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John Baez
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Circularly polarized light

This is a wave of circularly polarized light. As the wave moves forwards, but you stand in the same place and measure the electric field there, the electric field goes round and round. The magnetic field, not shown here, also goes round and round, at right angles to the electric field.

This movie shows right circularly polarized light. There's also left circularly polarized light, where the electric field turns around in the other direction.

All this stuff can be figured out mathematically by solving the vacuum Maxwell equations, which describe light with no matter around.

But where can you see circularly polarized light in nature?

Albert Michelson found some back in 1911!

You may know this guy: he won the Nobel prize with Robert Morley for discovering that light moves past you at the same speed no matter how you're moving. But he also discovered something else. Light reflected from a certain kind of beetle called a scarab tends to be left circularly polarized! The reason was discovered much later: at the microscopic level, the shells of these beetles are made of spiral-shaped molecules!

Light from certain firefly larvae is also circularly polarized, but nobody knows why yet.

And sometimes starlight is circularly polarized... slightly. It's actually a messy mix of different kinds of light. Sometimes it's linearly polarized - the electric field wiggles back and forth rather than round and round. This is because it scatters from elongated interstellar dust grains whose long axes tend to be oriented at right angles to the galactic magnetic field. But these grains spin rapidly, with their rotation axis along the magnetic field. This winds up creating a bit of circular polarization. The effect is tiny but measurable.

I was going to talk more about the math of circularly polarized light, but I got distracted. I wanted to explain how the polarization of light involves complex numbers. This is easier to talk about using quantum mechanics. To describe a photon with a certain energy in a certain direction, we need to use two complex numbers! A photon like

(1, 0)

is linearly polarized in one direction: say, its electric field wiggles back and forth. A photon like

(0, 1)

is linearly polarized in the other direction: say, its electric field wiggles up and down. So, a photon like

(1, 1)

would be linearly polarized in a diagonal way. But less obviously, a photon like

(1, i)

is right circularly polarized, and one like

(1, -i)

is left circularly polarized.

How did the complex numbers get into the game? We use them in quantum mechanics, but polarization of light is also there in the vacuum Maxwell equations, which were known before quantum mechanics. So the complex numbers should be lurking in the vacuum Maxwell equations!

They are. Mathematically, photons are solutions of the vacuum Maxwell equations. While these solutions involve two real vector fields, the electric and magnetic field, the space of solution is a complex Hilbert space. To multiply a solution by i you multiply its positive-frequency part by i and its negative-frequency part by -i.

In short: to fully understand light bouncing off a scarab beetle, you need to understand how the complex numbers are lurking in Maxwell's equations. The universe is cool. Let's be kind to our planet, so our civilization can stick around long enough to learn more. We're just getting started!

For more:

I got the animation from Wikicommons:


Animated Photo

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The battle against Elsevier begins in earnest
In Germany, the fight for open access and favorable pricing for journals is getting heated. At the end of last month (June 30), four major academic institutions in Berlin announced that they would not renew their subscriptions with the Dutch publishing giant Elsevier once they end this December. Then on July 7, nine universities in Baden-Württemberg, another large German state, also declared their intention to cancel their contracts with the publisher at the end of 2017.

These institutions join around 60 others across the country that allowed their contracts to expire last year.

The decision to cancel subscriptions was made in order to put pressure on Elsevier during ongoing negotiations. “Nobody wants Elsevier to starve—they should be paid fairly for their good service,” says Ursula Flitner, the head of the medical library at Charité–Berlin University of Medicine. “The problem is, we no longer see what their good service is.”

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Maryam Mirzakhani, 1977 - 2017

She died yesterday, a mathematician who had not yet reached the height of her powers: the first Fields medalist from Iran, and also the first woman to win that honor. Here's what I wrote when she won:

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find! She also watched television biographies of famous women like Marie Curie and Helen Keller. She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls. She did poorly in math her first year, and it undermined her confidence. “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject. She and a friend became the first women on Iranian math Olympiad team. She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate work at Sharif University in Tehran in 1999, she went on to grad school at Harvard. There she met Curtis McMullen, a Fields medalist who works on hyperbolic geometry and related topics.

