by Jonathan Kujawa

But even my teacher would admit that’s not much of an upside. Certainly, I was more motivated by the sticker you got for hitting 100 than the counting itself.

Another downside is that you can’t count to every number. If you need to count to sixteen, you can do it with twos, but not fives or tens. This is fixable, though. We just need to agree that 1 can be included when we count, regardless of how we are counting. Then counting by fives turns into 16 = 15 + 1 or 16 = 10 + 1 + 1 + 1 + 1 + 1 + 1. If it makes you feel better, you can think of 1 as a sort of degenerate two, five, and ten.

With 1 in hand, we can count to any number we like, so the question becomes what are the fewest numbers we could use? To count to seven using twos, you could do it as 7 = 1+1+1+1+1+1 or 7=4+1+1+1, but plainly 7=6+1 is the smallest sum that works.  But that question is still rather dull, to be honest. It seems counting is unavoidably boring.

Or is it?

I’m bummed my math education never got around to some of the interesting ways to count.

For example, how about the square numbers:

1, 4, 9, 16, 25, 36, ….?

The first question is if you can even use these to count. That is, can you get to any number you like by adding up squares? Sure. Since we have 1, we can always just count by ones. The real question is if we can do better. In 1770 Lagrange proved that every natural number (that is, 0, 1, 2, 3, 4, 5, 6, 7, …) can be written as a sum of four or fewer squares. For example, 14 = 9 + 4 + 1. In modern terms, we would state Lagrange’s theorem by saying that

w² + x² + y² + z²

is universal. Read more »

by Brooks Riley

A soft-spoken, self-effacing young man from Seoul may be the most listened-to living composer on the planet right now, with two blockbuster works of cinema and TV on his resumé. Not only did Jung Jaeil compose the score for the Oscar-winning Parasite, but his subsequent gig, Squid Game, has just stormed into the record books: Seen and heard by hundreds of millions by now, it has become a global phenomenon, another sign of South Korea’s approaching and encroaching hegemony over all things cultural.

Learning more about the elusive Mr. Jung is not as easy as it would seem, even if he’s all over YouTube and even if his English, if you can find it, is as elegant and formal as it is fluent: Thank you so very much, he said last week upon receiving a prize for Squid Game (that inserted ‘so’  a rarity of politesse). His Wikipedia entry is woefully thin, and mystery shrouds his early life. Most of his interviews are in Korean and not subtitled, including a Q&A on stage with Bong Joon-ho, director of Parasite, who discovered Jung Jaeil through a 2014 film Bong wrote and produced, Sea Fog (Haemoo).

As obscure as his biography may be, the task of placing this peripatetic music maker inside a category is even more daunting. From an astonishingly early age, as a quasi auto-didact, he has straddled the yawning divide between pop and classical, performing in a funk band while immersing himself in the Western canon. He wrote his first film music at 15, for an R-rated movie he wasn’t even old enough to see. It’s been a long journey from funk to punk to the barefoot-performing monk he resembles today at 39, but Jung is a master of metamorphosis, his musical transformations enhanced by fluctuating involvements in social and global issues, historical commemorations, theatre, art installations and pop music, as well as his attention to traditional Korean music—all adding up to many more commitments than one might expect from any other producer of tonal atmosphere for worldwide box-office hits. Read more »

Mary Kuper. “… our curious type of existence here.”

“A response to the close of David Jones’s introduction to ‘In Parenthesis’

This writing is called ‘In Parenthesis’ because I have written it in a kind of spaces between — I don’t know between quite what— but as you turn aside to do something; and because for us amateur soldiers (and especially for the writer, who was not only amateur, but grotesquely incompetent, a knocker-over-of –piles, a parade’s despair) the war itself was a parenthesis— how glad we were to step outside its brackets at the end of ’18—and also because our curious type of existence here is altogether in parenthesis.”

More here, here, and here.

