by Jonathan Kujawa

On December 22nd I started thinking about topics for this month’s 3QD essay. In a happy coincidence, someone posted to Twitter that Srinivasa Ramanujan was born on December 22, 1887. We’ve touched on Ramanujan’s work here at 3QD, but it seemed like a sign that we should dive a little deeper [0].

The story of Ramanujan is now famous, especially after the award-winning film “The Man Who Knew Infinity” [1]. He was born in southern India into a poor family. His talent in mathematics was noticed at an early age, but it wasn’t until he got hold of a copy of G. S. Carr’s “Synopsis of Pure and Applied Mathematics” at the age of fifteen that his talent was really revealed. Carr’s book was meant to be a Cliff Notes to undergraduate mathematics for students cramming for Cambridge University exams. It gave little to no explanations — just a thousand pages of raw, uncut mathematical formulae stated as gospel. Using Carr’s book, Ramanujan taught himself mathematics.

Ramanujan became consumed with his own mathematical explorations. So much so that he neglected his college studies and failed out after the first year. He continued to do math and live in poverty until his mother arranged for him to marry S. Janaki in 1909. Feeling the responsibility of marriage, Ramanujan eventually found employment as a clerk in the Madras Port Trust Office and in 1913, thanks to the encouragement of other mathematicians in India, finally sent a letter containing some of his results to several famous mathematicians in the UK.

Faithful 3QD readers might recognize the first of the following formulas from Ramanujan’s letter:

In one of my first essays for 3QD I talked about how you can make sense of infinite sums and how, properly interpreted, it is reasonable to think of the sum of all the counting numbers as equal to -1/12. Read more »

Elfriede Abbe. The Geese and The Cranes. c1980.

Wood engraving.

More here, here, and here.

by David Kordahl

Last month I worked on a modern sort of archaeological dig, going through the equipment in a college physics lab to see what sorts of devices were on hand. It reminded me of being a little kid, when I would tiptoe around my dad’s religious paraphernalia (he was a Lutheran pastor), not really knowing what everything was for, but being sure that each item had a definite purpose. My job in the lab was to construct setups for a modern physics course, demos for students to learn a few things about the empirical basis of special relativity and quantum theory, to cut through the layers of interpretative bullshit. Encountering unfamiliar items, I would rummage around for their service manuals, pushing aside brittle O-rings and chipped pipettes, stacking old printouts, believing without proof that the lab’s former occupants had found some use for these treasures.

In bed one night after a long day with the machines, it occurred to me that these educational toys might share some common purpose with the portable communion kits and illustrated Bibles of my childhood. In each case, the devices were technologies designed to strengthen belief in a distinct mask for the world of observed phenomena. And in each case, strengthened beliefs hold for believers the promise of new ways to navigate the world, ways that non-believers can neither appreciate nor access.

This is not to deny the obvious differences between a communion kit and a current amplifier. One obvious feature of technology is that it’s mostly belief-proof. Almost no one understands all the devices that they use, and many users hold views that explicitly contradict the theories used to construct the devices on which they rely. (Teaching high school science, I met smartphone savants who were supremely confident in the irrelevance of physics to their lives.) Yet the fact that I now entertained the possibility that my lab setups had anything to do with religious conversion already proved that I’d strayed pretty far from my early days. Read more »

by Tim Sommers

The Medieval Arabic philosopher Ibn Sina – Avicenna to Europeans – was rivaled in renown as a thinker in the Islamic world only by Al Farabi and hailed as “the leading eminent scholar” (ash-Shaykh ar-Ra¯sı ) of Islam. He worked in virtually every area of philosophy and science and influenced subsequent Jewish and Christian philosophers almost as much as Muslim ones. But he is probably known best for a single image, a heuristic more than a thought-experiment, “the falling person”.

“We say: The one among us must imagine himself as though he is created all at once and created perfect, but that his sight has been veiled from observing external things, and that he is created falling in the air or the void in a manner where he would not encounter air resistance, requiring him to feel, and that his limbs are separated from each other so that they neither meet nor touch. He must then reflect as to whether he will affirm the existence of his self. He will not doubt his affirming his self-existing, but with this he will not affirm any limb from among his organs, no internal organ, whether heart or brain, and no external thing. Rather, he would be affirming his self without affirming for it length, breadth and depth. And if in this state he were able to imagine a hand or some other organ, he would not imagine it as part of his self or a condition for its existence.”

