by Christopher Bacas

Catering hall loading docks smell of cleaning fluids, grease and rotting food. They rise from the shores of milky lakes continuously replenished by mop buckets. There's a dumpster nearby, mouth drooling effluents and green frame askew. Up concrete steps, through swinging doors, across a slippery red tile floor, PISO MOJADO! sign tossed aside, a stale hall leads to the kitchen; vast rain forest of garlic and meat odors suspended in a Hobart's steam cloud.

Public side of the building is hushed activity. Sidewinder vacuums exhaust stale air. Tuxedoed staff deal place settings from sprung stacks on casters. Musicians arrive solo, duo or trio. Bulky gear packed tight and wheeled in. Cases and bags pile as they set up. The PA forms a protective front; subwoofers root below suspended mains. The keyboards, light rack, sound board and mic stands mark the perimeter. Then, to the bathrooms, changing into work clothes: white ruffled shirt and bow tie or black on black or Joseph's Inflatable Vest of Many Colors; best worn with bedazzled cummerbund.

Every band has a leader. They might not even play anything, just make sure the musicians do what's expected. There might be two leaders: one for the music and one for the client and venue. No matter their number, division of labor or size of the cocktail-hour shrimp, sidemen will suspend treasured ideals for a (somewhat) steady paycheck.

The first leader I worked for out of college, ended each wedding singing "Embraceable You".

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by Paul Braterman

The now Vice-President of the United States stands accused of having said that evolution is "just a theory"; see here and here. No he did not say that. What he did say (full text below, with notes) was far, far worse. Much more detailed and much more dangerous.

After reminding us that he was trained in law and history, he mangles the historical facts and legal significance of a key court case (the Scopes trial).

L: Pence being sworn in as a member of the House Education and Workforce Committee (CNN)

By quotemining a secondary source, which he treats as if primary, he twists the then-recent discovery of Sahelanthropus into an argument against the underlying science. It is changeable, he argues, therefore it is uncertain.

He justifies this manoeuvre by harping on the ambiguous word "theory", and making a falsely rigid distinction between theory and fact.

R: Sahelanthropus tchadensis, photo from Smithsonian Human Origins website

And worst of all, he asks his colleagues to "demand [emphasis added] that educators around America teach evolution not as fact, but as theory". The proponent, when it suits him, of small Government wants Washington to tell teachers how to teach.

Pence has been accused of stupidity because of the factual and logical errors contained in his speech. On the contrary, the speech is a well-constructed piece of rhetoric directed at a specific intended audience. It skilfully deploys techniques of distortion, disinformation, and distraction to accomplish its goals; goals now crowned with personal success, and with the possibility of even greater personal success once Trump goes. To fail to recognise this is to remain in ignorance of some of the most powerful forces that have helped make the US what it is today.

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by Richard King

"How we gonna make this shit okay to be a Nazi out here?" demands a guy in a red beanie, his bearded face filling half the shot. "That's bullshit, bro, it's not okay! He will not divide us!" He paces the street like a lion in a cage, circling back to the camera, angry. "He will not divide us!" he shouts and the small crowd responds, "He will not divide us!" A young woman steps into shot and takes up the chant to a different rhythm: "He will not divide us he will not divide us he will not divide us he will not divide us." She holds up her palm: it has a love-heart on it. Meanwhile, in the background, the red beanie guy is quietly arrested by a team of cops. "Fuck you, you Nazis!" shouts a member of the crowd, as a stocky man walks forward, arms spread: "What the fuck just happened here?" Now it's two young women in the frame – Love-Heart and another one – repeating the line with a studied lack of affect, like cult members waiting in line for the Kool-Aid: "He will not divide us. He will not divide us. He will not divide us. He will not divide us."

Powerful stuff. Or, indeed, not. For whatever else "He Will Not Divide Us" has done, it's certainly divided opinion. For some it is merely a glorified selfie, a tedious bit of virtue signalling combining millennial narcissism and dull groupthink. For others, it is a message of hope and solidarity, of resistance in a time of defeat. Some have called it a work of genius. Writing in The Week, Jeva Lange described it as "the first great artwork of the Trump era".

