The Pacific Crest Trail and Its Wild Communities

by Katie Poore

Photo from visitcalifornia.com

A few weeks ago, one of my closest friends finished a thru-hike of the Pacific Crest Trail, the 2,650-mile footpath that snakes its way from Campo, California on the Mexican border to Mansfield Park, a few miles into Canada. It follows—as the name suggests—the crests of some of the West’s grandest mountain ranges: the Cascades in the Pacific Northwest, the Sierra Nevadas further south. It meanders through the Mojave Desert in southern California.

Ever since I read Cheryl Strayed’s 2012 memoir Wild: From Lost to Found on the Pacific Crest Trail as a fourteen-year-old, this footpath has occupied something of a sacred space in my imagination. And I am, evidently, not the only one. The trail granted 4,000 long-distance permits in 2016, the majority given to those intending to thru-hike—or walk the entire length of—the trail. Outside Magazine reports that the release of Wild’s 2014 film adaptation resulted in a 300% increase in web traffic on the official PCT website. If you’ve watched Netflix’s new installment of Gilmore Girls, you might recall a few scenes where Lorelai decides to remake her over-complicated life by following in Strayed’s footsteps. As she staggers to the PCT trailhead, however, she is greeted by a hoard of middle-aged divorcées and otherwise unsatisfied women with precisely the same idea. “Book or movie?” they ask each other. Gilmore Girls paints this journey as a kitschy one, the modern woman’s cliché strategy for shrugging off a mid-life crisis and walking off crappy ex-husbands. But here’s what’s true about those women, and the real people who hike this trail: most of them are there to remake themselves, to realize something, even if they don’t know what that something is just yet.

One can believe or not believe in this kind of spiritual journey, but it’s nonetheless an idea whose roots run deep in American soil. Think of Henry David Thoreau and Ralph Waldo Emerson and John Muir, of Robert Frost and Emily Dickinson and Walt Whitman. Consider Annie Dillard. Wendell Berry. Mary Oliver, whom the New York Times calls “one of the best-selling poets in the country.” Narratives of a redemptive natural world are everywhere. American wilderness, it seems, is nothing if not a spiritual and intellectual treasure trove. Where the flora and fauna run wild, these writers suggest, so may our souls. Read more »



Book Review: Drink More Wine! A Simple Guide to Peak Experiences NOW

by Dwight Furrow

It’s the holiday season and time to think about presents for the budding wine lover in your life. Of course, any season is the right time to think about that. You should always support your local wine lover. One place to begin is this compelling book by long-time food critic Jon Palmer Claridge entitled Drink More Wine! A Simple Guide to Peak Experiences Now. Most books on wine are meant to inform. This book is no exception, but it is also meant to inspire. It performs both tasks admirably and raises a philosophical issue to ponder as well.

Claridge delivers essential information about varietals and wine regions in easily digestible, bit-sized morsels along with helpful advice on topics such as how to read a wine label, wine and food pairings, setting up wine tastings, storing and serving wines. He covers just enough grape varietals and regions to pique the interest of people new to wine without weighing things down with too much information. (There are, thankfully, no dissertations on soil types or yeast strains.) He manages an authoritative voice without sounding like a snob and most of this information is disseminated via charming, personal vignettes from his extensive travel and entertainment experiences. Most helpful are his recommendations for wines that are affordable and available at even modestly well-stocked wine stores thus avoiding the common complaint that wine writers focus on wines that ordinary consumers can’t find. His advice about buying budget wine in the supermarket is particularly helpful. (Tip: Beware the bait and switch. Stores will use high scores from one superior vintage to sell that wine from a different vintage). Read more »

Stuck, Ch 6. Nowhere to Run: Bob Seger, “Night Moves”

Stuck is a weekly serial appearing at 3QD every Monday through early April. The Prologue is here. The table of contents with links to previous chapters is here.

by Akim Reinhardt

Image result for saturnWhen a song gets really stuck in my head, I break it down. I learn how to play it and even ponder ways to fiddle with it and improve it. In the throes of involuntary obsession, it gives me something to do. It’s a coping mechanism, a way to retain my sanity. And for this project, it also means writing, at least a little bit, about the song and artist. To create some context.

But I don’t need to talk about “Night Moves,” or any of a dozen other radio staples by Bob Seger. Why? Because Bob Seger is already a part of you, me, and everyone else. Bob Seger has sold over 50,000,000 albums.

