Look at either the red dot or the yellow dot. The circles near that dot will turn counterclockwise. The others turn clockwise!
Or: let your eyes bounce back and forth between the two.
Or: look away from both of them, but observe them from the 'corner of your eye'.
For details, see:
Around 2000, a guy named Robert Shawyer claimed he could bounce microwaves inside a fancy-shaped can and get them to push the can forwards, without anything leaving the can.
This would violate conservation of momentum. It's like sitting inside a car and making it roll forwards by pushing on the steering wheel. Standard physics doesn't allow this. He didn't claim to be using anything other than standard physics.
So: ho hum, just another guy with a really bad idea. I get emails like this all the time.
But in 2001, his company got a £45,000 grant from the British government to study this idea. He built his machine and claimed that with 850 watts of power he could get a force of 0.016 newtons. That's a bit less than the force of gravity from a penny pushing down on your hand. It could easily be an experimental error.
Why would people want a machine that uses lots of power to create a pathetically feeble force? Because — here's the great piece of salesmanship — if it existed, you could use it to build a reactionless drive! If you had a spaceship with huge amounts of power to spare — like, say, a nuclear reactor — you could use this gizmo to push your spaceship forwards without anything spewing out the back end.
Again, this is about as plausible as powering a spaceship by having the crew push on it from the inside. But if you don't know physics, it sounds very exciting.
The story goes on. And on. And on. It won't die. In 2012, some Chinese physicists claimed they could get a force of 0.720 newtons from a power of 2,500 watts using some version of Shawyer's device.
And now NASA is studying it!
They're claiming to see a force one thousandth as big as the Chinese £ probably because they are doing the experiment one thousand times more accurately. And still, some people are excited about this.
The new device comes with new improved mumbo-jumbo. Shawyer claimed that thanks to special relativity, classical electromagnetism can violate conservation of momentum. I took those courses in college, I know that's baloney. Now the NASA scientists say:
Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma.
This is baloney too — but now it's graduate level baloney. "Quantum vacuum virtual plasma" is something you'd say if you failed a course in quantum field theory and then smoked too much weed. There's no such thing as "virtual plasma". If you want to report experimental results that seem to violate the known laws of physics, fine. But it doesn't help your credibility to make up goofy pseudo-explanations.
I expect that in 10 years the device will be using quantum gravity and producing even less force.
For an article written by a severely optimistic blogger, see:
The NASA technical report is here:
Unfortunately only the abstract is free! I think someone with access should download the paper and make it publicly available. If my government is spending my money on this sort of thing, I'd at least like to see it.
There's a website about Guido Fetta's company and his device:
It says:
The Cannae Drive is a resonating cavity with design features that redirect the radiation pressure exerted in the cavity to create a radiation pressure imbalance on the cavity. This differential in radiation pressure generates an unbalanced force that creates thrust. The cavity is accelerated without use of propellant. Don't believe it? Study the theory. Replicate our numerical models. Review our experimental results. And draw your own conclusions.
Unfortunately, when I click on the links to theory, numerical models or experimental results, I get:
404 - Article not found
Hamilton Carter pointed out another paper by the NASA team, which explains the wild optimism behind this experiment:
NASA/JSC is implementing an advanced propulsion physics laboratory, informally known as "Eagleworks", to pursue propulsion technologies necessary to enable human exploration of the solar system over the next 50 years, and enabling interstellar spaceflight by the end of the century. This work directly supports the "Breakthrough Propulsion" objectives detailed in the NASA OCT TA02 In-Space Propulsion Roadmap, and aligns with the #10 Top Technical Challenge identified in the report. Since the work being pursued by this laboratory is applied scientific research in the areas of the quantum vacuum, gravitation, nature of space-time, and other fundamental physical phenomenon [sic], high fidelity testing facilities are needed. The lab will first implement a low-thrust torsion pendulum (<1 μN), and commission the facility with an existing Quantum Vacuum Plasma Thruster. To date, the QVPT line of research has produced data suggesting very high specific impulse coupled with high specific force. If the physics and engineering models can be explored and understood in the lab to allow scaling to power levels pertinent for human spaceflight, 400kW SEP human missions to Mars may become a possibility, and at power levels of 2MW, 1-year transit to Neptune may also be possible. Additionally, the lab is implementing a warp field interferometer that will be able to measure spacetime disturbances down to 150nm. Recent work published by White suggests that it may be possible to engineer spacetime creating conditions similar to what drives the expansion of the cosmos. Although the expected magnitude of the effect would be tiny, it may be a 'Chicago pile' moment for this area of physics.
