by Jonathan Kujawa

Mathematicians can be extraordinarily fussy about how they write. From having a near fetish on their choice of chalk to Donald Knuth taking 10 years in the middle of writing a multi-volume book series to develop an entirely new typesetting system [1], they spend an inordinate time thinking about how to write something. Indeed, a good choice of notation can be amazingly revealing.

Lately, I’ve become a bit obsessed with something a little more mundane: how we write numbers. The Arabic numeral system of 1, 2, 3, 4, … is so widespread and so ingrained that it is as invisible as the air we breathe. In elementary school, I remember learning the Roman numeral system of I, II, III, IV, …, but only use them occasionally when I need to read a clock or decode the year of a movie or Super Bowl. Certainly, if you asked me to compute

LXIV (CCCXXVIII – XXXVI) + DCCCXXVII

I would have a hard time figuring out that it equals XIXDXV.

Most of us ordinarily work using base ten. This means we use position to record powers of 10 (the tens place, hundreds place, and so on). This also means it is natural to have exactly 10 different symbols. You can have 0 tens, 1 ten, 2 tens, 3 tens, and so on, but 10 tens doesn’t need a symbol since it rolls over and is recorded as 1 hundred. Thus the Arabic system has 0, 1, 2, 3,4, 5, 6, 7, 8, and 9. Their shapes are designed to be easy to draw and read, and are maybe even suggestive of their value. When I was in elementary school, I did calculations by counting the three points of 3, the four corners of 4, and so on.

Altogether, the Arabic number system is efficient, practical, and pretty straightforward. It’s no surprise it became the standard. Roman numerals are terrible to use because they are written in a haphazard way that is disconnected from how we record, use, and calculate numbers. The Arabic system also has the advantage that how we use it to write numbers matches how we read numbers in English. No doubt, the rise of English and the Arabic number system are tied together. I recently saw a funny meme about this:

But it turns out there are lots of other interesting ways to write numbers. Read more »

by Brooks Riley

by Eric Bies

I picture the LORD God as a child psychologist—very much of a type, vaguely professorial, plucked from the ’50s. Picture him with me: shorn and horn-rimmed, his fingernails immaculate, he’s on his way to a morning appointment. As he kneels in the garden to tie his shoe, his starched white shirtfront strains against his gut.

Thus we find the LORD, seated in his air-conditioned office, placing birds and beasts before toddling Adam, whose first instinct, amusingly, is to name. “Horse!” he yells, flailing his arms as the dapple-gray Arabian rounds a copse of palms. “Horse!” he yells again, though this time it’s a penguin sliding by on its belly.

Those who can read Hebrew tell us that adam simply means “man,” which means, for all intents and purposes, that God named the first person “Person.” Of all the uncollared dogs that showed up on the family farm in Michigan when my father was a boy—the dogs that arrived, rambled around, and were inevitably flattened on the interstate—each was known in the same fashion, without any fuss, simply as “Dog.”

Which makes one wonder, what animal was it that St. Francis of Assisi encountered on the forested slopes above Gubbio? It’s true that that particular story gets less airtime than those in which we find il Poverello preaching to the birds or kissing lepers. And yet it may just mark his greatest conversion: not from this or that religion to Catholic, or from Catholic to yet more Catholic, but from terrorizing wolf to adoring doggie. It isn’t hard to imagine Francis with a smile, allowing the bristling thing’s big paw to eclipse his palm as he takes it in his hand for a good shake, as if to say, “You have eaten some of these kind people and their pets, chewed on them and enjoyed it, and I love you still; go along now and be a new man.”

A well-known prayer, apocryphally attributed to Francis, tells us that it is by pardoning others that one is pardoned. And the notion that our inward state bears a direct relation to our outward action does sound right. But does the structure hold up analogically? Is it by harming that one is harmed? By helping that one is helped? By naming that one is named? Read more »

Water lilies on a pond in Vahrn, South Tyrol.

by Ethan Seavey

September 7, 2021 (roughly 11,000 years ago)

A sad young novelist named Ethan Seavey wrote this sad scene in which the love interest is brutally honest and is revealed  to be less loving of Peter the person and more loving of Peter the artist. At the end of a three month long workshop, Peter invites only the love interest, Noah.

//

Seavey wrote:

I sot [sic.] on the floor of the empty gallery for a while and waited. I finally hear the door open and he walks in and I pat the ground next to me. He sits next to me and glances around the room.

“Yours isn’t here,” he says. “But I bet that Joan of Arc painting won.”

“It’s not even biblical.”

