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John Baez

John Baez 

Occupation: I'm a mathematical physicist. (Centre for Quantum Technologies)

Location: Riverside, California

Followers: 57,606

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Cream of the Crop: 11/05/2011

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Most comments: 106

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2016-08-27 04:43:12 (106 comments; 27 reshares; 210 +1s; )Open 

Dark mysteries

You probably heard the news this week: astronomers found a galaxy that's 98% dark matter. 

It's called Dragonfly 44.  It's extremely faint, so it doesn't have many stars.   But we can use redshifts to see how fast those stars are moving - over 40 kilometers per second on average.  If you do some calculations, you can see this galaxy would fly apart unless there's a lot of invisible matter providing enough gravity to hold it together.   (Or unless something even weirder is happening.)

Something similar is true for most galaxies, including ours.   What makes Dragonfly 44 special is that 98 percent of the matter must be invisible.   And this is just in the part where we see stars.   If we count the outer edges of the galaxy, the halo, the percentage could rise to 99% or more! 

By comparison, theMilky Way is... more »

Most reshares: 91

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2016-08-08 04:51:46 (0 comments; 91 reshares; 198 +1s; )Open 

What's wrong with Trump?

More and more people are wondering.  Here's an insightful analysis from a psychiatric social worker.  Please reshare.  It's not light reading, but we need to understand what we're dealing with here.

--------------------

The Billionaire's Baffling Behavior Explained

Recently, Mr. Trump's words and actions in various situations have become headline news. Suddenly, many people are alarmed and are questioning temperament, his emotional stability. Dementia? Campaign tactics?

No, it's not an illness that can be treated so he can return to his usual state of health. It's not like when a car's brakes don't work and the mechanic fixes them. It's more like the car came off the assembly line without them.

It's a structural problem.

We're witnessingte... more »

Most plusones: 332

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2016-08-14 02:05:13 (46 comments; 45 reshares; 332 +1s; )Open 

Not like Earth

At the end of August, the European Southern Observatory will announce a planet orbiting Proxima Centauri - the star closest to our Sun, 4.24 light years away.   They're trying to make this planet sound like Earth... and that's cool.   But I'll tell you some ways it's not.

Mainly, Proxima Centauri is really different from our Sun! 

It's a red dwarf.   It puts out just only 0.17% as much energy as our Sun.  So any planet with liquid water must be very close to this star.

And because it's cooler than the Sun, Proxima Centauri mainly puts out infrared light - in other words, heat radiation.   Its visible luminosity is only 0.005% that of our Sun!

So if you were on a planet as warm as our Earth orbiting Proxima Centauri, it would look very dim - about 3% as bright as our Sun.

Of course,if there... more »

Latest 50 posts

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2016-09-24 16:14:25 (20 comments; 11 reshares; 138 +1s; )Open 

Solar wind

This is the solar wind, the stream of particles coming from the Sun.  It was photographed by STEREO.  That's the Solar Terrestrial Relations Observatory, a pair of satellites we put into orbit around the Sun at the same distance as the Earth, back in 2006.  One  is ahead of the Earth, one is behind.  Together, they can make stereo movies of the Sun!

One interesting thing is that there's no sharp boundary between the 'outer atmosphere' of the Sun, called the corona, and the solar wind.  It's all just hot gas, after all!   STEREO has been studying how this gas leaves the corona and forms the solar wind.  This picture is a computer-enhanced movie of that process, taken near the Sun's edge.

What's the solar wind made of?   When you take hydrogen and helium and heat them up so much that theelectrons... more »

Solar wind

This is the solar wind, the stream of particles coming from the Sun.  It was photographed by STEREO.  That's the Solar Terrestrial Relations Observatory, a pair of satellites we put into orbit around the Sun at the same distance as the Earth, back in 2006.  One  is ahead of the Earth, one is behind.  Together, they can make stereo movies of the Sun!

One interesting thing is that there's no sharp boundary between the 'outer atmosphere' of the Sun, called the corona, and the solar wind.  It's all just hot gas, after all!   STEREO has been studying how this gas leaves the corona and forms the solar wind.  This picture is a computer-enhanced movie of that process, taken near the Sun's edge.

What's the solar wind made of?   When you take hydrogen and helium and heat them up so much that the electrons get knocked off, you get a mix of electrons, hydrogen nuclei (protons), and helium nuclei (made of two protons and two neutrons).   So that's all it is.

The Sun's corona is very hot: about a million degrees Celsius.  That's hotter than the visible surface of the Sun!  Why does it get so hot?  When I last checked, this was still a bit mysterious.   But it has something to do with the Sun's powerful magnetic fields. 

When they're this hot, some electrons are moving fast enough to break free of the Sun's gravity.   Its escape velocity is 600 kilometers per second.  The protons and helium nuclei, being heavier but having the same average energy, move slower.  So, few of these reach escape velocity.

But with the negatively charged electrons leaving while the positively charged protons and helium nuclei stay behind, this means the corona builds up a positive charge!   So the electric field starts to push the protons and helium nuclei away, and some of them - the faster-moving ones - get thrown out too.  

Indeed, enough of these positively charged particles have to leave the Sun to balance out the electrons, or the Sun's electric charge would keep getting bigger.   It would eventually shoot out huge lightning bolts!  The solar wind deals with this problem in a less dramatic way - but sometimes it gets pretty dramatic.  Check out this proton storm:

http://www.spaceweather.com/images2014/08jan14/x1s2_anim.gif

When storms like this happen, the US government sends out warnings like this:

Space Weather Message Code: WATA50
Serial Number: 48
Issue Time: 2014 Jan 08 1214 UTC
WATCH: Geomagnetic Storm Category G3 Predicted
Highest Storm Level Predicted by Day:
Jan 08: None (Below G1) Jan 09: G3 (Strong) Jan 10: G3 (Strong)
THIS SUPERSEDES ANY/ALL PRIOR WATCHES IN EFFECT
Potential Impacts: Area of impact primarily poleward of 50 degrees geomagnetic latitude.
Induced Currents – Power system voltage irregularities possible, false alarms may be triggered on some protection devices.
Spacecraft – Systems may experience surface charging; increased drag on low Earth-orbit satellites and orientation problems may occur.
Navigation – Intermittent satellite navigation (GPS) problems, including loss-of-lock and increased range error may occur.
Radio – HF (high frequency) radio may be intermittent.
Aurora – Aurora may be seen as low as Pennsylvania to Iowa to Oregon.

The solar wind is really complicated, and I've just scratched the surface.  I love learning about stuff like this, surfing the web as I lie in bed sipping coffee in the morning.  Posting about it just helps organize my thoughts - when you try to explain something, you come up with more questions about it.

For more on space weather, visit this fun site:

http://www.spaceweather.com/

You can see space weather reports put out by the National Oceanic and Atmospheric Administration here:

http://www.swpc.noaa.gov/products/alerts-watches-and-warnings

For more on the solar wind, see:

https://en.wikipedia.org/wiki/Solar_wind

For more on STEREO, see:

https://en.wikipedia.org/wiki/STEREO

#physics   #astronomy  ___

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2016-09-23 19:07:29 (19 comments; 10 reshares; 63 +1s; )Open 

Life on the Infinite Farm

This is a great book about infinity - for kids.   For example, there's a cow named Gracie with infinitely many legs.  She likes new shoes, but she wants to keep wearing all her old shoes.  What does she do?

Life on the Infinite Farm is by Richard Evan Schwartz, and it's free here:

https://www.math.brown.edu/~res/farm.pdf

Later it will be published on paper by the American Mathematical Society.  I really like turning the pages when I'm reading a book to a child.  Is that old-fashioned?  What do modern parents think?

Gracie's tale is just a retelling of the first Hilbert Hotel story.  There's a hotel with infinitely many rooms.  Unfortunately they're all full.  A guest walks in.  What do you do? 

You move the guest in room 1 to room 2, the guest in room 2 to room 3, andso on.  Now... more »

Life on the Infinite Farm

This is a great book about infinity - for kids.   For example, there's a cow named Gracie with infinitely many legs.  She likes new shoes, but she wants to keep wearing all her old shoes.  What does she do?

Life on the Infinite Farm is by Richard Evan Schwartz, and it's free here:

https://www.math.brown.edu/~res/farm.pdf

Later it will be published on paper by the American Mathematical Society.  I really like turning the pages when I'm reading a book to a child.  Is that old-fashioned?  What do modern parents think?

Gracie's tale is just a retelling of the first Hilbert Hotel story.  There's a hotel with infinitely many rooms.  Unfortunately they're all full.  A guest walks in.  What do you do? 

You move the guest in room 1 to room 2, the guest in room 2 to room 3, and so on.  Now there's a room available!

The Hilbert Hotel stories were introduced by the great mathematician David Hilbert in a 1924 lecture, and popularized by George Gamow in his classic One Two Three... Infinity.   That book made a huge impression on me as a child: one of my first times I tasted the delights of mathematics.    

But that book is not good for children just learning to read.  Life on the Infinite Farm is.  And there's nothing that smells like "education" in this book.  It's just fun.

You can read more Hilbert Hotel stories here:

https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

But it's probably more fun to read Gamow's One Two Three... Infinity.   He was an excellent astrophysicist who in 1942 figured out how the first elements were created - the theory of Big Bang nucleosynthesis.    He was also a coauthor of the famous Alpher-Bethe-Gamow paper on this topic, also known as the αβγ paper.    Alpher was a grad student of Gamow, and they added the famous nuclear physicist Hans Bethe as a coauthor just for fun - since 'Bethe' is pronounced like the Greek letter 'beta':

It seemed unfair to the Greek alphabet to have the article signed by Alpher and Gamow only, and so the name of Dr. Hans A. Bethe was inserted in preparing the manuscript for print. Dr. Bethe, who received a copy of the manuscript, did not object, and, as a matter of fact, was quite helpful in subsequent discussions. There was, however, a rumor that later, when the alpha, beta, gamma theory went temporarily on the rocks, Dr. Bethe seriously considered changing his name to Zacharias.

Gamow also had a real knack for explaining things in fun ways, with the help of charming pictures.   I don't do many advertisements for commercial products, but I will for this!  You can get his book for as little as $2.98 plus shipping:

https://www.amazon.com/One-Two-Three-Infinity-Speculations/dp/0486256642/

You should have read it by the time you were a teenager - but if you didn't, maybe it's not too late.

For more about Gamow, see:

https://en.wikipedia.org/wiki/αβγ_paper

#bigness___

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2016-09-22 06:29:24 (14 comments; 23 reshares; 110 +1s; )Open 

Poncelet's Porism

If you can fit a triangle snugly between two circles, you can always slide the triangle around.  The triangle may have to change shape, but it stays snug!   All 3 corners keep touching the outside circle, and all 3 sides keep touching the inside circle.

That's really cool.  But even better, it also works for polygons with more than 3 sides!

This amazing fact is called Poncelet's Porism

A porism is like a theorem, but much cooler.  Poncelet was a French engineer and mathematician who wrote a famous book on 'projective geometry' in 1822. 

What's a porism, really? 

Well, Euclid is famous for his Elements, but he also wrote a more advanced book called Porisms.  Unfortunately that book is lost.  I hear that someone checked it out from the library of Alexandria andnever ret... more »

Poncelet's Porism

If you can fit a triangle snugly between two circles, you can always slide the triangle around.  The triangle may have to change shape, but it stays snug!   All 3 corners keep touching the outside circle, and all 3 sides keep touching the inside circle.

That's really cool.  But even better, it also works for polygons with more than 3 sides!

This amazing fact is called Poncelet's Porism

A porism is like a theorem, but much cooler.  Poncelet was a French engineer and mathematician who wrote a famous book on 'projective geometry' in 1822. 

What's a porism, really? 

Well, Euclid is famous for his Elements, but he also wrote a more advanced book called Porisms.  Unfortunately that book is lost.  I hear that someone checked it out from the library of Alexandria and never returned it.   By now the overdue fee exceeds the annual GDP of Greece, so we'll never see that book again... and we'll never know exactly what Euclid meant by 'porism'.

Wikipedia starts by saying:

A porism is a mathematical proposition or corollary. In particular, the term porism has been used to refer to a direct result of a proof, analogous to how a corollary refers to a direct result of a theorem. In modern usage, a porism is a relation that holds for an infinite range of values but only if a certain condition is assumed, for example Steiner's porism.  [...]  Note that a proposition may not have been proven, so a porism may not be a theorem, or for that matter, it may not be true.

In short: nobody knows what a porism is, but people are willing to make stuff up.

Pappus of Alexandria managed to write down a few of Euclid's porisms around 400 AD, before the book got lost.  They are quite advanced facts about geometry.  Poncelet was inspired by Pappus, so when he proved his cool result, maybe he wanted to call it a porism too.  I don't know.

A slick modern proof of Poncelet's porism uses 'elliptic curves'.  Check out David Speyer's explanation:

https://sbseminar.wordpress.com/2007/07/16/poncelets-porism/

In case you're not a mathematician, beware!  An 'elliptic curve' is jargon for a surface shaped like a doughnut.  We just call them 'elliptic curves' to keep people like you confused.

For some truly amazing connections between Poncelet's Porism and other math problems, see this paper by J. L. King:

https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/King609-628.pdf

An elementary proof of Poncelet's Porism is here:

http://user.math.uzh.ch/halbeisen/publications/pdf/poncelet.pdf

In math, 'elementary' means that we don't use fancy concepts.  It doesn't mean 'easy'. 

When I retire, I want to quit proving theorems, and prove a porism.

#geometry  ___

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2016-09-21 15:17:59 (40 comments; 11 reshares; 54 +1s; )Open 

Black hole versus white hole

Last time I showed you a Schwarzschild black hole... but not the whole hole.  

Besides the horizon, which is the imaginary surface that light can only go in, that picture had a mysterious "antihorizon", where light can only come out.    When you look at this black hole, what you actually see is the antihorizon.    The simplest thing is to assume no light is coming out of the antihorizon.  Then the black hole will look black.

But I didn't say what was behind the antihorizon!

In a real-world black hole there's no antihorizon, so all this is just for fun.  And even in the Schwarzschild black hole, you can never actually cross the antihorizon - unless you can go faster than light.  So there's no real need to say what's behind the antihorizon.    And we can just decree that no light comesout of it.more »

Black hole versus white hole

Last time I showed you a Schwarzschild black hole... but not the whole hole.  

Besides the horizon, which is the imaginary surface that light can only go in, that picture had a mysterious "antihorizon", where light can only come out.    When you look at this black hole, what you actually see is the antihorizon.    The simplest thing is to assume no light is coming out of the antihorizon.  Then the black hole will look black.

But I didn't say what was behind the antihorizon!

In a real-world black hole there's no antihorizon, so all this is just for fun.  And even in the Schwarzschild black hole, you can never actually cross the antihorizon - unless you can go faster than light.  So there's no real need to say what's behind the antihorizon.    And we can just decree that no light comes out of it.

But inquiring minds want to know...  what could be behind the antihorizon?

This picture shows the answer.  This is the maximally extended Schwarzschild black hole - the biggest universe we can imagine, that contains this sort of black hole.

It's really weird.

It contains not only a black hole but also a white hole.  The wiggly lines are singularities.  Matter and light can only fall into the black hole from our universe... passing through the horizon and hitting the singularity at the top of the picture.   And they can only fall out of the white hole into our universe... shooting out of the singularity at the bottom of the picture and passing through the antihorizon.

If that weren't weird enough, there's also a parallel universe, just like ours.  

Someone from our universe and someone from the parallel universe can jump into the black hole, meet, say hi, then hit the singularity and die.    Fun!

But we can never go from our universe to the parallel universe.  :-(

Why not?   Remember, the only allowed paths for people going slower than light are paths that go more up the page than across the page - like the blue path in the picture.  To get from our universe to the parallel universe, a path would need to go more across than up.

If you could go faster than light for just a very short time, you could get from our universe to the parallel universe by zipping through the point in the very middle of the picture, where the horizon and antihorizon meet. 

Puzzle 1.  Suppose the parallel universe has stars in it more or less like ours.  You can't see it from our universe - but you could see it if you jumped into the black hole!  What would it look like?

Puzzle 2.   How would my story change if the "arrow of time" in the parallel universe pointed the other way from ours?  In other words, what if the future for them was at the bottom of the picture, rather than the top?

I should emphasize that we're playing games here, but they're games with rules.  We're not talking about the real world, but the math of this stuff is well-understood, so you can't just make stuff up.  Or you can, but it might be wrong.  These puzzles have right and wrong answers!

Unfortunately I haven't really explained things well enough, so you may need to guess  the answers instead of just figure them out.  For more info, try Andrew Hamilton's page, from which I took this picture:

http://jila.colorado.edu/~ajsh/insidebh/penrose.html

And for more, try this:

https://en.wikipedia.org/wiki/Schwarzschild_metric

#physics  ___

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2016-09-20 18:21:39 (69 comments; 25 reshares; 71 +1s; )Open 

Understanding black holes

This is a diagram of a Schwarzschild black hole - a non-rotating, uncharged black hole that has been around forever. 

Real-world black holes are different.  They aren't eternal - they were formed by collapsing matter.  They're also rotating.  But the Schwarzschild black hole is simple: you can write down a formula for it.  So this is the one to start with, when you're studying black holes.

This is a Penrose diagram.  It shows time as going up, and just one dimension of space going across.  The key to Penrose diagrams is that light moves along diagonal lines.  In these diagrams the speed of light is 1.   So it moves one inch across for each inch it moves up - that is, forwards in time.

The whole universe outside the black hole is squashed to a diamond. The singularity is the wiggly line attop.   T... more »

Understanding black holes

This is a diagram of a Schwarzschild black hole - a non-rotating, uncharged black hole that has been around forever. 

Real-world black holes are different.  They aren't eternal - they were formed by collapsing matter.  They're also rotating.  But the Schwarzschild black hole is simple: you can write down a formula for it.  So this is the one to start with, when you're studying black holes.

This is a Penrose diagram.  It shows time as going up, and just one dimension of space going across.  The key to Penrose diagrams is that light moves along diagonal lines.  In these diagrams the speed of light is 1.   So it moves one inch across for each inch it moves up - that is, forwards in time.

The whole universe outside the black hole is squashed to a diamond. The singularity is the wiggly line at top.   The blue curve is the trajectory of a cat falling into the black hole.  Since it's moving slower than light, this curve must move more up than across.  So, once it crosses the diagonal line called the horizon, it is doomed to hit the singularity. 

Indeed, anyone in the region called "Black Hole" will hit the singularity.   Notice: when you're in this region, the singularity is not in front of you!  It's in your future.  Trying to avoid it is like trying to avoid tomorrow.

But what is the diagonal line called the antihorizon?   If you start in our universe, there's no way to reach the antihorizon without going faster than light.     But we can imagine things crossing it from the other direction: entering from the left  and coming in  to our universe! 

The point is that while this picture of the Schwarzschild black hole is perfectly fine, we can imagine extending it and putting it inside a larger picture.   We say it's not maximally extended

The larger picture, the maximally extended one, describes a very strange world, where things can enter our universe through the antihorizon.   But that's another story, which deserves another picture.

If we stick with the diagram here, nothing can come out of the antihorizon, so it will look black.  In fact, to anyone in the "Universe" region, it will look like a black sphere.  And that's why a Schwarzschild black hole looks like a black sphere from outside!

The weird part is that this black sphere you see, the antihorizon, is different than the sphere you can fall into, namely the horizon.

If this seem confusing, join the club.   I think I finally understand it, but nobody ever told me this - at least, not in plain English - so it took me a long time.

What could be behind the antihorizon?   If you want to peek, try Andrew Hamilton's page on Penrose diagrams, where I got this picture:

http://jila.colorado.edu/~ajsh/insidebh/penrose.html
 
I wish that Wikipedia had a really nice Penrose diagram like this!  It's very important.  They have some more complicated ones, but the most basic important ones are not drawn very nicely.  You need to think about Penrose diagrams to understand black holes and the Big Bang!

Still, their article is worth reading:

https://en.wikipedia.org/wiki/Penrose_diagram

For more on the Schwarzschild black hole, read this:

https://en.wikipedia.org/wiki/Schwarzschild_metric

#physics  ___

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2016-09-18 18:48:33 (57 comments; 14 reshares; 79 +1s; )Open 

The mystical hexagram theorem

The picture explains this amazing result, which was discovered by Pascal in 1639, when he was only sixteen.

Take six points on an ellipse, called A,B,C,D,E,F.  Connect each point to the next by a line.

The red lines intersect in a point G.
The yellow lines intersect in a point H.
The blue lines intersect in a point K. 

And then the cool part:

The points G, H and K lie on a line!

I'm teaching a course on 'algebraic groups' starting on Thursday, so I need to review a bit of the history of projective geometry.   This result of Pascal, called the Hexagrammum Mysticum Theorem, was the first exciting theorem about projective geometry after the old work of Pappus.  So I'll mention it in my course!   But I don't really understand why it's true.  Do you know a niceexplana... more »

The mystical hexagram theorem

The picture explains this amazing result, which was discovered by Pascal in 1639, when he was only sixteen.

Take six points on an ellipse, called A,B,C,D,E,F.  Connect each point to the next by a line.

The red lines intersect in a point G.
The yellow lines intersect in a point H.
The blue lines intersect in a point K. 

And then the cool part:

The points G, H and K lie on a line!

I'm teaching a course on 'algebraic groups' starting on Thursday, so I need to review a bit of the history of projective geometry.   This result of Pascal, called the Hexagrammum Mysticum Theorem, was the first exciting theorem about projective geometry after the old work of Pappus.  So I'll mention it in my course!   But I don't really understand why it's true.  Do you know a nice explanation?