Hyperbolic geometry is about curved surfaces where the angles of a triangle add up to less than 180 degrees, like the surface of a saddle. It's more interesting than Euclidean geometry, or the geometry of a sphere. One reason is that if you have a doughnut-shaped thing with 2 or more holes, there are many ways to give it a hyperbolic geometry where its curvature is the same at each point. These shapes stand at the meeting-point of many roads in math. They are simple enough that we can understand them in amazing detail - yet complicated enough to provoke endless study.

Maryam Mirzakhani took a course from McMullen and started asking him lots of questions. “She had a sort of daring imagination,” he later said. “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Here's a question nobody knew the answer to. If an ant walks on a flat Euclidean plane never turning right or left, it'll move along a straight line and never get back where it started. If it does this on a sphere, it will get back where it started: it will go around a circle. If it does this on a hyperbolic surface, it may or may not get back where it started. If it gets back to where it started, facing the same direction, the curve it moves along is called a closed geodesic.

The ant can go around a closed geodesic over and over. But say we let it go around just once: then we call its path a simple closed geodesic. We can measure the length of this curve. And we can ask: how many simple closed geodesics are there with length less than some number L?

There are always only finitely many - unlike on the sphere, where the ant can march off in any direction and get back where it started after a certain distance. But how many?

In her Ph.D. thesis, Mirzakhani figured out a formula for how many. It's not an exact formula, just an 'asymptotic' one, an approximation that becomes good when L becomes large. She showed the number of simple closed geodesics of length less than L is asymptotic to some number times L to the power 6g-6, where g is the number of holes in your doughnut.

She boiled her proof down to a 29-page argument, which was published in one of the most prestigious math journals:

• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics 168 (2008), 97–125,

This is a classic piece of math: simple yet deep. The statement is simple, but the proof uses many branches of math that meet at this crossroads.

What matters is not just knowing that the statement is true: it's the new view of reality you gain by understanding why it's true. I don't understand why this particular result is true, but I know that's how it works. For example, her ideas also gave here a new proof of a conjecture by the physicist Edward Witten, which came up in his work on string theory!

This is just one of the first things Mirzakhani did. She's now a professor at Stanford.

"I don't have any particular recipe," she said. "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

She has a lot left to think about. There are problems she has been thinking about for more than a decade. "And still there’s not much I can do about them," she said.

"I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."

I got some of my quotes from here:

and some from here:

They're both good to read. For a mathematically informed obituary, see this by Terry Tao:

The animated gif is a clip from this video:


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A Chinese hero: Liu Xiaobo, 1955 - 2017

The Nobel Prize winner Liu Xiaobo died today, of liver cancer. Despite his family's pleas, the Chinese government would not let him leave the country, nor let him speak publicly.

Let's remember a bit of what he did! He began as a literary critic. But this changed:

In 1989, he was a visiting scholar at Columbia University when students in Beijing occupied Tiananmen Square to demand democratic changes and an end to party corruption. He returned to Beijing to support the protests. He later described that time as a turning point, one that ended his academic career and set him irrevocably into a life of political opposition.

Mr. Liu’s sympathy for the students was not unreserved; he eventually urged them to leave Tiananmen Square and return to their campuses. As signs grew that the Communist Party leadership would use force to end the protests, Mr. Liu and three friends, including the singer Hou Dejian, held a hunger strike on the square to show solidarity with the students, even as they advised them to leave.

“If we don’t join the students in the square and face the same kind of danger, then we don’t have any right to speak,” Mr. Hou quoted Mr. Liu as saying.

When the army moved in, hundreds of protesters died in the gunfire and the chaos on roads leading to Tiananmen Square. But without Mr. Liu and his friends, the bloodshed might have been worse. On the night of June 3, they stayed in the square with thousands of students as tanks, armored vehicles and soldiers closed in.

Mr. Liu and his friends negotiated with the troops to create a safe passage for the remaining protesters to leave the square, and he coaxed the students to flee without a final showdown.

“I understand what you’re feeling, but haven’t you considered how as soon as the first shot rings out, Tiananmen Square will become a river of blood?” Mr. Liu told the students, as he recounted in a memoir published in 1989.

