Global Math Week: Counting on Math

by Tim Chartier

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

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

 

 

 

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

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

 

 

 

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

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

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

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

 

 

 

 

 

 

 

 

 

 

 

 

 

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

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

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

Bird Fact Friday – The Wattled Jacana

From page 98 of Birds of Western Ecuador:

The Wattled Jacana is common in freshwater marshes, flooded rice paddies, ditches, and vegetated margins of lakes and sluggish rivers in the lowlands. The distinctive adult is not likely to be confused with any other species (W Ecuador birds have black scapular patches, not evident in this photo). Immature is extremely different from adult and has no similar species: it is all white below and has distinctive black-and-white head stripes.

The Wattled Jacana (Jacana jacana).

The Wattled Jacana forages methodically, in singles, pairs, or scattered groups, over matted and floating vegetation, where it is generally easy to see. Flight is slow, usually low to ground, with rather stiff wingbeats, legs and long toes protruding way beyond tail; when alighting, wings are often held outstretched, showing off yellow primaries. They can be quite noisy, emitting a series of loud yapping and yelping, cackling notes and churring sounds.

Birds of Western Ecuador
By Nick Athanas & Paul J. Greenfield
With special contributions from Iain Campbell, Pablo Cervantes Daza, Andrew Spencer & Sam Woods

Western Ecuador is famed for its astonishingly diverse birdlife, from colorful hummingbirds and outrageous toucans to more difficult groups like raptors, flycatchers, and ovenbirds. Here is the ultimate photographic guide to the spectacular birds of this region. Featuring nearly 1,500 stunning color photos of 946 species, this richly detailed and taxonomically sophisticated field guide will help you with even the toughest identification challenges. Species accounts, photos, and color distribution maps appear side by side, making it easier than ever to find what you are looking for, whether you are in the field or preparing for your trip.

  • Features nearly 1,500 photos of 946 species
  • Includes facing-page species accounts, photos, and maps
  • Provides photos of multiple plumages for many species
  • Helps you to differentiate between similar species

 

 

 

Read like a Nobel Prize-winning physicist

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

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

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

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

Five Books for Hawk Migration Season

From hawks, to falcons, to our illustrious bald eagle, raptors are the kings of the sky, so it seems only right to pay homage to them during this fall migration season. Whether you’re a birdwatching pro or new to the hobby, we’ve picked out five guides that can help you identify various raptors across America and learn more about birds as a whole.

Whether soaring or perched, diurnal birds of prey often present challenging identification problems for the bird enthusiast. Variable plumage, color morphs, and unique individual characteristics are just some of the factors bird watchers must consider when identifying the different species. In A Photographic Guide to North American Raptors, two of the world’s top experts on raptors provide an essential guide to the variations in the species, allowing for easier recognition of key identification points. All the distinguishing marks described have been exhaustively tested in a wide range of field conditions by the authors as well as the colleagues and students who have learned from them.
Raptors are among the most challenging birds to identify in the field due to their bewildering variability of plumage, flight silhouettes, and behavior. Raptors of Mexico and Central America is the first illustrated guide to the region’s 69 species of raptors, including vagrants. It features 32 stunning color plates and 213 color photos, and a distribution map for each regularly occurring species. Detailed species accounts describe key identification features, age-related plumages, status and distribution, subspecies, molt, habitats, behaviors, potential confusion species, and more.
Comprehensive and authoritative, The Crossley ID Guide: Raptors 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.
The ultimate must-have guide for identifying migrant raptors, Hawks at a Distance is the first volume to focus on distant raptors as they are truly seen in the field. Jerry Liguori, a leading expert on North American raptors, factors in new information and approaches for identifying twenty-nine species of raptor in various lighting situations and settings. The field guide’s nineteen full-color portraits, 558 color photos, and 896 black-and-white images portray shapes and plumages for each species from all angles. Useful flight identification criteria are provided and the accompanying text discusses all aspects of in-flight hawk identification, including flight style and behavior. Concentrating on features that are genuinely observable at a distance, this concise and practical field guide is ideal for any aspiring or experienced hawk enthusiast.
Hawks from Every Angle takes hawk identification to new heights. It offers a fresh approach that literally looks at the birds from every angle, compares and contrasts deceptively similar species, and provides the pictures (and words) needed for identification in the field. Jerry Liguori pinpoints innovative, field-tested identification traits for each species from the various angles that they are seen. Featuring 339 striking color photos on 68 color plates and 32 black & white photos, this is a unique in presenting a host of meticulously crafted pictures for each of the 19 species it covers in detail–the species most common to migration sites throughout the United States and Canada.