I'll start by reading this:

https://en.wikipedia.org/wiki/Pascal%27s_theorem

If you can manage to enable Java applets on your device - a task made ever harder by those worried for our safety - you should check out this:

http://www.cut-the-knot.org/Curriculum/Geometry/Pascal.shtml

You can move six points around a circle and see how things change.

#geometry___

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2016-09-17 02:15:36 (93 comments; 20 reshares; 109 +1s; )Open 

Exploring black holes - with cats!

There should be a series of videos exploring black holes with cats. 

So far all we have is this gif made by +Dragana Biocanin.   A cat can orbit just above the photon sphere of a non-rotating black hole, moving at almost the speed of light.   It's impossible for a cat to orbit below the photon sphere.   As long as it's outside the event horizon it can accelerate upwards and escape the black hole's gravitational pull.   But if it crosses the event horizon, it's doomed! 

The event horizon is an imaginary surface in spacetime that's defined by this property: once a cat crosses this surface, it can't come back without going faster than light!   This property involves events in the future, so there's no guaranteed way for the cat to tell when it's crossing an event horizon.

Forexample, if... more »

Exploring black holes - with cats!

There should be a series of videos exploring black holes with cats. 

So far all we have is this gif made by +Dragana Biocanin.   A cat can orbit just above the photon sphere of a non-rotating black hole, moving at almost the speed of light.   It's impossible for a cat to orbit below the photon sphere.   As long as it's outside the event horizon it can accelerate upwards and escape the black hole's gravitational pull.   But if it crosses the event horizon, it's doomed! 

The event horizon is an imaginary surface in spacetime that's defined by this property: once a cat crosses this surface, it can't come back without going faster than light!   This property involves events in the future, so there's no guaranteed way for the cat to tell when it's crossing an event horizon.

For example, if two supermassive black holes were shooting toward our Solar System right now and collided in an hour, forming a black hole that swallowed the Earth, at some moment your cat would cross the event horizon.  That's the moment when, no matter how hard it tried, it could no longer escape.  But this moment could be happening right now, and your cat might not notice!   No alarm bells ring at this moment.

What happens inside the event horizon?

For a non-rotating black hole formed by the collapse of matter, the answer is pretty well understood - except at the 'singularity', where the laws of physics we know break down.   

Your cat will fall in, getting stretched ever thinner.    For a hypothetical non-rotating black hole with the mass of our Sun, once it crosses the event horizon it will hit the singularity in about 10 microseconds.  That's not much time!

In fact, all known black holes are heavier than our Sun.   If you double the mass of the black hole, you double the amount of time it takes to hit the singularity, and so on.  So, for a non-rotating black hole 100,000 times the mass of our Sun, it takes 1 second to hit the singularity after  crossing the horizon.

The biggest known black holes are about 30 billion times the mass of our Sun.  For a non-rotating black hole this big, it would take three and a half days for your cat to hit the singularity after it crosses the horizon!   You might want to send it in with some cat food.

But there's a catch.  Real-world black holes are always rotating!  This makes them much more complicated.  For starters, frame-dragging tends to pull you along with the black hole's rotation.

We began to see that yesterday when I showed you +Leo Stein's website about how photons orbit a black hole.  There's not just one photon sphere - there's a bunch!   

There's also a region called the ergosphere where frame-dragging becomes so strong that your cat can't stand still.   And Penrose discovered something interesting about this.

You can send a cat into the ergosphere with rockets strapped to its back.  When it shoots back out, it can carry angular momentum and energy out of the black hole!   It's a bit like how we use Jupiter to fling satellites to Pluto - except we're using the rotation rather than the motion of the black hole!  

So, we can in theory "mine" a rotating black hole, removing energy from it until it's not rotating.

Beneath the ergosphere lies the horizon.  Inside the horizon of a rotating black hole, things get even weirder.  More on that later, I hope.  But probably not with cats.

For now, try this:

https://en.wikipedia.org/wiki/Ergosphere

#physics  ___

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2016-09-16 01:13:54 (35 comments; 19 reshares; 86 +1s; )Open 

Light moves around a rotating black hole

This gif by +Leo Stein shows a photon orbiting a black hole.  Since the black hole is rotating, the photon traces out a complicated path.  You can play around with the options here:

 https://duetosymmetry.com/tool/kerr-circular-photon-orbits/

If a black hole is not  rotating, light can only orbit it on circles that lie on a special sphere: the photon sphere

But if the black hole is rotating, photon orbits are more complicated!  They always lie on some sphere or other — but now there's a range of spheres of different radii  on which photons can move! 

The cool part is how a rotating massive object — a black hole, the Sun or even the Earth — warps spacetime in a way that tends to drag objects along with its rotation.  This is called frame-dragging.  
Frame-dragging... more »

Light moves around a rotating black hole

This gif by +Leo Stein shows a photon orbiting a black hole.  Since the black hole is rotating, the photon traces out a complicated path.  You can play around with the options here:

 https://duetosymmetry.com/tool/kerr-circular-photon-orbits/

If a black hole is not  rotating, light can only orbit it on circles that lie on a special sphere: the photon sphere

But if the black hole is rotating, photon orbits are more complicated!  They always lie on some sphere or other — but now there's a range of spheres of different radii  on which photons can move! 

The cool part is how a rotating massive object — a black hole, the Sun or even the Earth — warps spacetime in a way that tends to drag objects along with its rotation.  This is called frame-dragging.  

Frame-dragging was one of the last experimental predictions of general relativity to be verified, using a satellite called Gravity Probe B.    Frame-dragging was supposed to make a gyroscope precess a bit more.   This experiment was really hard.  It suffered massive delays and cost overruns.   When it was finally done, the results were not as conclusive as we'd like.   I believe in frame-dragging mainly because everything else about general relativity works great, and it's hard to make up a theory that differs in just this one prediction.

It's pretty bizarre that instead of following orbits that move in and out from the black hole - like ellipses, or something - photons can move only in orbits of constant radius, with a range of different possible radii  being allowed.   Leo Stein explains:

After you study the radial equation, you learn that the only bound photon trajectories — that is, orbits! — are those for which r=const in Boyer-Lindquist coordinates. This is why these photon orbits are sometimes called “circular” or “spherical.”

In the end, you see that for each angular momentum parameter a for the black hole, there is a one-parameter family of trajectories given by the radius r, which must be between the two limits

r₁(a) ≤ r ≤ r₂(a)

The innermost photon orbit is a prograde circle lying in the equatorial plane, and the outermost orbit is a retrograde circle lying in the equatorial plane.

Prograde means that this orbit goes around the same way the black hole is rotating; retrograde means it's moving in the opposite direction.

These orbits are all unstable.  Push the photon slightly inward and it will fall into the black hole.   Push it outward just a bit and it will fly away.  So, this stuff is mainly interesting for the math.  You won't actually find a lot of light orbiting a black hole.

For more of the math, see Leo Stein's website.  It's great!  But the most fun part is using some sliders to play with photon orbits.

For more on frame-dragging, see:

https://en.wikipedia.org/wiki/Frame-dragging

#physics  ___

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2016-09-15 03:41:43 (15 comments; 18 reshares; 161 +1s; )Open 

Just because someone's on crutches doesn't mean they're handicapped

Nomads kick ass.   James Dator explains:

The World Nomad Games concluded on Friday in what can only be described as the greatest week-long sporting event on the planet. The games, intended to showcase ethnic sports of Central Asia, featured things you have never heard of, athletes you’ll never learn about and sports that sound absolutely terrifying.

There were 16 sports with medals up for grabs. These are the ones that are the absolute wildest.

Cirit

This Turkish equestrian sport involves teams of riders chasing each other and throwing javelins at each other while on horseback. Yes, seriously.

Er Enish

It’s wrestling, except you’re on a horse. You win by pulling your opponent off their horse.

Kok-boru
more »

The World Nomad Games, Kyrgyzstan. ___Just because someone's on crutches doesn't mean they're handicapped

Nomads kick ass.   James Dator explains:

The World Nomad Games concluded on Friday in what can only be described as the greatest week-long sporting event on the planet. The games, intended to showcase ethnic sports of Central Asia, featured things you have never heard of, athletes you’ll never learn about and sports that sound absolutely terrifying.

There were 16 sports with medals up for grabs. These are the ones that are the absolute wildest.

Cirit

This Turkish equestrian sport involves teams of riders chasing each other and throwing javelins at each other while on horseback. Yes, seriously.

Er Enish

It’s wrestling, except you’re on a horse. You win by pulling your opponent off their horse.

Kok-boru

There’s no delicate way to explain Kok-boru. It’s horseback basketball using a goat carcass. You win by tossing the dead goat into your opponent’s well. It comes from a tradition of beating up wolves that attacked your herd of sheep and throwing a dead wolf to your friends who went wolf hunting with you.

Mas-wrestling

In this form a wrestling, athletes fight over a stick. Each wrestler is given part of the stick to hold and are seated facing each other with their feet on a plank. Whoever gets the stick wins.

Salbuurun

A three-step hunting sport involving animals.  Competitions are held in the following disciplines:

1. Burkut saluu - hunting with golden eagles. Composition of the team - 6 people: 1 leader and 5 berkutchi (hunter with eagles).

2. Dalba oynotuu - falcon flying to the lure. Composition of the team - 6 people: 1 leader and 5 Kushchu (falconer).

3. Taigan jarysh - dog racing among breeds of greyhound. Composition of the team - 6 people: 1 leader and 5 owners of dogs.

Traditional Archery

This has to be the biggest misnomer of the World Nomad Games. They say “traditional,” but really they mean on horseback and also this.

(The picture of this woman here.  Who is she?)

James Dator explains more games here:

http://www.sbnation.com/2016/9/12/12888720/world-nomad-games-burning-horseriders-dead-goat-basketball-eagle-hunting-wow

There's more here:

https://www.washingtonpost.com/news/early-lead/wp/2016/09/14/first-ever-u-s-team-plays-rugby-on-horses-with-a-decapitated-goat-at-world-nomad-games/

Not for the squeamish!  However, excellent pictures of hunters with their eagles, horse riders, etc.

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2016-09-13 00:41:47 (75 comments; 19 reshares; 103 +1s; )Open 

An even bigger particle accelerator?

This is Chen-Ning Yang.  He helped create Yang-Mills theory - the wonderful theory that describes all the forces in nature except gravity.    He helped find the Yang-Baxter equations, which describe what particles do when they move around on a thin sheet of matter, tracing out braids. 

He's one of China's top particle physicists... and he's come out against  building a new, bigger particle accelerator!   This is a big deal, because only China has the will to pay for the next machine.

In 2012, two months after the Large Hadron Collider (near Geneva) found the Higgs boson, a Chinese institute called for a bigger machine: the Circular Electron Positron Collider or CEPC.

This machine would be a ring 80 kilometers around.  It would collide electrons and positrons at an energy of250 GeV... more »

An even bigger particle accelerator?

This is Chen-Ning Yang.  He helped create Yang-Mills theory - the wonderful theory that describes all the forces in nature except gravity.    He helped find the Yang-Baxter equations, which describe what particles do when they move around on a thin sheet of matter, tracing out braids. 

He's one of China's top particle physicists... and he's come out against  building a new, bigger particle accelerator!   This is a big deal, because only China has the will to pay for the next machine.

In 2012, two months after the Large Hadron Collider (near Geneva) found the Higgs boson, a Chinese institute called for a bigger machine: the Circular Electron Positron Collider or CEPC.

This machine would be a ring 80 kilometers around.  It would collide electrons and positrons at an energy of 250 GeV, about twice what you need to make a Higgs.   It could make lots of Higgs bosons and study their properties.  It might find something new, too!  Of course that would be the hope.

It would cost $6 billion, and the plan was that China would pay for 70% of it.  Nobody knows who would pay for the rest.

On 4 September, Yang, in an article posted on the social media platform WeChat, says that China should not build a supercollider now. He is concerned about the huge cost and says the money would be better spent on pressing societal needs. In addition, he does not believe the science justifies the cost: The LHC confirmed the existence of the Higgs boson, he notes, but it has not discovered new particles or inconsistencies in the standard model of particle physics. The prospect of an even bigger collider succeeding where the LHC has failed is “a guess on top of a guess,” he writes. Yang argues that high-energy physicists should eschew big accelerator projects for now and start blazing trails in new experimental and theoretical approaches.

That same day, the director of the institute that wants to build the machine posted a rebuttal on WeChat.   I can't read it, because it's in Chinese:

http://chuansong.me/n/680325551051

It will be interesting to see how this plays out.  Personally I think we as a species need to focus on global warming and the Anthropocene: the way we're transforming the Earth. 

In the last 25 years, 10% of the world's remaining wilderness has disappeared.   Temperatures are rising at an ever-increasing rate.   If we keep it up, we'll melt Greenland and the Antarctic, eventually flooding all coastal cities.  Even now, weather patterns are changing, with big heat waves, floods and droughts becoming more common. 

Surviving the Anthropocene will require new math, new physics, new chemistry, new biology, new computer science, and new technology of many kinds.  Most of all, it will require new attitudes - new politics and economics.

One thing that won't  be required is new elementary particles.  I love fundamental physics.   But finding new particles can wait.  They'll still be here in a century or two.  Our civilization, and the natural world we love, may not.

What really matters here is not the money.  $6 billion is not much in the grand scheme of things.  For example, this fall California is voting on a $9 billion bond measure for its schools.    What really matters is where scientists put their energy. 

The quote is from Science magazine:

http://www.sciencemag.org/news/2016/09/debate-signals-cloudy-outlook-chinese-supercollider

The Earth's disappearing wilderness:

https://www.theguardian.com/environment/2016/sep/08/humans-have-destroyed-a-tenth-of-earths-wilderness-in-25-years-study

xkcd has a great graph of the Earth's temperature - check it out!  You'll learn a lot and have fun:

http://xkcd.com/1732/

#physics  ___

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2016-09-11 06:38:13 (25 comments; 20 reshares; 116 +1s; )Open 

Just above the photon sphere

This gif shows what it's like to orbit a non-rotating black hole just above its photon sphere.

That's the imaginary sphere where you'd need to move at the speed of light  to maintain a circular orbit.    At the photon sphere, the horizon of the black hole looks like a perfectly straight line!

But since you can't move at the speed of light, this gif shows you orbiting slightly above the photon sphere, a bit slower than light. 

We cannot go to such a place - not yet, anyway.  The gravity would rip us to shreds if we tried.   But thanks to physics, we can figure out what it would be like to be there!   And that is a wonderful thing.

The red stuff drawn on the black hole is just to help you imagine your motion.  You would not really see that stuff. 

The light above the blackhole is st... more »

Just above the photon sphere

This gif shows what it's like to orbit a non-rotating black hole just above its photon sphere.

That's the imaginary sphere where you'd need to move at the speed of light  to maintain a circular orbit.    At the photon sphere, the horizon of the black hole looks like a perfectly straight line!

But since you can't move at the speed of light, this gif shows you orbiting slightly above the photon sphere, a bit slower than light. 

We cannot go to such a place - not yet, anyway.  The gravity would rip us to shreds if we tried.   But thanks to physics, we can figure out what it would be like to be there!   And that is a wonderful thing.

The red stuff drawn on the black hole is just to help you imagine your motion.  You would not really see that stuff. 

The light above the black hole is starlight - bent and discolored by your rapid motion and the gravitational field of the black hole.

This gif was made by Andrew Hamilton, an expert on black holes at the University of Colorado.  You can see a lot more explanations and movies on his webpage:

http://jila.colorado.edu/~ajsh/insidebh/schw.html

#physics  ___

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2016-09-09 06:43:28 (50 comments; 5 reshares; 47 +1s; )Open 

The Ultimate Question, and its Answer

+David Madore has a lot of great stuff on his website - videos of black holes, a discussion of infinities, and more.   He has an interesting story that claims to tell you the Ultimate Question, and its Answer.  

(No, it's not 42.)

I like it, but I can't tell how much sense it makes.

Here's the key part:

What is the Ultimate Question, and what is its Answer? The answer to that is, of course: “The Ultimate Question is ‘What is the Ultimate Question, and what is its Answer?’ and its answer is what has just been given.”.  This is completely obvious: there is no difference between the question “What color was Alexander's white horse?” and the question “What is the answer to the question ‘What color was Alexander's white horse?’?”. Consequently, the Ultimate Questionis “What is the Answer t... more »

The Ultimate Question, and its Answer

+David Madore has a lot of great stuff on his website - videos of black holes, a discussion of infinities, and more.   He has an interesting story that claims to tell you the Ultimate Question, and its Answer.  

(No, it's not 42.)

I like it, but I can't tell how much sense it makes.

Here's the key part:

What is the Ultimate Question, and what is its Answer? The answer to that is, of course: “The Ultimate Question is ‘What is the Ultimate Question, and what is its Answer?’ and its answer is what has just been given.”.  This is completely obvious: there is no difference between the question “What color was Alexander's white horse?” and the question “What is the answer to the question ‘What color was Alexander's white horse?’?”. Consequently, the Ultimate Question is “What is the Answer to the Ultimate Question?” — but so that we can understand the Answer, I restate this as “What is the Ultimate Question, and what is its Answer?”, at which point it becomes obvious what the Answer is.

Of course it's meant to be funny.  I like it.   But I'm not sure how logical it is.   The logic is quite twisty, but it might make sense.   It's more funny if the logic is sound.

The whole story is here:

http://www.madore.org/~david/misc/totipsism.html___

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2016-09-08 08:39:04 (36 comments; 14 reshares; 75 +1s; )Open 

Cosmic censorship

Einstein's theory of gravity predicts singularities: places where you can fall off the edge of spacetime.   In reality, these may be places where Einstein's theory breaks down!  We don't really know.

Why not just go look?  Unfortunately, most singularities are hidden.  You can't see them and come back and tell us what you saw.

One singularity that's not hidden, according to Einstein's theory, is the Big Bang.  

Look into the sky in any direction and you are really looking back in time, because it takes time for light to travel.  If you look far enough - with the right kind of equipment - you can see a faint glow of microwaves left over from the Big Bang.   Actually this glow is from hot gas that cooled down enough to become transparent 380,000 years after the Big Bang.   It's harder to seebeyond that... more »

Cosmic censorship

Einstein's theory of gravity predicts singularities: places where you can fall off the edge of spacetime.   In reality, these may be places where Einstein's theory breaks down!  We don't really know.

Why not just go look?  Unfortunately, most singularities are hidden.  You can't see them and come back and tell us what you saw.

One singularity that's not hidden, according to Einstein's theory, is the Big Bang.  

Look into the sky in any direction and you are really looking back in time, because it takes time for light to travel.  If you look far enough - with the right kind of equipment - you can see a faint glow of microwaves left over from the Big Bang.   Actually this glow is from hot gas that cooled down enough to become transparent 380,000 years after the Big Bang.   It's harder to see beyond that, because farther back the gas was too hot and thick.  But we may be able to do it someday, using gravitational waves instead of microwaves.

What about black holes?  These have singularities too, according to Einstein's theory.  But these are hidden behind event horizons.  In other words, if you get too close to a black hole, you can't get back out.   For any signal to get out, it would have to go faster than light! 

In 1969 Roger Penrose proposed the cosmic censorship hypothesis.   In its original form, this says that any singularity created by the collapse of matter must be hidden behind an event horizon.  

In 1991, John Preskill and Kip Thorne made a bet against Stephen Hawking in which they claimed that cosmic censorship was false.   You may have heard about their famous bet about the black hole information paradox.  This is a different one!  These guys like bets.

Surprisingly, this bet was settled in 1997.    Guess who won?

Or don't guess - read my blog article, where I give away the answer:

https://www.physicsforums.com/insights/struggles-continuum-conclusion/

I also recommend this book, which has a great title:

• John Earman, Bangs, Crunches, Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes, Oxford U. Press, Oxford, 1993.   Available at http://www.pitt.edu/~jearman/Earman_1995BangsCrunches.pdf

John Earman is a philosopher of physics.  He's famous for actually understanding the physics in great detail, raising the standards for everyone else.   And he's kindly made this book available on his website!

#physics___

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2016-09-06 02:19:14 (35 comments; 9 reshares; 79 +1s; )Open 

Singularities - when spacetime goes bad

Physicists don't like it when things become infinite, but for Einstein's theory of gravity,  infinities are deeply connected to its most dramatic successful predictions: black holes and the Big Bang!  

 In this theory, the density of the Universe approaches infinity as we go back in time to the Big Bang.  The density of a star approaches infinity when it collapses to form a black hole.  The curvature of spacetime approaches infinity, too!   These situations where spacetime goes bad are called singularities.

Einstein didn't like singularities.  They could mean that his theory - general relativity - breaks down under extreme conditions.  But so far, they fit what we see very well.

In the 1960's, two guys named Roger Penrose and Stephen Hawking became famous by proving singularitytheorems... more »

Singularities - when spacetime goes bad

Physicists don't like it when things become infinite, but for Einstein's theory of gravity,  infinities are deeply connected to its most dramatic successful predictions: black holes and the Big Bang!  

 In this theory, the density of the Universe approaches infinity as we go back in time to the Big Bang.  The density of a star approaches infinity when it collapses to form a black hole.  The curvature of spacetime approaches infinity, too!   These situations where spacetime goes bad are called singularities.

Einstein didn't like singularities.  They could mean that his theory - general relativity - breaks down under extreme conditions.  But so far, they fit what we see very well.

In the 1960's, two guys named Roger Penrose and Stephen Hawking became famous by proving singularity theorems.  These theorems say that under certain conditions, a singularity is inevitable  if general relativity is true.  Penrose's theorem applies to black holes.  Hawking's applies to the Big Bang.  In 1970 they teamed up and combined their results into one big super-theorem.

But what, exactly, is  a singularity?  It's not a region in spacetime!  And when, exactly, is a singularity inevitable in Einstein's theory of gravity?  And what does his theory even say?   I explain all that here, in part 7 of my series on how physics battles with infinities.

