For my June 2014 diary, go here.

Diary - July 2014

July 1, 2014

The N-Light Membrane is a cube of mirrors with fluorescent lights as edges. 3 mirrors are one-way, so you can see inside. All you can see is reflections of the inside of the cube, extending to infinity!

The other 3 mirrors are flexible, and the cube is connected to an air tank. By inflating or deflating the air tank, you can make the cube convex or concave. The reflections bend in weird ways. The effect is hypnotic.

This cube was created by an art collective called Numen/For Use, and it was displayed in St. Petersburg. It's fun to watch videos of it shot from different angles.

What if you did a tetrahedron or octahedron? There's no need to imagine; you can see them here:

Numen/For Use is really three Croatian and Austrian guys, Sven Jonke, Christoph Katzler and Nikola Radeljkovi..

July 7, 2014

It seems a lot of ultra-high-energy cosmic rays are coming from a patch of the sky near the Big Dipper!

Cosmic rays are high-energy particles, mainly protons and atomic nuclei, which come from outer space and hit the Earth's atmosphere. When one hits, it produces a big shower of other particles. Most cosmic rays are believed to have picked up their energy by interacting with shock waves in the interstellar medium. But the most energetic ones remain mysterious — nobody knows how they could have acquired such high energies.

The record is a 1994 event seen by a detector in Utah called the Fly's Eye — because that's what it looks like. It saw a shower of particles produced by a cosmic ray with an energy of about 3 × 1020 electron volts. That's an insane amount of energy. It's about 50 joules: the energy of a one-kilogram mass moving at 10 meters/second, all packed into one particle!

To put it another way: the Large Hadron Collider, our best particle accelerator, speeds up protons to an energy of 7 trillion electron volts. The cosmic ray seen by the Fly's Eye had an energy of 300,000,000 trillion electron volts. We're not doing so well compared to nature. But we don't know how nature does it.

Anyway, now we've got a detector much better than the Fly's Eye: the Telescope Array. It's also in Utah, because the air is clear and the nights are dark. It's a jaw-dropping 760 square kilometers in size, because land is cheap. It consists of about 500 scintillation detectors in a square grid, each 1.2 kilometers away from the next. Each one is a solar-powered gadget containing plastic that lights up when a shower of particles hits it. There are also three telescopes that watch the air light up.

So, we can tell where the ultra-high energy cosmic rays are coming from!

Chart (a) shows where. Each dot is a cosmic ray with energy more than 57 quintillion eV. Well, the dot labelled GC is the galactic center, and the dot labelled anti-GC is the 'anti-galactic center': the direction in the sky pointing exactly away from the center of the Milky Way. GP is the plane of the galaxy, and there's some other stuff.

But the point is: the dots are clustered in a patch of the northern sky.

The colors in chart (b) show how many of these cosmic rays there are in a 20-degree circle around each point. This makes it easier to see where they're coming from. Their paths get bent by magnetic fields, so even if they all originate in one location they'd get smeared out.

What's making them? We don't know! That's the cool part: it's still a big mystery. Here's what the astronomers say:

Assuming the hotspot is real, two possible interpretations are: it may be associated with the closest galaxy groups and/or the galaxy filament connecting us with the Virgo cluster; or if cosmic rays are heavy nuclei they may originate close to the supergalactic plane, and be deflected by extragalactic magnetic fields and the galactic halo field.

What the heck is the supergalactic plane? It's the curve in chart (a) lablled SGP. It's major structure in the local universe: nearby galaxy clusters like the Virgo cluster, the Pisces-Perseus supercluster and the Great Attractor lie roughly in a plane!

Someday we'll figure out what's really happening. The paper is here:

July 13, 2014

A rotaxane is a 2-part molecule where one part is a ring that can rotate around the other part... but can't slip off!

People are starting to make molecular machines with rotaxanes. That's really cool, but let's talk about something simpler. How do you make a rotaxane?

The first one was made in 1967 by two chemists named Harrison. They used a simple but clever trick. Say you have a bunch of molecules that react and stick together in pairs to form a bigger dumbbell-shaped molecule. Say you let them do this when mixed with copies of some other ring-shaped molecule. Then a few of them will connect through the ring, forming a rotaxane!

By now there are better tricks:

  1. Capping: you let a rod-shaped molecule fit through a ring, and then cap it off with balls that keep the ring from sliding off.