Thanks for the introduction Vicki Sharp!

by Peter Wells

In Philip Pullman’s 2019 novel The Secret Commonwealth, the hero, Lyra, aged around twenty, suffers an attempted rape. If I say it is the most convincing description of a sexual assault I have ever read, this is not to say much, as I have never been raped, though in my youth I had some unpleasant encounters with predatory men that gave me some inkling of it. Anyway, it’s a creditable effort by Pullman to depict a nightmare experienced much more often by women than by men, and he should be applauded for attempting to help his readers (male readers especially) to imagine it.

The scene begins in a train, where Lyra finds herself, far from her own country, in a carriage occupied by soldiers whose language she does not know. There have already been grins and nudges, and alcohol has started to circulate.

The bottle went around the compartment again; the talk became louder and looser. They were talking about her, there was no doubt about that: their eyes moved over her body, one man was licking his lips, another clasping the crotch of his trousers.

Lyra attempts to escape, only for the man opposite to push her back into the seat and say something to the man by the door,

who reached up and pulled down the blind over the corridor window. Lyra stood up again, and again the soldier pushed her back, this time squeezing her breast as he did so.

Then the assault proper begins, as all the soldiers launch themselves upon her. Read more »

by Brooks Riley

by Tim Sommers

This past Friday, 3 Quarks Daily linked to a review by George Scialabba of the recent posthumous publication of a Richard Rorty lecture series called Pragmatism as Anti-Authoritarianism. The review was called, “Should Philosophy Retire?” I promised myself I wouldn’t respond to it. That I wouldn’t respond, for example, to the claim that philosophy “led Western thought into a dead end and should be retired”.

Or Scialabba’s claim that Hume, Mill, and William James would agree with this, and Rorty’s that Dewey, Wittgenstein, and Heidegger would too. But when Scialabba went on to insist that Rorty is “widely-revered”, I had, at least to ask this much. “Widely-revered” by whom? Not by philosophers, surely.

But let me start by saying something positive about Rorty. Rorty is a clear, crisp, concise writer whose  prose style fits firmly within the analytic tradition. Analytic philosophers are seldom credited as great writers, but the best are great. “I prefer desert landscapes,” Quine said in explaining his thinking, but it might as well as been his prose he was describing. “To be is to be the value of a bound variable,” was his answer to the mystery of existence. “Science,” he wrote “ is not a substitute for common sense, but an extension of it.” And Donald Davidson, another great writer, spare but whimsical, famously wrote that “Conceptual relativism is a heady and exotic doctrine or would be if we could make good sense of it. The trouble is, as so often in philosophy, it is hard to improve intelligibility while retaining the excitement.” (Keep that one in mind for later.) Rorty had a similar style and a similar talent for turns of phrase. “The world does not speak,” he wrote, “Only we do.” Since Rorty was one of the few analytic philosophers widely read outside the field, I think he is, as a writer, if not a thinker, our prose emissary to the wider academic world.

It was Rorty’s argumentation that was infuriating. Read more »

A colorful denizen of Brixen, South Tyrol. Photo taken last week.

by Varun Gauri

Do most people care a whit about foreigners? Would they be willing to reduce their own countries’ well-being for the benefit of foreign nationals? Global cooperation entails a variety of incentive-compatible deals among nation-states, but it rests, ultimately, on cosmopolitan values. If people can’t be bothered with the citizens of other countries, the prospect for long-term, stable solutions to crises like climate change, pandemic diseases, migration, and trade policy may be bleak. 

In series of large, representative surveys from Spain, the United Kingdom, Germany, China, Japan, the United States, Colombia, and Guatemala, my recent paper with Xuechunzi Bai and Susan Fiske finds more support for moral cosmopolitanism than a quick scan of the news headlines might lead one to suspect. 