He was arrested days later, and began the first of 4 prison terms. He just couldn't stay out of trouble! In 2009, at his last trial, he wanted to read a statement, but was not allowed to. When he won his Nobel Prize a year later, it was read out loud in Sweden. I'll quote just part:

I have no enemies

I have no enemies, and no hatred. None of the police who have monitored, arrested and interrogated me, the prosecutors who prosecuted me, or the judges who sentence me, are my enemies. While I’m unable to accept your surveillance, arrest, prosecution or sentencing, I respect your professions and personalities, including Zhang Rongge and Pan Xueqing who act for the prosecution at present. I was aware of your respect and sincerity in your interrogation of me on December 3.

For hatred is corrosive of a person’s wisdom and conscience; the mentality of enmity can poison a nation’s spirit, instigate brutal life and death struggles, destroy a society’s tolerance and humanity, and block a nation’s progress to freedom and democracy. I hope therefore to be able to transcend my personal vicissitudes in understanding the development of the state and changes in society, to counter the hostility of the regime with the best of intentions, and defuse hate with love [....]

I do not feel guilty for following my constitutional right to freedom of expression, for fulfilling my social responsibility as a Chinese citizen. Even if accused of it, I would have no complaints.

To understand why he went to jail for a fourth time in 2009, let's go back to 2008 and look at Charter 08. This is a manifesto he helped write, which was signed by 350 Chinese intellectuals and human rights activists. It begins:

This year is the 100th year of China's Constitution, the 60th anniversary of the Universal Declaration of Human Rights, the 30th anniversary of the birth of the Democracy Wall, and the 10th year since China signed the International Covenant on Civil and Political Rights. After experiencing a prolonged period of human rights disasters and a tortuous struggle and resistance, the awakening Chinese citizens are increasingly and more clearly recognizing that freedom, equality, and human rights are universal common values shared by all humankind, and that democracy, a republic, and constitutionalism constitute the basic structural framework of modern governance. A "modernization" bereft of these universal values and this basic political framework is a disastrous process that deprives humans of their rights, corrodes human nature, and destroys human dignity. Where will China head in the 21st century? Continue a "modernization" under this kind of authoritarian rule? Or recognize universal values, assimilate into the mainstream civilization, and build a democratic political system? This is a major decision that cannot be avoided.

It makes 19 demands, namely:

Amending the Constitution.

Separation of powers.

Legislative democracy.

An independent judiciary.

Public control of public servants.

Guarantee of human rights.

Election of public officials.

Abolition of Hukou system, which controls where citizens can live.

Freedom of association.

Freedom of assembly.

Freedom of expression.

Freedom of religion.

Civic education.

Free markets and protection of private property.

Financial and tax reform.

Social security.

Protection of the environment.

A federated republic.

Truth in reconciliation.

Finally, we should not forget his wife, Liu Xia, who remains under house arrest in China. Here's another passage from Liu Xiaobo's speech I Have No Enemies:

If I may be permitted to say so, the most fortunate experience of these past twenty years has been the selfless love I have received from my wife, Liu Xia. She could not be present as an observer in court today, but I still want to say to you, my dear, that I firmly believe your love for me will remain the same as it has always been. Throughout all these years that I have lived without freedom, our love was full of bitterness imposed by outside circumstances, but as I savor its aftertaste, it remains boundless. I am serving my sentence in a tangible prison, while you wait in the intangible prison of the heart. Your love is the sunlight that leaps over high walls and penetrates the iron bars of my prison window, stroking every inch of my skin, warming every cell of my body, allowing me to always keep peace, openness, and brightness in my heart, and filling every minute of my time in prison with meaning. My love for you, on the other hand, is so full of remorse and regret that it at times makes me stagger under its weight. I am an insensate stone in the wilderness, whipped by fierce wind and torrential rain, so cold that no one dares touch me. But my love is solid and sharp, capable of piercing through any obstacle. Even if I were crushed into powder, I would still use my ashes to embrace you.

My dear, with your love I can calmly face my impending trial, having no regrets about the choices I've made and optimistically awaiting tomorrow.