The "Chicago pile" was the experiment that demonstrated a nuclear chain reaction.
My last post on the NASA "quantum vacuum plasma thruster" was mainly about the shoddy theory behind it — like how there's no such thing as a "quantum vacuum plasma". But you could argue: hey, if the gizmo actually works, isn't that good enough? Unfortunately, the experiment has problems too. In brief:
In a bit more detail:
1. Their device, called the 'Cannae drive', was invented by a guy named Guido Fetta. You can see a picture below. It's not complicated! It's a hollow container made of metal, about 11 inches in diameter and 4-5 inches long. You pump radio waves in one end. At the other end, a copper wire serves as an antenna. This lets you measure the radio waves bouncing around inside the container, and adjust their frequency until you hit a resonance. Then this thing is supposed to generate thrust, for some unknown reason.
Fetta thought this device would work if you carve slots on one side of the flat part. The NASA guys tried a version with slots and one without slots. They claim both versions generate a thrust of 22-48 micronewtons when they pump 17-28 watts of radio waves into them:
Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article).
So, basically they found evidence against Fetta's idea: the slots make no difference. It's like giving someone a placebo and finding it works just as well as the drug you're testing.
They also tried a resistor instead of their device. They claim this produced no thrust. This rules out some possibilities of experimental error... but not others.
For example, if parts of their flat metal can get hot and create air currents, that might create the force they saw. It's a tiny force, less you'd get from 5 milligrams of mass pushing down due to gravity.
2. Their paper goes into great detail about the "vacuum chamber" their experiment was done in — but in the abstract to the paper, they say they didn't remove the air. This is important because of the issue of air currents.
It's also just weird. In their paper they say:
To simulate the space pressure environment, the test rig is rolled into the test chamber. After sealing the chamber, the test facility vacuum pumps are used to reduce the environmental pressure down as far as 5x10E-6 Torr. Two roughing pumps provide the vacuum required to lower the environment to approximately 10 Torr in less than 30 minutes. Then, two high-speed turbo pumps are used to complete the evacuation to 5x10E-6 Torr, which requires a few additional days. During this final evacuation, a large strip heater (mounted around most of the circumference of the cylindrical chamber) is used to heat the chamber interior sufficiently to emancipate volatile substances that typically coat the chamber interior walls whenever the chamber is at ambient pressure with the chamber door open. During test run data takes at vacuum, the turbo pumps continue to run to maintain the hard vacuum environment. The high-frequency vibrations from the turbo pump have no noticeable effect on the testing seismic environment.
They're working really hard to get a good vacuum, right? But in their abstract they say:
Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure.
At ambient atmospheric pressure? What's the point of the fancy vacuum chamber? A sentence in their conclusions gives a clue. Talking about future plans, they say:
Vacuum compatible RF amplifiers with power ranges of up to 125 watts will allow testing at vacuum conditions which was not possible using our current RF amplifiers due to the presence of electrolytic capacitors.
So it seems they couldn't actually test their device in a vacuum.
3. If you're trying to find some small effect, checking the ways you could have screwed up is the most important thing. The device they're testing is simple, but the test apparatus itself is very complicated, and lots of things could go wrong.
