Beauty is Not (Entirely) in the Eye of the Beholder

by Dwight Furrow

SunsetIn philosophy the most important development in the last 300 years has been the idea that what can be intelligibly said about reality is constructed out of our subjective responses, suitably constrained by social norms and intersubjective communication. This is the essence of Immanuel Kant's so-called Copernican Revolution in philosophy which converted us from naïve realists who took reality at face value to sophisticated anti-realists constructing reality via the structures of consciousness and language.

Kant's argument is sound but preposterous. One would have thought that reality's stubborn resistance to our ideas and expectations and the fact we are often surprised by this resistance might lead us to take the idea of a real world more seriously. The performative contradiction of claiming all reality is a social construction while traipsing off to the doctor when ill renders truth and knowledge the exclusive purview of scientists who have never shown much inclination toward anti-realism. But once these "naïve" realist thoughts are cast out in favor of Kant's fastidious, critical skepticism, common sense can't find a way back in. And so for 300 years we have been denying what to non-philosophers seems obvious—there is a real world out there with which our senses put us into contact.

In light of this revolution in thought we were, by now, supposed to be basking in the friendly solidarities of intersubjective agreement, a consequence that unfortunately appears to be increasingly remote. This idea that reality is a social construction ebbs and flows outside the philosophy class but in today's "post-truth" society it seems ascendant. Perhaps a new way must be found to anchor truth in something more substantial than contingent, collective agreements.

Read more »



Under The Radar, Part 1

by Misha Lepetic

"In economics, the majority is always wrong."
~ JK Galbraith

Diego-Rivera-work-998x698One of the unfortunate gifts of the current, star-crossed administration is that there's something for everyone that will get their knickers in a twist. If immigration or climate change isn't your thing, just wait a few days, and some administration official will come out with a statement that lands somewhere in the space between spectacularly ignorant or merely deeply ill-considered. My latest opportunity to double-take arrived a few days ago, when Secretary of the Treasury (and Goldman Sachs alum) Steven Mnuchin opined that the threat of artificial intelligence to employment is "not even on my radar screen".

To be fair, the clip is brief enough that it is difficult to conclude whether or not Mnuchin knows what he is talking about. Too often when we talk about technology we fixate on one aspect of it, and intend (although not always) that this aspect stands in for the entirety of the technological phenomenon. These days, favored metonymies are ‘AI', along with ‘robots' and ‘algorithms'. Keeping this in mind while listening to the Mnuchin clip, it's unclear what he actually means when referring to AI. Although I suspect he's talking about the holy grail of AI, which is artificial general intelligence, or an AI that is indistinguishable from human intelligence.

If that is the case, then he did a disservice to the question, which was about the impact of AI on employment. Or, if you'll allow me to pluck out the metaphor, the impact of technology on employment, which is much more amorphous. Mnuchin's dodge was to say that, since we won't have human-equivalent AI for the foreseeable future, it's something that's not worth thinking about, at least until it happens. Come to think of it, I've heard this dodge before, mostly from the mouths of climate change skeptics and deniers. In both cases, the purpose is to obfuscate and delay until the truly catastrophic comes to pass, then innocently maintain that "no one could have seen this coming" or some such nonsense.

Read more »

4B

by Tamuira Reid

The day Luna went mad her mother thought, finally. The signs had been there, hanging around at the dinner table, in the bathroom where she ironed her hair.

It had waited patiently in the corner of a room, under a chair, in the oven with the bread. Now they wouldn't need to wonder when it would all fall apart because it just had.

The day Luna went mad she was wearing pink lipstick. Her legs were waxed and smoothed down with cocoa butter because she was religious about that kind of thing. Never know who you're gonna see, she'd say, sliding a gold hoop through each ear.

It happened slowly and over a period of time. Shop closed. Her mind just closed-up on her. Went out of business.

Luna sang to the plants as she watered them. Would be normal except she thought she heard them sing back. Her mother turned up the radio and hung wet nylons from the fire escape.

It's hard to talk about it, when it's your daughter.

The emptiness in her eyes scared her mother. The empty blackness of her eyes. They held nothing but crazy and she knew that. And somewhere deep inside, her daughter knew what was happening too but she couldn't stop it.

The police said they had found her in the fetal position, on a sidewalk in Times Square. She was licking her arms like a cat. Her clothes sat next to her in a pile, perfectly folded. She wanted to go home if that was okay.

Sit. Eat.

My hair.

Your hair is perfect. Sit.