My first quote is from here:

For more on Liu Xiaobo and his wife, try these:

The full speech I Have No Enemies is here:

Charter 08 is here:


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Lately I've been listening to the music of William Bevan, who goes by the name Burial. I'm rarely on the cutting edge of anything - except in science - so I'm playing catch-up here. But starting around 2006 this guy has been a real sensation in British electronic music scene. He took elements from fashionable dance music - drum 'n' bass, dubstep and garage - and put a dark, soulful, gritty spin on them.

Burial decided at the outset to avoid at all costs the rigid, mechanistic path that eventually brought drum 'n' bass to a standstill. To this end, his percussion patterns are intuitively arranged on the screen rather than rigidly quantized, creating minute hesitations and slippages in the rhythm. His snares and hi-hats are covered in fuzz and phaser, like cobwebs on forgotten instruments, and the mix is rough and ready rather than endlessly polished. Perhaps most importantly, his basslines sound like nothing else on Earth. Distorted and heavy, yet also warm and earthy, they resemble the balmy gust of air that precedes an underground train.

He composes his tracks in SoundForge, a digital audio editor, avoiding trackers and sequencers, which tend to lock a piece into a rigid rhythm.

Once I change something, I can never un-change it. I can only see the waves. So I know when I’m happy with my drums because they look like a nice fishbone. When they look just skeletal as fuck in front of me, and so I know they’ll sound good.

As he progressed, he started writing longer, stranger pieces. They're pretty challenging, but I'm finding them rewarding once I get to know them. They often stop, go dead for a while, then start up again in a different mood. In this one here it starts to rain! You'll hear a little rain before the piece gets going... but in the pauses, the rain gets harder and you hear little drops hitting something hard in front of you. I don't know how that works when I'm using earbuds!

Here's a longer description of this piece, the title track of his 2012 EP Kindred:

The real progression on the Kindred EP relates to Burial’s use of musical time and space. The length of the tracks on Kindred is something that most reviewers have picked up on, if only in passing. Where the majority on Untrue clocked in at somewhere between three and five minutes, with the longest being the title track at 6:16, Kindred’s three tracks, by contrast, come in at 11:26, 7:28, and 11:44, respectively. Now, obviously bigger does not necessarily equal better; frequently the opposite, in fact. But the cuts on Kindred aren’t simply longer than before; they introduce a completely different sense of space and continuity. This is the point that, in their eagerness, everyone seems to have missed. But this is why Kindred is so strong.

Take the title track, for instance, the first on the record. It begins with the distant rumble of a storm and a voice peaking out through the fuzz and the rain. It’s nearly a minute before the beat scuttles in, and when it does, it feels like an intervention, an interruption of the urban peace. A couple of minutes later, though, it just falls away entirely. The wind blows. A fractured voice returns book-ended by cracked and bristling ‘silence,’ and the beat skips back on in again, more or less the same as before. At around 6:30, it begins to decompose again. A break in the beat becomes a long interlude. Voices. Nothingness. Space. Fragments. And then that same familiar pulse returns, except now with a brighter mood. A high synth. Hope, maybe. And then no synth at all, the beat naked. Another cracked silence. Clouds rumbling. Finally, a totally new theme emerges over an entirely new rhythm, fainter this time, more distant. And it doesn’t last long, barely a minute. Fading now. Quiet. Calm. The sound of the needle lifting? And it’s over.

There’s a sense of continuity here, of thematic variation, interruption, narrative, scale, that was only ever latent in Burial’s previous work. When it was there, it operated at the level of the album as a whole rather than at the level of individual tracks. By opening up the length of those tracks on Kindred, in other words, paradoxical as it might sound, Burial actually gives himself the time and space to focus. There’s something really self-conscious about it, something sculpted. It’s as if we’re being asked to listen a certain way, to consider each track as an independent ‘work.’ Not that Burial’s listeners were ever exactly reluctant in that respect, but the invitation this time seems far more overt.

We could almost reverse our original observation in relation to length then. It’s not so much that Burial is saying ‘look how long I can make these tracks last, look how much I can fit into them.’ What he’s really saying is ‘look how successfully I can distill the dynamics of an entire album into so little space.’

This is from James' Parker's review:

The first quote is from Derek Walmsley's guide to dubstep.