Notwithstanding that "the Trump era" is only two months old, this strikes me as an extraordinary claim. I mean to say, what about Hipster in Chief or Sean Spicer's surreal installation, White House Press Secretary in the Era of Fake News – a searing indictment of post-truth politics? (Watch this guy Spicer: he's going to be huge.) But the problem I have with this protest artwork is not its lack of artistic merit. No, the problem I have with it is the kind of protest it seeks to channel, and of which it is itself an example. My problem with it is political.

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by Carl Pierer

It is often the case in mathematics that by noticing some kind of symmetry, a problem can be simplified substantially. This makes them very useful. But, much like in art, mathematical symmetries also have an air of beauty and harmony. Perhaps this is one of the reasons why their study is a particularly satisfying branch of mathematics. A symmetry in mathematics is considered as an invariance under certain transformations. Consider, for instance, a square. There are the four rotational symmetries and four symmetries of reflection. While the vertices get permuted under these transformations, the configuration of the triangle is invariant. What this means is that if vertex 1 is joined to the vertices 2 and 4, then no matter what transformation we apply, these vertices will be joined afterwards as well. A transformation that does not keep these joints fixed will not be a symmetry. All these transformations taken together form a mathematical group. These can be, for a lack of a better word, considered as discrete symmetries and belong to the theory of finite groups. A different approach is to consider symmetries of continuous transformations. These are somewhat harder to visualise. Consider a circle. A rotation of the circle by any degree, no matter how small, will preserve the configuration of the circle. This is an example of a continuous transformation. The groups of these kinds of transformation find a natural place in Lie theory.

The person responsible for launching the early investigation of groups of continuous symmetries was Sophus Lie (1842-1899). In the 1860ies, the study of finite groups became a solid part of mathematics; by this time, tools had been developed and mathematicians started using them for various problems. In 1870, Camille Jordan published his Traité des substitutions et des équations algébriques. This was the first detailed study and clarification of Galois Theory. Evariste Galois (1811-1832) had studied algebraic equations and solutions to them. By finding symmetries in the roots of a polynomial and associating a group, he launched a wholly new and fruitful field of mathematical research. His work, possibly due to the highly tumultuous circumstances of his life and his early death, remained in sketches and it was not until others cleared up the ideas that the full impact of the theory was appreciated. Jordan's Traité was an effort to showcase and elaborate on the earlier work on groups by, amongst others Galois and Cauchy. But it also included substantially new contributions, introducing the concept of solvable groups, composition series and proving part of what is today known as the Jordan-Hölder theorem. The work has been credited with being an inspiration for many mathematicians and bringing group theory into the focus of late 19^th century and 20^th century mathematics.

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by Maniza Naqvi

I've traveled across the city from M.A. Jinnah Road and the Pioneer Book House in the neighborhood of Meriwether Tower to an art gallery off 26h street Block 4 Clifton in Karachi now in the shadow of another occupying towering tower. Same story. Of ground breaking points of references reaching back 1200 years. This route that encompasses galleys which brought Sidis and slaves and the Empires' soldiers, of alleys, and gullies and godowns and corridors, and mandirs and mazars and mosques, and synagogues. This route of the gods, part men-part women, and their many guest houses, whore houses, book houses, teahouses, sharab houses and more. I've crossed them all.

I have two hours before I call in to work—thousands of miles away–in the world where I am not quite like this. But still I hope the same. I'm here, this evening to meet my friend Hani. But instead in the moment I've walked into the opening reception in the courtyard for Taqseem the art exhibition. While I wait for Hani to arrive I go in to see the exhibit.

I stare at a photo shopped gigantic portrait of Jinnah by the artist Imran Channa—Jinnah in all his different iterations—perhaps seven different poses, now European now Indian, now Pakistani, so cool, so well dressed, debonair, effete, sophisticated, immaculate. And I'm there—gazing at him, this beautifully dressed man—and I'm dressed in my 20 year old khadi kurta—regretting not having washed my hands or feet or having taken a shower before I came here—And would it have killed me to have dragged a comb through my hair? But there wasn't enough time to fix things. For him. I mean. And I could've scrubbed my face. The one in the shades I'm picking that as the one I'm feeling…

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by Paul North

What do movies tell us? They tell stories; they tell about exotic places, wealth beyond our imagining, weapons beyond what would ever be necessary; they tell us about the idiosyncrasies of our celebrities. Besides all this, they almost always tell us something about ourselves. Imagine a screenwriter. What is her material? She works with plot and character yes, but her real material is us, our expectations. A screenwriter has to know, or think she knows, what the widest possible variety of viewers expects to see, so she can decide how to satisfy that in some respects and frustrate it in others. Before they type a word, screenwriters are psychic map makers, walking our internal landscapes, plotting the distant peaks and hidden valleys. They are the original mythographers. They tap into the unspoken myths that we keep secret—even from ourselves. Movies tell out loud secret beliefs we hide. Here is a test: next time you turn on a movie, if it captivates you, ask yourself which of your secrets is being revealed, what dark part of you is being torn out and lit up on the screen.