“Where’s yours?”

And so I took him all the way to the top, to the dome and to my great failed masterpiece, a graffiti tableau on top of the old cathedral. I thought I’d shock him but it had no such effect on his face. He frowned and looked on.

“It’s not your best. Just your boldest. The Joan of Arc one deserved the win.”

I look at him and wonder how he can be so cruel.

“Your use of color is all over the place. You can’t see the whole picture. All you can see is each little vignette. In one corner a man is flayed by the beast; in another four horses jockey for first place and over there is the heavenly sphere you have broken up. It is biblical but not in grandness or nuance. It is a meaningless bastard tomorrow without implication.

“But Joan is assertive and beautiful and unsure. She says a lot without opening her lips. The artist has less talent than you but they knew how to fight with integrity.

“You see that. You know this isn’t the peak of your work. But you’re stubborn and sad. And that will offer no more opportunities than…” and he gestures at the dome, “this soulless failure.”

I listen until those last words and then I leave him alone on the roof. I’m walking down the stairs and yes I am gone but I am picturing him sitting alone and glowing in his genius like he always is.

//

After discovering this text, my team of archaeologists focused on two main points. One is relatively short compared to the intricacies of the other. Read more »

by Oliver Waters

The first article of this series argued that in principle we should expect our personal identities to survive a transition to artificial brains. Obviously there remains the minor technical problem of how to actually build such brains. The most popular conception of how to approach this is known as ‘whole brain emulation’, which entails replicating the precise functional architecture of our current brains with synthetic components.

This is a cautious approach, in that the closer the design of your new brain to your old one, the more confident you can be that every precious memory and personality trait has been copied over. However, this also means copying over all the limitations and flaws that evolution bestowed upon our biological brains. Yes, you won’t have to worry about your cells ageing anymore – a definite upside! But you will remain stuck with outdated structures like the amygdala and hippocampus as well as the convoluted circuitry linking them together. It would be like upgrading your 1950s classic car engine with all new modern parts. It’s still the same, inefficient, loud, polluting machine, just shinier and more durable.

This is why we will choose to design far more advanced brains instead. Though this raises a risk of its own: what if we create kinds of minds that are far more powerful than our current ones and they destroy us before we have a chance to upgrade ourselves to rival them?

This is known as the ‘existential risk’ posed by artificial general intelligence (AGI). Read more »

by David J. Lobina

In an article on anarchist thought and action, Noam Chomsky draws a crucial but often neglected distinction for politically-inclined activists: that between visions, the ‘conception of a future society’ one might aspire to, and goals, the actual ‘choices and tasks that are within reach’, the latter ideally guided by one’s vision.^[i] These, Chomsky tells us, are often in conflict, as the most sensitive choices at some point may bring about changes and situations that can be far from, and perhaps even opposed to, the vision one is campaigning for.

The specific case that engaged Chomsky in the piece is the role of the corporation in modern society, a “legal entity” that can grow so powerful as to become ‘immune from popular interference and public inspection’ –  i.e., out of the reach of the state. Rather counter-intuitively, Chomsky concludes, an anarchist may well be advised to aim to strengthen public institutions and other spheres of the state in order to rein the corporations in, even if for an anarchist a future, desirable society would be one in which the state is in fact replaced by autonomous spheres of self-realisation (Chomsky’s preferred definition of anarchism); a clear discrepancy.

This state of affairs, however, is not exclusive to anarchist activists; indeed, the conflict between one’s goals and visions may well be a feature of normal life. The case I would like to consider in this two-parter is that of the international volunteer – those people who spend their unpaid time outside of their home countries to the benefit of others. In particular, I am interested in discussing some of the challenges a volunteer faces in a place like the occupied territories of Palestine. Read more »

by John Allen Paulos

Kurt Gödel was a logician whose work in mathematical logic was seminal and fundamental. His famous incompleteness theorems, in particular, have changed our view of mathematics and computer science. He was born in Austria and lived through political turmoil there before fleeing the country after the Nazis annexed it in 1938. He came to America and settled for a time at the Institute for Advanced Study in Princeton, New Jersey, where after the war in 1947 he applied for US citizenship. While preparing for the test, the ever punctilious Gödel noted a logical inconsistency in the Constitution, a loophole that would allow American democracy to legally become a dictatorship. His friends at the Institute, including Einstein, counseled him not to express his misgivings when he appeared before the judge lest he not be granted citizenship. He did, but happily the judge ignored them.