#physics  ___

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2016-09-05 04:37:57 (31 comments; 11 reshares; 65 +1s; )Open 

The photon sphere

A nonrotating black hole is surrounded by an imaginary sphere called the event horizon.  If you cross this sphere, you are doomed to fall in. 

If you carry a flashlight and try to shine light straight out, light emitted at the instant you cross the event horizon will basically stay there!  Why?  Because to stay on the horizon you must move outwards at the speed of light.   As the Red Queen said in Alice in Wonderland:

"Now, here, you see, it takes all the running you can do, to keep in the same place."

But there's another imaginary sphere outside the event horizon, called the photon sphere.  This is where light can go in circles around the black hole!

This picture by +David Madore shows the view from the photon sphere.  The black hole occupies exactly half the sky!   As he says:
This ... more »

The photon sphere

A nonrotating black hole is surrounded by an imaginary sphere called the event horizon.  If you cross this sphere, you are doomed to fall in. 

If you carry a flashlight and try to shine light straight out, light emitted at the instant you cross the event horizon will basically stay there!  Why?  Because to stay on the horizon you must move outwards at the speed of light.   As the Red Queen said in Alice in Wonderland:

"Now, here, you see, it takes all the running you can do, to keep in the same place."

But there's another imaginary sphere outside the event horizon, called the photon sphere.  This is where light can go in circles around the black hole!

This picture by +David Madore shows the view from the photon sphere.  The black hole occupies exactly half the sky!   As he says:

This is the distance at which, for an observer standing still, the black hole occupies precisely one half of the visual field. This is because it is the distance at which photons themselves will orbit the black hole circularly (this orbit is unstable, however).

In other words, the horizon is the distance at which photons emitted outward from the black hole are standing still, whereas the photon sphere is the distance at which photons emitted orthogonally from the black hole remain at this constant distance and circle around the black hole in an orbit: but since light rays always appear to be straight, to an observer standing still on the photon sphere, the photon sphere seems like an infinite plane, with the black hole occupying half of space beyond it, and the outside world occupying the other half of space.

Now I should admit, as David does, that it's unstable for light to stay exactly on the horizon, or to orbit the photon sphere in a circle.  It's like balancing a pencil on its tip!  In reality you can't make things so perfect. 

And this is especially true because light is a wave, not a particle - so it doesn't have a precise location, it's always a bit smeared out.   So, if you have a beam of light orbiting the photon sphere, it will spread out.  Some will fall in, and some will escape outwards.

I highly recommend David Madore's page on black holes:

http://www.madore.org/~david/math/kerr.html

and if I have the energy I will try to explain more about them here.  They're on my mind right now, because I'm writing a paper where I discuss them.

The photon sphere of a nonrotating black hole is one and a half times as big across as event horizon:

https://en.wikipedia.org/wiki/Photon_sphere

The radius of the event horizon is called the Schwarzschild radius and it's

2Gm/c²

where m is the black hole's mass, G is Newton's gravitational constant and c is the speed of light.  The radius of the photon sphere is

3Gm/c²

https://en.wikipedia.org/wiki/Schwarzschild_radius

#physics  ___

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2016-09-04 03:52:21 (4 comments; 6 reshares; 53 +1s; )Open 

Kummer surface

This picture by +Abdelaziz Nait Merzouk almost completes my series on surfaces with the maximum number of nodes - those places where the tips of two cones meet.   This surface has 16 nodes, the most possible for a surface described by a quartic equation: a polynomial equation of degree 4. 

Unlike other surfaces in this series, it's connected to some pretty deep math.  Take a complex curve of genus 2, form its Jacobian variety,  mod out by the Kummer involution, and you get a surface like this!  Whee!  Where's my "mad scientist" emoji?  😃

For an explanation of all that, go here:

http://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/

As usual, mathematicians seem to have a perverse desire to make things complicated.  For example, a "complex curve of genus 2" isbasically j... more »

Kummer surface

This picture by +Abdelaziz Nait Merzouk almost completes my series on surfaces with the maximum number of nodes - those places where the tips of two cones meet.   This surface has 16 nodes, the most possible for a surface described by a quartic equation: a polynomial equation of degree 4. 

Unlike other surfaces in this series, it's connected to some pretty deep math.  Take a complex curve of genus 2, form its Jacobian variety,  mod out by the Kummer involution, and you get a surface like this!  Whee!  Where's my "mad scientist" emoji?  😃

For an explanation of all that, go here:

http://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/

As usual, mathematicians seem to have a perverse desire to make things complicated.  For example, a "complex curve of genus 2" is basically just a doughnut with two holes in it.

Well, it's actually the surface of a 2-holed doughnut. 

Well, it's actually the surface of a 2-holed doughnut equipped with a given conformal structure: that is, a way to measure angles.

Well, it's actually the complex curve that's canonically associated to the surface of a 2-holed doughnut equipped with a given conformal structure. 

Okay: for short, let's say it's a complex curve of genus 2.

Hmm, so I guess what happens is this.  Mathematicians take a simple idea like a 2-holed doughnut, and notice that there's a lot of interesting variations on this idea.   They need to be precise, so they make up different names for these different variations.  So, what looks like a 2-holed doughnut to the naked eye might really be a complex curve of genus 2, or a compact 2-manifold of genus 2, or something else... all closely related things which differ in ways that take a while to explain!

Anyway, starting from such a thing you can build a Kummer surface, and my blog article says how. There are lots of different Kummer surfaces, but they all have 16 nodes.

The only surface left to do is the Togliatti quintic.   When I've this finished this series on Visual Insight I'll turn to crystals, and show you some pictures created by Greg Egan.  But before that, I may show you an interesting answer to an interesting puzzle about moving sofas.

By the way: you can now keep track of my new stuff on Twitter:

https://twitter.com/johncarlosbaez

#geometry  ___

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2016-09-02 00:37:26 (94 comments; 18 reshares; 199 +1s; )Open 

Black Saturns

Imagine a black hole with a black ring.  Physicists call such a thing a black Saturn

Nobody has ever seen one.  But we can still study them.

You see, we know the equation that describes black holes.  It's called Einstein's equation, the basic formula in Einstein's theory of gravity. 

We know this equation has solutions with a round event horizon - a surface that you can't escape if you fall through it.  These are black holes.  And we've seen plenty of black holes - or at least the hot gas falling into black holes.

Could there be a black ring - an event horizon shaped like a ring?   It would need to spin so it wouldn't collapse. 

Nobody has ever seen a black ring... and there's a reason why!  They're mathematically impossible.  There's nosolution of... more »

Black Saturns

Imagine a black hole with a black ring.  Physicists call such a thing a black Saturn

Nobody has ever seen one.  But we can still study them.

You see, we know the equation that describes black holes.  It's called Einstein's equation, the basic formula in Einstein's theory of gravity. 

We know this equation has solutions with a round event horizon - a surface that you can't escape if you fall through it.  These are black holes.  And we've seen plenty of black holes - or at least the hot gas falling into black holes.

Could there be a black ring - an event horizon shaped like a ring?   It would need to spin so it wouldn't collapse. 

Nobody has ever seen a black ring... and there's a reason why!  They're mathematically impossible.  There's no solution of Einstein's equation that describes a black ring just sitting there, or just spinning but staying the same shape.  Physicists have known this since the 1970's.  The options for stationary black-hole-like solutions are very limited.  You can have a black hole that just sits there, or you can have one that spins... and it can also have electric charge if you want.  That's it.

But suppose we had an extra dimension. 

Suppose space were 4-dimensional, instead of 3-dimensional.  We can still write down Einstein's equation and try to solve it.   You can still get round black holes.   But in 2001, two physicists proved that black rings are also possible!

Once you have round black holes and black rings, it's irresistible. You've got to see if you can create a black Saturn!  Can you get a black ring to orbit a black hole? 

Yes you can!  In 2007, Henriette Elvanga and Pau Figueras found black Saturn solutions of Einstein's equations in 4d space.  And this opened up lots of other fun questions.   Can you get the ring to rotate the opposite way than the black hole is spinning?  Can you get a black hole with more than one ring orbiting it?  Are black Saturns stable, or unstable?  And so on.

You might say this is just a game.  Or you might say it's important to understand what's so special about 3-dimensional space.  Either way, it's pretty cool. 

Puzzle 1.  Could a ring of dust be stable if there weren't a planet in the middle?   Does having a planet inside help stabilize the ring - and if so, how?

I think The Black Saturns would be a good name for a band... and here's one reason why:

Puzzle 2.  Why does the phrase 'black Saturn' make sense in terms of astrology?  A hint: Jupiter, or Jove, was supposedly responsible for making people 'jovial', or happy. 

Here is the first paper on black rings:

• R. Emparan and H. S. Reall,  A rotating black ring in five dimensions, Phys. Rev. Lett. 88 (2002) 101101.  Available at https://arxiv.org/abs/hep-th/0110260.

and here's the first paper on black Saturns:

• Henriette Elvang and Pau Figueras, Black Saturns, JHEP (2007), 0705:050.  Available at https://arxiv.org/abs/hep-th/0701035.

#physics___

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2016-09-01 06:06:53 (47 comments; 29 reshares; 83 +1s; )Open 

Waiting for the motivation fairy

Go ahead!   Procrastinate!   If you wait long enough, a fairy princess may suddenly appear and cast a spell motivating you to get work done. 

Here's what Hugh Kearns and Maria Gardiner have to say about this approach.  It contains good advice:

If you were trying to set up ideal conditions for procrastination, conducting a research project would provide them. Such projects tend to be large and time-consuming: completing a doctoral research project, for example, often takes three years or more. Deadlines and endpoints are often fuzzy and ill-defined. Then there’s the reward structure: you can put in a lot of effort with little to no positive feedback along the way, and the rewards, if there are any, take a long time to come.

Add to this the fact that scientists are often perfectionists with demanding, ifnot id... more »

Waiting for the motivation fairy

Go ahead!   Procrastinate!   If you wait long enough, a fairy princess may suddenly appear and cast a spell motivating you to get work done. 

Here's what Hugh Kearns and Maria Gardiner have to say about this approach.  It contains good advice:

If you were trying to set up ideal conditions for procrastination, conducting a research project would provide them. Such projects tend to be large and time-consuming: completing a doctoral research project, for example, often takes three years or more. Deadlines and endpoints are often fuzzy and ill-defined. Then there’s the reward structure: you can put in a lot of effort with little to no positive feedback along the way, and the rewards, if there are any, take a long time to come.

Add to this the fact that scientists are often perfectionists with demanding, if not idealistic, expectations, and it is little wonder that procrastination is the most discussed topic in our graduate-student and researcher workshops. Many researchers simply take for granted that they are at the mercy of the forces of procrastination, doomed to increased stress levels and stretched deadlines. But there are simple strategies for pushing yourself to get engaged. The first is to recognize the patterns that you’re falling into.

Some procrastination activities are pretty obvious. There’s the morning coffee break that creeps into lunchtime. Or watching videos on YouTube and sending them to all your friends. Or updating your Facebook status when you should be updating your lab book.   [I prefer posting to G+.]

But most procrastination is far more subtle, and can even be mistaken for productive work. For example, you might try to track down that elusive reference, even though you’ve already got more than you will ever have time to read. Or you could start a new experiment instead of analysing the old one. Or take stock of the glassware in the lab. Or check your e-mail. These activities make it seem as though you’re doing something useful, and you may well be, but it’s not the thing you should be doing right now.

So why is housekeeping, for example, so much fun when you’re supposed to be working on your dissertation or a paper? It’s a displacement activity, used to dispel the self-reproach or discomfort that we feel for not doing something else. Reading a novel or taking a nap causes too much guilt. But have you ever, say, reorganized your folders to make it easier to find the files? It would speed up your writing, after all. Or perhaps you’ve diligently labelled all the cupboards in the lab to make it easier to find things.

Although these activities or excuses seem acceptable, their fatal flaw is that once they’re over, you still haven’t finished that article, started that experiment or written your dissertation.  You probably have an increased sense of guilt because you’re not making progress on your goal. And although you’ve found and read that reference, you still don’t feel motivated to write. Sadly, while you were answering e-mails or counting the glassware, the motivation fairy didn’t stop by and make that difficult task look any more appealing. That’s just not how motivation works.

Most people have a fundamental misunderstanding: we like to think that motivation leads to action, or, more simply, that when you feel like doing something, you’ll do it. This model might work for things you enjoy doing, such as watching a film or going for a walk. But it’s not particularly good for huge tasks with fuzzy deadlines. The problem is that you may never feel motivated to revise and resubmit that paper — at least not until a hard-and-fast deadline appears. You need a different model.

Some psychology research shows that action leads to motivation, which in turn leads to more action. You have to start before you feel ready; then you’ll feel more motivated, and then you’ll take more action. You’ve probably had this experience yourself. You put off running an analysis for ages; eventually, you decide to do it, and once you start, you say to yourself, “This isn’t as bad as I thought. Why not keep going while I’m at it?”

Of course, starting before you feel motivated is difficult. But certain strategies can directly tackle the conditions that lead to procrastination in the first place.

First, big projects need to be broken down into steps. Not just small steps, but tiny steps. Instead of saying you’ll make the revisions to the paper — which probably seems overwhelming — the tiny step could be that you’ll read the reviewer’s comments or you’ll make the first two changes. Second, you need to set a time or deadline by which to perform that tiny step. Saying you’ll do it later or tomorrow isn’t enough — the deadline needs to have an ‘o’clock’ attached to it. Third, you need to build in an immediate reward. If you finish reading the comments by your deadline at 10:00 a.m., you can allow yourself to have a coffee, a brief chat or a quick e-mail exchange. It’s highly likely that once you start the task, your motivation will kick in and you’ll find yourself wanting to spend longer at it.

So if the motivation fairy hasn’t been stopping off at your lab or desk very frequently, perhaps you should give her a hand. The next time you catch yourself engaging in displacement activities, remember that there’s a way to recover that elusive drive. Follow our three rules and watch your motivation grow.

To waste more time reading articles about how to be more productive, visit Kearns and Gardiner's website:

http://www.ithinkwell.com.au/research

Personally, instead of trying to completely avoid procrastination, I try to make sure that all my "displacement activities" are themselves worthwhile.

The fairy princess here is from:

http://cdn.wallpapersafari.com/23/32/udCeSP.jpg

but I don't know who created it.___

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2016-08-31 05:17:00 (40 comments; 6 reshares; 72 +1s; )Open 

Cayley's nodal cubic surface

Arthur Cayley, born in 1821, was one of the first great pure mathematicians in Britain.   A guy named Newton had done some stuff connected to physics... and ultimately Newton's line of work led to Stephen Hawking, who occupies the same position at Cambridge, called the Lucasian Professorship.  But Cayley's work was more abstract.

He liked math a lot, and went to Cambridge at the age of 17, but when he got a degree and needed a job at the age of 25, he became a lawyer.  He worked as a lawyer for 14 years.  But then a new position opened up: the Sadleirian Professorship.   This professor was supposed to

explain and teach the principles of pure mathematics, and to apply himself to the advancement of that science

and that's what Cayley did!  

He helped invent group theory - he was the firstto give ... more »

Cayley's nodal cubic surface

Arthur Cayley, born in 1821, was one of the first great pure mathematicians in Britain.   A guy named Newton had done some stuff connected to physics... and ultimately Newton's line of work led to Stephen Hawking, who occupies the same position at Cambridge, called the Lucasian Professorship.  But Cayley's work was more abstract.

He liked math a lot, and went to Cambridge at the age of 17, but when he got a degree and needed a job at the age of 25, he became a lawyer.  He worked as a lawyer for 14 years.  But then a new position opened up: the Sadleirian Professorship.   This professor was supposed to

explain and teach the principles of pure mathematics, and to apply himself to the advancement of that science

and that's what Cayley did!  

He helped invent group theory - he was the first to give a modern definition of a group!    He helped invent graph theory.   And he also did a lot of great algebraic geometry!

For example, this is a picture of Cayley's nodal cubic surface.  It's famous because it's the surface described by a cubic equation with the largest possible number of nodes - meaning points where the surface looks like two cones meeting. 

It has 4 nodes, located at the corners of a tetrahedron.  And the whole surface has the same symmetries as a tetrahedron!   In fact, every cubic surface with 4 nodes is isomorphic to this one. 

Cayley was so prolific that there are two other famous cubic surfaces named after him.  And much more:

The Cayley–Hamilton theorem in linear algebra
The Cayley–Bacharach theorem about cubic curves
The Cayley–Menger determinant
Cayley's theorem – every group is a group of permutations
Cayley–Dickson construction – used to construct the octonions
The Cayley algebra – also called the octonions
The Cayley graph of a group
Cayley's sextic – a plane curve of degree 6
The Cayley table – the multiplication table of a group
Cayley's formula – saying there are n^(n-2) trees with n vertices
The Cayley–Klein metric – a metric on the complement of a quadric
The Cayley–Klein model of hyperbolic geometry
Cayley's Ω process – a way to get invariants of a group action
Cayley transform – a map from the upper halfplane to the unit disk
Cayley's mousetrap — a card game
The Cayleyan variety associated to a hypersurface
The Chasles–Cayley–Brill formula in algebraic geometry

By now Cayley has had over 7000 academic descendants working on math: for example, one of his student's student's was G. H. Hardy, the famous number theorist.

So, three cheers for old Arthur!

This picture was drawn by +Abdelaziz Nait Merzouk.   For more on Cayley's nodal cubic surface, visit my blog:

http://blogs.ams.org/visualinsight/2016/08/15/cayleys-nodal-cubic-surface/

You could have a lot of fun just learning the math Cayley did, and you can do it starting here:

https://en.wikipedia.org/wiki/Arthur_Cayley#Legacy

#geometry___

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2016-08-27 04:43:12 (106 comments; 27 reshares; 210 +1s; )Open 

Dark mysteries

You probably heard the news this week: astronomers found a galaxy that's 98% dark matter. 

It's called Dragonfly 44.  It's extremely faint, so it doesn't have many stars.   But we can use redshifts to see how fast those stars are moving - over 40 kilometers per second on average.  If you do some calculations, you can see this galaxy would fly apart unless there's a lot of invisible matter providing enough gravity to hold it together.   (Or unless something even weirder is happening.)

Something similar is true for most galaxies, including ours.   What makes Dragonfly 44 special is that 98 percent of the matter must be invisible.   And this is just in the part where we see stars.   If we count the outer edges of the galaxy, the halo, the percentage could rise to 99% or more! 

By comparison, theMilky Way is... more »

Dark mysteries

You probably heard the news this week: astronomers found a galaxy that's 98% dark matter. 

It's called Dragonfly 44.  It's extremely faint, so it doesn't have many stars.   But we can use redshifts to see how fast those stars are moving - over 40 kilometers per second on average.  If you do some calculations, you can see this galaxy would fly apart unless there's a lot of invisible matter providing enough gravity to hold it together.   (Or unless something even weirder is happening.)

Something similar is true for most galaxies, including ours.   What makes Dragonfly 44 special is that 98 percent of the matter must be invisible.   And this is just in the part where we see stars.   If we count the outer edges of the galaxy, the halo, the percentage could rise to 99% or more! 

By comparison, the Milky Way is roughly 90% dark matter if you count the halo.  We know this pretty well, because we can see a few stars out in there and measure how fast they're moving.

There are also galaxies like NGC 3379 that may have less than the average amount of dark matter in their halo, though this is debatable.

And most excitingly, sometimes clusters of galaxies collide and stop moving, but their dark matter keeps on going! 

We can see this because light from more distant galaxies is bent, not toward the colliding clusters, but toward something else.   The most famous example is the Bullet Cluster, but there are others.

All these discoveries - and more - make dark matter seem more and more like a real thing.  So it's more and more frustrating that we don't know what it is.  As I explained a while ago, recent experiments to detect particles of dark matter have failed.  So it could be something else, like black holes about 30 solar masses in size.  And intriguingly, the first black hole collision seen by LIGO involved a 35-solar-mass and a 30-solar-mass black hole.  These are too big to have formed from the collapse of a single star.  They might be primordial black holes, left over from the early Universe.

But more on that later.

For more on Dragonfly 44, see:

• Pieter van Dokkum, Roberto Abraham, Jean Brodie, Charlie Conroy, Shany Danieli, Allison Merritt, Lamiya Mowla, Aaron Romanowsky and Jielai Zhang, A high stellar velocity dispersion and ~100 globular clusters for the ultra diffuse galaxy Dragonfly 44, http://arxiv.org/abs/1606.06291.

For our failure to find dark matter particles, see this post of mine:

https://plus.google.com/117663015413546257905/posts/3U53iqtWYXk

For more on dark matter on the outer edges of galaxies, see:

https://en.wikipedia.org/wiki/Dark_matter_halo

For the Milky Way's dark matter halo, see:

• G. Battaglia et al, The radial velocity dispersion profile of the Galactic halo: constraining the density profile of the dark halo of the Milky Way, http://arxiv.org/abs/astro-ph/0506102

#astronomy___

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2016-08-26 05:35:36 (30 comments; 23 reshares; 102 +1s; )Open 

The driverless taxi is here

Singapore now has the world's first driverless taxi! 

Yes, just one so far.  Only 10 people are allowed to use it, and it will stay in the most futuristic part of town, near the research centers Biopolis and Fusionopolis.  But the company nuTonomy hopes to make this service commercially available by 2018, with a fleet of 75 cabs.  And it wants to boost the number to thousands by 2019.

Singapore just barely beat Pittsburgh: Uber plans to offer driverless rides there in a few weeks.

Here's a story from May 2016:

During this test drive, there were people; there was construction; there was even a fairly busy intersection.