Fate is one of these secrets. We may talk about freedom, we may think of our future as full of possibilities, we may choose our president, choose our deodorant, choose when to choose and when not to—but in the direst moments, when it becomes too frightening or too difficult to see a way forward, we indulge in our secret belief in the fateful nexus that makes us unable to act. I have heard the most radical intellectuals, whose freedom of thought and imagination dwarfs anyone else's, say that gender differences must be "hard-wired."

Obviously "hardwired" is a way we talk. Like movies though, the way we talk tells us the secrets we keep. Newspaper headlines are also "talk"—they can be equally revealing. Even when the answer is no, we are not hard-wired to do this or that, just raising the question points right at our worry: are we hard-wired for this or that? (Look at "Are We Hard-Wired for War?" (NYT 9/28/13)). It's funny: "hard-wired" or as it's sometimes written—as if it were a technical term—"hardwired," is most often used in the press these days to talk about human psychology. It is, though, a metaphor. To date, no psychologist has discovered any "wires" in us.

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by Michael Liss

My 40th college reunion is coming up. Yes, it's a jolt to the system to realize that I've gone from a skinny young nerd to a skinny vintage nerd in what seems roughly the amount of time it takes to play an Orioles-Yankees game. I'm making the calls and sending the emails to my far-flung (but "curated") group of friends, trying to decide whether Baltimore in Springtime is all that appealing…or should we just wait for 50?

It can get a little hot in April in Charm City. In fact, it can stay a little hot well into September. Along with hot, Baltimore has a well-deserved reputation for humid. It excels at humid. This, along with Chemistry, and, of all things, German, caused me briefly to wonder just what the heck I was doing when my guidance counselor suggested Johns Hopkins and I thought "Hopkins, wow, great idea, Cushing, Halsted, Osler, I'm going to be a doctor!"

Reality can be a cruel mistress. Yet there was something besides an absurd Heat-Index reading that was different about my first few days in college—there was also the sound of ROTC candidates training in the practice field behind my dorm. A reminder of Vietnam and a fate—perhaps my fate—rather narrowly escaped.

If you didn't live through it, it might be hard to grasp the turmoil, anger, and anxiety of the late 60s and early 70s. Turmoil, because no one knew when or how the war was going to end; anger, at politicians who seemed unable to find satisfactory answers; and anxiety—deep fear—that you, or a family member would somehow find himself in a place that few wanted to be for a cause in which many did not believe.

Richard Nixon had called for an all-volunteer army during the 1968 Campaign. Whether he actually believed in the concept or was merely using it as a tactic is hard to say. But he was also looking for a way to defuse the constant anti-war demonstrations. These, he thought, were led by middle and upper-middle class families who were concerned that once their boys completed their college deferments, they would be shipped off to die. Take away their risk, and they would no longer care, allowing him to pursue his strategic aims unencumbered by organized opposition.

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by Leanne Ogasawara

Nobel laureate Steven Weinberg had a wonderful piece in a recent edition of the New York Review of Books about "the trouble with quantum mechanics."

Trouble? You ask….?

Well according to science writer Tom Siegfried, "Quantum mechanics is science’s equivalent of political polarization." He says:

Voters either take sides and argue with each other endlessly, or stay home and accept politics as it is. Physicists either just accept quantum mechanics and do their calculations, or take sides in the never-ending debate over what quantum mechanics is actually saying about reality.

This is to draw attention to the fact that as the mathematical models become increasingly more sophisticated in representing a foundational picture of physical reality, the conclusions that can be drawn from the picture become "impossibly weird." Such weirdness is what led to Schrodinger's cat, for example. Or later on to the weirdness called "entanglement" and the multiverse; both which we can safely describe as being, "extreme weirdness."