Their paper should have a big section on this, but it doesn't. Instead it has a section on how if the gizmo works, you could scale it up and do great things:
Figure 23 shows a conservative 300 kilowatt solar electric propulsion roundtrip human exploration class mission to Mars/Deimos. Figure 24 shows a 90 metric ton 2 megawatt (MW) nuclear electric propulsion mission to Mars that has considerable reduction in transit times due to having a thrust to mass ratio greater than the gravitational acceleration of the Sun (0.6 milli-g's at 1 AU). Figure 25 shows the same spacecraft mass performing a roundtrip mission to the Saturn system spending over a year around two moons of interest, Titan and Enceladus.
This is called 'counting your chickens before the eggs have hatched'.
I would need to be more of an expert than I am to imagine all the things that could go wrong with their experiment. But just so you see what I mean, here's one thing they do mention:
one visible effect to the seismic environment is the periodic (about one-third to one-quarter Hertz) perturbation created by the waves from the Gulf of Mexico (about 25 miles southeast of Johnson Space Center), especially on windy days.
The thrust they're measuring is so small that waves in the ocean 25 miles away could screw up the experiment! They tried to deal with this... but it goes to show, you can't revolutionize physics until you carefully check all the sources of error.
I thank Greg Egan and Matt McIrvin for their help, but of course they're not to blame for any mistakes I made.
The paper I'm talking about was published here:
Beware: the abstract in the paper is different than the abstract on the NASA technical report server here:
This is where they say they didn't remove the air from the vacuum chamber.
August 4, 2014
Whether it's tucking tummies, contouring jaw lines, enlarging eyes and lips, brushing out cellulite, or full-out head swapping, I've seen it all as a photo editor. While the conversation about the media's portrayal and obsession with an unrealistic and unattainable beauty standard is not a new one, I think it's crazy how much retouching people don't notice. Over the last five years, having done many of the quick, subtle fixes that are the industry standard myself, I know that even an image considered to look 'natural' is anything but.
So, she changed a bunch of famous paintings. This is Titian's Danak With Eros. You can see the rest here:
Physicists often use a 'Cartesian coordinate system' — an imaginary grid, like 3d graph paper, that lets us name any point in space with 3 numbers. But what if it were real? You could climb around on it!
That's the idea of this art project by Numen/For Use, the guys who made that expanding and shrinking glowing cube with an infinity of reflections inside — I showed you a picture on July 1.
This is an inflatable structure. Ropes inside get stretched tight when it inflates. They form a 3d grid that's strong enough to climb around on. The inside walls are white, so it seems to go on infinitely. They tested it out in countryside near Vienna at the end of December 2013.
For more photos, try this:
After a decade-long chase, the Rosetta spacecraft has now reached a comet! This photo was taken from just 285 kilometers away. The comet's gravity is very weak, so Rosetta will move in a triangular orbit under its own power before moving closer.
On November 11th, Rosetta will send in a probe called Philae, which will harpoon the comet and land on it! The second picture below shows what that should look like. Philae will drill into the comet and carry out lots of experiments.
As the comet approaches the Sun, it will heat up. Gas will start to boil up from the surface, earthquakes will shake it, and I suppose Philae may even be destroyed. I haven't read any details about what to expect! But they will try to land Philae far away from places where jets of gas will erupt. The comet will makes its closest approach to the Sun on August 13th, 2015.
Here are the scientific instruments on the lander Philae:
For more great photos of the comet, go to the European Space Agency website.
Puzzle: what are these sciences?
People who can read Chinese will have a huge advantage. I don't think googling these words in English will help you much! Some websites use coppology to mean the study of film-maker Francis Ford Coppola, but that's not what it means here.
You know that mysterious crater that suddenly opened up in the Yamal Peninsula in northwest Siberia? Now an article in Nature blames it on melting permafrost:
A Russian archaeologist named Andrei Plekhanov led an expedition there. He and his team think it could be caused by melting permafrost due to abnormally hot summers in 2012 and 2013 — about 50°C warmer than usual. Air in the crater had up to 9.6% methane. The normal amount is closer to 0.0002%
Some scientists are already worrying about methane released from melting permafrost. Methane is a potent greenhouse gas: 90 times worse than carbon dioxide by weight, at least for the first 20 years. (It goes away faster.) Could we be in for a nasty feedback loop, where a warming climate melts permafrost, releases methane and warms the Earth even more?