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The uninhabitable Earth

Here's part of an article by David Wallace-Wells. This is why I quit work on pure math - except as a hobby - and started +Azimuth.

It is, I promise, worse than you think. If your anxiety about global warming is dominated by fears of sea-level rise, you are barely scratching the surface of what terrors are possible, even within the lifetime of a teenager today. And yet the swelling seas — and the cities they will drown — have so dominated the picture of global warming, and so overwhelmed our capacity for climate panic, that they have occluded our perception of other threats, many much closer at hand. Rising oceans are bad, in fact very bad; but fleeing the coastline will not be enough.

Indeed, absent a significant adjustment to how billions of humans conduct their lives, parts of the Earth will likely become close to uninhabitable, and other parts horrifically inhospitable, as soon as the end of this century.


Humans, like all mammals, are heat engines; surviving means having to continually cool off, like panting dogs. For that, the temperature needs to be low enough for the air to act as a kind of refrigerant, drawing heat off the skin so the engine can keep pumping. At seven degrees of warming, that would become impossible for large portions of the planet’s equatorial band, and especially the tropics, where humidity adds to the problem; in the jungles of Costa Rica, for instance, where humidity routinely tops 90 percent, simply moving around outside when it’s over 105 degrees Fahrenheit would be lethal. And the effect would be fast: Within a few hours, a human body would be cooked to death from both inside and out.

Climate-change skeptics point out that the planet has warmed and cooled many times before, but the climate window that has allowed for human life is very narrow, even by the standards of planetary history. At 11 or 12 degrees Celsius of warming, more than half the world’s population, as distributed today, would die of direct heat. Things almost certainly won’t get that hot this century, though models of unabated emissions do bring us that far eventually. This century, and especially in the tropics, the pain points will pinch much more quickly even than an increase of seven degrees.

The key factor is something called wet-bulb temperature, which is a term of measurement as home-laboratory-kit as it sounds: the heat registered on a thermometer wrapped in a damp sock as it’s swung around in the air (since the moisture evaporates from a sock more quickly in dry air, this single number reflects both heat and humidity). At present, most regions reach a wet-bulb maximum of 26 or 27 degrees Celsius; the true red line for habitability is 35 degrees. What is called heat stress comes much sooner.

Actually, we’re about there already. Since 1980, the planet has experienced a 50-fold increase in the number of places experiencing dangerous or extreme heat; a bigger increase is to come. The five warmest summers in Europe since 1500 have all occurred since 2002, and soon, the IPCC warns, simply being outdoors that time of year will be unhealthy for much of the globe. Even if we meet the Paris goals of two degrees Celsius warming, cities like Karachi and Kolkata will become close to uninhabitable, annually encountering deadly heat waves like those that crippled them in 2015.

At four degrees Celsius, the deadly European heat wave of 2003, which killed as many as 2,000 people a day, will be a normal summer. At six, according to an assessment focused only on effects within the U.S. from the National Oceanic and Atmospheric Administration, summer labor of any kind would become impossible in the lower Mississippi Valley, and everybody in the country east of the Rockies would be under more heat stress than anyone, anywhere, in the world today. As Joseph Romm has put it in his authoritative primer Climate Change: What Everyone Needs to Know, heat stress in New York City would exceed that of present-day Bahrain, one of the planet’s hottest spots, and the temperature in Bahrain “would induce hyperthermia in even sleeping humans.” The high-end IPCC estimate, remember, is two degrees warmer still.

By the end of the century, the World Bank has estimated, the coolest months in tropical South America, Africa, and the Pacific are likely to be warmer than the warmest months at the end of the 20th century. Air-conditioning can help but will ultimately only add to the carbon problem; plus, the climate-controlled malls of the Arab emirates aside, it is not remotely plausible to wholesale air-condition all the hottest parts of the world, many of them also the poorest.

And indeed, the crisis will be most dramatic across the Middle East and Persian Gulf, where in 2015 the heat index registered temperatures as high as 163 degrees Fahrenheit. As soon as several decades from now, the hajj will become physically impossible for the 2 million Muslims who make the pilgrimage each year.