Jesus, what kind of figure is that? 50,000,000. Is that a real number? If it does exist, where would I find that number? Somewhere between the Sun and Saturn, I reckon.

But even if you’re not among the many millions who’ve purchased a Bob Seger album during the last 40 years, he is still woven into every American’s existence. Even if you don’t listen to “classic rock,” or you’re a younger person who can’t put his name to his songs, you still know his music. You know Bob Seger even if you don’t know you know Bob Seger. Because if you’ve ever walked down the aisle of a supermarket, loitered in a 7-11, or simply stood there and pumped your gas, then you’ve heard more Bob Seger than you could possibly imagine. He’s had so many successful songs that simply listing them all would be tedious. Read more »

Monday, December 9, 2019

Taking Philosophy into the Field

by Robert Frodeman and Evelyn Brister

People sometimes express confusion about what public philosophy is. We see the point as straightforward: it’s a matter of location. Public philosophy consists of all those efforts that aren’t centered on university life. Public philosophers write op-eds for newspapers, work on disability issues and penal reform, serve on expert committees for government agencies, teach in prisons and schools, and help community groups balance considerations of justice with economic development. But while the possibilities for public philosophy are infinite, the distinction is clear: are your attentions directed toward other philosophers? That’s academic philosophy. Are your efforts aimed at the wider world? That’s public philosophy.

We’re pluralists in our attitude toward public philosophy: all of these varieties are useful in a world that too often assumes that the answers to societal questions come down to science or economics. But we want to emphasize one particular strain of public philosophy: what we call field philosophy. By analogy with field science, field philosophers work on-site with non-philosophers over an extended period of time. These are philosophers who are not simply writing about public problems but are engaged in projects, working alongside people as they confront real-world issues.

In a recent 3QD piece, Scott F. Aikin and Robert B. Talisse sound dubious about the usefulness of public philosophy. They claim that public philosophy has a distressing retrospective quality: by commenting on a situation philosophers are likely to affect that situation, and so are engaged in a continual process of catch-up. We grant the point, but we fail to see it as a problem. Public philosophy does not only consist of external, after-the-fact historical commentary. Particularly in the case of field philosophy, it actively participates in making sense of unfolding cultural events and reveals the conflicting pulls that make for difficult decisions. This iterative loop forms part of the dynamics of thinking, where an account adjusts to changed circumstances. The philosopher thinks with the scientist, the engineer, the businessperson, or the stakeholders’ group. Adjustment in the face of real-world conditions is how things are supposed to work. Read more »

Perceptions

Charles “Teenie” Harris. Girl Reading on Stack of Pittsburgh Courier Newspaper, 1940.

In the current “Truthiness and News” exhibition at DeCordova Museum, Lincoln, MA.

Silver gelatin print.

Truthiness and the News explores the evidentiary role of photography, from the heyday of newsprint in the first half of the twentieth century to the current age of post-truth politics. Presaging the contemporary turn to “alternative facts” and “fake news,” photographs in print journalism have always offered a multiplicity of truths depending on when and how editors chose to print them. Featuring works from the 1940s to the present, this exhibition highlights photojournalists and socially engaged photographers, such as Charles “Teenie” Harris and Barbara Norfleet, alongside spreads from the newspapers and magazines that published their photographs, and contemporary works responding to the dissemination of the news today.

More here, here, and here.

Pomegranates, or The Psychopharmacology of Everyday Myth

by Rafaël Newman

And the children of the moon / Were like a fork shoved on a spoon

Hedwig and the Angry Inch

1.

The goddess Demeter, having received the Earth as her domain in the post-Titanic dispensation that followed the parricidal murder of her father Kronos, had mated with her brother Zeus, lord of the Sky, and borne a daughter, Persephone, whom she adored. Their brother Hades, meanwhile, whose dominion was the Underworld, was as yet without a wife; and his gaze now fell on his niece, Persephone. With his brother Zeus’s connivance he kidnapped the object of his desire, whereupon her mother Demeter subsided into melancholy and perpetual winter was visited upon the Earth: until an agreement was reached, to forestall the death of all creatures, and Persephone was allowed to return to the surface, on condition that she not have eaten anything while below. But Hades had in fact persuaded her to swallow six pomegranate seeds; and thus she was condemned to return to the Underworld henceforth for six months of the year, during which period her mother, Demeter, mourned for her, and the Earth was cast into darkness, and cold.