Being able to understand traffic lights, navigate to a destination and not just detect obstacles but figure out when and how to pass them is no small feat for anaut... more »

The driverless taxi is here

Singapore now has the world's first driverless taxi! 

Yes, just one so far.  Only 10 people are allowed to use it, and it will stay in the most futuristic part of town, near the research centers Biopolis and Fusionopolis.  But the company nuTonomy hopes to make this service commercially available by 2018, with a fleet of 75 cabs.  And it wants to boost the number to thousands by 2019.

Singapore just barely beat Pittsburgh: Uber plans to offer driverless rides there in a few weeks.

Here's a story from May 2016:

During this test drive, there were people; there was construction; there was even a fairly busy intersection.

Being able to understand traffic lights, navigate to a destination and not just detect obstacles but figure out when and how to pass them is no small feat for an autonomous vehicle. Often, that clumsiness was simply a result of the vehicle being overly careful and leaving considerable space between it and the object it was skirting.

Determining when it's safe to overtake a stopped car is a significant challenge for autonomous cars. Many of today's semi and fully autonomous systems, which depend largely on vehicles around them to determine how fast or slowly to drive, would wait patiently behind the car in front of it until it moved. But nuTonomy cars use formal logic, Parker said.

"Essentially, we establish a hierarchy of rules and break the least important," he said. "For example, one rule is 'maintain speed.' Another is 'stay in lane.' We violate the 'stay in lane' rule because maintaining speed is more important."

At one point during the test drive, the car passed another car that was stopped on the left side of the road. To do that, it veered all the way to the right, then abruptly turned left to overtake the stopped car. Had it been a human driver taking a road test, the maneuver would have resulted in an automatic failure.

Though Parker joked that he was always telling his engineers they could reduce the "buffer space" the car gives other objects or people on the road, that buffer is a necessary safety net when deploying an autonomous car in a complex and unstructured environment.

nuTonomy is an MIT-based startup, and I'm happy they've come here to Singapore.  Here's why, according to the local newspaper:

nuTonomy chief operations officer Doug Parker told The Straits Times that it chose to try out the service in Singapore because of the high consumer demand for taxis here, well-maintained roads and clear government regulations for its tests. "Singapore is the best place in the world for self-driving cars," said Mr Parker.

When you're trying to do new stuff you don't want too many regulations, but it's equally important that the regulations be clear.  You don't want to have to guess whether something is okay.

The first quote is from here:

http://www.recode.net/2016/5/17/11689064/nutonomy-self-driving-car-singapore-test

The second one is from here:

http://www.straitstimes.com/singapore/transport/worlds-first-driverless-taxi-trial-kicks-off-in-singapore

You can see the nuTonomy car in action here:

http://nutonomy.com/___

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2016-08-25 10:03:24 (40 comments; 3 reshares; 46 +1s; )Open 

Transitions

I'm ashamed to say I've never been to a "rave" and danced the night away.   But if I ever do, this is what I want to hear. 

Because I somehow missed this sort of scene - spending my youth more quietly - I'm only now getting into various kinds of electronic dance music that I should have known about a long time ago.   I started with Photek's Modus Operandi, a masterpiece of icy cold, sometimes jazzy, vaguely sinister drum-and-bass.  Then I picked up Richie Hawtin's Consumed, just because I liked the spooky look of this CD, and discovered he too has the mysterious, "chilly" esthetic I often enjoy... though not the virtuosity Photek can muster.  

(I must sound strange.  Though I've become cheerful and romantic in the second half of my life, I'm still extremely fussy about music that acts that way. Why?  I ... more »

Transitions

I'm ashamed to say I've never been to a "rave" and danced the night away.   But if I ever do, this is what I want to hear. 

Because I somehow missed this sort of scene - spending my youth more quietly - I'm only now getting into various kinds of electronic dance music that I should have known about a long time ago.   I started with Photek's Modus Operandi, a masterpiece of icy cold, sometimes jazzy, vaguely sinister drum-and-bass.  Then I picked up Richie Hawtin's Consumed, just because I liked the spooky look of this CD, and discovered he too has the mysterious, "chilly" esthetic I often enjoy... though not the virtuosity Photek can muster.  

(I must sound strange.  Though I've become cheerful and romantic in the second half of my life, I'm still extremely fussy about music that acts that way.  Why?  I guess because most of it feels faked.  There are exceptions, which I treasure.)

Anyway, it was only when I got ahold of Photek's BBC Essential Mix  on YouTube that I started seeking hour-long "mixes" where a DJ blends different dance tunes. 

Unfortunately I'm extremely fussy about these, too, because certain musical cliches make me gag - and let's face it, dance music is mostly cliches repeated over and over for so long that you can't help starting to twitch in synch.  So, I haven't found many that I can tolerate, and if you suggest some, I'll probably hate 'em.   But I've gotten to like stuff by John Digweed.

At first I thought this was a stage name - the perfect name for a stoner DJ - but it's apparently real.  He hails from Hastings in the UK.  Later he became famous for playing sets that lasted between eight and twelve hours at his club Twilo in New York. 

I can completely understand this, because his albums tend to be hour-long solid blocks of energetic music that go on and on and on, slowly morphing and building to a series of climaxes... never very ferocious, much more friendly than guys I just mentioned... but with a huge emphasis on continuity. 

You'll see this here.  Starting very quietly, the music builds to a delirious psychedelic peak at 1:20, then thins to a steady, almost stolid drum beat with bass until 2:22.  Then a cymbal enters, making it sound like things are moving faster (though the beat remains steady), and a simple repeated descending melody enters.  This gradually grows louder and more complex, with an echoed vocal chorus slowly sneaking in... building to another crescendo at 4:58.   And then the music empties out again, leaving us at a quite place similar to where we were back at 2:22, but different.   And then it gradually builds again...

This is undoubtedly less fun to read than to listen to, but I hope you get an idea of the structure, which keeps unfurling in a similar way for an hour, somehow gradually becoming more intense all the time, despite many moments where things quiet and calm down.  I've never listened to a piece of music where there are so many moments where I say to myself "now it's really getting going". 

He is probably making use of some kind of cognitive illusion.  It reminds me of the Shepard tone illusion, where a note seems to rise in pitch endlessly.  Speaking of which, check out +Vi Hart's video about that:

https://www.youtube.com/watch?v=PwFUwXxfZss

But he's doing it much more subtly, more metaphorically, and to better musical effect.   There are certain passages, further along in this long album, where I say now it has finally achieved its full greatness.  And so I'm tempted to recommend jumping straight to 37:00 for the funky, bubbly bounce, 47:00 for the rather ominous blasts of sound, or 1:09:00, where a beat comes in that makes me want this thing to go on all night... but I suspect that would be completely missing the point.  It's not the destination, it's the journey.

Or, you might say: the transitions.

This album, from 2006, is a skillfully blended mix of other people's tunes.  You can see them listed here:

https://en.wikipedia.org/wiki/Transitions_(John_Digweed_album)

Mix tapes had been circulating informally for a long time, but Digweed was the first to officially market one as an album, in 1994. 

#favoritemusic  ___

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2016-08-24 11:38:23 (28 comments; 22 reshares; 138 +1s; )Open 

Quantum cryptography in space

Last week China launched Micius, the first of 20 satellites that will use quantum entanglement to create almost unbreakable codes. 

This satellite will broadcast pairs of photons to two ground stations.  These photons will be entangled - correlated in a way that's only possible through quantum mechanics.  If you share an entangled pair of photons with a friend, you can use them as a key to decode the messages you send each other.   And if someone tries to intercept this key, you can detect it!   No third party can access entangled information without affecting it.

This idea has already been tested over long distances - it's not just a crazy dream.  What's new is sending entangled photons from satellites orbiting the Earth.  China's new system is called QUESS: Quantum Experiments at SpaceScale.<... more »

Quantum cryptography in space

Last week China launched Micius, the first of 20 satellites that will use quantum entanglement to create almost unbreakable codes. 

This satellite will broadcast pairs of photons to two ground stations.  These photons will be entangled - correlated in a way that's only possible through quantum mechanics.  If you share an entangled pair of photons with a friend, you can use them as a key to decode the messages you send each other.   And if someone tries to intercept this key, you can detect it!   No third party can access entangled information without affecting it.

This idea has already been tested over long distances - it's not just a crazy dream.  What's new is sending entangled photons from satellites orbiting the Earth.  China's new system is called QUESS: Quantum Experiments at Space Scale.

Micius will attempt to send entangled photons to the Xinjiang Astronomical Observatory, out in the wild west of China, and an observatory near Beijing – about 2500 kilometers away!

If that works, they'll do it between China and the Institute for Quantum Optics and Quantum Information in Vienna – 7500 kilometers apart.

Later, the QUESS project will try to demonstrate violations of Bell's inequality at a distance of 1,200 kilometers. 

What are "violations of Bell's inequality"?  In very simple terms, it means quantum mechanics is weird.   More precisely, it means quantum mechanics allows correlations that would be impossible if ordinary probability theory were correct.

Then, QUESS will try to teleport a photon state from Tibet to a satellite.  Quantum teleportation is not the teleportation of matter – we're not talking "beam me up, Scotty!"  It's the complete transfer of quantum information from one place to another, which requires destroying the original copy of that information.

If these tests are successful, more satellites will be launched, allowing a European–Asian quantum-encrypted network by 2020, and a global network by 2030. 

Here at the +Centre for Quantum Technologies we've known this future was coming.  Indeed, the director, +Artur Ekert, helped invent quantum cryptography!  But soon this future will be here.

Puzzle: "Micius" is a rarely used romanization of a Chinese name.  You've probably heard of "Confucius", who was really Kong Fuzi.  You may have heard of the philosopher "Mencius", who was really Mengzi.  Who was Micius?  (Googling is easy; knowing things is harder.)

For more, see:

http://www.popsci.com/chinas-quantum-satellite-could-change-cryptography-forever

and

https://en.wikipedia.org/wiki/Quantum_Experiments_at_Space_Scale

which gives away the puzzle.

#physics___

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2016-08-23 14:32:26 (52 comments; 12 reshares; 100 +1s; )Open 

Jump for joy

Dolphins do this.  Why?   Maybe just for fun.  If you've ever seen the amazing games they play with air bubbles, you'll know what I mean.  If you haven't, check this out:

https://plus.google.com/117663015413546257905/posts/W8AAhgY1tCz

It was one of my most popular posts!

But people actually debate this question.  Here's what they say at Dolphins-World :

Why do dolphins jump out of the water?

There is an ongoing debate about why dolphins jump out of the water.  Scientists think about different reasons for this behavior.

Among them, some think that dolphins jump while traveling to save energy as going through the air consume less energy than going through the water.

Some other think that jumping is to get a better view of distant things, mainly food. So, inthis w... more »

Jump for joy

Dolphins do this.  Why?   Maybe just for fun.  If you've ever seen the amazing games they play with air bubbles, you'll know what I mean.  If you haven't, check this out:

https://plus.google.com/117663015413546257905/posts/W8AAhgY1tCz

It was one of my most popular posts!

But people actually debate this question.  Here's what they say at Dolphins-World :

Why do dolphins jump out of the water?

There is an ongoing debate about why dolphins jump out of the water.  Scientists think about different reasons for this behavior.

Among them, some think that dolphins jump while traveling to save energy as going through the air consume less energy than going through the water.

Some other think that jumping is to get a better view of distant things, mainly food. So, in this way, dolphins jump to locate food or food related activity like seagulls eating or pelicans hunting.

Other explanation suggest that dolphins use jumping to communicate either with a mate or with another pod.

Some people even think that dolphins jump for cleaning, trying to get rid of parasites while jumping.

Finally some scientists think that they are only having good fun, as playing helps to keep senses at their best.

http://www.dolphins-world.com/why-do-dolphins-jump-out-of-the-water/

The idea that this double flip "saves energy" is idiotic.   The other ideas are possible.  But I think it's likely that all sufficiently intelligent life forms do stuff "just for fun".  There are plenty of good biological reasons for this, I think.

#biology___

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2016-08-21 02:02:52 (45 comments; 12 reshares; 114 +1s; )Open 

Yu Jianchun - self-taught math whiz

Henan is one of the poorer provinces of China.  But there are beautiful mountains in the county of Xinxian.   That's where Yu Jianchun grew up.  Until recently he was a package delivery worker.   He says he barely knows calculus.  But he's been working on number theory.  It took him 8 years to get anyone to pay attention to his discoveries.  But recently he was invited to give a talk at Zhejiang University!

Yu is modest:

"I'm slow-witted.  I need to spend far more time studying math problems than others. Although I am sensitive to numbers, I barely have any knowledge about calculus or geometry."

But he's made some discoveries about Carmichael numbers.  I won't define those, but they're pseudoprimes: they pass a test for being prime that Fermat invented, butthey'... more »

Yu Jianchun - self-taught math whiz

Henan is one of the poorer provinces of China.  But there are beautiful mountains in the county of Xinxian.   That's where Yu Jianchun grew up.  Until recently he was a package delivery worker.   He says he barely knows calculus.  But he's been working on number theory.  It took him 8 years to get anyone to pay attention to his discoveries.  But recently he was invited to give a talk at Zhejiang University!

Yu is modest:

"I'm slow-witted.  I need to spend far more time studying math problems than others. Although I am sensitive to numbers, I barely have any knowledge about calculus or geometry."

But he's made some discoveries about Carmichael numbers.  I won't define those, but they're pseudoprimes: they pass a test for being prime that Fermat invented, but they're not actually prime.

What did Yu Jianchun actually discover, and how impressive is it?  Unfortunately I haven't been able to find out!  Can you help? 

An article in China Topix says:

Yu Jianchun developed five formulas for the Carmichael numbers, which are pseudo-prime numbers that occur as positive integers some 255 times per 100 million. He's also developed an alternative method to verify Carmichael numbers.

"I made my discoveries through intuition," said Yu. "I would write down what I thought when inspirations struck about the Carmichael. I have hard work and make a hard living, but I insist on my studies."

Yu sent his solutions to Dr. Cai Tianxin, a math professor at Zhejiang University, along with solutions to four other problems. He later presented his solutions to the public at a graduate student seminar at the invitation of Cai. Yu's solution to complex math problem has also amazed Chinese academics.

Yu said it took over eight years of writing letters to prominent Chinese mathematicians to get any recognition for his talent.
 
"It was a very imaginative solution," said Cai.

"He has never received any systematic training in number theory nor taken advanced math classes. All he has is an instinct and an extreme sensitivity to numbers."

 In late June, China Daily told a slightly different story, with some overlap but also this:

Yu was a migrant worker in many places, and everywhere he went, he would visit the math professors at the local university, hoping to get confirmation of his formulas.

Yu said he spent eight years developing the Carmichael formulas. He has reached out to academics through emails. Cai was the first to respond.

Cai found a formula proposed by Yu to be a more efficient way of identifying Carmichael numbers and invited him to share his thinking at the university with faculty members and doctoral and postdoctoral students in a class on June 13.

Six professors and advanced students in Zhejiang University's math department listened to Yu's lecture. Some of the experts considered Yu's idea to be a "novelty", while some said "his results have a certain depth".

Cai decided to include Yu's formula with his latest work in English, and he gave Yu a book to help the logistics worker in further study.

It seems he is no Ramanujan, but still a remarkable person who could use some help.  He may finally be getting it.  CNN writes:

After local and national media reported on his findings, Yu has become a local celebrity. A company that manufactures silk products has offered him a less labor-intensive job to give him more time to study math.

Yu had never heard of the movie "Good Will Hunting," but says he's curious to see it.

The 1997 drama, which stars Matt Damon and Robin Williams, tells the fictional story of a maths genius who works as a janitor at the Massachusetts Institute of Technology.

Slightly overwhelmed by his sudden fame, Yu said he is nevertheless grateful for the new opportunities that hopefully lie ahead.

However, at age 33 and still single, he says his primary concern is to get married.

People on MathOverflow are trying to figure out, from tiny clues, what Yu has done:

http://mathoverflow.net/questions/244751/what-did-yu-jianchun-discover-about-carmichael-numbers

The China Topix article is here:

http://www.chinatopix.com/articles/95664/20160718/slow-witted-chinese-math-genius-amazes-carmichael-numbers-formulas.htm

The China Daily article is here:

http://www.chinadaily.com.cn/china/2016-06/23/content_25813818.htm

The CNN article is here:

http://edition.cnn.com/2016/07/17/asia/china-migrant-worker-good-will-hunting/index.html

To learn about Carmichael numbers, go here:

https://en.wikipedia.org/wiki/Carmichael_number

#mathematics  ___

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2016-08-18 07:02:26 (62 comments; 53 reshares; 103 +1s; )Open 

The Equation Group

We live in a world of shadowy struggles.   A team of hackers called the Equation Group has remarkable powers:

• They can reprogram your hard drive firmware.  This lets them put software on your machine that will survive even if you reformat your hard drive and reinstall your operating system.  They can create an invisible, persistent area in your hard drive, store data there, and collect it later.

• They can retrieve data from networks not connected to the internet.  They can use an infected USB stick with a hidden storage area to collect information from a computer.   When this USB stick is later plugged into a computer they've subverted that does have an internet connection, they can retrieve this information.

• Since 2001, the Equation Group has infected thousands of computers in over 30 countries, focusing ongovernment ... more »

The Equation Group

We live in a world of shadowy struggles.   A team of hackers called the Equation Group has remarkable powers:

• They can reprogram your hard drive firmware.  This lets them put software on your machine that will survive even if you reformat your hard drive and reinstall your operating system.  They can create an invisible, persistent area in your hard drive, store data there, and collect it later.

• They can retrieve data from networks not connected to the internet.  They can use an infected USB stick with a hidden storage area to collect information from a computer.   When this USB stick is later plugged into a computer they've subverted that does have an internet connection, they can retrieve this information.

• Since 2001, the Equation Group has infected thousands of computers in over 30 countries, focusing on government and diplomatic institutions, telecommunications, aerospace, energy, nuclear research, oil and gas, military, nanotechnology, Islamic activists and scholars, mass media, transportation, financial institutions and companies developing encryption technologies. 

You can see a map of computers infected by the Equation Group here:

http://cdn.arstechnica.net/wp-content/uploads/2015/02/Victims-map.png

They also seem to be connected to StuxNet, the computer worm that destroyed centrifuges used by the Iranians for uranium enrichment.

Given all this, it's a good guess that the Equation Group is connected to the NSA, the National Security Agency of the US.  I sort of hope so - because while that's scary, the alternatives scare me more. 

Now another mysterious group called Shadow Brokers has released 256 megabytes of hacking tools that may be used by the Equation Group  - and has offered to sell the rest for $500 million!   They wrote:

We follow Equation Group traffic. We find Equation Group source range. We hack Equation Group. We find many many Equation Group cyber weapons. You see pictures. We give you some Equation Group files free, you see. This is good proof no? You enjoy!!! You break many things. You find many intrusions. You write many words. But not all, we are auction the best files.

At first researchers doubted that these guys had been able to steal software from the Equation Group.  But new research at the cybersecurity firm Kaspersky Labs seems to confirm it.

Read the linked article for more!  Also try these:

On how the Equation Group was found by researchers at Kapersky Labs last year:

http://arstechnica.com/security/2015/02/how-omnipotent-hackers-tied-to-the-nsa-hid-for-14-years-and-were-found-at-last/

http://www.kaspersky.com/about/news/virus/2015/equation-group-the-crown-creator-of-cyber-espionage

On how Shadow Brokers released 256 megabytes of hacking software on their blog:

http://arstechnica.com/security/2016/08/group-claims-to-hack-nsa-tied-hackers-posts-exploits-as-proof/

Wikipedia is collecting information on the Equation Group here, so this should eventually be the best place to access information about them:

https://en.wikipedia.org/wiki/Equation_Group___

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2016-08-16 05:31:43 (16 comments; 15 reshares; 69 +1s; )Open 

Points at infinity

+Abdelaziz Nait Merzouk made this amazing movie.  Be patient!   It may take a while to load.

This is a surface living in projective space.  Projective space is like ordinary 3-dimensional space except that it has some extra points called points at infinity.   In ordinary space, parallel lines never meet.  In projective space they do!   They meet at one of these points at infinity!  

It's not as weird as you think.

Imagine two parallel train tracks.  They never meet... but they look like they meet at some point on the horizon.   That's the idea of a point at infinity.   In projective space, points on the horizon are actual points!

The geometry of projective space is important for understanding perspective, so mathematicians started working on it in the Renaissance and got really good at it bythe 1800s.  Th... more »

Points at infinity

+Abdelaziz Nait Merzouk made this amazing movie.  Be patient!   It may take a while to load.

This is a surface living in projective space.  Projective space is like ordinary 3-dimensional space except that it has some extra points called points at infinity.   In ordinary space, parallel lines never meet.  In projective space they do!   They meet at one of these points at infinity!  

It's not as weird as you think.

Imagine two parallel train tracks.  They never meet... but they look like they meet at some point on the horizon.   That's the idea of a point at infinity.   In projective space, points on the horizon are actual points!

The geometry of projective space is important for understanding perspective, so mathematicians started working on it in the Renaissance and got really good at it by the 1800s.  They still love it.  You can do lots of extra stuff that you can't do with ordinary Euclidean geometry. 

For example, a surface like this one here can extend to infinity.... and actually get there!    And there are ways to rotate a shape so that its points at infinity get moved to ordinary points that aren't at infinity!  That's what is happening in this animation.

This surface is the Endrass octic.   It has lots of points where the tips of two cones meet.    However, in the usual picture of the Endrass octic, some of these conical points are at infinity.  In this animation, they swing into view as the surface gets rotated!

So, you are now actually seeing the pictures that mathematicians have in their heads when studying projective geometry!  You can see why it's fun... and you can see why mathematicians seem absent-minded.  We're not living in your reality.  We're off in projective space!