You can also check out this sample raptor ID guide from The Crossley ID Guide: Raptors for a taste of what you’ll find in these publications.

Bird Fact Friday – Townsend’s Warbler

From pages 440-442 in The Warbler’s Guide:

Townsend’s Warbler is easily identified by its high-contrast yellow face, which also contains a dark ear patch and yellow undereye arc. These warblers have variably black throats boarded by yellow, and dark streaking. In addition, they have a dark olive-green back and white wing bars. Their dark flight feathers contrast with their yellow bodies. Additionally, Townsend’s Warblers are identified by their white bellies and tails. They also have a distinctive, contrasty facial pattern.

The Townsend Warbler (Setophaga townsendi) perched on a branch. Photo courtesy of the Field Museum of Natural History, Chicago, IL. Copyright: Scott Whittle and Tom Stephenson.

This warbler breeds in conifers; during migration, they can use a range of habitats, but are often found in pines whenever available. Their breeding range overlaps with Hermit Warbler’s, and hybrids between the two are found annually. Townsend’s Warblers are typically found in the western part of the United States.

The Warbler GuideThe Warbler Guide
Tom Stephenson & Scott Whittle
Drawings by Catherine Hamilton

Warblers are among the most challenging birds to identify. They exhibit an array of seasonal plumages and have distinctive yet oft-confused calls and songs. The Warbler Guide enables you to quickly identify any of the 56 species of warblers in the United States and Canada. This groundbreaking guide features more than 1,000 stunning color photos, extensive species accounts with multiple viewing angles, and an entirely new system of vocalization analysis that helps you distinguish songs and calls.

The Warbler Guide revolutionizes birdwatching, making warbler identification easier than ever before. For more information, please see the author videos on the Princeton University Press website.

Bird Fact Friday – Virginia’s Warbler

From pages 446-448 of The Warbler Guide:

Virginia’s warbler is recognizable from its grayish back and head, the variable yellow patch on its breast, and the chestnut crown patch which is often hidden on the top of its head. This type of warbler also has a long, thin, gray tail, along with grayish wings, without any brighter edging. This warbler has a limited range and habitat and can be found in brushy areas during migrations.

Virginia’s Warbler (Oreothlypis virginae) perched on a branch. Photo credit: Jim Burns

There is some variance between these warblers. For example, their chestnut crown is sometimes more easily seen. Additionally, the yellow on their breast can vary from almost none to extending from their throat to mid breast. Some of these patches are bright and stand out, while others have been patchy with gray on their sides.

warblerThe Warbler Guide
Tom Stephenson & Scott Whittle
Drawings by Catherine Hamilton

Warblers are among the most challenging birds to identify. They exhibit an array of seasonal plumages and have distinctive yet oft-confused calls and songs. The Warbler Guide enables you to quickly identify any of the 56 species of warblers in the United States and Canada. This groundbreaking guide features more than 1,000 stunning color photos, extensive species accounts with multiple viewing angles, and an entirely new system of vocalization analysis that helps you distinguish songs and calls.

The Warbler Guide revolutionizes birdwatching, making warbler identification easier than ever before. For more information, please see the author videos on the Princeton University Press website.