Her mother sat her down at the table and did what she did best. Fed her. A hot plate of arroz con pollo, a Malta, tostones with the heat still rising off them.

Something is happening to me, she said and stared out the window. A plastic bag floated by, white and ripped on one side.

Eat.

Read more »

Relativity and relativism: stitching a world together

by Daniel Ranard

Stitching a treeIn the twentieth century, two important ideas arose with a nominal similarity: Einstein's theory of relativity on the one hand, and the idea of cultural or moral relativism on the other. It's probably fruitless to draw parallels between concepts that arose at distant ends of the intellectual spectrum—the hard sciences versus the humanistic disciplines—but sometimes you can't help yourself: "relativity" is right there in the name. In 1905, Einstein declared that certain facts about space and time are only true relative to a particular person or reference frame. In subsequent decades, philosophical "relativists" argued that questions of what is moral, what is true, or even what exists can only be answered relative to individuals or groups. Of course, Einstein's theory proved to be right, while the philosophical strand of relativism has evolved into a variety of contentious ideas.

First I will focus on Einstein's relativity, before touching on relativism in philosophy. To me, the story begins with two opposing accounts of what physics is. According to one account, physics provides an objective description of the world itself, like an encyclopedia entry on "The Universe." The encyclopedia tells you what stuff the world is made of and how that stuff behaves. This approach might be called the realist approach: physics presents objective facts about the real world.

Others prefer an "operationalist" account that focuses on the individual. By this account, physics is simply a collection of rules telling the individual what to expect in various circumstances. It's like a personal guidebook for experience: it predicts what you will observe when you follow various experimental procedures, like following a recipe in a laboratory. Unlike the realist's encyclopedia entry, the operationalist's guidebook does not attempt to describe the real world objectively. Instead, it prescribes how your experience should lead you to predict future experiences, using your own observations. Operationalists avoid referring to fundamental aspects of nature, like mass or length. To the operationalist, the length of an object is not some fundamental property – it's just a number you observe when you measure the object with a ruler, and any notion of length must be accompanied by well-specified procedure for how to measure it.

Read more »

Deep Disagreements and Argumentative Optimism

by Scott F. Aikin and Robert B. Talisse

ContemptWe all have had moments when we feel that those with whom we disagree not only reject the point we are focused on at the moment, but also reject our values, general beliefs, modes of reasoning, and even our hopes. In such circumstances, productive critical conversation seems impossible. For the most part, in order to be successful, argument must proceed against the background of common ground. Interlocutors must agree on some basic facts about the world, or they must share some source of reasons to with they can appeal, or they must value roughly the same sort of outcome. And so, if two parties disagree about who finished runners-up to Leister City in their historic BPL win last year, they may agree to consult the league website, and that will resolve the issue. Or if two travelers disagree about which route home is better, one may say, "Yes, your way is shorter, but it runs though the traffic bottleneck at the mall, and that adds at least ten minutes to the journey." And that may resolve the dispute, depending perhaps on whether time is what matters most.

But some disagreements invoke deeper disputes, disputes about what sources are authoritative, what counts as evidence, and what matters. Such disputes quickly become argumentatively strange. And so if someone does not recognize the authority of the soccer league's website about last year's standings, it is unclear how a dispute over last year's runners-up to Leister City could be resolved. What might one say to a disputant of this kind? Does he trust news sites, television reporting, or Wikipedia entries concerning the BPL? Does he regard the news sites and the league website as reliable sources of information concerning this year's standings or when the games are played? What if our interlocutor in the route-home case doesn't see why the quickest route is preferable to the shortest? Maybe our traveling companion regards our hurry-scurry as a part of a larger social problem, or maybe wants to enjoy the Zen of a traffic jam. Sometimes a disagreement about one thing lies at the tip of a very large iceberg of composed of many other, deeper, disagreements.

Read more »

Monday, March 20, 2017

Why technology won’t save biology

by Ashutosh Jogalekar

CarlWoese

Carl Woese’s integrated view of biology should help temper the application of technology to biological understanding

There seems to be no end to biology’s explosive progress. Genomes can now be read, edited and rewritten with unprecedented scope, individual neurons can now be studied in both space and time, the dynamics of the spread of viruses and ecological populations can be studied using mathematical models, and vaccines for deadly diseases like HIV and Ebola seem to hold more promise than ever. They say that the twentieth century belonged to physics and the twenty first belongs to biology, and everything we see in biology seems to confirm this idea.