In fact, I just lost my coffee cup.  I looked all over for it... and eventually found it, not at a point at infinity, but in the microwave!  Who put it there???

+Abdelaziz Nait Merzouk is great at making pictures of interesting surfaces.  You can see them in his collection here:

https://plus.google.com/u/0/collection/4tLusB

For more about the math of the Endrass octic, visit my blog:

http://blogs.ams.org/visualinsight/2016/08/01/endrass-octic/

This animation has a Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) copyright.  For details see https://creativecommons.org/licenses/by-sa/3.0/deed.en___

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2016-08-14 02:05:13 (46 comments; 45 reshares; 332 +1s; )Open 

Not like Earth

At the end of August, the European Southern Observatory will announce a planet orbiting Proxima Centauri - the star closest to our Sun, 4.24 light years away.   They're trying to make this planet sound like Earth... and that's cool.   But I'll tell you some ways it's not.

Mainly, Proxima Centauri is really different from our Sun! 

It's a red dwarf.   It puts out just only 0.17% as much energy as our Sun.  So any planet with liquid water must be very close to this star.

And because it's cooler than the Sun, Proxima Centauri mainly puts out infrared light - in other words, heat radiation.   Its visible luminosity is only 0.005% that of our Sun!

So if you were on a planet as warm as our Earth orbiting Proxima Centauri, it would look very dim - about 3% as bright as our Sun.

Of course,if there... more »

Not like Earth

At the end of August, the European Southern Observatory will announce a planet orbiting Proxima Centauri - the star closest to our Sun, 4.24 light years away.   They're trying to make this planet sound like Earth... and that's cool.   But I'll tell you some ways it's not.

Mainly, Proxima Centauri is really different from our Sun! 

It's a red dwarf.   It puts out just only 0.17% as much energy as our Sun.  So any planet with liquid water must be very close to this star.

And because it's cooler than the Sun, Proxima Centauri mainly puts out infrared light - in other words, heat radiation.   Its visible luminosity is only 0.005% that of our Sun!

So if you were on a planet as warm as our Earth orbiting Proxima Centauri, it would look very dim - about 3% as bright as our Sun.

Of course, if there's life on this planet, it would probably evolve to see infrared. 

But there's a more serious problem.  Proxima Centauri sometimes puts out big flares, with lots of X-rays!  That's not very nice.

Why does a wimpy little red dwarf have bigger flares than the Sun?

The Sun has a core where fusion happens, and helium produced down in the core mainly stays there.   A red dwarf doesn't have a core: it's fully convective.  In other words, heat moves through the star not by radiation, but by hot gas actually moving up to the surface. 

All this ionized gas moving around makes big magnetic fields.  The magnetic field lines get twisted up and sometimes explode out in flares!  These flares get so hot that they emit X-rays.  That's very  hot.

Our Sun has flares too, but on a smaller scale.  Even on a calm day, Proxima Centauri puts out as much X-ray energy as our Sun.  But when a big flare occurs, it can put out 10 times more.   This happens pretty often. 

So: any "Earth-like" planet orbiting this star will be a lot closer than the Earth is to our Sun, and get a lot more X-rays. 

Puzzle 1.  Use what I've told you to estimate how much closer a planet must be, to be at the same temperature as the Earth.

Puzzle 2.  Estimate how much more X-rays it will get.

On top of this, Proxima Centauri could be part of a triple star system!

The closest neighboring stars, Alpha Centauri A and B, orbit each other every 80 years. One is a bit bigger than the Sun, the other a bit smaller. They orbit in a fairly eccentric ellipse. At their closest, their distance is like the distance from Saturn to the Sun. At their farthest, it’s more like the distance from Pluto to the Sun.

Proxima Centauri is fairly far from both: a quarter of a light year away. That’s about 350 times the distance from Pluto to the Sun! We’re not even sure Proxima Centauri is gravitationally bound to the other stars. If it is, its orbital period could easily exceed 500,000 years.

On the bright side, Proxima Centauri will last a lot longer than our Sun. As it ages, it will get smaller and hotter, gradually changing from red to blue.  After about four trillion years it will grow to 2.5% of the Sun's luminosity.   When its hydrogen is exhausted, it will then become a white dwarf, without ever puffing out into a red giant like our Sun.

So, any planet orbiting this star will be a weirdly different world.  But if we ever get there, we could stay for trillions of years, long after our Sun has become a red giant, roasting life on Earth.

For rumors of ESO's announcement, see this:

http://www.universetoday.com/130276/earth-like-planet-around-proxima-centauri-discovered/

For more on Proxima Centauri, try this:

https://en.wikipedia.org/wiki/Proxima_Centauri

#astronomy  ___

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2016-08-13 06:32:47 (27 comments; 30 reshares; 157 +1s; )Open 

And even in defeat... victory!

This shows great presence of mind, and a sense of humor.

And even in defeat... victory!

This shows great presence of mind, and a sense of humor.___

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2016-08-12 05:18:30 (93 comments; 41 reshares; 257 +1s; )Open 

How big is a proton?

We thought we knew.  New measurements say we were 4% off.  That may not seem like much - but it's enough to be a serious problem!

We can measure the proton radius by bouncing electrons off it, or by carefully studying the energy levels of a hydrogen atom.  People have measured it many times, and the different measurements agree pretty well.  Here's the answer:

0.8775 ± 0.0051 femtometers   

A femtometer is 10 to the minus 15th meters, or a quadrilionth of a meter. 

But you can make a version of hydrogen with a muon replacing the electron.  The muon is the electron's big brother.  It's almost the same, but 207 times heavier.   So, muonic hydrogen is about 1/207 times as big across.  And that makes the effects of the proton radius easier to detect! 

So, in principle, weshould be abl... more »

How big is a proton?

We thought we knew.  New measurements say we were 4% off.  That may not seem like much - but it's enough to be a serious problem!

We can measure the proton radius by bouncing electrons off it, or by carefully studying the energy levels of a hydrogen atom.  People have measured it many times, and the different measurements agree pretty well.  Here's the answer:

0.8775 ± 0.0051 femtometers   

A femtometer is 10 to the minus 15th meters, or a quadrilionth of a meter. 

But you can make a version of hydrogen with a muon replacing the electron.  The muon is the electron's big brother.  It's almost the same, but 207 times heavier.   So, muonic hydrogen is about 1/207 times as big across.  And that makes the effects of the proton radius easier to detect! 

So, in principle, we should be able measure the radius of a proton more accurately using muonic hydrogen. 

So that's what they did - in Switzerland, back in 2010.  They repeated the experiment in 2013.   Here's what they got:

0.84087 ± 0.00039 femtometers
 
In theory, this is about ten times more accurate.  However, it's way off from all the earlier measurements!  7 standard deviations off.

This story is in the news again today.  The same team just used muons to measure the radius of deuterium - a proton and a neutron stuck together.  And again, they're getting a different answer than what people get using electrons.

Could some new physics be responsible?  Some serious mistake in our theory of particles?   The guy who led the new experiment, Randolph Pohl, said:

“That would, of course, be fantastic.  But the most realistic thing is that it’s not new physics.”

I like that.  A good experimentalist does not  jump to dramatic conclusions.  Pohl guesses that we're wrong about the value of the Rydberg constant, a number that goes into calculating the proton mass from the experimental data. 

However, it's worth noting that there's another puzzle about muons. Electrons and muons are like tiny magnets.  When we calculate how strong the magnetic field of an electron is, we get results that match experiment incredibly well.  But when we do the same calculation for the muon, we're off by 3.4 standard deviations.

So maybe, just maybe, there's something funny going on with muons, which hints at new physics beyond the Standard Model.  I doubt it.  But you never know.  

Check out this for more:

https://www.quantamagazine.org/20160811-new-measurement-deepens-proton-radius-puzzle/

If our estimate of the Rydberg constant were 4 standard deviations off, that would do the job.  That sounds like a lot... but if you look at the graphs here, you'll see other cases when we were way off about things!

 For even more, check out this:

• Carl E. Carlson, The proton radius puzzle, https://arxiv.org/abs/1502.05314

#physics #protonRadiusPuzzle
#spnetwork arXiv:1502.05314___

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2016-08-09 12:26:55 (16 comments; 10 reshares; 63 +1s; )Open 

WWW: the Wood Wide Web

The world wide web was not the first powerful communication network!  Long before came the wood wide web, underground in every forest.

This picture was produced by a program called Mycelium, which takes a picture and evolves it using the rules by which fungi send out tiny threads... sort of like roots... that absorb nutrients. 

A mycelium is the name for this network of threads formed by a fungus - or a bunch of fungi.   A mycelium can be huge!  In his book Mycelium Running, Paul Stamets writes:

"Is this the largest organism in the world? This 2,400-acre [970-hectare] site in eastern Oregon had a contiguous growth of mycelium before logging roads cut through it. Estimated at 1,665 football fields in size and 2,200 years old, this one fungus has killed the forest above it several times over, and in sodoing ... more »

WWW: the Wood Wide Web

The world wide web was not the first powerful communication network!  Long before came the wood wide web, underground in every forest.

This picture was produced by a program called Mycelium, which takes a picture and evolves it using the rules by which fungi send out tiny threads... sort of like roots... that absorb nutrients. 

A mycelium is the name for this network of threads formed by a fungus - or a bunch of fungi.   A mycelium can be huge!  In his book Mycelium Running, Paul Stamets writes:

"Is this the largest organism in the world? This 2,400-acre [970-hectare] site in eastern Oregon had a contiguous growth of mycelium before logging roads cut through it. Estimated at 1,665 football fields in size and 2,200 years old, this one fungus has killed the forest above it several times over, and in so doing has built deeper soil layers that allow the growth of ever-larger stands of trees."

Many plants have fungi in their roots called mycorrhizal fungi.  The mycelium of the fungus helps the plant get phosphorus and nitrogen.  In exchange, the plant feeds the fungus. 

Recently a writer for New Yorker went on a hike with an expert on this stuff named Merlin Sheldrake.    He wrote:

"Sheldrake is an expert in mycorrhizal fungi, and as such he is part of a research revolution that is changing the way we think about forests. For centuries, fungi were widely held to be harmful to plants, parasites that cause disease and dysfunction. More recently, it has become understood that certain kinds of common fungi exist in subtle symbiosis with plants, bringing about not infection but connection. These fungi send out gossamer-fine fungal tubes called hyphae, which infiltrate the soil and weave into the tips of plant roots at a cellular level. Roots and fungi combine to form what is called a mycorrhiza: itself a growing-together of the Greek words for fungus (mykós) and root (riza). In this way, individual plants are joined to one another by an underground hyphal network: a dazzlingly complex and collaborative structure that has become known as the Wood Wide Web."

What can the Wood Wide Web actually do?  We're just beginning to find out!   As I said, plants feed fungi in exchange for help getting phosphorus and nitrogen.

"The implications of the Wood Wide Web far exceed this basic exchange of goods between plant and fungi, however. The fungal network also allows plants to distribute resources—sugar, nitrogen, and phosphorus—between one another. A dying tree might divest itself of its resources to the benefit of the community, for example, or a young seedling in a heavily shaded understory might be supported with extra resources by its stronger neighbors. Even more remarkably, the network also allows plants to send one another warnings. A plant under attack from aphids can indicate to a nearby plant that it should raise its defensive response before the aphids reach it. It has been known for some time that plants communicate above ground in comparable ways, by means of airborne hormones. But such warnings are more precise in terms of source and recipient when sent by means of the myco-net."

Read the whole article here:

http://www.newyorker.com/tech/elements/the-secrets-of-the-wood-wide-web

The program Mycelium was created by Ryan Alexander, who writes:

"Hyphae grow into the lighter areas of the image while avoiding their own trails. Branching and growth speed are also functions of the available food (brightness) in the image. Type can be added by splitting the trails up into phrase-sized chunks of different colors. Each color is then stroked with text in Adobe Illustrator."

That's right: the little hairs or 'hyphae' are actually strings of text if you look at them closely!  You can see that here:

https://www.flickr.com/photos/onecm/sets/72157600033861485/

Merlin Sheldrake is the son of Rupert Sheldrake, and I hope he is a better scientist - otherwise I can't really trust his work.  ___

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2016-08-08 04:51:46 (0 comments; 91 reshares; 198 +1s; )Open 

What's wrong with Trump?

More and more people are wondering.  Here's an insightful analysis from a psychiatric social worker.  Please reshare.  It's not light reading, but we need to understand what we're dealing with here.

--------------------

The Billionaire's Baffling Behavior Explained

Recently, Mr. Trump's words and actions in various situations have become headline news. Suddenly, many people are alarmed and are questioning temperament, his emotional stability. Dementia? Campaign tactics?

No, it's not an illness that can be treated so he can return to his usual state of health. It's not like when a car's brakes don't work and the mechanic fixes them. It's more like the car came off the assembly line without them.

It's a structural problem.

We're witnessingte... more »

What's wrong with Trump?

More and more people are wondering.  Here's an insightful analysis from a psychiatric social worker.  Please reshare.  It's not light reading, but we need to understand what we're dealing with here.

--------------------

The Billionaire's Baffling Behavior Explained

Recently, Mr. Trump's words and actions in various situations have become headline news. Suddenly, many people are alarmed and are questioning temperament, his emotional stability. Dementia? Campaign tactics?

No, it's not an illness that can be treated so he can return to his usual state of health. It's not like when a car's brakes don't work and the mechanic fixes them. It's more like the car came off the assembly line without them.

It's a structural problem.

We're witnessing textbook Cluster B Personality Disorders come to life, revealing his intra-psychic structure, particular lens on reality and associated defense mechanisms.

Clinically, it's fascinating.

Politically, it's frightening.

This is who Trump is, how he sees the world and others in it and how he will continue to function. At 68, without acknowledging any internal difficulties and/or any desire to change them, this is how he will continue forever. Introspection and self-analysis are rarely typical of personality disordered individuals. These behaviors are no surprise; in fact they're utterly predictable.

Before I continue though, let me head off some opposition.

YES, everyone has some level of narcissism; a certain amount is actually healthy. It allows one to advocate for oneself, not be taken advantage of and, based on a reasonable assessment of one's strengths, take risks to apply those abilities to start a new business, try out for a minor league MLB slot or take a step up the occupational ladder, for instance. Politicians, ALL of them, have more than the average person, required to withstand the vagaries of our current election process.

But, "healthy narcissism " differs from Trump's version. His is "grandiosity ", a rigidly held, yet fragile exaggerated sense of self-importance where one is special, unique, superior to others, often without the associated level of grand accomplishment.

"Healthy narcissism " is reasonable self-confidence when an accomplished person says "I have some good ideas that could help solve this problem."

In contrast, you see Trump's "grandiosity " in the statement "I alone can fix it."

How grandiose to believe one can run for the highest political office in the land without a day of previous experience or even a modicum of interest in geo-political issues. Trump's grandiosity led him to waltz into the casino & "education" businesses with no prior experience and look at the results. Anyway, back to psychology:

A personality disorder is essentially a developmental arrest, a mosaic of maladaptive personality traits which create a distorted lens through which one views self and others and influences one's interactions. We all have these aspects to our personalities, but with PD's [personality disorders], it's a matter of greater frequency and degree. Certain psychic defense mechanisms are correlated with specific phases of development in more or less chronological order. They basically function to help the person moderate internal needs and desires to the demands of reality. When those are at odds, defenses are meant to help protect the core "self" from the resultant anxiety. When lower level, more primitive defense mechanisms are the characteristic mode of behavior one relies on, it moves into the personality disorder category.

Underlying all PDs, no matter the external "flavor", is the failure to have reached the psychic developmental level where disparate, opposing aspects of self and other are able to be mentally integrated into a cohesive whole. This underlies one of the most important associated defense mechanisms, that of "splitting ", which becomes the filter through which self, others & events are perceived.

In splitting, discrepant aspects of an image or object cannot be held in consciousness at the same time. Everything's either "all bad" or "all good" but never both together at the same time. Look at Trump's constant usage of these superlatives when describing others. No integrated "sometimes he's ok, sometimes not." If you listen carefully, you won't hear this type of response unless the wording has been previously crafted by another in a speech or statement. No supportive factual content, just one sided emotional reactivity. Never an explanation why a person is "horrible, the worst" or "very good guy, great person", just the judgemental superlatives.

This non-integration usually goes hand in hand with "projection" and "projective identification " (it's complicated.) It's much simpler to categorize others that way and initially, it wards off anxiety associated with cognitive dissonance,but it prevents the assimilation of all information. Without all the discrepant data about self or other though, invariably the "unexpected " will appear, for which one is unprepared, then: anxiety! This leads to that chronic hyper-vigilance often seen with PDs. The fear provoked by this amorphous unknown is then "projected" onto an object, which becomes a concrete target.

Negative aspects of the self cannot be integrated into a positive self-image (i.e. criticism like "ignorant " or "arrogant ") so are often projected onto another and then denigrated. The most recent example of projective identification is that for the past week, people have been questioning Trump's mental stability. Yesterday, he called Hillary Clinton "unstable" and "unhinged ", the same words recently used to describe him. No example to support the claim... I imagine he was vaguely instructed to criticize Hillary without specific guidance. Although there is more than enough ammunition, his obsession with "self" and "image" is apparent in his choice of off the mark insults.

Back to splitting:

Because self and others aren't seen in their full conflicting, complex reality, PDs hold mental representations akin to superficial caricatures. They tend to disregard the thoughts and feelings of others and fail to consider the consequences of their own actions on others because their mental representations of others just aren't imbued with these qualities. The self focus of NPDs is so constant and obsessive, there's no room or concern for consideration of others. In other words, others just don't matter. This behavior is what some happily, but mistakenly announce is his not caring about being "politically correct". Actually, it's really a symptom of his disturbance.

Splitting is also the explanation behind what are his constant examples of contradictory statements about a multitude of subjects over time. It differs qualitatively from "lying" per se, although I'm sure he does that too.

Lying is an intentional deceptive act often associated with some secondary gain, such as avoidance of consequences. The person is fully aware that what they are saying differs from the actual facts. In splitting, the contradictory concepts cannot mentally coexist at the same time. Trump believes what he says when he it. Because his mental state may differ today from two weeks ago, his view point on the same subject will vacillate too. Contradictions for most cause conflict but his psychic makeup disavows discrepancy before it gets to that point. But remember, this is an unconscious process... it just doesn't go in, it remains foreign, it's not "owned" and explained (in spite of video). Contradictory statements will, at best, be minimally acknowledged in terms that they've occurred, but disregarded as unimportant, shrugged off because they no longer connect on an intra-psychic level. He's almost surprised that these discrepancies are attributed to him all. Thus, they cause no anxiety.

I truly pity his team of campaign strategists having to negotiate this mine field. PDs are notorious for leaving chaos and distress in their wake while they go happily along without any care in the world.

PD's are a product of both nature and nurture. As one goes through maturational phases, the demands of reality increase and through experiencing the invariable failures, frustrations and disappointments, more evolved mechanisms like "repression " or "rationalization " ideally develop and replace the more inadequate primitive ones. For most people, but not all.

We are seeing Mr. Trump struggle to use his inadequate set of rigid, primitive defense mechanisms to manage real world demands, apparently for the FIRST TIME.

The very rich really ARE different.

If you recall, while Donald was growing up, his father Fred was one of the richest men in the world.

The very wealthy have the resources to create a universe which, while protective, also serves to reinforce any dysfunction. Critics or nay-sayers are removed from their orbit, replaced with loyalists who rationalize or ignore the dysfunction. Often in the presence of celebrity or great wealth, otherwise intelligent reasonable people become fawning syncophants.

Trump never had to follow any rules; they didn't apply to him. Punch a teacher? Simple fix: change schools. Potential draft material? Find a doctor to submit a medical deferment (bone spurs in the foot prevent military service but don't prevent playing baseball?). He went into the family business so never had a critical boss. Keep digging and you find his claims of great ability exaggerated or actually non-existent; doesn't matter that the narrative is false as long as it reinforces the self-image.

Anyway, back to the present:

The goal with an NPD [narcissistic personality disorder] person is to protect & reinforce the simultaneously fragile & grandiose core. It's almost as if without the constant attention, it's feared that the self may disintegrate. Because the self-image is so tenuous, they need inordinate amounts of external approval & rely on a defense called "mirroring"... You're great because you think I'm great, etc.... He gets this at his rallies with core supporters. This inordinate need for excessive approval may also underlie his reluctance to disavow questionable supporters, like David Duke.

With criticism, an ego this brittle experiences it as an impending attack which threatens the very existence of the core self and triggers what's called "narcissistic rage" followed often by a reflexive aggressive response.

He calls it "counter-punching" but it's truly acting out in response to the rage.

This has always been his response.

Within the security of Trump World, no one criticized this behavior before, ever. In one video of him, he seems truly baffled that anyone would view him differently than he views himself. He says "Even if you don't like me, you have to vote for me. You have to."

He's had no prior experience with this type of ego threat from long-term microscopic scrutiny. Previously, it's been intermittent or his public presentation has been structured to coincide with his inflated self-image, such as his reality show.

Someone with such a fragile self-image will take the bait constantly , whether it's from a Gold Star American family or another world leader.

He cannot help himself. It's ego life or death.

Splitting also explains his lack of coherent political philosophy; issues are presented piecemeal, disconnected from other. If some of the data is conflictual it can't exist in the consciousness, so no possible way to create a grand plan based on a cohesive frame of reference. Just not possible. It also explains the apparent self-defeating behavior toward prominent Republicans. Each slight is responded to in isolation without any comprehension how one spat, like with McCain or Ryan, affect his relationship to the whole group.

No, he isn't "calculating" and "crazy like a fox", although he may be decompensating under stress.