 

 

Just in Time for Migration Season: The Warbler Guide

The Warbler GuideWarblers are among the most challenging birds to identify. But, as we enter the fall migration season, Princeton University Press has the perfect tool for identifying these beautiful birds: The Warbler Guide.

This helpful guide enables readers to quickly identify any of the 56 species of warblers in the United States and Canada, with more than 1,000 stunning color photos, extensive species accounts with multiple viewing angles, and an entirely new system of vocalization analysis that helps you distinguish songs and calls.

This is the perfect tool for birdwatching, making warbler identification easier than ever before. But fear not: we are pleased to offer some of these tools to print, laminate, and take with you as you set out on your own adventures. Below, we have eight different finder keys – you can also download them in a complete set as a PDF or JPG. Additionally, we have a tip sheet on identifying the age and sex of warblers, including those from the West Coast. Take these with you on your next birdwatching trip, and then check out the complete Warbler Guide for additional information and insights.

 

Face Quick Finder

Face Quick Finder PDF | JPG

45 Degree Quick Finder

45 Degree Quick Finder    PDF | JPG

East Fall Quick Finder

East Fall Quick Finder        PDF | JPG

East Spring Quick Finder

East Spring Quick Finder    PDF | JPG

Side Quick Finder

Side Quick Finder PDF | JPG

Undertails Quick Finder

Undertails Quick Finder     PDF | JPG

Underview Quick Finder

Underview Quick Finder     PDF | JPG

West Quick Finder

West Quick Finder PDF | JPG

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Browse Our New Politics Catalog

Our new Politics catalog includes a comprehensive look at human rights laws and institutions, an examination of the role social media plays in our democracy, and a guide to forming opinions on some of the most controversial topics currently under the spotlight.

If you’ll be at APSA 2017 in San Francisco, please join us at Booth 511, or stop by any time to see our full range of politics titles and more.

 

Kathryn Sikkink makes the case that, yes, human rights work. Drawing on decades of research and fieldwork, this book provides a rigorous rebuttal to pessimistic doubts about human rights laws and institutions, demonstrating that change comes slowly and as the result of struggle. Evidence for Hope looks at how these essential advances can be supported and sustained for decades to come.

As the Internet grows more sophisticated, it is creating new threats to democracy. In his revealing new book, Cass Sunstein shows how today’s Internet is driving political fragmentation, polarization, and even extremism—and what can be done about it. In addition, Sunstein proposes practical and legal changes to make the Internet friendlier to democratic deliberation.  Once finished, readers will understand why #Republic need not be an ironic term.

Let’s be honest, we’ve all expressed opinions about difficult hot-button issues without always thinking them through. With so much media spin, political polarization, and mistrust of institutions, it’s hard to know how to think about these tough challenges, much less what to do about them. One Nation Undecided takes on some of today’s thorniest issues and walks you through each one step-by-step, explaining what makes it so difficult to grapple with and enabling you to think smartly about it. No other book provides such a comprehensive, balanced, and accessible analysis of these urgent social controversies.

Bird Fact Friday — The Sword-billed Hummingbird

From page 134 of Wildlife of Ecuador:

The Sword-billed Hummingbird has the longest bill in proportion to its body of any bird on earth. Reaching up to 11cm (4.25in) long, the bill nearly equals the length of its large body. Males are solid green, and females are speckled white and green from throat to belly; both have a brown-bronzy shine on the head.

The Sword-billed Hummingbird

The Sword-billed Hummingbird (Ensifera ensifera) mid-flight. Photo credit: Andres Vasquez, Tropical Birding Tour.

The species has coevolved with long tubular flowers to be their exclusive pollinator; it favors red Datura flowers and Purple Passionflower, or Taxo. Pleasingly, this stunner visits feeders and is fairly common throughout its range, which stretches along both slopes from 2,500m to about 3,400m (8,200–11,150ft). It is present close to small towns and in agricultural areas that grow its favored flowers as ornamentals.

