hunters, but they were up against the most efficient and effective killer the planet has ever seen. Given the dodo’s clumsy body design—large and flightless—and that it had nowhere to run, it’s clear that dodos were in the wrong place at the wrong time, though being stupid didn’t help! 

More than 50 percent of birds are members of the songbird family or passerines. In fact, most of the birds we encounter every day in our gardens and parks are passerines, including sparrows, thrushes, finches, titmice, robins, blackbirds, and crows. Although not all members of this family are melodious singers, as anyone who has experienced the loud cawing of a crow will testify, all learn vocalizations specific to their species and, indeed, have evolved a special brain circuit to do so. This ability, rare in the animal kingdom, shares properties with human language which will be examined in Chapter 3.

Although birds have been studied with respect to the structure and function of their brains, their learning, and cognition for over a century, very little is known about the cognitive abilities of more than a tiny proportion of species. Most species are not kept in laboratories and thus are unavailable for experimental study, so our best ideas about their intelligence are only guesses based on their relative brain size (in comparison to their body size; see Chapter 1), their diet, social system, habitat, and life history (how long the species lives and how long the young take to develop to independence). These clues help build a picture of what these species may need their brains for—finding food, relating to others, building a home—but without being able to run experiments the picture can only be a sketch. Nonetheless, this technique is still useful for making predictions as to how intelligence may have evolved, specifically in those species we would expect to be the intellectual heavyweights. Three groups of birds— woodpeckers, hornbills, and falcons—possess some or all of the traits displayed by species known to be smart (The Clever Club; Chapter 1) but have yet to be tested. All three groups are outside the passerines but are closely related, so any cognitive skills they may have are likely to have evolved independently (that is, not from a common ancestor).

Bird Brain
An Exploration of Avian Intelligence
By Nathan Emery with a foreword by Frans de Waal

Birds have not been known for their high IQs, which is why a person of questionable intelligence is sometimes called a “birdbrain.” Yet in the past two decades, the study of avian intelligence has witnessed dramatic advances. From a time when birds were seen as simple instinct machines responding only to stimuli in their external worlds, we now know that some birds have complex internal worlds as well. This beautifully illustrated book provides an engaging exploration of the avian mind, revealing how science is exploding one of the most widespread myths about our feathered friends—and changing the way we think about intelligence in other animals as well.

Bird Brain looks at the structures and functions of the avian brain, and describes the extraordinary behaviors that different types of avian intelligence give rise to. It offers insights into crows, jays, magpies, and other corvids—the “masterminds” of the avian world—as well as parrots and some less-studied species from around the world. This lively and accessible book shows how birds have sophisticated brains with abilities previously thought to be uniquely human, such as mental time travel, self-recognition, empathy, problem solving, imagination, and insight.

Written by a leading expert and featuring a foreword by Frans de Waal, renowned for his work on animal intelligence, Bird Brain shines critical new light on the mental lives of birds.