There have been roughly six revolutions in biology during the last five hundred years or so that brought us to this stage. The first one was the classification of organisms into binomial nomenclature by Linnaeus. The second was the invention of the microscope by Hooke, Leeuwenhoek and others. The third was the discovery of the composition of cells, in health and disease, by Schwann and Schleiden, a direct beneficiary of the use of the microscope. The fourth was the formulation of evolution by natural selection by Darwin. The fifth was the discovery of the laws of heredity by Mendel. And the sixth was the discovery of the structure of DNA by Watson, Crick and others. The sixth, ongoing revolution could be said to be the mapping of genomes and its implications for disease and ecology. Two other minor revolutions should be added to this list; one was the weaving of statistics into modern genetics, and the second was the development of new imaging techniques like MRI and CT scans.

These six revolutions in biology resulted from a combination of new ideas and new tools. This picture is consistent with the general two-pronged picture of scientific revolutions that has emerged through the ages: a picture consisting in equal parts of revolutions of ideas and revolutions of technology. The first kind was popularized by Thomas Kuhn in his book “The Structure of Scientific Revolutions”. The second was popularized by Peter Galison and Freeman Dyson; Galison in his book “Image and Logic”, and Dyson in his “The Sun, the Genome and the Internet”. Generally speaking, many people are aware of Kuhn but few people are aware of Galison or Dyson. That is because ideas are often considered loftier than tools; the scientist who gazes at the sky and divines formulas for the universe through armchair calculations is considered more brilliant than the one who gets down on her hands and knees and makes new discoveries by gazing into the innards of machines.

Read more »

Monday Poem

Coffe and whistlers mother

Having Coffee

i’m having coffee
i’m dreaming I’m having coffee with Whistler’s mother
i’m scratching a knuckle with my nose
i’m not listening to my wife while gazing out a window
i’m imagining our small distant sun rising over the horizon of Neptune
i’m having coffee, paper cup with a heat sleeve
i’m playing with two small stones, twiddling them in my palm like Queeg
i’m remembering throwing stones through a neighbor’s bias
i’m sitting, but you don’t want to know where
i’m wondering if death is simply the mirror parenthesis of birth
i’m lying in bed staring at the ceiling slightly chilled. I need another
blanket

i’m fooled again
i’m not fooled again
i’m having coffee, dark roast, the only kind
i’m wrong about a lot of things, too many
i’m dumber than a stump but smarter than a breadbox
i’m still wondering what it’s all about Alfie
i don’t care what it’s all about, I’m picking asparagus
i’m inside a cosmic question bouncing off its walls
i’m having coffee, Colombian this time, but dark, as I said…
i’m puffed as a peacock but simultaneously beside the point
i’m over the hill but still climbing
i’m loose as a goose and tight as a fundamentalist’s ass
i’m unknown, thank god, remembering Elvis
i’m anonymous as a red leaf in the Berkshires in Fall
i’m having coffee gazing over the rim of a mountain watching a small cloud glide
i’m as unbelievable as your average Mohammed or Mike
i’m at least as believable as your average Mohammed or Mike
i’m beating my head against the wall again painlessly
i’m taking an aspirin just in case
i’m having tea , green, trying to take coffee’s edge off
i’m under the gun, but still over the clover
i’m not sure
i’m cock sure
i’m as fraught with anticipation as I was when I was twenty, just not as often
i’m remembering something, but quickly change channels
i’m thinking again of a Dylan line, so many good ones blowin in the wind

time out of mind

I am having coffee
I am not having
I am not not

yet
.

Jim Culleny
May 2009

A Confession in the Age of Trump

by Elise Hempel

TrumpHair03Sometime during college, back home in the Chicago area for the summer, I found a job as a secretary for a successful real estate agent who kept two offices in his condo – his own out of sight in a bedroom, and the other, for his secretary, right there as you walked in, the large, dark wrap-around desk commanding a good portion of the living room. I don't recall my exact secretarial duties, except for answering the phone, but I remember my boss's name and his face, as well as my overall discomfort with having no fellow employees, with being in an office that was also someone's home – just the two of us there together all day long.

And I remember what he asked me to do for him on my last day of work before I returned to school for the fall semester: Would I let him take my picture? Would I get down on the shag carpet on all fours and stick my butt up in the air while he sat on the sofa with his camera and snapped a permanent image of his favorite part of me?…

What did I say at that moment, and how long did I pause before I complied? Why didn't I shout no or spit in his face? Why didn't I grab my purse and my final paycheck and storm out of that condo, resolutely slamming the door behind me? How many more suggestive comments had there been before then, inappropriate remarks I'd tried to ignore, laughed off because I had no idea what to say?