  2. Clipping: you let a short C-shaped molecule fit around the middle of a dumbbell, and then get it to close off and form a ring.

  3. Slipping: sometimes at high temperatures a ring can stretch and fit around the end of a dumbbell... but at low temperatures it can't slip off.

The picture shows a rotaxane made in 1998. The paper describing this is not open-access, and I'm too lazy to get ahold of it and find out what trick they used. The picture was made by James Fraser Stoddart or one of his coworkers — he runs a big lab and is a specialist on rotaxanes. You can see it here:

This article also explains molecular machines made using rotaxanes!

July 17, 2014

This is a mural by Natalia Rak in Białystok, Poland. It reminds me of Alice in Wonderland, and the great Jefferson Airplane song "White Rabbit" with its line

Ask Alice... when she's ten feet tall.

And that reminds me of this magnificent version of the same song:

If you love the original, you must listen to this! I can't give away what's so great about it: that would spoil the surprise. Grace Slick's vocals are so powerful on the original I had thought no other version could be enjoyable, but I was wrong. As with the mural, good art wants a good idea.

July 21, 2014

Boron is the 5th element in the periodic table, right next to carbon. But we don't hear much about it. Why not? Because stars skip boron when building up elements, so it's rather rare!

It does, however, form interesting molecules, a bit like carbon. This is borospherene, a cage of 40 boron atoms. Earlier this year, a team of Chinese chemists synthesized molecules made of 40 borons and did computer simulations to guess what they'd made. This is their best guess!

It has a confusing shape. Each boron atom is connected to 4 or 5 others, and they make 48 triangles, 2 big hexagons - and 4 heptagons, which are on the top, bottom, left and right.

It's a bit like the famous buckyball made of 60 carbons. But it's much less symmetrical, and it doesn't have any hydrogens hanging off it. It has 8 symmetries. For starters, you can:

  1. leave it alone,
  2. rotate it 180 degrees around the axis pointing towards you,
  3. switch the top and bottom in a certain way, or
  4. do first 2 and then 3.

Abstractly this group of symmetries is called the Klein 4-group, because 'klein' means 'small' in German.

Puzzle 1: spot the joke.

Puzzle 2: explain why it's not just a joke; it's also sort of true.

Puzzle 3: how was most of the boron here on Earth made?

Puzzle 4: can you describe all 8 symmetries of borospherene?

If you get stuck on Puzzle 4, read what Layra Idarani wrote on G+. For more on symmetries of objects in 3d space, see:

The symmetry group of borospherene is called D2d, and you can learn what that means.

Here's the paper, unfortunately not free:

I thank Mark Bruce for alerting me to this discovery! The picture above, made by 'Materialscientist', is on Wikicommons:

July 24, 2014

Cinnabar is a mineral made of mercury — the silver balls here — and sulfur — the yellow ones. It's fascinated people for thousands of years. When you grind it up, you get vermilion: a brilliant red pigment.

Vermillion was used in murals in Çatalhöyük, one of the world's oldest cities, in Turkey, back around 7000 BC. It's been used in the art and lacquerware of China since the Han Dynasty! You'll also find it in the Tomb of the Red Queen built by the Mayans around 650 AD:

It was precious in Rome, used for art and decoration. Since mercury is poisonous, a term in working in the cinnabar mines was a virtual death sentence. Pliny the Elder wrote:

Nothing is more carefully guarded. It is forbidden to break up or refine the cinnabar on the spot. They send it to Rome in its natural condition, under seal, to the extent of some ten thousand pounds a year. The sales price is fixed by law to keep it from becoming impossibly expensive, and the price fixed is seventy sesterces a pound.

The Chinese were probably the first to make a synthetic vermilion, back in the 4th century BC. A Greek alchemist named Zosimus of Panopolis mentioned the process around the 3rd century AD. In the early ninth century the alchemist Jabir ibn Hayyan described it in a book — and it then spread to Europe.

The process is pretty simple. You mix mercury and sulfur together, forming a black compound called Aethiopes mineralis. You heat it in a flask. The compound vaporizes, and recondenses on the top of the flask. Then you break the flask, take out the vermilion, and grind it. At first the stuff is almost black, but the more you grind it, the redder it gets.

Puzzle 1: Where did they get the mercury in the first place, if not from cinnabar?