The short answer is: probably not very soon.
There are certainly things that make me nervous. Back in 2011, a Russian research cruiser found methane bubbling up from the ocean floor:
In late summer, the Russian research vessel Academician Lavrentiev conducted an extensive survey of about 10,000 square miles of sea off the East Siberian coast. Scientists deployed four highly sensitive instruments, both seismic and acoustic, to monitor the .fountains. or plumes of methane bubbles rising to the sea surface from beneath the seabed."In a very small area, less than 10,000 square miles, we have counted more than 100 fountains, or torch-like structures, bubbling through the water column and injected directly into the atmosphere from the seabed," Dr Semiletov said. "We carried out checks at about 115 stationary points and discovered methane fields of a fantastic scale. I think on a scale not seen before. Some plumes were a kilometre or more wide and the emissions went directly into the atmosphere — the concentration was a hundred times higher than normal."
Others argued that this could have been going on for centuries; nobody had looked very hard! A group of experts called the Permafrost Carbon Network polled themselves and guessed that up to 2040, they expected the effect of melting permafrost to be roughly 1/8 to 1/4 of the direct effect of burning carbon. That would be bad but not disastrous... at least not soon.
One obvious question about this crater is whether it's an unusual event or the start of a trend. Local reindeer herders have reported a similar but smaller hole nearby. But most of us, who aren't doing research on permafrost, will just have to wait and see.
Hey, I've got an idea! In the meantime, how about cutting greenhouse gas emissions?
For more background, see:
There's a big network of trails and parks in Singapore. You can climb up a huge wooden bridge and suddenly see this futuristic apartment complex amid the jungle.
My friend Jamie Vicary is visiting the Centre for Quantum Technologies. Today he showed Lisa and me how to walk through park land to Vivocity, a fancy shopping mall by the sea. There are some elevated walkways through the jungle, that really let you see the trees and vines.
There's a World War II museum that shows how the Japanese invaded, and the battles fought around here. It was open for free because it was National Day — the 49th anniversary of the birth of Singapore as an independent country. It's weird to be in a country that's younger than I am.
Walking across the Henderson Wave Bridge, we spotted these buildings, called Reflections at Keppel Bay, on the horizon near the sea. They were designed by Daniel Libeskind, who also created the plan for the World Trade Center Memorial.
Once a Chinese billionaire invited Lisa and me to lunch near those apartments! He wanted me to work with him on his physics theories. Alas, I couldn't bring myself to do it.
When we reached Vivocity, we were really tired — it was a cool day by Singapore standards, but still sweaty after a 4-hour hike. We watched a crowd of Chinese folks doing country-western dancing outdoors by the mall. It's fun to see a middle-aged Chinese guy wearing cowboy boots and a hat slowly dancing to country music as if it were some sort of tai chi exercise. I really wonder how this fad got started. Then we went to an overpriced restaurant called The Queen and Mangosteen and had beers and dinner by the water.
Life is stranger and more interesting than I'd expected.
There's a map for this walk online.
Both rectangles are moving at constant speed
At least that's what the creator of this illusion says! It looks like the yellow and blue rectangles are taking turns going forward — one step at a time.
This is an illusion that's so good it's hard to believe it's an illusion. When the black and white lines disappear, it's easy to see the rectangles are moving at constant speed. But before that they seem to be taking turns, and pausing when they reach each new line.
Could the creator of this illusion be cheating — fooling you into thinking there's an illusion? How can you tell, except by making your own version of this animated gif?
Hide one rectangle with your hand. Then look closely at the other. Try not to look at the black and white lines. I think you'll see the rectangle is moving at constant speed.
But if you look away, and watch the rectangle with your peripheral vision, it will seem to move in steps.
We don't just 'see what's there'. We construct a mental model of reality from sensory data. We need to do this. But people can manipulate this.