Read more »

The Chickening of America, or Why We Don’t Eat Fish (But Could Eat More)

by Carol A Westbrook

It's Lent. For many people, that means you have to deprive yourself of food that you like to eat, and instead punish yourself by eating fish. In actuality, you are not required to eat fish during the forty days of Lent, devout Catholics and other Christians are only required to abstain from meat on Lenten Fridays. Fish is merely a protein can be conveniently substituted for the missing meat course–or you can eat eggs, cheese, pizza or eggplant Parmesan instead.

Yet some people are so unused to eating fish that when it appears in their diets it is memorable. Eating fish means "Lent." And they hate it.

During Lent we "try" to eat fish, and for many, McDonald's Filet-O-Fish is the answer. Fillet1The company sells nearly a quarter its filling, 390-calorie sandwiches during the six-week Lenten season. Although it contains wild-caught Alaskan Pollock, the sandwich contains only 2.8 oz. this fish (as I calculated from the protein content provided in McDonald's online nutritional information). Since 2.8 g of Alaskan Pollock has only 73 calories and 0.8 g of fat, the Filet-O-Fish's 390 calories and 18.2 g of fat can only be attributed to the bread, tartar sauce, and melted cheese.

I don't eat Filet-O-Fish because I honestly like fish a great deal more than I like bread, tartar sauce and melted cheese. Truly, I love fish. I love eating it in any way, shape or form — from smoked and pickled, to raw, fried, steamed and everything between. For example, while vacationing in Martinique, I had a plate of whole fried ballaboo, a local reef fish with a cute pointy nose that was meant to be eaten whole after deep-frying, sans pointy nose. Yum! (See the picture on the right). But most Americans don't share my passion, they hate fish.

Read more »

If You Could Have Any Superpower, What Would It Be?

by Max Sirak

IMG_0667Would you soar through the skies flying as most our feathered friends do?

Would you lord over light, bending beams this way and that, going invisible, and launching lasers?

Would you opt for elemental mastery? Controlling fire, air, wind, or water could definitely have its perks.

Would you wish to wrangle the weather? No more rained-out picnics, bike rides, rounds of golf, beach days, etc. doesn't sound bad. Ideal conditions for all outdoor outings would be swell.

Wielding weather was always my choice when I was kid. I remember lying in bed at night and thinking how much better it'd be if I could just make it snow instead of hoping the meteorologists on TV were right. Then school would be canceled whenever I felt like it, whether the flakes fell or not.

Now, my answer is a bit different. If I could choose to have any superpower it would be the ability to travel by teleportation. No more airfare. No more gas stations. No more traffic. No more delays. Just close my eyes and pop.

Italy for grocery shopping (and morning espresso with Abbas). Back to the States for a late breakfast with Tim. Over to San Francisco to see nieces and nephews. Happy hour in DC with Jonah and Rachel. Bounce back to Europe for a bottle of Bordeaux or to pick up a port from Portugal, depending on my mood. Then on to Ohio for home-cooked dinner before calling it a night under the Colorado sky.

Read more »

Poem

For My Nephew Omar On His Engagement to Nadia

This small box hides a porcelain elephant
rigged up in howdah and trimmings,
a Kashmir-style sapphire
on the forehead­­ — an inner eye;

conch shell ears fan out,
supple raised trunk
cradles a bird’s nest
without breaking the eggs.

“A matriarch of her herd,”
said the woman who sold it,
“175 years old, maybe more.
One-of-a-kind.”

Parting with this thing,
(Raj kitsch or art?)
I have long held dear
with my childhood’s faith

I have this dream
you will one day walk
like an elephant
joyously on water.

by Rafiq Kathwari, Beaver Dam, 29 October 2005
rafiqkathwari.com/@brownpundit

The Wedding Singer: Charlie’s Angels or Two-Buck Chuck

by Christopher Bacas

ImageCatering 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".

Read more »

Monday, March 13, 2017

Artificial Stupidity

by Ali Minai

"My colleagues, they study artificial intelligence; me, I study natural stupidity." —Amos Tversky, (quoted in “The Undoing Project” by Michael Lewis).