To understand what physicists mean when they call something "weird," Weinberg pointedly contrasts the situation in quantum mechanics to the ever-reliable consolation that is classical Newtonian physics; in which one can quite accurately calculate where a ball will land if its velocity and direction are known. Not so in our new universe; for in the crazy upside-down world of quantum mechanics no one can say for sure where an electron will be if it is measured–only where the probability wave is most intense.

Even Einstein lost his nerve at this point, famously saying, "God does not throw dice." And Weinberg wonderfully describes how both Schrodinger and Einstein distanced themselves from quantum mechanics later in their careers for just this reason; as the observational results have led particle physicists into saying the damnedest things.

And interestingly this weirdness eventually led to the two different approaches to the issues, so wonderfully described by Tom Siegfried above. Before reading Weinberg's piece I wasn't actually aware that particle physicists thought in terms of "realism" versus "instrumentalism;" as this is a dichotomy that I associated with an older period in the history and philosophy of science.

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by Dave Maier

As a philosophical term of art, pragmatism is a uniquely difficult to define. This is because pragmatists don’t care about essences or definitions, and when presented with apparent problems with this or that definition of pragmatism, they (we) are likely to shrug. Who cares what something is called, when what matters is what good it is? But surely “pragmatism” has a meaning like any other word – or, if we don’t want to bring meaning into it, we can appeal to pragmatist sympathies in this matter by noting that the concept can be useful, but only if we are clear on how to use it best. This can be tricky, as pragmatists don’t like to be pinned down on anything, semantic or otherwise, without knowing how the issue has come up and why we care, and of course there’s a wide variety of potential answers to those questions.

I mention all this because I have been reading Alan Malachowski’s 2010 book The New Pragmatism, by which, at least in this brief introduction to the subject, he mainly means Richard Rorty and/or Hilary Putnam (whose death a year ago (at 89) I am ashamed to admit I did not notice. One of the book’s epigraphs is from Rorty himself, who tells us, typically, that “I do not think that pragmatism has a True Self.” Throughout the book, Malachowski is pretty consistently a staunch defender of Rorty’s thought, but I wonder here if he has chosen this particular Rortyan formulation to motivate our sense that for all its virtuous resistance to metaphysical sin, it still leaves something important yet undone. Who said anything about a True Self? We just want to know what we’re talking about.

We might naturally start by distinguishing pragmatism from one of its neighbors. In contemporary parlance, in philosophy and in general, while “pragmatism” is generally neutral in tone, the term “postmodernism” is mainly used dismissively. So used, it picks out a (thankfully) short-lived intellectual and cultural movement characterized by trendy nihilism, radical skepticism and relativism, and naive, tendentious, sanctimonious identity politics of the primarily left-wing variety. In linguistic matters at least, vox populi, vox Dei, so I can’t really complain; but it does leave us with some work to do if we are to avoid confusion – which is what we’re here for, so let’s get to it.

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by Sarah Firisen

Science fiction has always run the gamut from extreme prescience on one end to paranoid fantastical delusions at the other, and everything in between. But it has always done more than merely try to predict future technologies, it has played its part in our imagining of the future. From the imaginations of writers and filmmakers spring fantastical creations that generations of science and tech geeks dedicate themselves to making a reality – there may be no better example of this than the fervor around creating Marty McFly’s hoverboard from Back to the Future. And while there is a very long list of fictional universes that have clearly inspired generations of scientists, maybe none has had quite such a direct and sustained impact as Neal Stephenson’s Snow Crash has had on the envisioning, creation and even lexicon of virtual and augmented reality. The impact is so clear that Stephenson was stalked by the founders of the extremely hyped but uber secretive augmented reality firm Magic Leap and was eventually persuaded to join them as their Chief Futurist. Stephenson even coined the terms avatar and metaverse in his rather dark tale of a pretty dystopian early 21st century.

Actual virtual reality technology has been around maybe 20 years or more in one form or another. But it’s really only in the last few years that a perfect storm of cheap and plentiful data storage, extreme advances in computing power, and perhaps most opportunely, the rise in quality and drop in cost of tiny hi-res screens thanks to the proliferation of smartphones, has meant that finally, despite many false starts, we may be on the cusp of realizing a level of virtual and augmented reality that may come close to Stephenson’s vision.