He may not become truly psychotic in the classic Axis I sense of the definition; however, there seems to be more paranoia emerging as he hasn't developed psychic resources capable of effectively warding off the disequilibrium brought on by the onslaught of scrutiny and criticism. Recently he's said the current administration has allowed "thousands upon thousands " of terrorists into the country, fears the election will be "rigged" without ANY factual basis for support.

This kind of thinking will probably remit when there's less pressure, but it will resurface anytime stress intensifies.

It is no surprise that his children function better than he; for much of their lives they were raised in separate home environments by his ex-wives. Both divorce settlements were accompanied by "non-disclosure agreements", aka "gag orders".

Trump's "missteps", "misstatements" and "walk backs" which characterize his campaign are not due to his "rookie" politician status. They are a true reflection of how he functions.

And the "he tells it like it is" assertion? That actually used to be a euphemism meaning "truthful ". He tells you what he's thinking at the moment but it doesn't mean it has any connection to reality or fact.

Please stop "Waiting for him to change". He cannot. (There's no Easter Bunny either, by the way.)

Just admit you were star-struck, misled by his grandiosity or made incorrect assumptions about his business acumen based on 24k gold bathroom fixtures and call it a day.

--------------------

This is from here:

https://www.yabberz.com/post/the-billionaires-baffling-behavior-explained/86689585/

I thank +Boris Borcic for pointing it out.___

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2016-08-05 15:24:03 (30 comments; 12 reshares; 87 +1s; )Open 

The quest for beauty

This is a nice interview of Miranda Cheng, an assistant professor at the University of Amsterdam working on the math of string theory.   She's on a quest to understand the connection between strings and some mysterious functions in Ramanujan's lost notebook.

It's sort of spooky how much of Ramanujan's work makes more sense with the help of string theory.   But perhaps it shouldn't be surprising.  String theory hasn't really done anything to predict the results of experiments - it's mainly attractive because of its mathematical beauty.  Ramanujan, too, was motivated by the quest for beauty.   He got there sooner... but he only saw the tip of the vast iceberg we're exploring now.

What's "mathematical beauty"?    Here's what Cheng says:

It’s kind of hard to say why it isbeautiful. I... more »

The quest for beauty

This is a nice interview of Miranda Cheng, an assistant professor at the University of Amsterdam working on the math of string theory.   She's on a quest to understand the connection between strings and some mysterious functions in Ramanujan's lost notebook.

It's sort of spooky how much of Ramanujan's work makes more sense with the help of string theory.   But perhaps it shouldn't be surprising.  String theory hasn't really done anything to predict the results of experiments - it's mainly attractive because of its mathematical beauty.  Ramanujan, too, was motivated by the quest for beauty.   He got there sooner... but he only saw the tip of the vast iceberg we're exploring now.

What's "mathematical beauty"?    Here's what Cheng says:

It’s kind of hard to say why it is beautiful. It’s beautiful not the same way as a song is beautiful or a picture is beautiful.  Typically a song is beautiful because it triggers certain emotions. It resonates with part of your life. Mathematical beauty is not that. It’s something much more structured. It gives you a feeling of something much more permanent, and independent of you. It makes me feel small, and I like that.

The interviewer asked if she always had a knack for math, and she replied:

As a child in Taiwan I was more into literature — that was my big thing. And then I got into music when I was 12 or so — pop music, rock, punk. I was always very good at math and physics, but I wasn’t really interested in it. And I always found school insufferable and was always trying to find a way around it. I tried to make a deal with the teacher that I wouldn’t need to go into the class. Or I had months of sick leave while I wasn’t sick at all. Or I skipped a year here and there. I just don’t know how to deal with authority, I guess.

And the material was probably too easy. I skipped two years, but that didn’t help. So then they moved me to a special class and that made it even worse, because everybody was very competitive, and I just couldn’t deal with the competition at all. Eventually I was super depressed, and I decided either I would kill myself or not go to school. So I stopped going to school when I was 16, and I also left home because I was convinced that my parents would ask me to go back to school and I really didn’t want to do that. So I started working in a record shop, and by that time I also played in a band, and I loved it.

Long story short, I got a little bit discouraged or bored. I wanted to do something else aside from music. So I tried to go back to university, but then I had the problem that I hadn’t graduated from high school. But before I quit school I was in a special class for kids who are really good in science. I could get in the university with this. So I thought, OK, great, I’ll just get into university first by majoring in physics or math, and then I can switch to literature. So I enrolled in the physics department, having a very on- and off-again relationship to it, going to class every now and then, and then trying to study literature, while still playing in the band. Then I realized I’m not good enough in literature. And also there was a very good teacher teaching quantum mechanics. Just once I went to his class and thought, that’s actually pretty cool. I started paying a bit more attention to my studies of math and physics, and I started to find peace in it. That’s what started to attract me about math and physics, because my other life in the band playing music was more chaotic somehow. It sucks a lot of emotions out of you. You’re always working with people, and the music is too much about life, about emotions — you have to give a lot of yourself to it. Math and physics seems to have this peaceful quiet beauty. This space of serenity.

How true, how true!   Read the whole interview!

For more on what Cheng is up to, try this Wikipedia article:

https://en.wikipedia.org/wiki/Umbral_moonshine

I wish I had time to really dig into this stuff!  It combines lots of things I like: string theory, K3 surfaces, the 24 even unimodular lattices in 24 dimensions, the Mathieu group M24... hmm, did you notice how the number 24 keeps coming up here?  That's part of the charm and mystery of this part of math.

Thanks to +David Roberts for pointing out this interview. 

#physics  ___

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2016-08-04 05:25:21 (16 comments; 10 reshares; 65 +1s; )Open 

Endrass octic

This surface looks cute - but it's also the best known solution to a hard math problem.  It's called the Endrass octic

Why 'Endrass'?  Because was discovered in 1995 by Stephan Endrass while he was writing his Ph.D. thesis. 

Why 'octic'?  Because it's described by a polynomial equation of degree 8.

You'll notice it has lots of points where the tips of two cones meet.   It has 168 of them, though not all are visible here.  And this is, so far, the largest number of such points that people have gotten for an octic.

It may not be the best possible.   But it's the best so far.  In 1984, a guy named Miyaoka showed that you can't get get more than 174 of these conical points in an octic.  So, there's a gap between what we know is possible and what might be possible.   (If you're... more »

Endrass octic

This surface looks cute - but it's also the best known solution to a hard math problem.  It's called the Endrass octic

Why 'Endrass'?  Because was discovered in 1995 by Stephan Endrass while he was writing his Ph.D. thesis. 

Why 'octic'?  Because it's described by a polynomial equation of degree 8.

You'll notice it has lots of points where the tips of two cones meet.   It has 168 of them, though not all are visible here.  And this is, so far, the largest number of such points that people have gotten for an octic.

It may not be the best possible.   But it's the best so far.  In 1984, a guy named Miyaoka showed that you can't get get more than 174 of these conical points in an octic.  So, there's a gap between what we know is possible and what might be possible.    (If you're into algebraic geometry you might like Miyaoka's paper - he used some pretty fancy techniques.)

Endrass actually found two octics with 168 conical points.  You can see pictures of both, drawn by +Abdelaziz Nait Merzouk, over at my blog:

http://blogs.ams.org/visualinsight/2016/08/01/endrass-octic/

They're very beautiful.  You can also see the equations of these surfaces.  They're not very beautiful, at least not to me.  Endrass found them with the help of a computer algebra system. 

The animation I'm showing you here comes from a German math website:

• IMAGINARY: open mathematics, https://imaginary.org/tr/node/626

Request: Can someone draw beautiful pictures of the Cayley cubic, the Kummer quartic and the Togliatti quintic?  Those are the surfaces described by equations of degree 3, 4, and 5 with the maximum number of conical points.  They're pretty nice:

https://en.wikipedia.org/wiki/Cayley%27s_nodal_cubic_surface
https://en.wikipedia.org/wiki/Kummer_surface
https://en.wikipedia.org/wiki/Togliatti_surface

Wikicommons has decent pictures of the first and last ones. I'd like to discuss these surfaces on my blog.  It would be nice to have truly spectacular pictures.

#geometry  ___

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2016-08-03 05:12:57 (29 comments; 72 reshares; 147 +1s; )Open 

Primes with no sevens

This is a prime number whose decimal digits are all ones.  It has 317 ones.  It's not the world record.  The number with 1031 ones is also known to be prime! 

Even larger guys like this are suspected  to be prime.  Are there infinitely many?   Mathematicians believe so, but they can't prove it.

Why do they believe it?   The main reason is that they have an estimate of the "probability" that a number with some number of digits is prime. We can use this to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here.  A number is either prime or not: the math gods do not flip coins to decide which numbers are prime! 

Nonetheless, treating primes as if  they were random turns out to be useful.   Mathematicians have made many guesses using this idea, andthen proved ... more »

Primes with no sevens

This is a prime number whose decimal digits are all ones.  It has 317 ones.  It's not the world record.  The number with 1031 ones is also known to be prime! 

Even larger guys like this are suspected  to be prime.  Are there infinitely many?   Mathematicians believe so, but they can't prove it.

Why do they believe it?   The main reason is that they have an estimate of the "probability" that a number with some number of digits is prime. We can use this to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here.  A number is either prime or not: the math gods do not flip coins to decide which numbers are prime! 

Nonetheless, treating primes as if  they were random turns out to be useful.   Mathematicians have made many guesses using this idea, and then proved these guesses are right, using a lot of extra work.

Of course it's subtle.  If I wrote down a number with 317 twos in its decimal expansion, you'd instantly know it's not prime - because it would be even.

In the European Congress of Mathematics, a number theorist named James Maynard just announced something cool.  There are infinitely many prime numbers with no sevens in their decimal expansion!

And his proof works equally well for any other number: there infinitely many primes without 0 as a digit, or 1, or 2, or 3, or 4, or 5, and so on.

This is big news, but not because mathematicians really care about primes with no sevens in them.  It's because proving something like this requires a deep and delicate understanding of "the music of primes" - the way prime numbers are connected to wave patterns.  For more on that, here's something easy to read:

https://plus.maths.org/content/missing-7s

Thanks to +Luis Guzman for pointing out this article, and thanks to +David Roberts for finding James Maynard's paper on this subject, which is here:

• James Maynard, Primes with restricted digits, http://arxiv.org/abs/1604.01041.

He shows that if your base b is sufficiently large, you can find infinitely many primes that are lacking a chosen set of digits, where this set can contain up to b^(23/80) of the digits.  Unfortunately I don't see  how large b must be - he may not have worked this out.  If b = 10 counts as sufficiently large, then since 10^(23/80) is about 1.94, this result would let you avoid any one digit in base 10, but not two.  In any event, he does prove, separately, that you can find infinitely many primes that avoid any one digit in base 10.

  It uses cool techniques, like "decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dictate when the Fourier transform of numbers with restricted digits is large".  It also uses ideas from Markov process theory - that is, the theory of random processes - as well as hard-core number theory concepts.

#bigness   #spnetwork arXiv:1604.01041 #numberTheory #primes  ___

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2016-08-01 02:27:09 (8 comments; 12 reshares; 108 +1s; )Open 

Single-minded determination meets gentle courtesy

Single-minded determination meets gentle courtesy___

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2016-07-31 02:44:02 (37 comments; 18 reshares; 103 +1s; )Open 

The search for dark matter

In South Dakota, in a town named Lead, there was a gold mine.  Now it's abandoned.   But at the bottom of this mine, more than a mile underground, there sits a one-meter-tall, 12-sided container.  It contains 370 kilograms of a noble gas chilled to liquid form.  Liquid xenon!  

It's called the Large Underground Xenon experiment, or LUX.  It's been looking for particles that could explain dark matter.   If such a particle interacts with a xenon atom, LUX can detect it. 

Of course, we also need to distinguish these particles from other things. Xenon, a gas at room temperatures, chilled to liquid form, is a great choice here.  For one thing, it's self-shielding!  Xenon is so dense that most gamma rays and neutrons don't get through more than a few centimeters of the stuff.  But it's perfectlytransparent t... more »

The search for dark matter

In South Dakota, in a town named Lead, there was a gold mine.  Now it's abandoned.   But at the bottom of this mine, more than a mile underground, there sits a one-meter-tall, 12-sided container.  It contains 370 kilograms of a noble gas chilled to liquid form.  Liquid xenon!  

It's called the Large Underground Xenon experiment, or LUX.  It's been looking for particles that could explain dark matter.   If such a particle interacts with a xenon atom, LUX can detect it. 

Of course, we also need to distinguish these particles from other things. Xenon, a gas at room temperatures, chilled to liquid form, is a great choice here.  For one thing, it's self-shielding!  Xenon is so dense that most gamma rays and neutrons don't get through more than a few centimeters of the stuff.  But it's perfectly transparent to ordinary light... so if a dark matter particle hits an atom of xenon in the middle of the tank, LUX will see a flash of light.  It can also detect electrons that shoot out from the collision.

Four other experiments had reported hints of dark matter particles about 5 times heavier than a proton.  But LUX is much more sensitive!

The LUX team, with over a hundred scientists, has been looking for dark matter since 2014.  Ten days ago they announced their results: no dark matter particles seen.

This "non-discovery" is actually an important discovery.  The most popular theory of dark matter - that it consists of weakly interacting massive particles - has taken a serious hit. 

We now know that if these hypothetical particles, affectionately called WIMPs, are responsible for most of the dark matter and have a mass between 1/5 and 1000 times the mass of a proton, they must be very, very unwilling to interact with ordinary matter. 

There's no rule saying particles have to interact with ordinary matter.  So, we can't rule out such WIMPs, but they're looking less plausible.  People are getting more interested in other theories:

1) theories with very light WIMPs, such as axions or new kinds of neutrinos

2) theories with very heavy WIMPs, jokingly called WIMPzillas

3) theories where dark matter consists of large objects such as black holes.

In case you're wondering whether dark matter really exists: there's so much evidence for this that very few scientists question it anymore.

Theory 3) is getting a lot of attention, because the gravitational wave detector called LIGO is now able to detect black hole collisions!  It's seen two collisions so far, and the first one involved black holes that seem quite strange, not like the ones we know.  They might be primordial black holes, left over from the early Universe.   Perhaps dark matter consists of primordial black holes!

More on that later.  For now, try these.  The new announcement from the LUX team is here:

http://luxdarkmatter.org/LUX_dark_matter/Talks_files/LUX_NewDarkMatterSearchResult_332LiveDays_IDM2016_160721.pdf

For how the LUX detector works, read this nice article:

http://www.quantumdiaries.org/2014/04/17/searching-for-dark-matter-with-the-large-underground-xenon-experiment/

For a nice intro to the LUX results by Ethan Siegel, on a website that requires you to look at ads, try this:

http://www.forbes.com/sites/startswithabang/2016/07/21/dark-matter-may-be-completely-invisible-concludes-worlds-most-sensitive-search/

For primordial black holes as dark matter, try this:

http://resonaances.blogspot.com/2016/06/black-hole-dark-matter.html

The picture is from this article:

http://www.symmetrymagazine.org/image/april-2012-dark-matter-underground

#physics  ___

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2016-07-30 05:17:01 (33 comments; 9 reshares; 73 +1s; )Open 

Death of the diphoton bump

In June 2015, after a two-year upgrade, the Large Hadron Collider turned on again.  In its first run it had discovered the Higgs boson, a particle 133 times heavier than the proton — and the main missing piece of the Standard Model.   When the collider restarted, with a lot more energy, everyone was hoping to see something new.

In December 2015, two separate detectors saw something: pairs of photons, seemingly emitted by the decay of a brand new particle 6 times heavier than the Higgs boson.  

But was it for real?   Maybe it was just a random fluctuation — noise, rather than a true signal. 

It seemed unlikely to be just chance.  Combining the data from both detectors, the chance of coincidentally seeing a bump this big at this location in the photon spectrum was one in 100 thousand. 

But in particle physicsthat's n... more »

Death of the diphoton bump

In June 2015, after a two-year upgrade, the Large Hadron Collider turned on again.  In its first run it had discovered the Higgs boson, a particle 133 times heavier than the proton — and the main missing piece of the Standard Model.   When the collider restarted, with a lot more energy, everyone was hoping to see something new.

In December 2015, two separate detectors saw something: pairs of photons, seemingly emitted by the decay of a brand new particle 6 times heavier than the Higgs boson.  

But was it for real?   Maybe it was just a random fluctuation — noise, rather than a true signal. 

It seemed unlikely to be just chance.  Combining the data from both detectors, the chance of coincidentally seeing a bump this big at this location in the photon spectrum was one in 100 thousand. 

But in particle physics that's not good enough.  Physicists are looking for lots of different things in these big experiments, so rare coincidences do happen.  To feel safe, they want to push the chance down to one in 3 million.  That's called a 5 sigma event.

So they looked harder. 

Meanwhile, theoretical physicists wrote 500 papers trying to explain this so-called diphoton bump.  It turned out to be easy to make up theories that have a particle of the right sort.  Not so easy, though, to make a convincingly elegant theory.

New data have come in.  The bump is gone.

Theorists are bummed.  A particle physicist named Adam Falkowski wrote:

The loss of the 750 GeV diphoton resonance is a big blow to the particle physics community. We are currently going through the 5 stages of grief, everyone at their own pace, as can be seen e.g. in this comments section. Nevertheless, it may already be a good moment to revisit the story one last time, so as  to understand what went wrong.

In the recent years, physics beyond the Standard Model has seen 2 other flops of comparable impact: the faster-than-light neutrinos in OPERA, and the cosmic microwave background tensor fluctuations in BICEP.  Much as the diphoton signal, both of the above triggered a binge of theoretical explanations, followed by a massive hangover. There was one big difference, however: the OPERA and BICEP signals were due to embarrassing errors on the experimentalists' side. This doesn't seem to be the case for the diphoton bump at the Large Hadron Collider. Some may wonder whether the Standard Model background may have been slightly underestimated,  or whether one experiment may have been biased by the result of the other... But, most likely, the 750 GeV bump was just due to a random fluctuation of the background at this particular energy. Regrettably, the resulting mess cannot be blamed on experimentalists, who were in fact downplaying the anomaly in their official communications. This time it's the theorists who  have some explaining to do.

For more, see Adam Falkowski's blog.  He goes by the name of "Jester":

http://resonaances.blogspot.sg/2016/07/after-hangover.html

By now we have to admit it's quite possible that the Large Hadron Collider will not see any new physics not predicted by the Standard Model.   Unfortunately, this triumph of the Standard Model would leave a lot of big questions unanswered... for now.

The video explains the diphoton bump in simple terms.  It was made back in the early optimistic days.

#physics  ___

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2016-07-29 04:16:41 (0 comments; 28 reshares; 107 +1s; )Open 

Melania Trump has disappeared

Her website was deleted on Wednesday.   Check it out:

http://www.melaniatrump.com

But it's not so easy to make things disappear on the internet!  You can still see what it looked like ten days ago:

https://web.archive.org/web/20160719142534/http://www.melaniatrump.com/

Why was it deleted?   Melania Trump didn't really get a degree of architecture.  Her website said:

After obtaining a degree in design and architecture at University in Slovenia, Melania was jetting between photo shoots in Paris and Milan, finally settling in New York in 1996.

But in fact she dropped out before getting a degree.   She attended the University of Ljubljana’s architecture school... but quit after her freshman year! 

I don't think this lie - or her plagiarized speech - is a bigdeal com... more »

Melania Trump has disappeared

Her website was deleted on Wednesday.   Check it out:

http://www.melaniatrump.com

But it's not so easy to make things disappear on the internet!  You can still see what it looked like ten days ago:

https://web.archive.org/web/20160719142534/http://www.melaniatrump.com/

Why was it deleted?   Melania Trump didn't really get a degree of architecture.  Her website said:

After obtaining a degree in design and architecture at University in Slovenia, Melania was jetting between photo shoots in Paris and Milan, finally settling in New York in 1996.

But in fact she dropped out before getting a degree.   She attended the University of Ljubljana’s architecture school... but quit after her freshman year! 

I don't think this lie - or her plagiarized speech - is a big deal compared to Trump's other lies.   It's just another small example of the dishonesty and utter lack of respect for reality  displayed by Donald Trump and his minions. 

Do we really want a president who repeatedly pretended to be someone else, then admitted in court that he did this... and now says he never did it?

The voice is instantly familiar; the tone, confident, even cocky; the cadence, distinctly Trumpian. The man on the phone vigorously defending Donald Trump says he’s a media spokesman named John Miller, but then he says, “I’m sort of new here,” and “I’m somebody that he knows and I think somebody that he trusts and likes” and even “I’m going to do this a little, part time, and then, yeah, go on with my life.”

A recording obtained by The Washington Post captures what New York reporters and editors who covered Trump’s early career experienced in the 1970s, ’80s and ’90s: calls from Trump’s Manhattan office that resulted in conversations with “John Miller” or “John Barron” — public-relations men who sound precisely like Trump himself — who indeed are Trump, masquerading as an unusually helpful and boastful advocate for himself, according to the journalists and several of Trump’s top aides.

In 1990, Trump admitted in a court case that “I believe on occasion I used that name", meaning John Miller.  But this year he lied again:

In a phone call to NBC’s “Today” program Friday morning after this article appeared online, Trump denied that he was John Miller.  “No, I don’t think it — I don’t know anything about it. You’re telling me about it for the first time and it doesn’t sound like my voice at all,” he said. “I have many, many people that are trying to imitate my voice and then you can imagine that, and this sounds like one of the scams, one of the many scams — doesn’t sound like me.” Later, he was more definitive: “It was not me on the phone. And it doesn’t sound like me on the phone, I will tell you that, and it was not me on the phone. And when was this? Twenty-five years ago?”

Or maybe the person on the phone to NBC wasn't Trump!  Maybe it was John Miller!