Broadly speaking, respondents everywhere distinguish preventing harm to foreign citizens, which almost everyone supports, from redistributing resources, which about half of respondents endorse. These two psychological dimensions of moral cosmopolitanism, equitable security (preventing harm) and equitable benefits (redistributing resources), are correlated with attitudes toward contested international policies, such as support for international organizations, reducing a nation’s carbon footprint, enforcing anti-bribery rules, and expanding international migration. The equitable benefits dimensions also predicts the likelihood of sending real resources to international, rather than domestic, NGOs, as well as support for the global distribution of masks to fight Covid-19. The equitable security dimension predicts responses to a thought experiment protecting foreigners, as well as support for vaccinating the world against Covid-19. In short, people tend to temper their altruism with a dose of moral parochialism, or patriotism, when redistributing benefits, but they are moral altruists when preventing harms.  Read more »

by David Oates

A scar is a shiny place with a story.

A skink is a story you could never imagine.

It leaves a bright streak across your vision and an after-image you might notice even years later, neon greeny blue flashing amidst weed and dry stone and buckbrush and bending sumac trees. Our mountains were called the San Gabriels, a name somehow just barely noble enough for these creatures. In their foothills skinks appeared to us like tiny fragile dragons, fully astonishing, sinuous, and menacing. They liked to writhe. Would bite, the bony jaws clamping onto a fingertip, a ten-year-old’s screaming terror – until it was seen that the grim little mouth could not break the skin. The beast just hung on there, flailing, until screams turned to laughter and showing off, “Lookit, lookit, lookit. . .!”

If someone tried to tell you about skink, it would sound like a lie, an exaggeration. Just seeing it certainly outstripped the lame awe-mongering of, for example, Superman comic books.

And made you wonder what else might be out there.

When my mother’s voice rose up on a summer eve, and we had been allowed to play outside after dinner. When I noticed the mourning doves silhouetted on telephone wires above us, repeating and repeating their strangeness and sadness. Perhaps I would see her standing in the illuminated doorway, in the warm air full of chaparral scent drifting downhill off the mountains. Her voice calling then falling still, while the blue-black sky gathered evening under itself. And us in it.

Then the boys would come barging back into the house, and the mood would break and be replaced with all the reassuring commotion we could muster.

 Once in a while my mom would accidentally back into the truth, like hitting something in the garage with her fender. “Well, we raised them by hand, so. . .” This was not really apology, just what we were: three dusty, slightly used boys, with dents here and there and unstraightened teeth. Read more »

by Pranab Bardhan

All of the articles in this series can be found here.

When I first attended the occasional Harvard-MIT joint faculty seminar I was dazzled by the number of luminaries in the gathering and the very high quality of discussion. Among the younger participants Joe Stiglitz was quite active, and his intensity was evident when I saw Joe chewing his shirt collar, a frequent absent-minded habit of his those days. Sometimes one saw the speaker incessantly interrupted by questions, say from one of the big-name Harvard professors, Wassily Leontief (soon to be a Nobel laureate). At Solow’s prodding I agreed to present a paper at that seminar, with a lot of trepidation, but fortunately Leontief was not present that day.

At Harvard the economist I knew best was Steve Marglin whom my friends, George Akerlof and Mrinal, had introduced me to. He was at that time regarded as a whiz kid who was one of the youngest tenured professors at Harvard. He had earlier spent some time in India and became an admiring friend of Punjab’s strong-man Chief Minister Partap Singh Kairon. He was very friendly with me and Kalpana (Steve gave her useful comments on her dissertation), but I had seen him behaving somewhat abrasively with others, including senior professors.

Steve’s early work was on investment and evaluation of development projects. Then by the late 60’s his research and politics took a major turn in a heterodox, radical direction. When he gave me the first draft of his later widely-known paper titled “What Do Bosses Do?”—arguing that the Industrial Revolution was less a technological advance and more an organizational restructuring, with capitalists getting dominant control of the labor process– I was quite impressed reading it. Read more »

by Charlie Huenemann

Over years of teaching philosophy, I have observed that people fall into two groups with regard to the Biggest Question. The Biggest Question is one that is so big it is hard to fit into words, but here goes: When everything that can be explained has been explained, when we know the truths of physics and brains and psychology and social interactions and so on and so forth, will there still be anything worth wondering about? I am assuming the “wonder” here is a philosophical wonder, not the sort of wonder over whatever happened to my old pocket knife or whatever. It’s the sort of wonder that has a “why-is-there-something-rather-than-nothing” flavor to it. It’s the sort of wonder that doesn’t go away no matter how much is explained.