Humans-vs-AINot only is this quote by Tversky amusing, it also offers profound insight into the nature of intelligence – real and artificial. Most of us working on artificial intelligence (AI) take it for granted that the goal is to build machines that can reason better, integrate more data, and make more rational decisions. What the work of Daniel Kahneman and Amos Tversky shows is that this is not how people (and other animals) function. If the goal in artificial intelligence is to replicate human capabilities, it may be impossible to build intelligent machines without "natural stupidity". Unfortunately, this is something that the burgeoning field of AI has almost completely lost sight of, with the result that AI is in danger of repeating the same mistakes in the matter of building intelligent machines as classical economists have made in their understanding of human behavior. If this does not change, homo artificialis may well end up being about as realistic as homo economicus.

The work of Tversky and Kahneman focused on showing systematically that much of intelligence is not rational. People don’t make all decisions and inferences by mathematically or logically correct calculation. Rather, they are made based on rules of thumb – or heuristics – driven not by analysis but by values grounded in instinct, intuition and emotion: Kludgy short-cuts that are often “wrong” or sub-optimal, but usually “good enough”. The question is why this should be the case, and whether it is a “bug” or a “feature”. As with everything else about living systems, Dobzhansky’s brilliant insight provides the answer: This too makes sense only in the light of evolution.

The field of AI began with the conceit that, ultimately, everything is computation, and that reproducing intelligence – even life itself – was only a matter of finding the “correct” algorithms. As six decades of relative failure have demonstrated, this hypothesis may be true in an abstract formal sense, but is insufficient to support a practical path to truly general AI. To elaborate Feynman, Nature’s imagination has turned out to be much greater than that of professors and their graduate students. The antidote to this algorithm-centered view of AI comes from the notion of embodiment, which sees mental phenomena – including intelligence and behavior – as emerging from the physical structures and processes of the animal, much as rotation emerges from a pinwheel when it faces a breeze. From this viewpoint, the algorithms of intelligence are better seen, not as abstract procedures, but as concrete dynamical responses inherent in the way the structures of the organism – from the level of muscles and joints down to molecules – interact with the environment in which they are embedded.

Read more »

Why aren’t we working less?

by Emrys Westacott

Back in 1930, the economist John Maynard Keynes predicted that the continuous increase in productivity characteristic of industrial capitalism would lead within a century to much more leisure for everyone, with the typical working week being reduced to about fifteen hours. UnknownThis has obviously not come about. To be sure, in virtually all relatively prosperous countries the average number of hours worked annually has fallen over the last few decades. Between 1950 and 2010, in the US, for instance, this number dropped from 1,908 to 1,695, in Canada from 2,079 to 1,711, and in Denmark from 2,144 to 1,523. Even in Japan, famed for its workaholism, the average number of hours worked per year went from a high of 2,224 in 1961 to 1,706 in 2011.[1] But even the lackadaisical Danes are still working twice as hard as Keynes predicted.

Given the increases in productivity and prosperity in the industrialized world, one could have reasonably hoped for more. People in the UK are now four times better off than they were in 1930, but they work only twenty percent less, and that is fairly typical of other advanced economies. The rich, who used to relish their idleness, now boast about how hard they work, while for many of the poor unemployment is a persistent curse.

Moreover, according to economist Staffan Linder, economic growth is typically accompanied by a sense that we have less time available for the things we wish to do. This feeling is not mistaken, but the lack of time is in large part due to the fact that members of affluent societies will opt for more money over more leisure if given the choice. They then start to carry the mentality and values of workplace productivity into every part of their lives, resulting in what Linder calls the "harried leisure class."[2]

So why was Keynes wrong? According to Robert and Edward Skidelsky in How Much Is Enough? his mistake was to underestimate the difficulty of reining in the forces unleashed by capitalism, particularly people's desire for ever increasing wealth and the things it can buy. Our natural concern for improved relative status, hardwired into us by evolution, is inflamed by the capitalist system, complete with incessant advertising and free market ideology, so that we always want more than we have and more than we really need.[3]

Read more »

Sahelanthropus, evolution, and the word “theory”; what Mike Pence really said

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).

PenceSwearingL: 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.

Sahelanthropus tchadensis SmithsonianR: 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.

Read more »

‘POST-THIS, POST-THAT, ANTI-THIS, ANTI-THAT’: EVERYTHING THAT’S WRONG WITH LIBERAL POLITICS IN ONE, SELF-DEFEATING ARTWORK

by Richard King

He_Will_Not_Divide_Us_logo.svg"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.

Read more »

A sketch of early Lie Theory

by Carl Pierer

Sophus_LieIt 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 19th century and 20th century mathematics.

Read more »