It's not optical illusions we need to worry about. It's political illusions, economic illusions, social illusions. We think we're just seeing what's there... but we're actually constructing a model of reality. And politicians and other people are busy trying to shape your model, so you'll do what they want. Escaping their illusions is much, much harder than escaping this optical illusion.
You can probably think of many examples of other people who are fooled by politicians, ideologies, doctrines and dogmas. Now list the ways in which you are being fooled.
Oh, you think you're better than average? Join the club.
Puzzle 1: name the biggest way you've been fooled by a cultural, political or religious illusion.
Puzzle 2: name a way you're just starting to realize that you're being fooled by such an illusion.
For Puzzle 2, it should be just as hard to really believe you're being fooled as it is with this optical illusion. For example: I'm just starting to realize that I've been fooled into wanting to be a 'bigshot': well-known, and seemingly 'important'. But it's hard to break out of this belief. Even now, I'm trying to get you to pay attention to me. I'm sorry — at least I try to make it worth your while.
There was a very nice long discussion about all this on Google+. Carlos Schedegger made a version of this illusion with a higher framerate. Gustav Delius made an open source version of the illusion where you can read the code and edit it yourself.
Maryam Mirzakhani won the Fields medal yesterday.
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:
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 fun to read.
Manjul Bhargava is another of this year's Fields medalists. He works on number theory, which in its simplest form is the study of integers:
$$ ..., -3, -2, -1, 0, 1, 2, 3, ... $$
So when I say 'number' in this post, I'll always mean one of these!
When Bhargava was a grad student at Princeton, he read a book on number theory by the famous mathematician Gauss. Gauss was interested in quadratic forms, which are things like this:
$$ x^2 + 3xy + y^2 $$
or this
$$ -3x^2 + y^2 + 4xz + yz - 7z^2 $$
Gauss was mainly interested in quadratic forms with two variables, but it's also fun to think about more variables.
I can hand you a quadratic form and ask: what numbers can you get if you plug in any numbers you want for the variables?
Start with something really easy. For this one
$$ x^2 $$
you can only get the perfect squares
$$ 0, 1, 4, 9, 16, \dots $$
But what about this one?
$$ x^2 + y^2 $$
Can you find numbers \(x\) and \(y\) that make \(x^2 + y^2 = 100\)? How about \(x^2 + y^2 = 99\)? Remember, I'm using 'numbers' to mean numbers like these:
$$ \dots, -3, -2, -1, 0, 1, 2, 3, \dots $$
And what about this quadratic form?
$$ w^2 + x^2 + y^2 + z^2 $$
It's a famous fact that for this one, you can get any positive number by plugging in numbers for \(w, x, y\) and \(z\).
What about this?
$$ x^2 + y^2 + z^2 $$
Now you can't get every positive number. Do you see why?
We say a quadratic form is positive definite if whenever you plug numbers into it, you get something positive — unless all those numbers were zero. For example,
$$ x^2 + y^2 + z^2 $$
is positive definite, but
$$ x^2 + y^2 - z^2 $$
is not.
Okay, now you're ready. Here's something amazing that Manjul Bhargava proved with Jonathan Hanke in 2005: the 290 theorem.
Here's how to tell if you can get every positive number by plugging in numbers for the variables in a positive definite quadratic form. It's enough to check that you can get every number from 1 to 290.
In fact, it's enough to get these numbers:
$$ 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290. $$
Weird!
This is just one of many things Bhargava has done. Most are a bit harder to explain, but I described one a while ago here. It's about 'elliptic curves', another really popular topic in number theory.
And in fact, the 290 theorem I just explained is secretly about elliptic curves! As usual in number theory, the statement of a theorem may sound simple, cute, and pointless... but the proof reveals a very different world, and that's what really matters.
Here's a nice explanation of the proof:
The original paper is here:
There's a lot left to do. For example, Jonathan Rouse tried to show that a positive definite quadratic form gives all odd positive numbers if gives the odd numbers from 1 up to 451... but he only succeeded in showing this assuming something called the Generalized Riemann Hypothesis! Proving this is an extremely hard problem in its own right.
