by Jonathan Kujawa

Every institution has its founding myths. In mathematics, one of ours is that mathematical truths are unassailable, universal, and eternal. And that any intelligent being can discover and verify those same truths for themself.

This is why movie aliens who want to communicate with us usually use math [1]. The cornerstone of this myth is that mathematicians give airtight logical arguments for their truths. After all, Pythagoras knew his eponymous theorem 2500 years ago and it’s as true as it ever was. And it was equally true in Mesopotamia 3500 years ago and in China and India 2000+ years ago.

The idea of a “mathematical proof” is what makes math, math.

This semester I am teaching our introduction to mathematical proofs course. The not-so-secret purpose of the class is to help students transition from being mathematical computers to being mathematical creators. The students learn what it means to think mathematically. This includes how to take vague and ill-framed questions and turn them into mathematics, how to creatively solve those problems, and how to communicate those solutions in written and verbal form.

A huge part of the course is teaching the students what it means to give a valid proof. They learn about direct proofs (a direct logical march to the desired result), proofs by contradiction (if the desired result weren’t true, then one is forced to a logical impossibility), proofs by induction (using a recursive loop to verify the desired result), and more. They also learn some of the common pitfalls like pre-supposing the desired result and thereby begging the question.

The topics of the course are basic number theory, set theory, logic, functions, and the like, but the real content is how to read and write proofs. Read more »

Ekua Holmes. There’s No Place Like Home.

More here and here.

by David Oates

We are always looking for the book it is necessary to read next. —Saul Bellow

That quote hangs over my writing desk. Its purpose is to remind me of the urgency of writing. Not the correctness of writing, not its sentiment or fashionability or mild amusement: its urgency. Bellow wants what I want – what every reader wants: the book that is necessary and of the moment, now.

It’s what drives me as a writer. As a reader. And as a small-press publisher.

In the marketplace of books, it can be hard to find that next, necessary book. I keep a list of what to read next – lots of people do. But what is offered to me? Mostly big books from big names, published in editions up into the millions of copies (Michelle Obama’s initial print run for Becoming was 3.4 million, increased to 4.3 million because of demand). The big publishers want sure-fire bestsellers. . . but are these really the necessary books? The “Big Six” publishers who dominate the English-speaking book world have consolidated yet again – it’s the “Big Five” now – and they want a guaranteed return on investment. Until authors can guarantee sales – until they are already in some way famous – why would Penguin Random House give them a contract?

Profit is their necessity, but it’s not mine. I want what is of the heart and of the moment, not merely what is salable.

This disconnect is what has brought small publishers to the fore. They take chances. They can afford to look for excellence, freshness, that je ne sais quoi. I think they follow trends that no trends that aren’t trends yet. And they look above all for urgency. They give writers their first and second books. They edit, sometimes fiercely. They create for writers time and space to grow.

In the economy of creativity, this is how it works now. It’s the little presses who are performing these crucial services. While the big guys make money. Read more »

by Tim Sommers

Children are natural philosophers. Some combination of imagination, maybe, and lack of knowledge. Philosophy is all theory and no data, after all. In any case, in my experience, one of the most popular philosophical puzzles among young people is this.

When I look at something red, it looks red to me. But it’s hard to say what “red” is other than not green, not blue, etc. How do I know that when you look at something red it doesn’t actually look like what I see as green – and vice versa. Philosopher’s call this “The Inverted Spectrum Problem”.

John Locke was the first to write about it. It’s surprising that no one wrote about earlier since, as I said, many, many people, including children, come up with the basic idea all on their own. I think that maybe the problem is a product of the way our view of the mind changed in the early modern period. Specifically, it’s a side effect of the increased emphasis on the idea of idea of a private, internal, inaccessible self. Anyway, in the end, Locke didn’t think it was very important. Maybe it isn’t. But like many philosophical puzzles, it points to something important.

Back up. We learn colors by being shown samples of colors and learning to name them. Back in my day, it was crayons. So, we learn colors by discrimination. But maybe colors are, beyond that, “featureless”, as the philosophical behaviorist said. Yet non-color-blind people are seeing something when they see a color. What is it?

When I ask my students what “red” is, I invariably get the answer, it’s a certain frequency of light. What frequency? I always ask. In the olden days, most of the time, they had to admit they didn’t know. Nowadays, they google it on their phone and say “between 635 and 700 nanometers”. But when you go to the grocery store you don’t tell red apples from green by looking for apples in a certain frequency range, do you? Read more »

by Brooks Riley

by Brooks Riley

Of all the secondary discomforts imposed by the pandemic, the most treacherous may be inertia. Life, interrupted, can be characterized as an absence of movement, like a stream that stops running, stagnating as the surface begins to cloud with algae and other still-standing detritus. Inertia that stems from the current situation can quelch any creative impulse. Even cinema, that paradigm of life in motion—the moving picture—isn’t much help if we expect our own lives to keep moving as well as movies do. They don’t, at least not right now.

Now we sit at home and consume an ersatz elixir of motion on our streaming platforms, and without quite realizing it, get our kinetic gratification by surfing a narrative, instead of going out for a drive or a walk and seeing our visual field alter naturally.