For more details about Trump pretending to be his own spokesman:

https://www.washingtonpost.com/politics/donald-trump-alter-ego-barron/2016/05/12/02ac99ec-16fe-11e6-aa55-670cabef46e0_story.html

For more details about Melania's amazing disappearing website:

http://www.huffingtonpost.com/entry/melania-trump-biography-deleted_us_57990c1ae4b02d5d5ed3fed9

http://www.huffingtonpost.com/entry/melania-trump-college-claims_us_578dd95ce4b0c53d5cfac0dc___

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2016-07-27 04:02:07 (59 comments; 12 reshares; 96 +1s; )Open 

Satanic crystal found in ancient meteorite

Just kidding!  There's nothing devilish about the pentagram here.  It's what scientists saw when they shot X-rays through a tiny piece of a meteorite found in the far northeast of Russia. 

No ordinary crystal can produce this pattern  - it takes a quasicrystal, where the atoms are packed in a way that never quite repeats.  Scientists have made lots of quasicrystals in the lab, but only two have been found in nature, both in meteorites!

This is the second one.  It contains a mineral called icosahedrite, made of aluminum, copper and iron.  It's only stable at high temperatures and pressures, so it must have formed in a collision.  It's been slowly decaying ever since, but very slowly.  It could be billions of years old.

To see how this mineral could have formed, scientistssimulate... more »

Satanic crystal found in ancient meteorite

Just kidding!  There's nothing devilish about the pentagram here.  It's what scientists saw when they shot X-rays through a tiny piece of a meteorite found in the far northeast of Russia. 

No ordinary crystal can produce this pattern  - it takes a quasicrystal, where the atoms are packed in a way that never quite repeats.  Scientists have made lots of quasicrystals in the lab, but only two have been found in nature, both in meteorites!

This is the second one.  It contains a mineral called icosahedrite, made of aluminum, copper and iron.  It's only stable at high temperatures and pressures, so it must have formed in a collision.  It's been slowly decaying ever since, but very slowly.  It could be billions of years old.

To see how this mineral could have formed, scientists simulated the collision between two asteroids in their lab.  They took thin slices of minerals found in the Khatyrka meteorite and sandwiched them together in a gadget that looks like a a steel hockey puck.  They attached it to the muzzle of a four-meter-long gun and blasted it with a projectile moving nearly one kilometer per second! 

Yup.  Icosahedrite.

For details and more pictures, see:

• Paul D. Asimow, Chaney Lin, Luca Bindi, Chi Ma, Oliver Tschauner, Lincoln S. Hollister and Paul J. Steinhardt, Shock synthesis of quasicrystals with implications for their origin in asteroid collisions, Proceedings of the National Academy of Sciences 113 (2016), 7077-7081.  Freely available at http://authors.library.caltech.edu/67876/

Puzzle: how did pentagrams get associated with Satan in the first place?

#astronomy #geometry
#spnetwork DOI:10.1073/pnas.1600321113___

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2016-07-26 06:47:27 (0 comments; 9 reshares; 72 +1s; )Open 

What Sanders thinks about Clinton and Trump

I've never lived through an election where the choice is so stark - where the consequences of our vote will be so huge.  Bernie Sanders laid it out clearly at the Democratic National Convention yesterday:

This election is about which candidate understands the real problems facing this country and has offered real solutions – not just bombast, fear-mongering, name-calling and divisiveness.

We need leadership in this country which will improve the lives of working families, the children, the elderly, the sick and the poor. We need leadership which brings our people together and makes us stronger – not leadership which insults Latinos, Muslims, women, African-Americans and veterans – and divides us up.

By these measures, any objective observer will conclude that – based on her ideas andher lead... more »

What Sanders thinks about Clinton and Trump

I've never lived through an election where the choice is so stark - where the consequences of our vote will be so huge.  Bernie Sanders laid it out clearly at the Democratic National Convention yesterday:

This election is about which candidate understands the real problems facing this country and has offered real solutions – not just bombast, fear-mongering, name-calling and divisiveness.

We need leadership in this country which will improve the lives of working families, the children, the elderly, the sick and the poor. We need leadership which brings our people together and makes us stronger – not leadership which insults Latinos, Muslims, women, African-Americans and veterans – and divides us up.

By these measures, any objective observer will conclude that – based on her ideas and her leadership – Hillary Clinton must become the next president of the United States. The choice is not even close.

This election is about a single mom I saw in Nevada who, with tears in her eyes, told me that she was scared to death about the future because she and her young daughter were not making it on the $10.45 an hour she was earning. This election is about that woman and the millions of other workers in this country who are struggling to survive on totally inadequate wages.

Hillary Clinton understands that if someone in America works 40 hours a week, that person should not be living in poverty. She understands that we must raise the minimum wage to a living wage. And she is determined to create millions of new jobs by rebuilding our crumbling infrastructure – our roads, bridges, water systems and wastewater plants.

But her opponent – Donald Trump – well, he has a very different view. He does not support raising the federal minimum wage of $7.25 an hour – a starvation wage. While Donald Trump believes in huge tax breaks for billionaires, he believes that states should actually have the right to lower the minimum wage below $7.25. What an outrage!

This election is about overturning Citizens United, one of the worst Supreme Court decisions in the history of our country. That decision allows the wealthiest people in America, like the billionaire Koch brothers, to spend hundreds of millions of dollars buying elections and, in the process, undermine American democracy.

Hillary Clinton will nominate justices to the Supreme Court who are prepared to overturn Citizens United and end the movement toward oligarchy in this country. Her Supreme Court appointments will also defend a woman’s right to choose, workers’ rights, the rights of the LGBT community, the needs of minorities and immigrants and the government’s ability to protect the environment.

If you don’t believe this election is important, if you think you can sit it out, take a moment to think about the Supreme Court justices that Donald Trump would nominate and what that would mean to civil liberties, equal rights and the future of our country.

This election is about the thousands of young people I have met who have left college deeply in debt, and the many others who cannot afford to go to college. During the primary campaign, Secretary Clinton and I both focused on this issue but with different approaches. Recently, however, we have come together on a proposal that will revolutionize higher education in America. It will guarantee that the children of any family this country with an annual income of $125,000 a year or less – 83 percent of our population – will be able to go to a public college or university tuition free. That proposal also substantially reduces student debt.

This election is about climate change, the greatest environmental crisis facing our planet, and the need to leave this world in a way that is healthy and habitable for our kids and future generations. Hillary Clinton is listening to the scientists who tell us that – unless we act boldly and transform our energy system in the very near future – there will be more drought, more floods, more acidification of the oceans, more rising sea levels. She understands that when we do that we can create hundreds of thousands of good-paying jobs.

Donald Trump? Well, like most Republicans, he chooses to reject science. He believes that climate change is a "hoax," no need to address it. Hillary Clinton understands that a president’s job is to worry about future generations, not the short-term profits of the fossil fuel industry.

This campaign is about moving the United States toward universal health care and reducing the number of people who are uninsured or under-insured. Hillary Clinton wants to see that all Americans have the right to choose a public option in their health care exchange. She believes that anyone 55 years or older should be able to opt in to Medicare and she wants to see millions more Americans gain access to primary health care, dental care, mental health counseling and low-cost prescription drugs through a major expansion of community health centers.

And what is Donald Trump’s position on health care? No surprise there. Same old, same old Republican contempt for working families. He wants to abolish the Affordable Care Act, throw 20 million people off of the health insurance they currently have and cut Medicaid for lower-income Americans.

Hillary Clinton also understands that millions of seniors, disabled vets and others are struggling with the outrageously high cost of prescription drugs and the fact that Americans pay the highest prices in the world for their medicine. She knows that Medicare must negotiate drug prices with the pharmaceutical industry and that drug companies should not be making billions in profits while one in five Americans are unable to afford the medicine they need. The greed of the drug companies must end.

This election is about the leadership we need to pass comprehensive immigration reform and repair a broken criminal justice system. It’s about making sure that young people in this country are in good schools and at good jobs, not in jail cells. Hillary Clinton understands that we have to invest in education and jobs for our young people, not more jails or incarceration.

In these stressful times for our country, this election must be about bringing our people together, not dividing us up. While Donald Trump is busy insulting one group after another, Hillary Clinton understands that our diversity is one of our greatest strengths. Yes. We become stronger when black and white, Latino, Asian-American, Native American – all of us – stand together. Yes. We become stronger when men and women, young and old, gay and straight, native born and immigrant fight to create the kind of country we all know we can become.

Click on 13:12 if you want to hear him say this on the video!___

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2016-07-25 15:39:23 (0 comments; 20 reshares; 82 +1s; )Open 

Endorsed by Putin

Putin, eager to weaken the EU and NATO, has been backing right-wing demagogues throughout Europe.   So it came as no surprise when he started complimenting Trump.  Not only is Trump would-be strongman of Putin's ilk (only less clever), he's also been threatening to break US commitments to NATO.

In December, Putin called Trump "an outstanding and talented personality".  Trump, in a rare moment of sweetness, replied:

"It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond."

Putin?  Respected?

Putin now appears to be backing Trump even more strongly, with Russian operatives hacking into Democratic National Committee (DNC) computers and trying to embarrass them shortly before the convention.

On June 14th, thecybe... more »

Endorsed by Putin

Putin, eager to weaken the EU and NATO, has been backing right-wing demagogues throughout Europe.   So it came as no surprise when he started complimenting Trump.  Not only is Trump would-be strongman of Putin's ilk (only less clever), he's also been threatening to break US commitments to NATO.

In December, Putin called Trump "an outstanding and talented personality".  Trump, in a rare moment of sweetness, replied:

"It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond."

Putin?  Respected?

Putin now appears to be backing Trump even more strongly, with Russian operatives hacking into Democratic National Committee (DNC) computers and trying to embarrass them shortly before the convention.

On June 14th, the cybersecurity firm CrowdStrike, under contract with the DNC, announced in a blog post that two separate Russian intelligence groups had gained access to the DNC network.  One, called FANCY BEAR or APT 28, gained access in April. The other, COZY BEAR or APT 29, first breached the network in the summer of 2015.

You can read a more detailed analysis here:

https://www.crowdstrike.com/blog/bears-midst-intrusion-democratic-national-committee/

Let me quote some:

CrowdStrike Services Inc., our Incident Response group, was called by the Democratic National Committee (DNC), the formal governing body for the US Democratic Party, to respond to a suspected breach. We deployed our IR team and technology and immediately identified two sophisticated adversaries on the network – COZY BEAR and FANCY BEAR. We’ve had lots of experience with both of these actors attempting to target our customers in the past and know them well. In fact, our team considers them some of the best adversaries out of all the numerous nation-state, criminal and hacktivist/terrorist groups we encounter on a daily basis. Their tradecraft is superb, operational security second to none and the extensive usage of ‘living-off-the-land’ techniques enables them to easily bypass many security solutions they encounter. In particular, we identified advanced methods consistent with nation-state level capabilities including deliberate targeting and ‘access management’ tradecraft – both groups were constantly going back into the environment to change out their implants, modify persistent methods, move to new Command & Control channels and perform other tasks to try to stay ahead of being detected. Both adversaries engage in extensive political and economic espionage for the benefit of the government of the Russian Federation and are believed to be closely linked to the Russian government’s powerful and highly capable intelligence services.

COZY BEAR (also referred to in some industry reports as CozyDuke or APT 29) is the adversary group that last year successfully infiltrated the unclassified networks of the White House, State Department, and US Joint Chiefs of Staff. In addition to the US government, they have targeted organizations across the Defense, Energy, Extractive, Financial, Insurance, Legal, Manufacturing Media, Think Tanks, Pharmaceutical, Research and Technology industries, along with Universities. Victims have also been observed in Western Europe, Brazil, China, Japan, Mexico, New Zealand, South Korea, Turkey and Central Asian countries. COZY BEAR’s preferred intrusion method is a broadly targeted spearphish campaign that typically includes web links to a malicious dropper. Once executed on the machine, the code will deliver one of a number of sophisticated Remote Access Tools (RATs), including AdobeARM, ATI-Agent, and MiniDionis. On many occasions, both the dropper and the payload will contain a range of techniques to ensure the sample is not being analyzed on a virtual machine, using a debugger, or located within a sandbox. They have extensive checks for the various security software that is installed on the system and their specific configurations. When specific versions are discovered that may cause issues for the RAT, it promptly exits. These actions demonstrate a well-resourced adversary with a thorough implant-testing regime that is highly attuned to slight configuration issues that may result in their detection, and which would cause them to deploy a different tool instead. The implants are highly configurable via encrypted configuration files, which allow the adversary to customize various components, including C2 servers, the list of initial tasks to carry out, persistence mechanisms, encryption keys and others. An HTTP protocol with encrypted payload is used for the Command & Control communication.

FANCY BEAR (also known as Sofacy or APT 28) is a separate Russian-based threat actor, which has been active since mid 2000s, and has been responsible for targeted intrusion campaigns against the Aerospace, Defense, Energy, Government and Media sectors. Their victims have been identified in the United States, Western Europe, Brazil, Canada, China, Georgia, Iran, Japan, Malaysia and South Korea. Extensive targeting of defense ministries and other military victims has been observed, the profile of which closely mirrors the strategic interests of the Russian government, and may indicate affiliation with Главное Разведывательное Управление (Main Intelligence Department) or GRU, Russia’s premier military intelligence service. This adversary has a wide range of implants at their disposal, which have been developed over the course of many years and include Sofacy, X-Agent, X-Tunnel, WinIDS, Foozer and DownRange droppers, and even malware for Linux, OSX, IOS, Android and Windows Phones. This group is known for its technique of registering domains that closely resemble domains of legitimate organizations they plan to target. Afterwards, they establish phishing sites on these domains that spoof the look and feel of the victim’s web-based email services in order to steal their credentials. FANCY BEAR has also been linked publicly to intrusions into the German Bundestag and France’s TV5 Monde TV station in April 2015.

At DNC, COZY BEAR intrusion has been identified going back to summer of 2015, while FANCY BEAR separately breached the network in April 2016. We have identified no collaboration between the two actors, or even an awareness of one by the other. Instead, we observed the two Russian espionage groups compromise the same systems and engage separately in the theft of identical credentials. While you would virtually never see Western intelligence agencies going after the same target without de-confliction for fear of compromising each other’s operations, in Russia this is not an uncommon scenario. “Putin’s Hydra: Inside Russia’s Intelligence Services”, a recent paper from European Council on Foreign Relations, does an excellent job outlining the highly adversarial relationship between Russia’s main intelligence services – Федеральная Служба Безопасности (FSB), the primary domestic intelligence agency but one with also significant external collection and ‘active measures’ remit, Служба Внешней Разведки (SVR), the primary foreign intelligence agency, and the aforementioned GRU. Not only do they have overlapping areas of responsibility, but also rarely share intelligence and even occasionally steal sources from each other and compromise operations. Thus, it is not surprising to see them engage in intrusions against the same victim, even when it may be a waste of resources and lead to the discovery and potential compromise of mutual operations.

You can even see some of the code that was used. Another security group, Fidelis, did an independent study confirming CrowdStriker's findings:

http://www.threatgeek.com/2016/06/dnc_update.html

Of course, none of this excuses the DNC's dastardly behavior as revealed by the hacked emails.  But it's another sign of how sickening a disaster a Trump presidency would be.

------------------------------------------------------------

Putin's compliment, and Trump's reply, is here:

http://www.cnn.com/2015/12/17/politics/russia-putin-trump/

Here's an article on Putin's "useful idiots" in Europe:

http://foreignpolicy.com/2016/02/23/why-europe-is-right-to-fear-putins-useful-idiots/

A quote, which contains lots of links in the original:

Prior to 2010, one would be hard-pressed to find public statements in praise of Putin by far-right leaders. Today, they are commonplace. UKIP’s Nigel Farage is a self-proclaimed fan of the Russian president. Jobbik’s head, Gabor Vona, is a frequent invited guest in Moscow. And, of course, Madame Le Pen, whose party was the beneficiary of a 9.4 million euro loan from a Russian-owned bank, is a consistent voice of support for Russian foreign policy in Ukraine and the Middle East. Even Germany, where the far right has failed to gain a foothold, is not immune to Moscow’s narrative. Supporters of PEGIDA, the increasingly popular xenophobic group whose acronym stands for “Patriotic Europeans Against the Islamization of the West,” often carry Russian flags and anti-government posters begging for Putin’s help.___

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2016-07-24 04:19:04 (13 comments; 10 reshares; 77 +1s; )Open 

New kinds of quasiparticles

You can get electrons to behave in many strange ways in different materials.   They act like various kinds of particles... but they're not truly fundamental particles, so they're called quasiparticles

For example, the spin, charge and position of electrons can move in completely independent ways. 

Imagine an audience at a football game holding up signs, and then creating a wave by wiggling their signs.  This wave can move even even if the people stand still! 

Similarly, we can have electrons more or less standing still, with their spins lined up.   Then their spins can wiggle a bit, and this wiggle can move through the material, even though the electrons don't move.  This wave of altered spin can act like a particle!  It's called a spinon.

You can also imagine a hole in a densecrowd of... more »

New kinds of quasiparticles

You can get electrons to behave in many strange ways in different materials.   They act like various kinds of particles... but they're not truly fundamental particles, so they're called quasiparticles

For example, the spin, charge and position of electrons can move in completely independent ways. 

Imagine an audience at a football game holding up signs, and then creating a wave by wiggling their signs.  This wave can move even even if the people stand still! 

Similarly, we can have electrons more or less standing still, with their spins lined up.   Then their spins can wiggle a bit, and this wiggle can move through the material, even though the electrons don't move.  This wave of altered spin can act like a particle!  It's called a spinon.

You can also imagine a hole in a dense crowd of people, moving along as if it were an entity of its own.  When this happens with electrons it's called a holon, or more commonly just a hole.  A hole acts like a particle with positive charge, since electrons have negative charge. 

Since holes have positive charge and electrons have negative charge, they attract.   Sometimes they orbit each other for long enough that this combined thing acts like a particle of its own!   This kind of quasiparticle is called an exciton.

There are also other quasiparticles.  If you're a student who wants to do particle physics, please switch to studying quasiparticles!  The math is almost the same, and you don't need huge particle accelerators to make cool new discoveries.  Some are even useful.

One of the most fundamental things about a quasiparticle, or for that matter an ordinary particle, is its energy.  Its energy depends on its momentum.  The relation between them is called the dispersion relation.  This says a lot about how the quasiparticle acts.

Right next door to the +Centre for Quantum Technologies where I'm working in Singapore, there's a lab that specializes in graphene - a crystal made of carbon that's just one atom thick.  When you've got a very thin film like this, a quasiparticle inside it acts like it's living in a 2-dimensional world!   Since it can't go up and down, only 2 components of its momentum can be nonzero.

The picture here shows a graph of energy as a function of momentum for a new kind of quasiparticle they're studying.  They haven't made it in the lab yet; they've just shown it's possible. 

The three colored sheets show that 3 different energies are possible for each momentum - except momentum zero, where all three sheet meet, and also a line of momenta where two sheets meet.

If we only had the green and blue sheets, that would be the dispersion relation for a massless particle.  People already know how to make massless quasiparticles with graphene.

The new thing is the yellow sheet!  This will make very strange things happen, I'm sure.

I got interested in these new quasiparticles thanks to this article pointed out by +rasha kamel:

• Unconventional quasiparticles predicted in conventional crystals, ScienceDaily, https://www.sciencedaily.com/releases/2016/07/160721151219.htm

But I got the picture from here:

• Guoqing Chang et al, New fermions on the line in topological symmorphic metals, http://arxiv.org/abs/1605.06831.

Here's the abstract, for you physics nerds out there:

Abstract. Topological metals and semi-metals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. The most studied TMs, i.e., Weyl and Dirac semi-metals, feature quasiparticles that are direct analogues of the textbook elementary particles. Moreover, the TMs known so far can be characterized based on the dimensionality of the band crossing. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM which breaks the above paradigms. Firstly, the TM features triply-degenerate band crossing in a symmorphic lattice, hence realizing emergent fermionic quasiparticles not present in quantum field theory. Secondly, the band crossing is neither 0D nor 1D. Instead, it consists of two isolated triply-degenerate nodes interconnected by multi-segments of lines with two-fold degeneracy. We present materials candidates. We further show that triply-degenerate band crossings in symmorphic crystals give rise to a Landau level spectrum distinct from the known TMs, suggesting novel magneto-transport responses. Our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm.

Weirdly, I had learned the word 'symmorphic' just yesterday.  Greg Egan are writing a paper on crystals, and he explained that a crystal is symmorphic if it contains a point where every symmetry of the crystal consists of a symmetry fixing this point followed by a translation.   It was important for our work to notice that a diamond is not symmorphic.

#spnetwork arXiv:1605.06831 #condensedMatter #physics  ___

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2016-07-23 02:54:41 (22 comments; 4 reshares; 43 +1s; )Open 

The quest for larger infinities

There are different kinds of bigness.   But they're connected.

There's a fascinating contest where you try to write the computer program of a certain length that would print out the largest possible integer.    This contest was actually carried out on the xkcd blog, and Eliezer Yudkowsky won.  Unless you know more about logic than he does, you won't be able to beat him.

There's another contest where you try to name the largest "computable ordinal", and that's what my post is about:

https://johncarlosbaez.wordpress.com/2016/07/07/large-countable-ordinals-part-3/

And there's another contest where you try to name the largest "cardinal".   Here we get into inaccessible cardinals, indescribable cardinals, huge cardinals, superhuge cardinals and the like. 
But th... more »

The quest for larger infinities

There are different kinds of bigness.   But they're connected.

There's a fascinating contest where you try to write the computer program of a certain length that would print out the largest possible integer.    This contest was actually carried out on the xkcd blog, and Eliezer Yudkowsky won.  Unless you know more about logic than he does, you won't be able to beat him.