It is not just the hajj, and it is not just Mecca; heat is already killing us. In the sugarcane region of El Salvador, as much as one-fifth of the population has chronic kidney disease, including over a quarter of the men, the presumed result of dehydration from working the fields they were able to comfortably harvest as recently as two decades ago. With dialysis, which is expensive, those with kidney failure can expect to live five years; without it, life expectancy is in the weeks. Of course, heat stress promises to pummel us in places other than our kidneys, too. As I type that sentence, in the California desert in mid-June, it is 121 degrees Fahrenheit outside my door. It is not a record high.

The whole article is here, and it has a lot more in it:

I've added clarifications about which temperatures are in Fahrenheit, because the author has an annoying habit of switching back and forth between Celsius and Fahrenheit.

Thanks to +Alexander Kruel for pointing out this article. I apologize, Alexander, for not simply resharing your post! I think this way of spreading the information will work a tiny bit better. I donate all my +1's to you.

For more scientific detail on this one issue - how hot is too hot for humans? - see this article I wrote on the Azimuth blog:

"Fossils" of the sort shown below are on sale here:

Get yours before they become common!


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Chmutov octic – 3d printer version

The Chmutov octic is a cool-looking surface with 154 singularities, described by a polynomial of degree 8. A while ago +Abdelaziz Nait Merzouk made some great pictures of it here on G+. Now someone with the handle Alpheccar has made a version using a 3d printer! It's here:

You can download a zip file containing an stl file for printing this shape – it has a Creative Commons license. I had no idea what an stl file actually is, but I clicked on it, and a program I'd never heard of called 3D Builder popped open and let me view this shape.

The singularities in the Chmutov octic should look like points where two cones meet. But if you actually tried to make something like that, it would fall apart. So the singularities have been smoothed out in this version.

Okay, so what's an stl file?

STL (STereoLithography): A file format native to the stereolithography CAD software created by 3D Systems. STL has several after-the-fact backronyms such as "Standard Triangle Language" and "Standard Tessellation Language". This file format is supported by many other software packages; it is widely used for rapid prototyping, 3D printing and computer-aided manufacturing.[5] STL files describe only the surface geometry of a three-dimensional object without any representation of color, texture or other common CAD model attributes. The STL format specifies both ASCII and binary representations. Binary files are more common, since they are more compact.

An STL file describes a raw unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. STL coordinates must be positive numbers, there is no scale information, and the units are arbitrary.

Cool! And in the process, I learned two new words:

Backcronym: A specially constructed phrase that is supposed to be the source of a word that is, or is claimed to be, an acronym. Backronyms may be invented with serious or humorous intent or may be a type of false etymology or folk etymology.

It's presumably a portmanteau word formed by blending 'back-formation' and 'acronym'. More important:

Stereolithography: also known as optical fabrication, photo-solidification, or resin printing, this is a form of 3-D printing technology used for creating models, prototypes, patterns, and production parts in a layer by layer fashion using photopolymerization, a process by which light causes chains of molecules to link, forming polymers. These polymers then make up the body of a three-dimensional solid. Research in the area had been conducted during the 1970s, but the term was coined by Chuck Hull in 1986 when he patented the process. He then set up 3D Systems Inc to commercialize his patent.

All this wisdom is from the almighty Wikipedia. For Abdelaziz's pictures of the Chmutov octic and more on the math of this beast, go here:


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Replacing men in suits with robots

Modern technology has been eliminating a lot of routine jobs. Why pay a bunch of people to answer phone calls if a computer can do it? In principle this could benefit all of society, but so far the benefits have flowed mainly to the very rich. It's been great for people in the finance industry. But now AI is starting to displace even them!

The financial firm Goldman Sachs is a great example. In 2000, its U.S. cash equities trading desk in New York employed 600 traders. Now they have just two. Machines do the rest of the work!

And the trend is just beginning:

Human traders and hedge fund managers don’t stand a chance, in large part because they’re human. “Humans have biases and sensitivities, conscious and unconscious," says Babak Hodjat, co-founder of Sentient and a computer scientist who played a role in Apple’s development of Siri. "It's well-documented we humans make mistakes. For me, it's scarier to be relying on those human-based intuitions and justifications than relying on purely what the data and statistics are telling you."