Ibn Sina’s ultimate aim was to prove the existence of the soul. Let’s leave that more complicated task aside and stick to the question of what “the falling person” might tell us just about the existence of a self.

Ibn Sina, by all accounts, didn’t count “the falling person” as proof of the reality of the soul or self. He taught his students a whole chain of sophisticated arguments for that purpose. He described “the falling person” more as “alerting” or “reminding” us of the self. It’s not quite a thought-experiment. It’s not about how you would react. It’s not a puzzle with a solution. It’s a question. And the question is, if you were without a past and shut off from any input external or internal, would you have or be a self? Or, maybe, would a self still be there? Would you, could you, think, I am here? Or I am me. Or I am something.

What would this bare self’s awareness of its self be like?

I picture a hum.

Just to the right of where I sit now there’s a freezer on the other side of a closed door. But I can still hear the hum. It only comes into my awareness when there’s dead silence and my mind goes blank for a moment. But it’s always there. The kind of self that “the falling person” might have, I picture as that hum. No content just…there. But is it really there? Couldn’t the falling man think? Read more »

by Brooks Riley

by David Oates

We are entering the aftermath. Two of the most epic and wrenching struggles in American history are finally playing out to their conclusions. At last we see a conclusive democratic rejection of a presidency built on systematic lying and racism. At the same time we look just weeks or months ahead for vaccines that will liberate us from our deadly yearlong pandemic.

Of course the two catastrophes are entwined, most wrenchingly in the excess numbers of Americans who died not just because of the disease, but by the incompetence and malfeasance of the president’s handling of it. According to a summary by the Center for Infectious Disease Research and Policy (October 2020), “If the coronavirus death rate in the United States were similar to that of Australia, it would have had 187,661 fewer COVID-19 deaths . . . and, compared with Canada, it would have had 117,622 fewer deaths.” And another hundred thousand US deaths have accumulated since October. So amplify those numbers accordingly, please, as this president’s personal death-toll on the nation.

Our collective house in disorder, occupied by thugs and dying by the thousands. All coming, at last, to an end! An end to constant alarm and worry. An end to the adrenaline-rush of hyperalertness, the daily fight-or-flight. The four-year emergency. The cavalcade of death. The pageant of ignorance.

Who are we now? we might soon be asking ourselves, as we step out, one by one, from our psychological foxholes and almost-literal bunkers. Can we relax now? Can we pick up normal life again?

Can we? Will we?

The after-blight is beginning. How shall we then live, in the aftermath of so much sustained stress and fear and misery? Read more »

by Varun Gauri

The spirit of gift exchange animates democracy. In exchange for letting you control government, giving you power over the security forces, the common treasure, and the agencies and civil service — which is power over me — you agree to grant me those same powers —  and power over you —  in the future. I am then entitled to control government and its coercive powers in exchange for agreeing to transfer those powers back to you, or your representatives, when the time comes.

Aristotle emphasized this, arguing that in political regimes where citizens are more or less equal, the citizens alternate governing, “ruling and being ruled in turn.” Rawls believed this notion of reciprocity in democratic societies is widely relevant across a range of social and economic practices, including taxation: Because society should be seen “as a fair system of cooperation over time,” not only public offices but the common surplus should be divided in a way that acknowledges mutual contributions over time. My firm profited from those highways and airports and bridges that others paid for and built; now I pay it forward, in the form of taxes.