It’s never been clear what Gödel’s logical objection was, but it’s likely, as F. E. Guerra-Pujol speculated in his 2012 paper, “Gödel’s Loophole,” that it centered around Article V of the U.S. Constitution, which described the procedure by which the Constitution might be amended. Given that Gödel’s proof of his first incompleteness theorem involves a sort of self-reference, it’s not surprising that his loophole arises from the observation that Article V’s procedures to amend the Constitution might be employed to amend itself. Article V could be modified to make it easier to amend Article V. Thus, although Article V makes the Constitution difficult to amend, an amended Article V could make it easier to do so. There could also be amendments to the amendments to make it easier still, allowing future politicians to do away with the constitutional safeguards of fundamental rights in the Constitution. Read more »

Jeffrey Gibson. Chief Black Coyote, 2021.

Mixed media collage, acrylic paint, vintage beads, nylon thread etc.

More here and here.

by Mindy Clegg

I had plans this month for a discussion of the phenomenon of easter eggs in film and TV. Instead, the sudden death of singer/songwriter Sinead O’Connor demands our attention, although I doubt I’ll have much of an argument about her career, other than it matters, much as Allyson McCabe argued in her new book.¹ Much like McCabe, I want to remind us of how and why the life and career of this extraordinary women matters, and to dwell a bit on what she can tell us about the past and present. This will mostly a bit of disconnected ramblings, so I hope you bear with me to honor this incredible woman, who refused to be cowed and always told her truth, whatever it cost her. So, let’s discuss a bit about her feminism and women in music, what she told us about the history of Ireland and the Catholic Church, and what her very public struggles with mental health tell us about our evolving understanding of mental illness.

As a historian of punk and postpunk musics, I harbor a healthy skepticism of artists who hit the big time—or rather I find myself critical about how the recording industry shapes artists to make them more palatable to the widest possible audience. It rarely is about pure talent but about marketability. In the face of this, O’Connor stood firm on her own artistic ground, even as there were attempts to market her in particular ways. The industry demands women shape their image to primarily appeal to men’s tastes, so she rebelled, shaving her head and wearing baggy clothing. This has been changing in recent years, as more women dominate the charts, more often on their own terms–that seems in part thanks to O’Connor. Despite all this pressure, she flatly refused to play the adorable manic pixie girl role that some in the industry hoped to slot her into. She insisted on her voice being heard and her experiences being honored above the misogynistic din of the recording industry. Read more »

by Richard Farr

Lucky you, reading this on a screen, in a warm and well-lit room, somewhere in the unparalleled comfort of the twenty-first century. But imagine instead that it’s 800 C.E., and you’re a monk at one of the great pre-modern monasteries — Clonard Abbey in Ireland, perhaps. There’s a silver lining: unlike most people, you can read. On the other hand, you’re looking at another long day in a bitterly cold scriptorium. Your cassock is a city of fleas. You’re reading this on parchment, which stinks because it’s a piece of crudely scraped animal skin, by the light of a candle, which stinks because it’s a fountain of burnt animal fat particles. And your morning mug of joe won’t appear at your elbow for a thousand years.

What could be worse than the cold, the fleas, the stink, and no coffee? Well. The script you are reading is minuscule, to save ink and space, and it’s written in scriptio continua. That’s right: you are plagued by headaches because spacesbetweenthewordsaremodernconveniencesthathavelikepunctuationandcoffeeandreadingglassesanddeodorantforthatmatternotyetbeeninvented. Even for someone like you, with years of prayer and special training under your greasy rope belt, this is a constant source of difficultyambiguityfrustrationeyestrainanderrer.

Thank goodness for modernity, eh? Except for one strange fact. In our smugly “digital” age, our numbers are still waiting for modernity to happen.  Read more »

by Brooks Riley

by Nate Sheff

Harry Frankfurt died on July 16, 2023. As a philosophy student I came to appreciate him for his work on freedom and responsibility, but as a high school word nerd, I came to know him the way other shoppers did: as the author of one of those small books near the bookstore checkout line. That book, On Bullshit, had exactly the right title for impulse-buying, which has to explain how Frankfurt became a bestselling author in a field not known for bestsellers.

Happily for all of us, On Bullshit turned out to be philosophically rich, not just by impulse-buy standards, but by the standards of academic philosophy. I like to imagine that when members of the book-buying public got home and sat down grinning with the funny little hardcover in their bag, they cracked it open and read straight through to the end, not even realizing that an hour or two had slipped through their fingers.

