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 »