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by Scott F. Aikin and Robert B. Talisse

Wisdom is a product of experience and reflection. As a consequence, it's often quite a long road to that goal. It's for this reason that the poetic expression, "the Owl of Minerva Flies at Dusk," has its effect. Only at the end of the day, once the work is done and we recline in thought, do the insights of what we ought to have done, what the best option was, and what was wrong about a particular decision become clear. We live forward, but we understand backward. And that can occasion distinctive problems.

In democratic politics, this point about insight is certainly true. And it extends not only to the errors we may make as a country, but also to the errors we make in understanding ourselves and our decision-making. In its current form, much democratic theory is focused on the decision-making and argumentative elements of modern political life. This deliberative democratic movement casts democratic life as that of participating in ongoing discussions, wherein all have a voice, no issue is beyond question, and every decision must be justifiable to all those whom it effects. There are admirable ideals, but we understand the ways we can fail those ideals only in making mistakes, only in witnessing the pathologies to which public reason is prone.

We experience living in a democracy and then we see the particular kinds of challenges and errors to which reasoning together can be prone. Perhaps we should have anticipated the effects of group polarization that seem to define contemporary political discourse, but we understand it all too well now that we live under its conditions. The incurious dogmatism of epistemic closure, the slippery euphemism of Orwellian Newspeak, and the abuses of and visceral reactions to political correctness are all political phenomena that require we see as developments from histories and arising within particular social settings. We do now know them a priori.

The Owl of Minerva Problem at first looks like a simple point about the retrospective nature of knowledge: You must first have experience to know, so knowledge must be dependent on (at least some) events of the past. But the Owl of Minerva Problem raises distinctive trouble for our politics, especially when politics is driven by argument and discourse. Here is why: once we have a critical concept, say, of a fallacy, we can deploy it in criticizing arguments. We may use it to correct an interlocutor. But once our interlocutors have that concept, that knowledge changes their behavior. They can use the concept not only to criticize our arguments, but it will change the way they argue, too. Moreover, it will also become another thing about which we argue. And so, when our concepts for describing and evaluating human argumentative behavior is used amidst those humans, it changes their behavior. They adopt it, adapt to it. They, because of the vocabulary, are moving targets, and the vocabulary becomes either otiose or abused very quickly.

Consider the use of fallacy vocabulary less as a device for the cool evaluation of arguments, now, but rather as a tool of evasion or attack.

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by Jonathan Kujawa

While laying in bed on the night of January 20, 1884, Lewis Carroll conjured up the following puzzle:

Three Points are taken at random on an infinite Plane. Find the chance of their being the vertices of an obtuse-angled Triangle.

That is, since any three points on a sheet of paper can be connected to form a triangle, what's the likelihood that one of the angles is more than ninety degrees if you pick those points at random?

If you only know Lewis Carroll from Alice in Wonderland you may be surprised that his thoughts turned to mathematics. In fact, his day job was to be a mathematician at Christ Church college in Oxford under the name Charles Dodgson. In addition to his more famous works of fiction, he was known for writing several mathematical texts. When teaching linear algebra I always take a day to talk about Dodgson Condensation [1].

Lewis Carroll working on a pillow problem.

One of the books he wrote is Curiosa Mathematica, Part II: Pillow Problems Thought Out During Wakeful Hours. It is the compendium of 72 math problems Dodgson pondered and solved while waiting to fall asleep. Helpfully he also gives the date he dreamt up the problem and the solution he devised. Go here if you'd like to take a look at the other 71 problems.

The Obtuse Triangle Problem is No. 58. Before we take a look at his solution we should step back a minute. What does it mean to pick three points at random? Like most politicians' speeches, it sounds good but falls apart under the slightest scrutiny. Are we to pick x and y coordinates for each of these points? Alternatively, we could pick an angle between 0 and 360 degrees and a distance and, starting at the origin, take the point at that angle and distance. Or, since all we care about is the resulting triangle, maybe we should randomly pick an angle between 0 and 180 degrees, pick two side lengths at random, and make the triangle made by drawing two sides of those lengths with that angle between them. I'm sure we could come up with a dozen different ways to randomly pick a triangle.

If a random triangle was a random triangle, and if the world was fair and just, then the odds of an obtuse triangle would be the same regardless of our method. Sadly, the world is neither fair nor just. It will matter how we choose to pick a random triangle [2].

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