Andrés Vásquez Noboa
Photography by Pablo Cervantes Daza
Preview a Chapter

Mainland Ecuador’s spectacular wildlife makes it a magnet for nature tourists, but until now there hasn’t been a go-to, all-in-one guide geared to the general reader. With this handy and accessible guide, visitors now have everything they need to identify and enjoy the majority of birds and animals they are likely to see. Written and illustrated by two of Ecuador’s most experienced nature guides and photographers, this book covers more than 350 birds, mammals, amphibians, and reptiles. It features over 400 stunning color photographs and includes a range map for each species, as well as a brief account of the country’s natural history and biogeography. With its extensive coverage, attractive and easy-to-use layout, beautiful photographs, and nontechnical text, this is an essential guide for anyone who wants to explore the natural wonders of Ecuador.

Omnia El Shakry: Psychoanalysis and Islam

Omnia El Shakry‘s new book, The Arabic Freud, is the first in-depth look at how postwar thinkers in Egypt mapped the intersections between Islamic discourses and psychoanalytic thought.

What are the very first things that pop into your mind when you hear the words “psychoanalysis” and “Islam” paired together?  For some of us the connections might seem improbable or even impossible. And if we were to be brutally honest the two terms might even evoke the specter of a so-called “clash of civilizations” between an enlightened, self-reflective West and a fanatical and irrational East.

It might surprise many of us to know, then, that Sigmund Freud, the founding figure of psychoanalysis, was ever-present in postwar Egypt, engaging the interest of academics, novelists, lawyers, teachers, and students alike. In 1946 Muhammad Fathi, a Professor of Criminal Psychology in Cairo, ardently defended the relevance of Freud’s theories of the unconscious for the courtroom, particularly for understanding the motives behind homicide. Readers of Nobel laureate Naguib Mahfouz’s 1948 The Mirage were introduced to the Oedipus complex, graphically portrayed in the novel, by immersing themselves in the world of its protagonist—pathologically erotically attached and fixated on his possessive mother. And by 1951 Freudian theories were so well known in Egypt that a secondary school philosophy teacher proposed prenuptial psychological exams in order to prevent unhappy marriages due to unresolved Oedipus complexes!

Scholars who have tackled the question of psychoanalysis and Islam have tended to focus on it as problem, by assuming that psychoanalysis and Islam have been “mutually ignorant” of each other, and they have placed Islam on the couch, as it were, alleging that it is resistant to the “secular” science of psychoanalysis. In my book, The Arabic Freud, I undo the terms of this debate and ask, instead, what it might mean to think of psychoanalysis and Islam together, not as a “problem,” but as a creative encounter of ethical engagement.

What I found was that postwar thinkers in Egypt saw no irreconcilable differences between psychoanalysis and Islam. And in fact, they frequently blended psychoanalytic theories with classical Islamic concepts. For example, when they translated Freud’s concept of the unconscious, the Arabic term used, “al-la-shuʿur,” was taken from the medieval mystical philosopher Ibn ʿArabi, renowned for his emphasis on the creative imagination within Islamic spirituality.

Islamic thinkers further emphasized similarities between Freud’s interpretation of dreams and Islamic dream interpretation, and they noted that the analyst-analysand (therapist-patient) relationship and the spiritual master-disciple relationship of Sufism (the phenomenon of mysticism in Islam) were nearly identical. In both instances, there was an intimate relationship in which the “patient” was meant to forage their unconscious with the help of their shaykh (spiritual guide) or analyst, as the case might be. Both Sufism and psychoanalysis, then, were characterized by a relationship between the self and the other that was mediated by the unconscious. Both traditions exhibited a concern for the relationship between what was hidden and what was shown in psychic and religious life, both demonstrated a preoccupation with eros and love, and both mobilized a highly specialized vocabulary of the self.