My daughter saw it immediately. We had just spent a week in Istanbul, and our daily dose of nar suyu, fresh-squeezed pomegranate juice, was still a pleasant sense memory; so she was primed to spot the plump fruit on the poster in the lobby of the cinema where we had gone to see Dora, oder die sexuellen Neurosen unserer Eltern (“Dora, or The Sexual Neuroses of Our Parents”). This was the pomegranate that had afforded her so much pleasure in Asia Minor, and which is reputed to have been the snake’s gift to Eve, and thus hers to Adam, in the Garden of Eden. This particular pomegranate, however, was part of a story of natural origins from a different cultural tradition, but was to prove no less my fruit of knowledge that evening as I began to decipher Stina Werenfels’ retelling of a myth central to western culture. A myth about fertility, and death, and love, and sex. And food. Read more »

The Responsibility Of Intellectuals Who Teach

by Eric J. Weiner

There are two ways to be fooled. One is to believe what isn’t true; the other is to refuse to believe what is true. ― Soren Kierkegaard

A lot has changed since 1967, the year Noam Chomsky published “The Responsibility of Intellectuals.” His essay threw damning shade at the intelligentsia—particularly those in the social and political sciences—as well as those that supported what he called the “cult of expertise,” an ideological formation of professors, philosophers, scientists, military strategists, economists, technocrats, and foreign policy wonks, some of who believed the general public was ill-equipped (i.e., too stupid) to make decisions about the Vietnam war without experts to make it for them. For others in this cult, the public represented a real threat to established power and its operations in Vietnam, not because they were too stupid to understand foreign policy, but because they would understand it all too well. They had a sense that the public, if they learned the facts, wouldn’t support their foreign policy. Of course, in retrospect, we know that this is exactly what happened. Once the facts of the operation leaked out or were exposed by Chomsky and others like him, the majority of people disagreed with the “experts.” Soon there were new experts to provide rationalizations for why and how the old experts got it wrong, but not before a groundswell of popular protest and resistance turned the political tide and gave a glimpse at the power of everyday people—the “excesses of democracy”—to control the fate of the nation and the world.

Chomsky has consistently been confident that people who were not considered experts in foreign affairs were as capable if not more so to decide what was right and wrong without the expert as a guide. This is one of the things that continues to make Chomsky such a threat to the established order. He has faith in the public’s ability to think critically (i.e., reasonably, morally, and logically) about foreign affairs and other governmental actions at the local and national levels. For Chomsky, the promise of democracy begins and ends with the people. He does not have the same confidence that those in positions of power will give the public the facts so that they can make good and reasonable decisions. But this does not mean that Chomsky uncritically embraces the public simply because it is the public. He does not support, nor has he ever, the cult of willful ignorance; that is, those members of the public—experts, intellectuals or laypeople—who, as Kierkegaard wrote, “refuse to believe what is true.” Read more »

The Cancer Questions Project, Part 19: Mark Heaney

Dr. Mark Heaney is a hematologist and an active principal investigator of several clinical trials that have aimed at developing novel treatments for leukemia. His research has focused on metabolic differences between leukemia cells and normal cells that can provide understanding into how leukemias behave in the individual patient and how they respond to treatment. He chiefly focussed on the new treatments of the myeloproliferative neoplasms, primary myelofibrosis, polycythemia vera and essential thrombocythemia, however, has also studied new treatments for chronic myeloid leukemia, mastocytosis and Langerhans cell histiocytosis in keeping with his clinical expertise in rare blood cancers. He currently serves as Professor of Medicine and Director of Hematology and Medical Oncology Fellowship Program at Columbia University Medical Center.

Azra Raza, author of The First Cell: And the Human Costs of Pursuing Cancer to the Last, oncologist and professor of medicine at Columbia University, and 3QD editor, decided to speak to more than 20 leading cancer investigators and ask each of them the same five questions listed below. She videotaped the interviews and over the next months we will be posting them here one at a time each Monday. Please keep in mind that Azra and the rest of us at 3QD neither endorse nor oppose any of the answers given by the researchers as part of this project. Their views are their own. One can browse all previous interviews here.

1. We were treating acute myeloid leukemia (AML) with 7+3 (7 days of the drug cytosine arabinoside and 3 days of daunomycin) in 1977. We are still doing the same in 2019. What is the best way forward to change it by 2028?