This principle of reciprocity applies not only to taxation and to ceding control of government — conceding after an election loss — but to forbearance in the exercise of power. When I’m in power, the principle requires me to appreciate that the security forces, the common treasure, and the civil service are not mine to control forever. One day they will be yours. So I shouldn’t break or repurpose them in a way that leaves them not useful to you, for your objectives, when it becomes your turn to rule. It’s hard to specify the point at which the pursuit of ordinary policy objectives amounts to breaking or repurposing institutions and agencies, but the line certainly exists. An outgoing administration repurposing the civil service by installing loyalists, or by raiding the treasure, is, after a certain point, normatively equivalent to an executive embezzling funds from a business partner (or worse). Read more »

A specimen of the Peruvian grasshopper Lophacris cristata mounted in a vitrine. Photo taken in my living room in December of 2020.

by Brooks Riley

The first time I ever left home without leaving home I was twelve years old, recently back from a winter trip to Mexico. Routinely sent to bed at 8 pm (my parents were old and old-fashioned), always wondering how to fill the inevitable two hours of insomnia, I opted to return to Mexico, not as the sleepless chiquita that I was, but as the fierce guerilla chief I would become in the narrative, leading a band of outlaw Aztecs in raids against a host of injustices from base camp in a desert. No precedents existed for my leadership skills in real life, but within the carefully sculpted storyline of the daydream, I was both charismatic and respected, not merely proficient but also inspired, a warrior queen to rival any Amazon.

Where did this come from, this semi-androgenous role so foreign to my timid female self? I may have been feeling powerless back then, on the verge of puberty and alone in my ignorance. My daydream could just as easily have come from a twelve-year-old boy but more likely it incubated in the tomboy I sometimes was. Gender had little to do with it, though. Empowerment is what mattered, something I desperately needed, as well as a jolly exciting way to pass the time until I fell asleep.

Daydreams have served the needs of human beings since the evolution of the imagination a few million years ago. The caveman who dreamed of bagging a boar pictured an encounter in his mind and practiced his moves. Except for those with aphantasia, we can all visualize places we’ve been and people we’ve seen. This ‘inner eye’ allows us to do much more than that—to create people and places that we’ve never seen, that don’t exist, and to give them life, context, and raisons d’être. This is how fiction is born, before the first word has even hit the page.

We all indulge in daydreams, those reticules in the mind that hold our most vivid hopes in the form of mise-en-scène, endowing our bucket list with emotional nuance and narrative—however improbable the reality. With age, however, imagining a dazzling future no longer seems viable, as the scope of our hopes and desires shrink, like the law of diminishing returns. Daydreaming is eventually reduced to hardly more than an imagined walk in the park when you’re stuck at home. Much of my bucket list has been accomplished, in sometimes surprising ways. My life has been eclectic, peripatetic, unexpected, and gratifying. I’ve been places, done things. What more could there be to dream about? Read more »

by Hari Balasubramanian

This year marks two decades since I moved from India to the United States. I look back at how it all began in Arizona.

In the summer of 2000, after completing my bachelor’s degree in engineering, I had to decide where to go next. I could either take up a job offer at a motorcycle manufacturing plant in south India, or I could, like many of my college friends, head to a university in the United States. Most of my friends had assistantships and tuition waivers. I had been admitted to a couple of state universities but did not have any financial support. Out a feeling that if I stayed back in India, I’d be ‘left behind’ – whatever that meant: it was only a trick of the mind, left unexamined – I took a risk, and decided to try graduate school at Arizona State University. I hoped that funding would work out somehow.

So in August 2000, I found myself traveling across continents to this powerful country that I knew little about. It was my first ever time outside India and my first ever flight. From Chennai, I flew to Kuala Lumpur, then, after an eight-hour layover which I didn’t mind at all, to Los Angeles and finally, after the worry of a missed connection, to Phoenix, Arizona. The gleaming, modern airports, the meals and the movies, the turbulence and the clouds: it was all very exciting, a glimpse of an elite world that had once seemed inaccessible.

At the Phoenix airport, someone from the Indian Students Association at ASU came to pick me up. After what seemed like a recklessly fast drive – in fact it was normal: it’s just that I’d never experienced a 70-miles-an-hour ride on a highway before – he dropped me off at an apartment shared by three Indian grad students. One of them, my host until I found an apartment, wore a veshti, the wraparound skirt common in south India. He spoke Tamil fluently; he spoke it so well that I could well have been in my home state. I had a nagging suspicion at the time that people might change as soon as they landed in a foreign country – that they might change their attire, even forget their mother tongue. It was reassuring to know that wasn’t true. At the heart of such doubts, I see now, was a fear that I would quickly surrender my Indianness. Read more »