Some people think that on that sunny day when everything that can be explained has been explained, well then, that will be that. We will understand why things have happened, and how we came to exist, and what we should do if we want to be healthy and happy, and why works of art move us as they do. It’s not that such people are in any way shallow or unimaginative or tone deaf. They are open to the most wonderful experiences of life, along with the most heart-wrenching and most tragic. It’s just that they think these experiences can be explained and understood in all their glory through that explanation. If there is anything “left over” — some stubborn bit of incredulous wonder we just can’t shake — then that too will be explained through some feature of human psychology, like the way those patterns still seem to swirl in a static optical illusion even when you know the trickery behind it. The feeling that there is a Mystery can itself be explained as an illusory sort of feeling, an accidental by-product of the cognitive engine we happen to think with.

But other people think that the Mystery is not an illusion or accident, and that there still would be something worthy of genuine philosophical wonder even when the grand explainers have completed their grand task. Maybe the Mystery is worthy of some kind of worship or spiritual reverence. Maybe it can be reflected in a poem or in music or in a painting, or even in a shared and silent moment with friends. Maybe it is exactly what remains when all explaining is done — as Wittgenstein the Sage once wrote, “Not how the world is, is the mystical, but that it is”. In his terms, the Mystery is precisely that of which we must remain silent, simply because no amount of talking will capture it. These people would say that the first group of people are the ones with the illusion: namely, the illusion that what can’t be explained isn’t real. Read more »

by John Allen Paulos

In politics, business, and education, the issue of how to ensure proportional representation of groups is often salient. A salient issue, but usually an impossible task. Why?

Since group identity and wokeness arouse so much emotion, a “geologic upheaval of thought” as Proust characterized it, it’s probably best to discuss a couple of simple illustrative scenarios abstractly. Consider, for example, a well-meaning institution, the Earnest Enterprises Foundation say, operating in a community that contains a numerically dominant majority group, Maj, and two subgroups – a substantial minority group, Min, and a smaller minority group, Sm, which has members in group Maj as well as members in group Min.  Let’s assume that the group Maj constitutes 75% of this imaginary community, Min the remaining 25%, and let’s also assume that 10% of the community belongs to group Sm, whose members are known to be somewhat marginalized and less likely to self-identify as Sm, self-identity being a somewhat nebulous notion. This latter assumption introduces complications since the extent to which the groups differ, self-identify, and intersect is unknown to the foundation or even to the community. Let’s further assume that only 4% of group Min members self-identify as Sm and 8% of the group Maj members self-identify as Sm.

Making a well-intended attempt to assemble a workforce of 1,000 which “fairly” reflects the community, the foundation most naturally (but not necessarily) prioritizes the Maj-Min dichotomy and hires 750 members of group Maj and 250 members of group Min. But this is problematic since just 10 members of the group Min (4% of 250) would self-identify as being in group Sm, AND 60 members of the group Maj (8% of 750) would self-identify as being in group Sm. Thus ONLY 70 or 7% of all 1,000 workers would be self-identified members of group Sm.