Puzzle 2: If they had cinnabar, why not just grind that to make vermillion?

Puzzle 3: Why does the stuff start out black?

Here's one possible answer to Puzzle 3. Cinnabar contains one crystal form of mercury sulfide, the so-called α form, shown here. It's a hexagonal crystal, and it's red. But there's also another form, the β form, which is black. This is sometimes called 'metacinnabar' — a cool word if I ever saw one.

In Taoist alchemy in China, cinnabar and gold were used in various potions that were supposed to give long life. Cinnabar was considered to have a lot of yang and gold a lot of yin. According to their theories, gold naturally transmutes into cinnabar over time, much as yin becomes yang (and vice versa). The evidence? Deposits of cinnabar are sometimes found beneath veins of gold.

Unfortunately, some people got mercury poisoning thanks to these potions!

Isaac Newton also spent a lot of his later life doing alchemy. This is not as dumb as it sounds, because at that time alchemy included what we now call 'chemistry', along with more mystical things. Some hairs from Newton's body have been found to contain 4 times as much lead, arsenic and antimony as normal — and 15 times as much mercury! This might explain Newton's tremors, severe insomnia, and paranoia.

I love the look of this crystal! The picture, made by Ben Mills, is on Wikipedia:

Some of my text is quoted or paraphrased from these articles:

For the use of cinnabar in Taoist alchemy, see:

July 25, 2014

Can you see what's happening here?

Each square is rotated by some angle compared to the square directly below it. This angle increases as time passes.

The angle starts out being zero, so the stack is straight. As the angle increases, the stack of squares starts to twist. When the angle becomes big, the stack twists so much that it becomes very complicated! But when the angle reaches 90 degrees, the stack becomes straight again — because when you rotate a square by 90 degrees, it looks exactly the same!

So, the stack seems to twist more and more... and then straighten out again.

Moral: a symmetry is a way to change something so that it doesn't change.

This 'paradox' is why symmetry is so powerful. We see it in action here. We twist the squares so much they are untwisted.

This gif was created by a mysterious person known only as intothecontinuum. I'll guess it's a he, because he uses a picture of Erwin Schrödinger as his icon. He puts his gifs here:

Here's the Mathematica code for this particular gif:
v[x_, y_, z_] =
Flatten[Table[ {(-1)^i*x, (-1)^j*y, (-1)^k*z}, {i, 0, 1}, {j, 0,
1}, {k, 0, 1} ], 2];

f = {{1 , 2 , 4 , 3 }, {1 , 2 , 6 , 5 }, {5 , 6 , 8 , 7 }, { 3, 4 ,
8 , 7 }, { 1, 3 , 7 , 5 }, { 2, 4 , 8 , 6 } };

G[x_, y_, z_, s_, H_ , t_] :=
Table[
Translate[
Rotate[
GraphicsComplex[v[x, y, z], Polygon[f]],
h (Cos[t] + 1) Pi/4, {0 , 0, 1 }],
{0, 0, s*h}],
{h, 1, H}]

Manipulate[
Graphics3D[
G[2, 2, .1, .25, 30, t],
Lighting -> "Neutral", ViewPoint -> Front, ViewAngle -> 35 Degree,
Boxed -> False, ImageSize -> 500],
{t, 0, Pi}]
Puzzle 1: What's the significance of these numbers?
f = {{1 , 2 , 4 , 3 }, {1 , 2 , 6 , 5 }, {5 , 6 , 8 , 7 }, { 3, 4 ,
8 , 7 }, { 1, 3 , 7 , 5 }, { 2, 4 , 8 , 6 } };
For some answers, go to my G+ post on this subject and read the comments.

July 26, 2014

This 'hypersnake' made by Davidope is cool, but here's something much cooler:

It starts out intense... and then keeps getting more so.

You can control the shape of the little rectangles by moving your cursor over the screen. Do it! Try to keep your eye on just one little rectangle! It moves up and down, not very fast... but sometimes it's impossible to keep your eye on it, because all the rectangles together produce patterns that grab your attention. These are called Moiré patterns.

I think the 'hypersnake' above is attention-grabbing because your brain has parts that are good at detecting snakes even before you are conscious of it. Your amygdala is one of these parts:

Information from an external stimulus reaches the amygdala in two different ways: by a short, fast, but imprecise route, directly from the thalamus; and by a long, slow, but precise route, by way of the cortex.