by Ali Minai

One of the most interesting and memorable characters in sci-fi films is the T-1000, the shape-shifting, nearly indestructible robot from the classic film Terminator 2: Judgment Day, starring Arnold Schwarzenegger. There are other, less prominent examples of shape-shifting intelligent beings in sci-fi – for example Odo, the chief of security on Star Trek’s Deep Space Nine, or the electromagnetic, gaseous, and otherwise inchoate life-forms encountered in various Star Trek episodes. These fictional examples raise the interesting question of whether intelligent beings without a fixed structure are feasible in practice – naturally or through technology (In fact – speaking of Star Trek – the question could potentially be extended to teleportation as well since that would presumably involve the re-assembly of a disassembled body, but that is too remote a possibility to consider for now.)

Recently, several research groups have worked on building robots that can reconfigure themselves autonomously into different shapes and perform different types of actions suitable to their current form. For example, a robot consisting of a large group of small, identical modules could turn itself into a compact sphere to roll down smooth surfaces, flatten itself to slide under doors, grow limbs to climb stairs, or take a snake-like form to crawl away. Such robots, with various degrees of reconfigurability, have now been implemented extensively, both in simulation and in actuality. Some of these robots are, in fact, controlled by external computers to which they are connected or by a centralized brain built into the robot, but the more interesting ones are based on distributed autonomous control: Each module in the robot communicates with other modules near it and, based on the information obtained, triggers one of several simple programs it is pre-loaded with. These programs might cause the module to send out a particular signal to its neighbor or make a simple move such as a rotation, alignment, detachment, or attachment. As all these mechanically connected modules signal and move in response to their triggered programs, the robot assumes different shapes and global behaviors such as locomotion or climbing emerge through self-organized coordination.

The primary feature in these robots is what might be termed radical reconfigurability, i.e., no elementary component has a fixed location in the body or is specialized to a task; like Lego pieces, it can serve any role anywhere. However, this property depends on another, more general attribute: radical distributedness. A radically distributed system consists of identical and exchangeable modules with no permanent functional specialization: Any module can take on any role as needed. Read more »

by Mike O’Brien

There’s a concept in education, particularly science education, called “lies-to-children”. It roughly means this: some matters are so complicated that they cannot be clearly understood when accurately presented. So, if you want a naive audience (“children”) to eventually understand how these complex matters actually work, you need to prepare their minds with inaccurate but helpfully simplified analogies, which are discarded and replaced by ever more complicated and accurate analogies, until they are finally ready to understand the most complicated and accurate version of the truth presently available. A concrete example is teaching Newtonian physics in high school, then telling university physics students arriving for their first day of class that everything they’ve been taught is a lie (and everything they’re about to learn is also a lie, but necessarily so).

The concept of rights, both human and non-human, is like this. It is different from concepts in physics or chemistry in that it is fundamentally prescriptive rather than descriptive, but operates exactly like “lies” in scientific education in that the simplicity and certainty of false portrayals serve to accomplish a useful end. In the case of science education, that end is a mental “formatting” that prepares the student for incrementally more complicated pictures of reality. In the case of moral advocacy, the end is to introduce a predicate that can be attached to objects in moral calculation, allowing moral discussions to proceed in a descriptive, concrete mode rather than a prescriptive, contentious one.

Do rights exist? That strikes me as a nonsensical question. Is there a moral state of affairs that is usefully analogised by “rights” discourse? Now you’re talking. I’m not sure that there is, or that any objective state of moral affairs can be objectively shown to obtain, but at least rights talk seems to be an activity that morally interested, language-using beings can engage in with useful results. We can talk about how people have rights, and what obligations those rights impose on how people are treated by others. We can talk about how animals have rights, and what obligations those rights impose on how animals are treated. We can even talk about according rights to trees, mountains, and legally incorporated businesses, if we want to. But the trees don’t know they have rights, nor do the mountains, nor do the animals. And, given the dismal state of moral and civic education in many places, nor do many people. If they don’t think of themselves as having rights (or, furthermore, lack any clear concept of legal or moral right), and don’t experience any special treatment or status as rights-holders, what does it matter if some philosopher or judge believes them to have rights? Read more »