So what’s going to happen to the finance people who find themselves standing in front of the oncoming AI bus? Well, average compensation for staff in sales, trading and research at the 12 largest investment banks is $500,000, according to business intelligence company Coalition Development. Many traders earn in the millions. In 2015, five hedge fund managers made $1 billion or more, according to an industry survey. If you think Carl’s Jr. is motivated to replace $8-an-hour fast-food workers with robots, imagine the motivation to dump million-dollar-a-year ($500 an hour!) traders.

This could be a good thing, according to Mark Minevich, a New York-based investor in AI:

As the surest, fastest path to million-dollar paydays, Wall Street trading and hedge fund managing have long soaked up a large chunk of America’s best and brightest. About one-third of graduates from the top 10 business schools go into finance. Only a tiny sliver, usually around 5 percent, go into health care. An even smaller percentage go into energy or manufacturing businesses, and you can count on two hands the number who take jobs at nonprofits each year.

Most of the rest of society looks at that and sees selfishness. Yeah, sure, we need liquid markets and financial instruments and all that. But if we’re going to pay a group of people so much money, maybe we’d be better off if they were inventing electric cars that go 1,000 miles on a charge, or healthy vegetarian kielbasa, or babies who don’t cry on airplanes. Just do something that brings tangible benefits to the masses.

“Some of these smart people will move into tech startups, or will help develop more AI platforms, or autonomous cars, or energy technology,” Minevich says. That could be really helpful right now, since the tech industry is always fretting that it doesn’t have enough highly skilled pros and might be facing a geek drought in the age of Trump travel bans. If the MBA elite leave Wall Street but stay in New York, Minevich adds, “New York might compete with Silicon Valley in tech.”

As math Ph.D.’s no longer find that hedge fund recruiters are salivating over them, they might leap into efforts to model climate change or the behavior of cancer cells in the body.

However, in our society as it is today, it also means that the very richest will get even richer:

For the highly paid who remain, there is a growing income spread that mirrors the broader economy, says Babson College professor Tom Davenport. “The pay of the average managing director at Goldman will probably get even bigger, as there are fewer lower-level people to share the profits with,” he says.

The "American dream" can't survive in a world like this. We may adapt in intelligent ways... or we may just have an ugly revolution.

David Brin is writing a lot these days about the rebellion against competent elites. I don't think he's offered a convincing explanation for why it's happening.

Here's my theory: it's the revolt of the humans. More and more people are feeling that the sophisticated world of globalization and modern technology will leave no room for them. The out-of-work steel workers and coal miners - they'll never get good jobs back. They don't see their children living better lives than they did. They've all been rendered obsolete by computers and AI. All the benefits of this new technology are going to the rich and well-educated. So what will they do? They may decide that a descent into deliberate stupidity and chaos is their only way to stop a future in which most humans are unnecessary. Brexit and the election of Trump may be just the first step.

The first bunch of quotes are from this Newsweek article, which I've linked to:

The last one is from here:

I find this trend fascinating!

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If we impeach Trump, this genius will become president

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The end of the gasoline era

The end isn't here - but it's coming! Yesterday Volvo announced that starting in 2019, all its cars would be hybrids or electric. The company's chief executive said:

This announcement marks the end of the solely combustion engine-powered car.

And today, the environment minister of France announced that sales of gasoline and diesel powered cars would be banned starting in 2040!

David Bailey, an automotive industry expert at Aston University, said:

The timescale involved here is sufficiently long term to be taken seriously. If enacted it would send a very clear signal to manufacturers and consumers of the direction of travel and may accelerate a transition to electric cars.

And France is not the only country moving in this direction! Norway has set a target of only allowing sales of 100% electric or plug-in hybrid cars by 2025. The Netherlands is considering a 2025 ban for gasoline and diesel cars, and some states in Germany want to phase them out by 2030.

Tony Seba, a Stanford University economist, argues that electric cars will take over even sooner:

Banning sales of diesel and gasoline vehicles by 2040 is a bit like banning sales of horses for road transportation by 2040: there won’t be any to ban.

Still, announcing this ban will help people see the handwriting on the wall - we can start innovating and adapting as needed.

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