This opal from South Australia is beautiful... but why does it look like this? It's actually a photonic crystal!
Opal is made of small spheres of silicon dioxide, the same stuff as quartz. These spheres are between 150 to 300 nanometers in diameter, and they're arranged in a regular pattern.
When light waves pass through an opal, funny stuff happens when the distance between these spheres is half the wavelength of the light. Imagine water waves trying to fight their way through a regular pattern of round logs standing in the water and you'll get the picture. The waves start to bounce back and interfere with themselves.
So, light of certain wavelengths winds up bouncing back off the opal instead of going through! Since the opal is not perfectly the same everywhere, different parts reflect different colors of light.
When a repeating pattern strongly affects the behavior of light, it's called a photonic crystal. Nowadays people are making artificial photonic crystals. Way back in 1887, the English physicist Lord Rayleigh experimented with stacking layers of different materials to make light of certain wavelengths interfere with itself and bounce back. When this happens, we now call it a photonic band gap. But Rayleigh only got this effect to occur in a single direction — at right angles to the layers.
Now people can make 3d arrays of tiny spheres that act as photonic crystals. We might be able to use them to make color-changing paints and inks. But the first commercial products involving photonic crystals are photonic-crystal fibers — a bit like ordinary optical fibers, but different.
Photonic crystals are one example of a metamaterial — a material whose optical or electronic properties depend not just on their composition, but from carefully designed tiny structures.
In the Middle Ages, some thought an opal could make you invisible if you wrapped it in a fresh bay leaf and held it in your hand. Now people are designing metamaterials that can act like a 'cloak of invisibility'. But more about that later.
Puzzle: I said opal is made of tiny spheres of silicon dioxide (called silica), but what's in the spaces between these spheres?
The photo is from Dpulitzer, and the opal was found in Coober Pedy, Australia.
Wouldn't it be cool if we could turn one dimension of space into an extra dimension of time? We can't — but we can fake it!
Einstein showed the only difference between space and time is a minus sign. So: make a material where light obeys equations with an extra minus sign!
How? Just take lots of microscopic metal wires and put them in transparent stuff that doesn't conduct electricity. Line them all up. You'll get something that conducts electricity like a metal in one direction but not the other two directions!
It's called a hyperbolic metamaterial. The video explains why.
But why is this like converting a dimension of space into a dimension of time?
Einstein showed that if you have a photon — a particle of light — in a vacuum, it obeys
$$ k_x^2 + k_y^2 + k_z^2 - k_t^2 = 0 $$
where:
(Momentum in the time direction is basically just energy.)
Photons in other stuff obey more complicated equations. In a hyperbolic metamaterial with wires lined up in the z direction, they obey an equation basically like this:
$$ k_x^2 + k_y^2 - k_z^2 - k_t^2 = 0$$
So, the \(z\) direction is acting like an extra time dimension! And this lets us do very weird things.
Here's a nice video that explains more:
A few warnings if you watch the video:
You can learn more about hyperbolic metamaterials here:
This is an intriguing conjectural map of Sub-Roman Britain.
I've been a fan of the legends of King Arthur for a long time. I love how they continue to inspire new versions, from Marion Zimmer Bradley's Tales of Avalon (where Morgaine is recast as a hero in the doomed struggle of the Druids against encroaching Christians) to the goofy but fun TV series Merlin (where a black Guinevere starts as a serving-girl and winds up ruling Camelot).
But I'm only just now poking into the mysterious centuries from 400 to 600 AD in Britain, after the collapse of Roman rule, when Arthur would have lived... if he existed.
It's really cool to imagine life in former Roman towns and villas during these 'dark ages'. We have some archaeological evidence, but very little written history: mainly just the writings of Saint Patrick and a book called On the Ruin and Conquest of Britain, written by a guy called Saint Gildas or 'Gildas the Wise'.