Prayer

I thank Thee for this couch
and the room it inhabits
and the chair which, being its partner
in undeserved comfort, leaves itself available
to any weary stander who might take advantage
of its open invitation to sit,
and for those two aptly-named bolsters
plumped at one of the couch’s ends
near the bookcase of stacked knowledge,
as incorrect as some of it might be
as spot-on as some of it might be
as brimming with the juice of knowing
or not, as the case may be,
those bolsters which in moments of fatigue
are there to do what their name suggests
in both guises, noun and verb,
to support that which seems to
uphold this scene in some place,
in some thing, a cathedral of a skull,
and thank you for the dark and tiny landscape
between the bookcase and the chair
which appeared out of nowhere as I drew,
in what had been a small white void
needing something there that
did not before exist,
amen

Jim Culleny
12/13/20

by N. Gabriel Martin

In 2017, the Nobel prize in economics attracted more attention than it usually does, when it was awarded to Richard Thaler. Articles in leading newspapers everywhere explained Thaler’s revolutionary insight: whereas economic orthodoxy was premised on the belief that humans are essentially selfish, Thaler’s work assumed that we are also stupid.

Thaler was the perfect laureate for a world trying to come to grips with Brexit and the election of Trump, even if the novelty of his theories was exaggerated. For many, faith in the decision-making ability of the public was shaken, and so was the conception of human nature underpinning liberal economics and democracy—that humans act in their own self-interest. How else could the decisions of tens of millions of Brits to tank their economy, or of more than a hundred million Americans to elect an unqualified, corrupt bigot be explained than by calling into question our ability to figure out what’s in our own best interests?

Thaler, though not all that original in this regard, has espoused a theory of human behaviour that maintains the assumption that self-interest drives our actions, but rejected the idea that we know what our interests are. This reimagining of human nature called for a reimagining of political possibilities. Thaler’s behaviourist economic view doesn’t support free market liberalism without conditions. A free market can, supposedly, be counted on to yield optimal results on the assumption that its members are able to choose what’s in their own interests, but if we are too stupid either to know what’s really in our own interests or to make the better choice most of the time, then there’s no reason to expect a free market to produce optimal outcomes. Read more »

Bisa Butler. The Safety Patrol. 2018.

Quilted and appliquéd cotton, wool, and chiffon. 90 x 82 in.

More here and here.

by Liam Heneghan

In Memoriam Tim Robinson (1935 – 2020) and Máiréad Robinson (1934 – 2020)

In Connemara: Listening to the Wind (2006), the first volume of cartographer and writer Tim Robinson’s trilogy of books about that rugged part of Co. Galway, Robinson records an illuminating and slightly fraught exchange that he had with landscape artist Richard Long about the fate of the artist’s work left exposed to the battering Irish coastal elements.

Work of Long’s include pieces sculpted from rocks and other materials found as he traversed natural landscapes on foot. The sculptures are gradually re-arranged by forces in the landscape, though the images have greater durability and are often displayed in galleries and preserved in archives.

In his excursus about Connemara to complete his trilogy, Robinson located one of Long’s sculpture on a small headland near the town of Roundstone The piece, entitled Connemara Sculpture (1971), is comprised of beach pebbles arranged in a distinctive pattern. This was not the first of Long’s pieces that Robinson had located and mapped. As a gift for Long, Robinson’s wife Máiréad had sent Long a copy of a map on which Robinson had marked a couple of pieces on Inishmore, the largest of the Aran Islands.

Long took umbrage to the gift, writing to Robinson that he was “very surprised and aghast when someone told me years ago that my work was marked on a map.” It had not been his intention, he went on to write, for the sculptures “to be marked sites.” Long concludes his letter to Robinson noting that fortunately the “map that you kindly sent… didn’t have my sculpture on it.”

Robinson—that consummate map-maker—replied to Long, pointing out explicitly where these sculptures were marked on the map. Of course they were mapped!

Along with Robinson’s spirited defense of the fidelity of his mapmaking, he makes the following point: “…once the artist has made an intervention in the landscape and left it there, it contributes to other peoples experience of place, which may well be expressed in someone’s else work of art.” He goes on to write, “…your marks on the landscape will have a career of their own; they are no longer defined by their origin in your creativity.” Read more »