Movement in this case is not about physical activity, or what we do, but rather about what we see, the perception of changing location in one or another direction—forward, out, away, off, back. On a walk, we may be thinking about our muscles, or about the surrounding nature. But we are mostly oblivious to the subtle changes in our field of vision as we move forward—that constant progress of our steps which alters the panorama ever so slightly. Seen this way, movement feeds our perceptions at the instinctual level. This is where the brain boards a train, metaphorically, to exercise its ability to adjust to change.

I miss trains. I miss the way the scene outside the window rapidly evolves as the miracle of speed presses ever new images on my retina. I miss the way my mind comes alive and cranks out thoughts and ideas at a similar speed. That there is a connection between what we see and what we think, even if none seems to exist, can be explained this way: Motion embodies two accelerators of thought, energy and change, both of which are in short supply if we’re locked down somewhere. The more sedentary and static our lives become the more we depend on the illusion of motion provided by second-hand sources. As the pandemic wears on, I find myself spending less time reading and more time on YouTube, not chasing stories to get lost in, but seeking some kind of eye candy that moves. Read more »

My wife and I went for a snow hike on the massif named Plose in Brixen, South Tyrol, on Saturday. Here, she is climbing up a fairly steep ski run on the mountain. The mountains look deceptively small from a distance but have vast fields of snow and ice. It was not cold though.

by Ashutosh Jogalekar

In many ways, the story of my life is the story of books that I have read and loved. Books haven’t just shaped and dictated what I know and think about the world but they have been an emotional anchor, as rock solid as a real ship’s anchor in stormy seas. As the son of two professors with a voracious appetite for reading, it was entirely unsurprising that I acquired a love of reading and knowledge very early on. The Indian city of Pune that I grew up in was sometimes referred to as the “Oxford of the East” for its emphasis on education, museums and libraries, so a love of learning came easy when you grew up there. For 35 years until their mandatory retirement, my parents both taught at Fergusson College in Pune.

The college which became one of the premier institutions of undergraduate education in India was founded in 1885 by prominent intellectuals who were active in the Indian independence movement. Named after the governor of Bombay, James Fergusson, the British allowed the college to remain largely autonomous and this autonomy allowed the college to experiment with its own blend of nationalism and modernity. Among many others, two prominent leaders of the independence movement, Bal Gangadhar Tilak and Gopal Krishna Gokhale, taught there. It was Gokhale who became an early mentor to Gandhi and who encouraged Gandhi to know his country better by traveling across it after the former lawyer returned to India from South Africa where he had lit the spark of his nonviolence movement. Read more »

by Camille Noûs^1,#

¹ Cogitamus laboratory, France
^# Correspondence to: [email protected]

Camile Noûs is a collective author intended to embody the collective dimension of scientific research. The sense of collective work has been devalued and forgotten for two decades in academia, through various neoliberal research policies that prioritize competition over cooperation, and thereby favor individualism at all levels. Many issues in academia worldwide, regarding any kind of fraud or misconduct, stem from these ill-conducted policies and their deleterious emphasis on individuals as competitors.  In this manifesto, Camille Noûs, recently portrayed in Science Magazine, calls for resistance against the pervasiveness of individualism in science and its nefarious consequences upon the reliability and quality of research.

I was Socrates’s master as well as Hypatia’s student. I wondered why apples fell while the moon did not, long before Newton proposed that they both did. I was Lavoisier’s better half and Darwin’s ship mate, Giordano Bruno’s publisher and the Curies’ assistant, Hardy’s collaborator and Leibniz’s rival, Einstein’s contradictor and Hobbes’ disciple, Freud’s patient and Arendt’s penfriend. I am the nameless reviewer who read your work and suggested a control experiment that led you to reconsider your model. I am this discussion around the coffee machine that you joined with your mind a shamble and left with two key parts of the puzzle assembled. I am the former adviser or the new colleague who encouraged you to test a daring hypothesis. I am the tricky question that drove you to push your thoughts further. I am the unseen hands that maintained the environment needed for your work. I represent the sum of findings that were cited by the authors you cited, the chain of thoughts that, seamlessly, gave way to your own. I will also be the scientists who later read, debate and use your work as a basis for theirs.

You who work in research know me of old. And yet, only last year did I start co-authoring your publications. You and I, who search for a living and often dedicate our lives to science, are fully aware of what our results owe to collective construction, to the timely collegial process that shapes the landscape of knowledge by accretion and erosion, seldom disturbed by earthquakes. Indeed, although genius is a convenient fiction, science relies on the strength of its probation process much more than on the personality of its enunciator; it would be nothing without a complete state-of-the-art and, above all, without disputatio.