2. There are 3.5 million papers on cancer, 135,000 in 2017 alone. There is a staggering disconnect between great scientific insights and translation to improved therapy. What are we doing wrong?

3. The fact that children respond to the same treatment better than adults seems to suggest that the cancer biology is different and also that the host is different. Since most cancers increase with age, even having good therapy may not matter as the host is decrepit. Solution?

4. You have great knowledge and experience in the field. If you were given limitless resources to plan a cure for cancer, what will you do?

5. Offering patients with advanced stage non-curable cancer, palliative but toxic treatments is a service or disservice in the current therapeutic landscape?

The General and the Attorney General

by Michael Liss

How do you feel about an Imperial Presidency?  

Attorney General William Barr has been on a bit of a bender recently. He’s suggested that communities that are critical of law enforcement will lose police protection, disagreed with the Inspector General’s report about the FBI and the Russia investigation, and warmed the hearts of the faithful at Notre Dame in decrying a “war on religion.”

While Mr. Barr rarely fails to make news, his most consequential opinions came in a speech he gave to the Federalist Society on November 15, 2019, in which he went on, at some length, as to why he supports the broadest possible interpretation of Presidential powers. 

If you have read reports about Mr. Barr’s remarks, you probably already know they have been criticized for their ferocious partisanship. There is unquestionably a considerable amount of energy devoted to critiquing those who get in President Trump’s way (Congress, the federal courts, Progressives, and private citizens who exercise their right of free speech). But Mr. Barr is not only a man of intensity, he is also one of words (over 6000 here), and, when moved to talk about substance, he has a lot to say. You can find the text on the Department of Justice website. Read more »

A list of books of some sort or another

by Dave Maier

Here we have either a) a holiday gift guide; b) just another ordinary book roundup; or c) a bunch of mini-reviews each of which just didn’t have the oomph to deserve its own post. Answer provided below!

First up:

Theodore M. Bernstein – Miss Thistlebottom’s Hobgoblins: The Careful Writer’s Guide to the Taboos, Bugbears, and Outmoded Rules of English Usage (1971)

Rodney Huddleston and Geoffrey K. Pullum – A Student’s Introduction to English Grammar (2005)

I rarely read Columbia’s alumni magazine, but I did happen to see an interesting exchange (“Verbal Dispute”) in the Feedback section of the Fall 2019 issue. Apparently the cover of the previous issue had read “About 8 million tons of plastic ends up in the ocean every year,” and, perhaps not surprisingly, numerous quasi-literate chuckleheads had conveyed their righteous outrage at the offense to grammar so publicly displayed. Two are quoted; one explains to us that “‘Tons’ is a plural subject that takes the plural verb ‘end up,” continuing witheringly, “Are you a native English speaker? From California? [ooh, snap!] Are you intent on sabotaging Columbia or unqualified and irresponsible?” and so on.

The editor’s response is at once coolly civil and delectably devastating.

While it is certainly true that “end up” is the standard plural form, a singular verb is often used instead when the subject is a phrase that can be viewed as a single unit. This is particularly common when the subject is an expression of quantity or measure, as in “eight million tons.”

He then provides supporting examples from the above authors. I’ve listed the Huddleston and Pullum book I own; the actual quote is from their previous work, The Cambridge Grammar of the English Language (2002), on which the former is based. Their examples are simply brutal. (Try to say these sentences out loud with the plural form of the verb; you won’t even be able to.)

Twenty dollars seems a ridiculous amount to pay to go to the movies. Five miles is rather more than I want to walk this afternoon. Three eggs is plenty. [Yow.]

From Bernstein’s book (which I immediately ordered upon reading this):

You would not [or, you know, maybe you would, if you were a quasi-literate chucklehead] write “Three inches of snow have fallen,” because you are not thinking of individual inches; you are thinking of a quantity of snow that accumulates to that depth. Likewise you would not write “About $10,000 were added to the cost of the project,” because again you are thinking of a sum of money, not of individual dollars.

I’m tempted to quote as well what Huddleston and Pullum say about singular uses of “they,” because it also combines definitive analysis with deliciously polite snark, but let’s move on. Read more »

On the Road: Ngorongoro Crater

by Bill Murray

Godfrey points the Land Rover toward Ngorongoro Crater. The road is fine to lull the unwary, but before you know it there is one lane, then no tarmac, then mud and potholes and empty hills.