This book is a grumpy attack on various kings, including:
There were many other kingdoms that Gildas didn't bother to write about. Gildas is himself rather mysterious; one later biography tells of how he helped mediate a struggle between King Arthur and a king who had abducted and raped Guinevere... but this is all just legend.
'Medieval Bex' has a lively blog on medieval matters, and here's what she says about the two biographies of Gildas:
The earlier account, written in the ninth century in Rhuys, Brittany, tells how Gildas son of Caw was born in the north of Britain. He moved to a monastic college to begin his education and then to Iren (probably Ireland) to continue his studies, before returning to north Britain to preach to those naughty heathens. St Brigid (d. 524) asked Gildas for a token so he made her a bell. As you do. After these high-jinks he then travelled around a bit before settling in Rhuys, where he built a monastery and lived out his days preaching and writing epistles about kings that he didn.t like very much. When he died his body was placed in a boat and set adrift according to his wishes. Just a floating corpse; not set aflame or anything. Imagine being the person to find a boat containing a decomposing monk. which someone actually did (the HORROR!!) . his boat washed up a few months later and was found by some men from Rhuys. They did the sensible thing and took his body back to Rhuys and buried it there. Gildas. corpsified wandering days were over.The other book, however, depicts Gildas as a sort of monk-cum-Arthurian action hero. It seems like the writer of the twelfth-century biography, Caradoc of Llancarfan, read the earlier book and said "Oh ho! I think we can do better than that!" and essentially pimped the Life of Gildas. The twelfth-century version has Gildas educated in Gaul before settling near Glastonbury—all normal enough so far, if ever-so-slightly at odds with the ninth-century version of events. but then things get a little bit more exciting when Guinevere and Arthur arrive on the scene! That's right, no floating corpses here!
According to Caradoc's biography of Gildas, King Melwas abducted Queen Guinevere and Arthur then proceeded to throw a massive wobbly. He stormed over to Melwas. stronghold in Glastonbury with his knights, ready to attack. It was all getting a bit intense. until Gildas stepped in and saved the day! He happened to be in the neighbourhood and persuaded Melwas to release Guinevere, before unbelievably managing to make the two kings kiss and make up. They probably all went for a beer and a good chortle about it all afterwards. As an interesting aside, this is the first recorded instance of the Guinevere abduction scene, a plot which becomes a recurring motif in subsequent redactions of the Arthurian stories. So a highly imaginative biography of a monk has helped to shape the legend of Arthur as we know it today. Who.d have thought! There is also something in this version about Gildas. brothers rising up against Arthur, and one of them being killed, and Gildas being rather upset about this. Apparently the large stone in Ruthin town square (north Wales) is the chopping block that was used when Arthur decapitated Gildas. brother. It's still there, you can go and see it!
Wolves run through the air, hit a glass wall and fall down. Then they pick themselves up, go back and do it again.
This piece, called 'Head On', is just one of the remarkable and unsettling works by Chinese artist Cai Guo-Qiang.
He recently made the news by creating a kind of Noah's ark with endangered animals and floating it down the river past the main financial district of Shanghai. The animals aren't real — but they look pretty real, like these wolves.
The boat is now on display in Shanghai, along with the wolves, in an exhibit that's become very popular. You can see more of it here:
A piece called 'Silent Ink' features a waterfall of ink plunging into a 5,300-gallon lake excavated from the museum's floor. The lake is ringed by mounds of crushed concrete and iron bars. It looks like a scene from a Chinese landscape painting—made of industrial waste. It's hard to stay there for very long, because the smell of the ink becomes overpowering.
But in its own strange way it's beautiful.
Of course, if you don't know the politics of China you'll miss part of the meaning of this wolf pack. If you don't know that 16,000 dead pigs were found floating down a river in Shanghai last year, you won't fully understand that ark. If you don't know a bit about the pollution crisis in China and the art of landscape painting, you'll miss some of what's going on in 'Silent Ink'. But this art is good because it's not merely commentary on politics and the pollution crisis in China. It's visually stunning, mysterious and tragic.
© 2014 John Baez
baez@math.removethis.ucr.andthis.edu