However, in the past decades a myth has propagated, among our institutions and then among us, that research is essentially a matter of individual performance. Far from maintaining a healthy research environment where collegiality drives us ahead, production indicators that we are each expected to satisfy corrupt the quality of scientific interactions, and the fear of concurrence precludes sharing information and building collaborations so as to secure one’s own success. These enticements also constitute the primary cause of scientific misconduct due to the direct benefits of cutting corners. Read more »

by Charlie Huenemann

Observations are laden with theories, or so we are told, and theories are laden with cultures. There’s a good reason for thinking this. Theories, after all, spring out from people’s heads. But people’s heads grow within languages and cultures, along with whatever biological constraints lay at the foundations of our being. So anything coming out of our heads is going to bear the imprint of those complex systems. When you speak, a culture is speaking through you, with your own distinctive garnish.

This plausible observation, however, exists in tension with one of the guiding principles our culture speaks through us. That guiding principle is methodological individualism, or the basic strategy of understanding the big stuff by understanding the little stuff. Society is just people, we observe, and languages are just how these people say what they say. So if we understand the people, we will understand the larger cultures and languages they compose en masse. Better yet, understand the individual brains of these individual people; for certainly anything they do will be issuing from what is inside their heads. Better yet still, understand neurons and their local neighborhoods, for certainly the brain is not doing anything more than they are doing. Keep at it, and pretty soon you’ll just be paying attention only to what the quantum physicists say. And at that point you’re a goner, for sure.

We live in an epoch of nominalism: a general distrust of any explanation that proceeds from the big stuff downward. All causality is a local exchange between concrete individuals; larger patterns result from these, just as — in not a wholly unrelated way — economies exist through the exchanges of rationally self-interested individuals. Our culture is formed around the crucial notion that all social facts rest on the consent of individuals disposing of their individual liberties as their own reasons see fit. As Nietzsche once recognized, as scientists we generously extend these republican ideals to nature as a whole, interpreting it as a state teeming with wayward individuals governed by stern and inviolable laws. What is done in the large is only as real as what is done in the small.

But we just might be oversimplifying things a tad. Read more »

by Callum Watts

At the 100th anniversary of John Rawls’ birth back in February, some of the most generous op-eds, whilst celebrating the brilliance of his thought, lamented the torpor of his impact. ‘Rawls studies’ are by no means the totality of political philosophy, but they are one of its most significant strands, and his approach has been dominant for the past 50 years. I’m an admirer of political philosophy, having happily spent much time and energy studying it, specifically looking at theories of deliberative democracy, an area with important connections to Rawls’ thought. That political philosophy does not have much to say that is of direct practical concern does not bother me, the sense that it is not just uninfluential, but is disconnected from the reality of the present moment does though.

Although I’ve been out of academia for 5 years or so, my work in large organisations focussed on change programmes and innovation has meant that deep questions about how people work together, and how we understand the purpose and ontology of collective action, have never really left my mind. When you are trying to encourage and inspire new behaviours in organisations of hundreds of thousands of people, it’s almost impossible not to ask about the fundamentals. Specialists in this field have elaborate theoretical apparatuses of varying rigour explaining different models of change, different accounts of human motivation, and ultimately, normative accounts of what is desirable. Even though much of this has developed in the business literature, it cannot help but stray into the broader social realm as the outsized impact of businesses that are often more powerful than states become impossible to ignore. One particular area of interest is in the idea of systems thinking. Read more »

Anderson Ambroise. Rubble Sculpture.

More here and here.

by Mindy Clegg

By now over 100,000,000 Americans have received the Covid-19 vaccine and we seem on track to double that by the end of President Biden’s hundredth day. Efforts to reach herd immunity continue apace with many states opening up access to more groups in recent weeks. It’s a hopeful feeling, seeing more people receiving this promise of a return to normality. But some dark clouds are obscuring this (global) goal of herd immunity. We might see yet another surge before we’re done, both here and in other countries. Many of the states struggling to get their populations vaccinated have begun to roll back various mandates for distancing, masking, and capacity limits in businesses. There is still a vocal minority who continue to insist that masking and distancing are useless “health theater”, a direct threat to our civil liberties, that Covid-19 is no worse than the flu, and will refuse getting the vaccine as it’s “their body” (ignoring how their actions impact others in their communities).

This vaccine hesitancy—which despite the media narrative that it’s prevalent among Black Americans is really now a problem among white Republicans—can easily disrupt our goal of herd immunity and draw out the liminal state many of us have been living through. This hesitancy stems from a longer history of initially pro-health, anti-corporate movements that have been twisted and weaponized. As a result, the people who have been historically hurt the most by our government and other institutions are now suffering the most. Their pro-life rhetoric only extends to theoretical life, not to actual humans already alive and in need of support and protection via widespread vaccinations. Here I argue that skepticism of government and even corporations has become weaponized to a dangerous degree, even when it comes to settled science such as vaccinations. Read more »

Phoenix

after Iqbal

Unveil your face
A star is witness

Stop flickering
Blaze

How long will you beg like Moses on the mountain?
Fan the flame within you

Create a new Mecca with every speck of your embers
Rid yourself of idolatry

Observe the limits in this temple
Even if you want to boast

First create the confidence of Alexander
Then lust after the splendor of Darius

 ***

By Rafiq Kathwari. His new collection of poems, My Mother’s Scribe, is available here  and  here.