Close cropped with a natty little mustache, Godfrey is kempt, forties, paunch-softened,  with an easy smile. A veteran guide, he has been here before. Says it will take five hours to do the 250 kilometers to the crater and so it does.

No package tour jets preceded us when we flew into Kilimanjaro International Airport aboard a small plane from Nairobi, so the airport bank wasn’t open. Consequently, we have no Tanzanian Shillings.

Oxen pull plows across the fields. Buses are occasional and private cars are rarer than cows. At the time of this visit (several years ago), the road is primarily for foot traffic, human and animal. No matter how far from a village, people are everywhere walking on the roads, always. They only move to the verge, reluctantly, when a Land Rover thunders by.

The few vehicles you do pass are either chock full of ride-sharing local folks, or they’re hauling two or three white Europeans on safari, or maybe they’re jeeps that read something like, “Africa Wildlife Research Project, funded by Belgian government.”

What do you know, way out here Godfrey knows where to buy a few beers. Two hot Tuskers from Kenya, two hot Safari beers from Tanzania, a roadside bodega, no power, no refrigeration, just a handful of dusty beers on a shelf for four for five dollars at an anonymous shack, friendly enough, opaque to a stranger. Godfrey’s got this round. Read more »

Stations of the mind: Om to Eureka and beyond

by Bill Benzon

I’ve been thinking about it a lot recently, how we regulate our minds. It can be simply things, like listening to some music, taking a walk, taking a few deep breaths, a time-out, maybe we take in a movie, or have some coffee, wine or liquor? perhaps smoke some weed – it’s legal now in America, at least in some states. Maybe one meditates, perhaps every now and then, perhaps daily; perhaps you go on a retreat for a week, a month, two or three. One can see a shrink, get a prescription or two. Read a good novel? Take an evening class at the local community college. For that matter, isn’t education about training the mind?

It’s what we do, one of the things. Regulating the mind. The list could grow and grow.

But I’ve got something more specific in mind. I’m interested in those various moments either when: one’s mind impresses itself on you as a stranger, as something perhaps a little perhaps a lot foreign, or you take a leap to see whether or not your mind will catch you. Welcome to your mind. And welcome to the world.

Herewith I offer a collection of experiences. I’m embarrassed to say that they’re my own. I don’t regard them as particularly special. They’re just the experiences I know about. They span my life from about age four to perhaps thirty.

We all have such liminal experiences, each in our own way.

Fiddle-De-Dee

That’s the earliest more or less distinct memory I’ve got, Burl Ives singing that song. I’m told I played the record over and over, on one occasion driving my visiting Uncle Harry to distraction. As I note in the preface to Beethoven’s Anvil, “It is my mind’s tether to history, my umbilical to the world.“

Since that particular experience happened at the house on Cherry Lane, I would have to have been four years old or so at the time. Though, come to think of it, there is an exceedingly vague impression of the house in Ellsworth, where we’d lived before moving to Cherry Lane in Johnstown, Pa. Read more »

The tale of Joanne the Roomba, Or, does work have to be such…work?

by Sarah Firisen

When I moved into a new, larger apartment with my boyfriend a couple of months ago, I decided to buy a Roomba, robot vacuum cleaner. I named her Joanne. I love Joanne, my boyfriend is less of a fan. He finds her hour and a half or so a day moving around the apartment to be intrusive. He doesn’t appreciate me going around beforehand and picking his things off the floor so that she doesn’t get caught in them. When I was at work one day and she got stuck, it was a toss up whether he was going to rescue her or not – he did, but grudgingly. He says to me, “Why does she have to vacuum every day? You don’t vacuum every day”. My response, “Let’s set the bar a little higher than my housekeeping”. And it’s true, Joanne does takes a long time to do what I can do pretty quickly. And she can’t, and doesn’t get to every spot. On the other hand, she can get to spots under cabinets, or beds, that I can’t, or at least don’t get to. Does she clean as well in one session as a professional cleaner would? No. Does she clean better over the course of a week than I do, definitely. Read more »

Stuck, Ch. 5. Your America: Redbone, “Come and Get Your Love”

Stuck is a weekly serial appearing at 3QD every Monday through early April. A Prologue can be found here. A table of contents with links to previous chapters can be found here.

by Akim Reinhardt

Europeans spent 400 years killing, raping, lying to, and robbing Indigenous Americans. And then, when they’d taken most everything they wanted, they turned Native peoples into tokens, costumes, mascots, and fashion accessories. Like most fashion trends, it’s gone in cycles.