There's another contest where you try to name the largest "computable ordinal", and that's what my post is about:

https://johncarlosbaez.wordpress.com/2016/07/07/large-countable-ordinals-part-3/

And there's another contest where you try to name the largest "cardinal".   Here we get into inaccessible cardinals, indescribable cardinals, huge cardinals, superhuge cardinals and the like. 

But these three contests turn out to deeply related!   There's a way to name huge integers using fast-growing functions that you can describe using large computable ordinals.  And Yudkowsky won the contest to write a program that prints out a large integer by taking advantage of a very large cardinal.

So, there's a spooky connection between large finite numbers, large computable ordinals - which are all countable, by the way - and large cardinals, which are not countable.  Many theorems point at this connection, but the full story remains obscure.  I believe when it becomes clear we'll get a whole new idea of what the infnite is all about.

As for me, I need a break.  My post takes you up to the large Veblen ordinal, a whopping large computable ordinal... but I know people have studied others that dwarf this one.  As Bilbo said:

The Road goes ever on and on
Out from the door where it began.
Now far ahead the Road has gone,
Let others follow it who can!
Let them a journey new begin,
But I at last with weary feet
Will turn towards the lighted inn,
My evening-rest and sleep to meet.

#bigness  ___

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2016-07-21 23:28:18 (0 comments; 18 reshares; 102 +1s; )Open 

Republicans for Trump

Cruz caused a stir at the Republican convention by not endorsing Trump.  But here's what other Republicans say:

“He’s a race-baiting, xenophobic religious bigot. He doesn’t represent my party. He doesn’t represent the values that the men and women who wear the uniform are fighting for.” — Senator Lindsey Graham, Republican of South Carolina

“I don’t think this guy has any more core principles than a Kardashian marriage.” — Senator Ben Sasse, Republican of Nebraska

“We saw and looked at true hate in the eyes last year in Charleston. I will not stop until we fight a man that chooses not to disavow the K.K.K. That is not a part of our party.” — Nikki Haley, Republican governor of South Carolina

“Donald Trump is a madman who must be stopped,” — Bobby Jindal, former Republican governor ofLouisiana

“I won’t vo... more »

Republicans for Trump

Cruz caused a stir at the Republican convention by not endorsing Trump.  But here's what other Republicans say:

“He’s a race-baiting, xenophobic religious bigot. He doesn’t represent my party. He doesn’t represent the values that the men and women who wear the uniform are fighting for.” — Senator Lindsey Graham, Republican of South Carolina

“I don’t think this guy has any more core principles than a Kardashian marriage.” — Senator Ben Sasse, Republican of Nebraska

“We saw and looked at true hate in the eyes last year in Charleston. I will not stop until we fight a man that chooses not to disavow the K.K.K. That is not a part of our party.” — Nikki Haley, Republican governor of South Carolina

“Donald Trump is a madman who must be stopped,” — Bobby Jindal, former Republican governor of Louisiana

“I won’t vote for Donald Trump because of who he isn’t. He isn’t a Republican. He isn’t a conservative. He isn’t a truth teller. ... I also won’t vote for Donald Trump because of who he is. A bigot. A misogynist. A fraud. A bully.” — Norm Coleman, former Republican senator from Minnesota

“To support Trump is to support a bigot. It’s really that simple.” — Stuart Stevens, chief strategist to Mitt Romney’s 2012 presidential campaign

“Donald Trump is unfit to be president. He is a dishonest demagogue who plays to our worst fears. Trump would take America on a dangerous journey.” — Meg Whitman, Hewlett-Packard Enterprise C.E.O. and former national finance co-chairwoman for Chris Christie’s presidential campaign

“I thought he was an embarrassment to my party; I think he’s an embarrassment to my country. … I can’t vote for him.” — Tom Ridge, former Republican governor of Pennsylvania and secretary of homeland security under George W. Bush

“I would not vote for Trump, clearly. If there is any, any, any other choice, a living, breathing person with a pulse, I would be there.” — Mel Martinez, former Republican senator from Florida and former chairman of the Republican National Committee

“The G.O.P., in putting Trump at the top of the ticket, is endorsing a brand of populism rooted in ignorance, prejudice, fear and isolationism. This troubles me deeply as a Republican, but it troubles me even more as an American. … Never Trump.” — Henry M. Paulson Jr., Treasury secretary under George W. Bush

“Donald Trump is a phony, a fraud. His promises are as worthless as a degree from Trump University.” — Mitt Romney, 2012 Republican nominee for president

“When you’ve got a guy favorably quoting Mussolini, I don’t care what party you’re in, I’m not voting for that guy.” — Ken Cuccinelli, president of the Senate Conservatives Fund

“Donald Trump is a scam. Evangelical voters should back away... Trump is a misogynist and philanderer. He demeans women and minorities. His preferred forms of communication are insults, obscenities and untruths.” — The Christian Post, a popular U.S. evangelical website

“A moral degenerate.” — Peter Wehner, evangelical Christian commentator who served in last three Republican administrations

“A man utterly unfit for the position by temperament, values and policy preferences … whose personal record of chicanery and wild rhetoric of bigotry, misogyny and misplaced belligerence are without parallel in the modern history of either major party.” — Eliot A. Cohen, a senior State Department official under George W. Bush

“Leaders don’t need to do research to reject Klan support. #NeverTrump” — Ken Mehlman, former chairman of the Republican National Committee

“God bless this man” — Daily Stormer, white supremacist website

----------------------------------------------------------

Sources for all these quotes can be found by clicking on the links here:

http://www.nytimes.com/2016/07/21/opinion/what-republicans-really-think-about-trump.html___

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2016-07-19 02:19:16 (13 comments; 11 reshares; 70 +1s; )Open 

Into the clouds

Frigatebirds are amazing:

Ornithologist Henri Weimerskirch put satellite tags on a couple of dozen frigatebirds, as well as instruments that measured body functions such as heart rate. When the data started to come in, he could hardly believe how high the birds flew.

“First, we found, ‘Whoa, 1,500 meters. Wow. Excellent, fantastique,’ ” says Weimerskirch, who is with the National Center for Scientific Research in Paris. “And after 2,000, after 3,000, after 4,000 meters — OK, at this altitude they are in freezing conditions, especially surprising for a tropical bird.”

Four thousand meters is more than 12,000 feet, or as high as parts of the Rocky Mountains. “There is no other bird flying so high relative to the sea surface,” he says.

Weimerskirch says that kind of flying should take a hugeamount of energy.... more »

Into the clouds

Frigatebirds are amazing:

Ornithologist Henri Weimerskirch put satellite tags on a couple of dozen frigatebirds, as well as instruments that measured body functions such as heart rate. When the data started to come in, he could hardly believe how high the birds flew.

“First, we found, ‘Whoa, 1,500 meters. Wow. Excellent, fantastique,’ ” says Weimerskirch, who is with the National Center for Scientific Research in Paris. “And after 2,000, after 3,000, after 4,000 meters — OK, at this altitude they are in freezing conditions, especially surprising for a tropical bird.”

Four thousand meters is more than 12,000 feet, or as high as parts of the Rocky Mountains. “There is no other bird flying so high relative to the sea surface,” he says.

Weimerskirch says that kind of flying should take a huge amount of energy. But the instruments monitoring the birds’ heartbeats showed that the birds weren’t even working up a sweat. (They wouldn’t, actually, since birds don’t sweat, but their heart rate wasn’t going up.)

How did they do it? By flying into a cloud.

“It’s the only bird that is known to intentionally enter into a cloud,” Weimerskirch says. And not just any cloud—a fluffy, white cumulus cloud. Over the ocean, these clouds tend to form in places where warm air rises from the sea surface. The birds hitch a ride on the updraft, all the way up to the top of the cloud.

But this is far from the only amazing thing about frigatebirds!  For the full story, read this:

https://johncarlosbaez.wordpress.com/2016/07/18/frigatebirds/

You'll also learn the dark side of frigatebirds: they're kleptoparasites.

The quote is from here:

• Christopher Joyce, Nonstop flight: how the frigatebird can soar for weeks without stopping, All Things Considered, National Public Radio, 30 June 2016, http://www.npr.org/sections/thetwo-way/2016/06/30/484164544/non-stop-flight-how-the-frigatebird-can-soar-for-months-without-stopping

and the photo is from here:

https://www.pinterest.com/pin/237353842833650981/

#biology  ___

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2016-07-16 00:51:06 (25 comments; 4 reshares; 72 +1s; )Open 

A winning septic

A septic tank is a system for disposing of sewage.  A septic surface is a surface described by a polynomial equation of degree 7.

This picture by +Abdelaziz Nait Merzouk shows a septic surface discovered by Oliver Labs when he was working on his PhD thesis. 

It looks like a beautiful flower of some strange sort.  But it's famous because it's the septic with the largest known number of points that look like two cones meeting tip to tip. 

How many?  Ninety-nine!  We know that no septic can have more than 104 of these ordinary double points, as they're called.  But we don't know any with more than 99.  So this is currently one of the winners.  There are others, too, also discovered by Labs.

This surface is called the Labs septic, which reminds me of yet another meaning of the word'sep... more »

A winning septic

A septic tank is a system for disposing of sewage.  A septic surface is a surface described by a polynomial equation of degree 7.

This picture by +Abdelaziz Nait Merzouk shows a septic surface discovered by Oliver Labs when he was working on his PhD thesis. 

It looks like a beautiful flower of some strange sort.  But it's famous because it's the septic with the largest known number of points that look like two cones meeting tip to tip. 

How many?  Ninety-nine!  We know that no septic can have more than 104 of these ordinary double points, as they're called.  But we don't know any with more than 99.  So this is currently one of the winners.  There are others, too, also discovered by Labs.

This surface is called the Labs septic, which reminds me of yet another meaning of the word 'septic'.  

Sepsis occurs when harmful bacteria start to grow in tissue.  So, 'septic' also means 'infected with bacteria'... and 'Labs septic' has a strangely medical sound.   But this septic is pure and beautiful.

For more on how the Labs septic was found, and another view of it, visit my blog Visual Insight:

http://blogs.ams.org/visualinsight/2016/07/15/labs-septic/

#geometry  ___

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2016-07-12 04:25:39 (24 comments; 26 reshares; 92 +1s; )Open 

Global warming: demand the truth

After announcements that 2015 was the hottest year on record and February 2016 was the hottest month, the news station CNN aired five times more fossil fuel advertising than actual climate reporting!

So, please sign this petition to CNN.  Tell them: start reporting on climate change.   And please reshare this message.

A study by the group Media Matters showed that the American Petroleum Institute is getting more coverage than actual news about global warming.  This doesn't even include the ads from individual fossil fuel companies and the Koch brothers.

Here's some actual news, in case you hadn't heard:

1) The extent of Arctic sea ice in June was the lowest in recorded history for that month of the year: 260,000 square kilometers less than ever before!   It's on track to break allrecor... more »

Global warming: demand the truth

After announcements that 2015 was the hottest year on record and February 2016 was the hottest month, the news station CNN aired five times more fossil fuel advertising than actual climate reporting!

So, please sign this petition to CNN.  Tell them: start reporting on climate change.   And please reshare this message.

A study by the group Media Matters showed that the American Petroleum Institute is getting more coverage than actual news about global warming.  This doesn't even include the ads from individual fossil fuel companies and the Koch brothers.

Here's some actual news, in case you hadn't heard:

1) The extent of Arctic sea ice in June was the lowest in recorded history for that month of the year: 260,000 square kilometers less than ever before!   It's on track to break all records this year.

2) Recently every month from October until May has been the hottest on record worldwide.  June was the second hottest, since the El Niño is fading.

3) India recorded its hottest day ever on May 19th. The temperature in Phalodi hit 51 degrees Celsius (124 degrees Fahrenheit), and a nationwide drought has affected more than 300 million people marched on, leaving armed guards at dams, and reservoirs well below their usual levels.

4) Alaska, along with the rest of the Arctic, has experienced record-breaking heat this year.  Its average year-to-date temperature has been 5.5C above the long term average.

5) In the atmosphere, carbon dioxide has been increasing every year for decades - but this year the speed of increase is also record-breaking!   The increase for 2016 is expected to be 3.1 parts per million, up from an annual average of 2.1.

6) The Great Barrier Reef, a natural wonder and world heritage site, recently experienced its worst ever coral bleaching event.  An aerial study found that just 7% of the reef escaped bleaching. 

7) A new study in Nature argues that even despite the actions pledged in the Paris Agreement, the Earth is still on course for a temperature increase of 2.6 - 3.1C by the end of this century.  Read this:

http://www.nature.com/nature/journal/v534/n7609/full/nature18307.html

The Paris agreement is a step in the right direction, but we need to ratchet it up.  We can't afford to slack off now.  One piece of the puzzle is clear information about the crisis we're in.

------------------------------------------------

Media Matters writes:

In Week After Hottest Year Announcement, CNN Aired Less Than One Minute Of Climate-Related Coverage And 13.5 Minutes Of Oil Industry Ads.

From January 20 to January 26, CNN morning, daytime and primetime programming included only 57 seconds of coverage about climate change or the announcement that 2015 was the hottest year on record. Over that same time period, CNN aired 13.5 minutes of American Petroleum Institute ads. The climate-related segments included one on the January 21 edition of Early Start, in which anchor Christine Romans reported that 2015 was the hottest year on record and that officials say “the planet is still warming with no apparent change in the long term global warming rate.” Additionally, CNN senior legal analyst Jeffrey Toobin briefly mentioned Republican climate science denial during a discussion of Hillary Clinton’s emails on Anderson Cooper 360, and CNN host Fareed Zakaria noted that the “The World Economic Forum said this year that the greatest global risk is the failure of climate change mitigation and adaptation,” during a Fareed Zakaria GPS segment about a study finding that humans have entered a new geological epoch known as the Anthropocene.

Following Announcement That February 2016 Was Most Unusually Hot Month Ever, CNN Aired Four Minutes Of Climate-Related Coverage And 10 Minutes Of Fossil Fuel Ads.

In the one-week period beginning March 17, when NOAA released data showing that February 2016 was the most unusually hot month ever recorded, CNN aired only four minutes of coverage about climate change or the temperature record during its morning, daytime, and primetime coverage. During that same time period, CNN aired ten minutes of American Petroleum Institute ads. On March 18, CNN anchors Christine Romans and John Berman delivered nearly-identical reports on February’s “astounding” temperature record during the 4 a.m. and 5 a.m. editions of Early Start, respectively, but neither explicitly mentioned climate change or the role fossil fuel pollution and other human activities play in driving climate change. The March 20 edition of Fareed Zakaria GPS featured an interview with astronaut Piers Sellers about his climate change advocacy, followed by a brief report about International Energy Administration (IEA) data showing a decline in carbon emissions from energy production, which Zakaria described as “some good news on the climate front” and a “welcome update in the climate battle.” Finally, on the March 20 edition of New Day Sunday, anchor Christi Paul reported that major cities around the world were participating in Earth Hour, an event meant to bring awareness to climate change, by switching off their lights.

For more details see:

http://mediamatters.org/research/2016/04/25/study-cnn-viewers-see-far-more-fossil-fuel-advertising-climate-change-reporting/209985

Here's the data for the statements 1)-6):

https://www.theguardian.com/environment/2016/jun/17/seven-climate-records-set-so-far-in-2016

https://www.theguardian.com/environment/2016/jul/07/arctic-sea-ice-crashes-to-record-low-for-june

http://www.netnewsledger.com/2016/07/05/june-2016-second-hottest-june-ever/___

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2016-07-10 15:13:26 (49 comments; 23 reshares; 128 +1s; )Open 

Gimbal lock

Here you see 3 rotating rings called gimbals.  Gimbals are used in gyroscopes and inertial measurement units, which are gadgets that measure an object's orientation - like a drone, or a spacecraft.   Gimbals are also used to orient thrusters on rockets.

With 3 gimbals, you can rotate the inner one to whatever orientation you want.  The basic reason is that it takes 3 numbers to describe a rotation in 3 dimensional space.  This is a special lucky property of the number 3. 

But when two of the gimbal's axes happen to be lined up, you get gimbal lock.   In other words: you lose the ability to rotate the inner gimbal a tiny bit in any way you want.   The reason is that in this situation, rotating one of the two aligned gimbals has the same effect on the inner gimbal as rotating the other!  

I've always foundgimbal lock... more »

Gimbal lock

Here you see 3 rotating rings called gimbals.  Gimbals are used in gyroscopes and inertial measurement units, which are gadgets that measure an object's orientation - like a drone, or a spacecraft.   Gimbals are also used to orient thrusters on rockets.

With 3 gimbals, you can rotate the inner one to whatever orientation you want.  The basic reason is that it takes 3 numbers to describe a rotation in 3 dimensional space.  This is a special lucky property of the number 3. 

But when two of the gimbal's axes happen to be lined up, you get gimbal lock.   In other words: you lose the ability to rotate the inner gimbal a tiny bit in any way you want.   The reason is that in this situation, rotating one of the two aligned gimbals has the same effect on the inner gimbal as rotating the other!  

I've always found gimbal lock to be a bit mysterious, so I'm trying to demystify it here. 

As the wise heads at Wikipedia point out,

The word lock is misleading: no gimbal is restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals' axes there is no gimbal available to accommodate rotation along one axis.

Gimbal lock can actually be dangerous!  When it happens, or even when it almost happens, you lose some control over what's going on.

It caused a problem when Apollo 11 was landing on the moon.  This spacecraft had 3 nested gimbals on its inertial measurement unit. The engineers were aware of the gimbal lock problem but decided not to use a fourth gimbal.  They wrote:

"The advantages of the redundant gimbal seem to be outweighed by the equipment simplicity, size advantages, and corresponding implied reliability of the direct three degree of freedom unit."

They decided instead to trigger a warning when the system came close to gimbal lock.  But it didn't work right:

"Near that point, in a closed stabilization loop, the torque motors could theoretically be commanded to flip the gimbal 180 degrees instantaneously. Instead, in the Lunar Module, the computer flashed a 'gimbal lock' warning at 70 degrees and froze the inertial measurment unit at 85 degrees."

The spacecraft had to be manually moved away from the gimbal lock position, and they had to start over from scratch, using the stars as a reference.

After the Lunar Module had landed, Mike Collins aboard the Command Module joked:

"How about sending me a fourth gimbal for Christmas?"

Fun story!  But ultimately, it's all about math.  If you don't like math, stop reading here.

























Don't say I didn't warn you!

Puzzle: show that gimbal lock is inevitable with just 3 gimbals by showing that every smooth map from the 3-torus to SO(3) has at least one point where the rank of its differential drops below 3.

See what I mean?  Math.  This result shows not only that gimbal lock occurs with the setup shown here, but that any scheme of describing a rotation by 3 angles - or more precisely, 3 points on the circle - must suffer gimbal lock.

https://en.wikipedia.org/wiki/Gimbal_lock

#geometry___

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2016-07-08 08:08:55 (11 comments; 1 reshares; 43 +1s; )Open 

Adventures in Asia

I'm back in Singapore, the land of explosive cuisine.  This is the menu from our favorite Chinese restaurant.  It's on Southbridge Road across from the Sri Mariamman Temple - a popular Hindu temple where they do firewalking on the holiday called Theemithi.  Maybe they do it to cool down after eating here. 

I hadn't known it was called The Explosion Pot Barbecue.  They sell excellent barbecued fish, roast skewers of lamb with cumin, roast chives, dumplings, and other Szechuan delights.  The food is a bit spicy, but I haven't seen any exploding pots, so this may be a mistranslation of something that makes more sense in Chinese. 

As usual I'm working at the +Centre for Quantum Technologies and my wife +Lisa Raphals is teaching at the philosophy department at NUS.  You can see her in the background ordering ourfood.more »

Adventures in Asia

I'm back in Singapore, the land of explosive cuisine.  This is the menu from our favorite Chinese restaurant.  It's on Southbridge Road across from the Sri Mariamman Temple - a popular Hindu temple where they do firewalking on the holiday called Theemithi.  Maybe they do it to cool down after eating here. 

I hadn't known it was called The Explosion Pot Barbecue.  They sell excellent barbecued fish, roast skewers of lamb with cumin, roast chives, dumplings, and other Szechuan delights.  The food is a bit spicy, but I haven't seen any exploding pots, so this may be a mistranslation of something that makes more sense in Chinese. 

As usual I'm working at the +Centre for Quantum Technologies and my wife +Lisa Raphals is teaching at the philosophy department at NUS.  You can see her in the background ordering our food.

Meanwhile, my student +Blake Pollard is in a small town in the hills of Yunnan Province in southern China, helping teach some local students science, English... and American folk songs!  

This seems much more adventurous than what I'm doing.  But he has a good reason for doing it.   His great grandfather, Sam Pollard, was a Methodist missionary in this area - and he invented a script that is still used by the locals:

https://en.wikipedia.org/wiki/Pollard_script

The Miao are an ethnic group that includes the Hmong, Hmub, Xong, and A-Hmao.  These folks live in the borderlands of southern China, northern Vietnam, Laos, Myanmar and Thailand.  The A-Hmao had a legend about how their ancestors knew a system of writing but lost it. According to this legend, the script would eventually be brought back some day.  When Sam Pollard introduced his script for writing A-Hmao, it became extremely popular, and he became a kind of hero.  Blake and his family visited this part of China last year.  He enjoyed it a lot, so he decided to do some teaching there this summer. 

I hope to say more about both our adventures in a while...

Watch firewalking at the Sri Mariamman Temple:

https://www.youtube.com/watch?v=nxPuTKx3OEI

and if you live around here, check out the Explosion Pot Barbecue:

https://www.google.com/maps?daddr=1.282462,103.845405___

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