It is the short, more direct route that lets us start preparing for a potential danger before we even know exactly what it is. In some situations, these precious fractions of a second can mean the difference between life and death.

Here is an example. Suppose you are walking through a forest when you suddenly see a long, narrow shape coiled up at your feet. This snake-like shape very quickly, via the short route, sets in motion the physiological reactions of fear that are so useful for mobilizing you to face the danger. But this same visual stimulus, after passing through the thalamus, will also be relayed to your cortex. A few fractions of a second later, the cortex, thanks to its discriminatory faculty, will realize that the shape you thought was a snake was really just a discarded piece of garden hose. Your heart will then stop racing, and you will just have had a moment.s scare.

The 'moiré eel' was made by Darius Bacon. You can see more of his stuff here:

Davidope makes a lot of cool animated gifs, which you can see here:

July 27, 2014

The first report of a fast radio burst appeared in 2007. An astronomer named Duncan Lorimer found a signal buried in recordings made at the Parkes radio telescope in Australia. It lasted for less than 5 milliseconds and it seemed to come from outside our galaxy. It didn't match anything we'd seen in visible light, X-rays or anything else. A complete mystery!

Last year people found 4 more. But all at the Parkes telescope. Maybe there was an error of some sort?

But now they've seen one at Arecibo, the famous radio telescope in Puerto Rico. Duncan Lorimer says several more confirmations will soon be announced.

So what causes these fast radio bursts?

We don't know. But here's one theory: a 'blitzar'.

When a supernova blasts the outer layers of a big star into space, the remaining core collapses down to a ball of neutronium heavier than our Sun and the size of a small city: a neutron star.

If this spins fast enough, like a thousand times a second, it's highly magnetic. It produces regular pulses of intense radiation — and we call it a pulsar.

If it's too heavy, though, the neutron star collapses into a black hole.

But suppose it's spinning really fast! Then the centrifugal force might pull it out and keep it from collapsing into a black hole!

Until it slowed down. Then it would collapse into a black hole. The magnetic field lines would suddenly get cut by an event horizon. They don't like that. WHAM — a blast of radio waves. A blitzar.

One newspaper headline describes it this way: "as if millions of voices suddenly cried out in terror and were suddenly silenced". It's good to see that purple prose isn't dead in science journalism.

This is just a theory, so far. We'll get more evidence as we see more short radio bursts.

For more, read these:

They're well-written!

And here's the paper that introduced the blitzar theory. The calculations are surprisingly sketchy. It's really hard to calculate what happens when a ball of neutronium suddenly collapses into a black hole, so they use simple estimates:

Abstract. Several fast radio bursts have been discovered recently, showing a bright, highly dispersed millisecond radio pulse. The pulses do not repeat and are not associated with a known pulsar or gamma-ray burst. The high dispersion suggests sources at cosmological distances, hence implying an extremely high radio luminosity, far larger than the power of single pulses from a pulsar. We suggest that a fast radio burst represents the final signal of a supramassive rotating neutron star that collapses to a black hole due to magnetic braking. The neutron star is initially above the critical mass for non-rotating models and is supported by rapid rotation. As magnetic braking constantly reduces the spin, the neutron star will suddenly collapse to a black hole several thousand to million years after its birth. We discuss several formation scenarios for supramassive neutron stars and estimate the possible observational signatures {making use of the results of recent numerical general-relativistic calculations). While the collapse will hide the stellar surface behind an event horizon, the magnetic-field lines will snap violently. This can turn an almost ordinary pulsar into a bright radio "blitzar": Accelerated electrons from the travelling magnetic shock dissipate a significant fraction of the magnetosphere and produce a massive radio burst that is observable out to z > 0.7. Only a few percent of the neutron stars needs to be supramassive in order to explain the observed rate. We suggest that fast radio bursts might trace the solitary formation of stellar mass black holes at high redshifts. These bursts could be an electromagnetic complement to gravitational-wave emission and reveal a new formation and evolutionary channel for black holes that are not seen as gamma-ray bursts. Radio observations of these bursts could trace the core-collapse supernova rate throughout the universe.

For my August 2014 diary, go here.


© 2014 John Baez
baez@math.removethis.ucr.andthis.edu

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