During the mid-19th century, when secretive men’s fraternal societies such as the Masons and Shriners became popular, the Improved Orders of Red Men was one such organization. Members occasionally dressed as make believe Indians and “whooped” it up. Although most people today have not heard of them, some Red Men societies held on until the late 20th century. Indeed, my own Baltimore neighborhood had a Tecumseh chapter building when I moved here in 2003.

By the early 20th century, dressing up as Indians had become a trendy pursuit for boys. The Boy Scouts promoted this appropriation, and it soon spread to countless summer camps across America. This childish cosplay was widespread during the first half of the Cold War, when Hollywood Westerns were at their peak of popularity, both in movie theaters and on TV. Countless backyard games of cowboys and Indians ensued, along with a fresh wave of children dressing up as both. Read more »

Monday, December 2, 2019

The Owl of Minerva Problem for Public Philosophy

by Scott Aikin and Robert B. Talisse

I.

The Owl of Minerva flies only at dusk. That’s a philosophical chestnut attributed to the German idealist, G.W.F. Hegel. It’s a poetic way of saying that wisdom is achieved only in hindsight. The Owl of Minerva, the representation of the goddess of wisdom, begins its activity only at the end of the day, only once the deeds in need of wisdom’s guidance are done. Our plan here is to present what we see as a central feature of why the Owl of Minerva must fly only at dusk and then turn that critical thought to some, by our lights, unjustifiably optimistic calls for public philosophy.

Let’s start with a pretty intuitive distinction between different kinds of things. There are, on the one hand, things that behave how they do independently of how we talk about them or how we classify them. So, Helium behaves that way it does regardless of who we talk about it or classify it. The same goes for plenty of other things – planets, microbes, physical substances, and so on. They take no heed of what we think about them and just do their own thing. On the other hand, there are things that behave differently when we classify or talk about them differently. For example, people are that way. If you talk about a group or an individual and they hear about it, they will often start behaving differently in light of what you said. Ian Hacking calls these two different kinds of things indifferent and interactive kinds, respectively. Interactive kinds are such that “the classification and the individual classified interact.”

But interaction isn’t a one-way street. When it comes to interactive kinds, how they behave can change how we think about them, too. There’s an informational loop, then, between our concepts of interactive kinds and individuals of those kinds. That looping phenomenon between concepts and kinds occasions interesting diachronic phenomena. In essence, our concepts of interactive kinds, so long as individuals of those kinds are responsive to the content of those concepts, will change the behavior of those individuals. The kind, because it is interactive with the concept, will, from the perspective of the conceptualizer, be a moving target. Our concepts, with interactive kinds, then, will always be incomplete, because as we develop them and make them explicit, we end up changing the way the interactive kind behaves. Read more »

Pentagonal Billiards and other Geometric Oddities

by Jonathan Kujawa

Each year my department hosts an all-day event for high school students interested in math. Nowadays we have approximately 400 students and 20-30 teachers join us from all across Oklahoma and north Texas. Some drive 2+ hours each way to come!

The students’ goal? Probably getting out of class is high on the list :-).

Our goal is for the students to have fun and see interesting math they are likely to have never seen before. More generally we hope the students see math as a lively, engaging, and creative subject with lots of interesting open questions which are areas of active research. It’s meant to be an antidote to the dusty, rigid, cut-and-dry subject they usually see in an educational system focused on standardized tests and the like.

Diana Davis

The highlight of the day, at least for me, is a talk by a visiting mathematician chosen for their reputation as an excellent speaker. It gives me an all-to-rare chance to hear a non-technical introduction to some cool math. This year we had the pleasure of hosting Diana Davis. Dr. Davis earned her Ph.D. from Brown University in 2013 and is now faculty at Swarthmore College. She gave a fantastic talk about playing billiards on a pentagonal billiard table.

Since we are mathematicians who are untroubled by the real world, we will always assume there is no friction nor spin to our billiard balls. This means the angle of incidence equals the angle of reflection and a ball can bounce around the table forever. We’ll also assume the table has no pockets and the ball never hits a corner. This is because our interest will be in understanding the trajectories a ball could take as it bounces around the table and pockets and corners would cause complications. A fundamental first question is if there is always a periodic trajectory: that is, a path that eventually repeats itself and, hence, repeats over and over forever. Read more »