What, precisely, are we to make of this close connection between Islamic mysticism and psychoanalysis? On the one hand, it helps us identify something of a paradox within psychoanalysis, namely that for some psychoanalysis represents a non-religious and even atheistic world view. And there is ample evidence for this view within Freud’s own writings, which at times pathologized religion in texts such as The Future of an Illusion and Civilization and Its Discontents. At the same time, in Freud and Man’s Soul, Bruno Bettelheim argued that in the original German Freud’s language was full of references to the soul, going so far as to refer to psychoanalysts as “a profession of secular ministers of souls.” Similarly, psychoanalysis was translated into Arabic as “tahlil al-nafs”—the analysis of the nafs, which means soul, psyche, or self and has deeply religious connotations. In fact, throughout the twentieth century there have been psychoanalysts who have maintained a receptive attitude towards religion and mysticism, such as Marion Milner or Sudhir Kakar. What I take all of this to mean is that psychoanalysis as a tradition is open to multiple, oftentimes conflicting, interpretations and we can take Freud’s own ambivalence towards religion, and towards mysticism in particular, as an invitation to rethink the relationship between psychoanalysis and religion.

What, then, if religious forms of knowledge, and the encounter between psychoanalysis and Islam more specifically, might lead us to new insights into the psyche, the self, and the soul? What would this mean for how we think about the role of religion and ethics in the making of the modern self? And what might it mean for how we think about the relationship between the West and the Islamic world?

FreudOmnia El Shakry is Professor of History at the University of California, Davis. She is the author of The Great Social Laboratory: Subjects of Knowledge in Colonial and Postcolonial Egypt and the editor of Gender and Sexuality in Islam. Her new book, The Arabic Freud, is out this September.

PUP Celebrates The Total Eclipse with Three Giveaways

In celebration of the solar eclipse on August 21, Princeton University Press will be hosting three giveaways. If you’d like the chance to learn more about astronomy after next week’s solar event, you’re in luck. We’ll be giving away three of our favorite books via Goodreads:

These giveaways will run through Tuesday, August 22.

Welcome to the Universe Searching for the Oldest Stars The Cosmic Cocktail

Bird Fact Friday – A Look at Pied-billed Grebes

From page 74 of Wildlife of Ecuador:

Superficially like a short-tailed duck in general shape and habits, [the Pied-billed Grebe] shows a quite obvious dark band across a pale, cone-shaped bill. The overall coloration is rich or grayish buff-brown, lighter on the flanks and darker on the wings. This grebe is found exclusively on water, inhabiting ponds, lakes, and estuaries in the western lowlands and large lakes in highlands.

The Pied-billed Grebe

The Pied-billed Grebe (Podilymbus podiceps)Photo by Sam Woods, Tropical Birding Tours & samwoodsbirding.blogspot.com

It is fairly confiding, rarely flying when disturbed, and rarely comes ashore. Grebes walk with difficulty because their legs are located near the rear end of the body, which works great for swimming and diving but not for walking. They feed on invertebrates and fish, which are caught when diving up to several feet underwater.

Wildlife of Ecuador
Andrés Vásquez Noboa
Photography by Pablo Cervantes Daza
Preview a Chapter

Mainland Ecuador’s spectacular wildlife makes it a magnet for nature tourists, but until now there hasn’t been a go-to, all-in-one guide geared to the general reader. With this handy and accessible guide, visitors now have everything they need to identify and enjoy the majority of birds and animals they are likely to see. Written and illustrated by two of Ecuador’s most experienced nature guides and photographers, this book covers more than 350 birds, mammals, amphibians, and reptiles. It features over 400 stunning color photographs and includes a range map for each species, as well as a brief account of the country’s natural history and biogeography. With its extensive coverage, attractive and easy-to-use layout, beautiful photographs, and nontechnical text, this is an essential guide for anyone who wants to explore the natural wonders of Ecuador.