I’ve taught On Bullshit to intro philosophy students. The title makes them laugh (they can’t believe what they’re getting away with in college), but things get real quickly. Frankfurt is having fun, but he isn’t messing around. He takes his topic seriously, and even if you find his analysis unconvincing, the problem of bullshit lingers. It’s a platitude that we seem to be up to our necks in the stuff, but hardly anyone ever thought to say what this stuff is. Characteristic of the best philosophy, Frankfurt asks a question that seems obvious in hindsight, but if it was so obvious, how come nobody asked it? Light chuckling gives way to nervous laughter, which gives way to furrowed brows. This is the legacy of Socrates.

Good philosophy has a tendency to keep on giving. It furnishes you with new tools, new ways to see the world. Good philosophy is productive and fruitful because it allows you to ask questions you didn’t know how to ask before. Read more »

A small demonstration of America’s global cultural hegemony in Franzensfeste, South Tyrol. 🙂

by Mary Hrovat

I had my first experience with Daylight Saving Time when I was 9 or 10 years old and living in Phoenix. Most of the country was on DST, but Arizona wasn’t. I knew DST as a mysterious thing that people in other places did with their clocks that made the times for television shows in Phoenix suddenly jump by one hour twice a year. In a way, that wasn’t a bad introduction to the concept. During DST, your body continues to follow its own time, as we in Phoenix followed ours. Your body follows solar time, and it can’t easily follow the clock when it suddenly jumps forward.

When I moved to Indiana as a young adult, I was relieved that my new home, like Arizona, didn’t observe DST. The history of time zones in Indiana is complex. When I moved here in 1980, most of Indiana was on Eastern time. Because the state is on the western edge of Eastern time (and arguably ought to be on Central time), DST makes less sense for Indiana. We already have relatively late sunrises and late sunsets. Eastern time is one zone east of where we should probably be. We don’t need DST to effectively move us one time zone even further east.

Before standard time zones existed, all time was based on local solar noon. Indianapolis is closer to the center of the Central time zone than to the center of the Eastern time zone, as currently defined, and until 1960, the entire state was on Central time. However, for various reasons, the state crept into the Eastern time zone, first just half of it and then most of the rest. The exception is 12 counties in the northwestern and southwestern corners, which chose to be on the same time as nearby regions on Central time. Read more »

In Praise of Mirza Ghalib

—a transcreation after Mohammad Iqbal (1877-1938)

Imagine a bird with agile wings introduce the gathering
Now imagine the flawless bird seduce the gathering

You glimpse the fire of life veiled in everything
A hidden crown jewel imbues the gathering

Bringing forth Spring, coloring our world green
In silent foothills, a river renews the gathering

Curls of Urdu are forever grateful to the comb
You show us how not to obtuse the gathering

Your words grace not just ghazals — mischievous —
Even frozen lips in photos suffuse the gathering

Heart’s rage is a moth candle burns; your gaze foretold
sun and moon in sand grains infuse the gathering

Your regal flight entrances even the Pleiades
Rose of Shiraz bud of Delhi salutes the gathering

Your dust conceals a thousand million pearls, laments
from thresholds to rooftops induce the gathering

O Shahjahanabad — cradle of learning
Is Hindustan now out to traduce the gathering?

Ghalib buried in New Delhi’s jungle, Goethe
Interred in Weimar’s garden muse the gathering

____________________________________
Goethe (1749- 1832); Ghalib (1797 – 1869)

by Rafiq Kathwari

by Mike Bendzela

The idea that “the only intolerable thing is intolerance” wears its contradiction on its sleeve. It also violates the Golden Rule–to behave toward others as you would have them behave toward you. We all have limits to our tolerance–call them “intolerances”–and it’s not too much to ask others to tolerate them, within reason. Let them hold the backs of their hands against their foreheads and declaim their forbearance of poor, weak us. Like they’ve never been a pain in someone else’s ass.

It’s unfortunate we have to use the word “tolerance” to express the capacity to interact with various kinds of people. It has a whiff of victimhood about it, as if one were asking to be admired for one’s stamina and not for one’s humanity. “Tolerance” seems as if it were a physical capacity to withstand repugnant stimuli: One has high or low levels of “tolerance” for cigarette smoke, alcohol, pollen, toxins, sunlight, and cats. So, the same goes for homosexuals, Jews, and Republicans?  “Tolerance” doesn’t adequately express that the issue is one’s comportment, not one’s fortitude, when it comes to facing others who differ from oneself.

Here’s Karl Popper on the Paradox of Tolerance, as served up by Wikipedia:

Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them.

For this to be graspable, we need a demonstration of just what the intolerance of intolerance would look like in everyday life. Read more »