It follows that, despite their best efforts, Earnest Enterprises would still be liable to charges of bias. It could obviously be accused by its Min employees of being anti-SM since only 4% of the Min employees (10 of 250) would be in group Sm, not the assumed community‑wide 10%. Interestingly, the foundation’s group Sm employees could likewise claim that the foundation was anti-Min since only 14.3% of the self-identified Sm members (10 of 70) would be from group Min, not the community‑wide 25%. Read more »

“Facts are surprisingly delible things.”
………….— Bill Bryson, author

“Trump won.”
……….…— Fox Skews

Facts Are Delible

facts are not indelible after all—
imagine that

now U S headspace is one of delibility,
if such a word exists
—but of course it may, nothing
moors every word to dictionaries:
fresh definition embraced, case closed.
now we just say: fact’s indelibility is erased

what’s interesting though is that
those who scorn indelible facts
genuflect before them when fact is essential
—no heart transplant’s performed through routines
of delible facts, that’s a certainty; nor have
kidneys enjoyed dialysis through ignorance,
or deliberate, delible inconstancy
—nor does any pact, personal or political
survive in a miasma of delible truth or law
by which, instead, we suffer lives of
tooth and claw

Jim Culleny
11/19/21

by Nicola Sayers

Clickety clack, clickety clack. All aboard the twilight train, a Scottish man with a deep voice announces over the sound of a train heading off into the night. This story is the only one on the Moshi app that I can happily listen to over and over as I wait for my kids to fall asleep. I lie on the floor of their bedroom and think of Before Sunrise, a movie that takes place mostly in Vienna but whose defining image is of the opening, the eroticism of the young couple’s meeting on the train; I think of the sweeping, freighted snowy train journey of Dr Zhivago; I think of Anna Karenina, standing defiantly on the train platform, and of her eventual death. I think, too, of the apartment in Chicago that I so miss, of the view, and the sound, of the L-train clattering loudly past the window at five minute intervals. And I think of a train journey I once took across Europe. 

That they would use the sound of a train for a children’s bedtime story is unsurprising. It is repetitive, soporific. But to me, lying there, it is enlivening, as though I might myself just hop on board the twilight train and be transported right on out of here: away from this room, this moment, this world. 

*

It was the end of  the Christmas holidays a few years ago, and I was due to fly back from Stockholm to London, a flight I have taken dozens of times. The familiarity of this particular journey usually alleviates the mild fear of flying I sometimes suffer. Waiting at the gate I felt completely relaxed, and I boarded happily. But after boarding and sitting down in my seat for a few minutes I was hit, for whatever reason, by a paralysing fear. This was not something that I could breathe through; I had to get off the plane. So I sheepishly exited back down the jetway, watched by many curious eyes as I took refuge behind my escort, the flight attendant, like a celebrity might behind their bodyguard, or a criminal behind their captor. Cast back into the waiting area and left to my own devices, I uploaded a series of badly designed apps and began to plot an alternative route home from Arlanda airport to Oxford, England. 

The story of my two day journey home across Europe is, I confess, an uneventful one. If it has anything to offer it is simply in the account of the minutes and hours that make up such a journey, and of the very particular ways in which travelling long distances by train today alters your sense of space and time.  Read more »

by Mary Hrovat

My books are arranged more or less the way a library keeps its books, by subject and/or author, although I don’t use call numbers. I also have various piles of current and up-next and someday-soon reading. In addition, I have a loose set of idiosyncratic categories that guide my choice of what to read right now, out of several books I’m reading at any given time. I choose books for occasions the way more sociable people choose wines to complement their menus.

Books To Read With A Meal

I read while I’m eating, even though I’ve been told it’s a bad habit. I prefer not to read grisly books during a meal: no noir, nothing about the digestive system or skin diseases (eyeball diseases, brain diseases…really, nothing medical), no travel books of the sort where terrible accidents are likely. I think I tried to read Jon Krakauer’s Into Thin Air with a meal and couldn’t.

It’s best if I read something that doesn’t make me cry while I’m eating, although that’s difficult these days because so many things make me cry. (My sister died this summer. Also…you know, everything.)

It’s even harder to tell when something you’re reading is going to make you laugh. I was reading a novel by Barbara Pym in a restaurant once and found something so hilarious that I had to set the book down and stop eating for several minutes while I laughed. Every time I thought I was finished laughing, I’d pick up the book, and there was the funny bit again to set me off. I can’t remember what was so funny, but I’m smiling as I type this. Thank you, Barbara Pym. Read more »