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Narendra Bharathi
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Narendra Bharathi

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A climate hero

This is Alberto Behar in Greenland with the robotic boat he designed.  How fast is Greenland melting due to global warming?  Where does the water go?  Some people sit around and argue.  Others go and find out.

It was very warm in Greenland from July 11th to 13th, 2012.  Scientists from NASA traveled by helicopter to study the melting ice.  They mapped rivers and streams over 5400 square kilometers of Greenland.   They found 523 separate drainage systems - small streams joining to form larger streams and rivers.

The water in every one of these flowed into a moulin!  A moulin is a circular, vertical shaft.  Water pours down the moulin and goes deep below the surface - sometimes forming a layer between ice and the underlying rock.  This layer can help glaciers slide down toward the ocean.  And this water reaches the ocean fast. 

In the area they studied, a total of between 0.13 and 0.15 cubic kilometers of water were flowing into moulins each day.  That's a lot!  That would be enough to drain 2.5 centimeters of water off the surface each day. 

To study the flow of water, Alberto Behar designed two kinds of remotely controlled boats.  One was a drone boat that measured the depth of the water and how much light it reflected, allowing the researchers to calibrate the depth of the surface water from satellite images. They used this boat on lakes and slow-flowing rivers.  But for dangerous, swift-flowing rivers, Behar developed disposable robotic drifters that measured the water's velocity, depth and temperature as they swept downstream.

Just a few days ago, Alberto Behar died in a plane crash.  The plane he was flying crashed shortly after he took off from a small airport near NASA’s Jet Propulsion Laboratory in Pasadena, California. 

So, his coauthors dedicated their paper on this research to him.  Here is is:

• Laurence C. Smith et al, Efficient meltwater drainage through supraglacial streams and rivers on the southwest Greenland ice sheet, Proc. Nat. Acad. Sci.,

Check out the cool images and maps.
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Cosmological billiards and spacetime crystals

In 1970, Belinksii, Khalatnikov and Lifschitz discovered that when you run time backwards toward the Big Bang, a homogeneous universe behaves like a billiard ball.  As you run time back, the universe shrinks, but also its shape changes.  Its shape moves around in some region of allowed shapes... and it 'bounces' off the 'walls' of this region!

These guys considered the simplest case: a universe with 3 dimensions of space and 1 dimension of time, containing gravity but nothing else.   In this case the region of allowed shapes is a triangle in the hyperbolic plane.  I showed it to you last time. 

So, running time backwards in this kind of universe is mathematically very much like watching a frictionless billiard ball bounce around on a strangely curved triangular pool table.

But you can play the same game for other theories: gravity together with various kinds of matter, in universes with various numbers of dimensions.  And when people did this, they discovered something really cool.   Different possibilities gave different kinds of pool tables!

When space has some number of dimensions, the pool table has dimension one less.   As far as I know, it's always sitting inside 'hyperbolic space', a generalization of the hyperbolic plane.  And it's always a piece of a hyperbolic honeycomb - a very symmetrical way of chopping hyperbolic space into pieces.  

The picture here, drawn by +Roice Nelson, shows a hyperbolic honeycomb in 3-dimensional hyperbolic space.   So, one tetrahedron in this honeycomb could be the 'pool table' for a theory of gravity where space has 4 dimensions.  (In fact it doesn't quite work like this: we have to subdivide each tetrahedron shown here into 24 smaller tetrahedra to get the 'pool tables'.  But never mind.)

Even better, these stunningly symmetrical patterns arise from what I called spacetime crystals.   The technical term is 'hyperbolic Dynkin diagrams', and I told you about them earlier.   The picture here, in 3 dimensions, arises from a spacetime crystal in 4 dimensions.  That's how it always works: the crystal has one more dimension than the pool table.

And here's the really amazing thing: mathematicians have proved that the highest possible dimension for a spacetime crystal is 10.   This gives you a 9-dimensional pool table, which is the sort of thing that could show up in a theory of gravity where space has 10 dimensions.

And there is a theory of gravity in where space has 10 dimensions:  it's called 11-dimensional supergravity, because there's also 1 dimension of time in this theory.   String theorists like this theory of gravity a lot, because it seems to connect all the other stuff they're interested in. 

It turns out this particular theory of gravity gives a spacetime crystal called E10.  There are several other 10-dimensional spacetime crystals, but this is the best.

For a while I've been thinking that we should be able to describe E10 using the octonions, an 8-dimensional number system that shows up a lot in string theory.  I had a guess about how this should work.   And last week, my friend the science fiction writer Greg Egan proved this guess is right!

For the details, go here:

This result probably came as no surprise to the real experts on cosmological billiards - I'm no expert, I just play a game now and then.   Here is a nice introduction by a real expert:

• Thibault Damour, Poincaré, relativity, billiards and symmetry,

And here are some more detailed papers:

• Thibault Damour, Sophie de Buyl, Marc Henneaux and Christiane Schomblond, Einstein billiards and overextensions of finite-dimensional simple Lie algebras,

• Axel Kleinschmidt, Hermann Nicolai, Jakob Palmkvist, Hyperbolic Weyl groups and the four normed division algebras,

#spnetwork arXiv:0805.3018 arXiv:hep-th/0206125 arXiv:hep-th/0501168 #gravity #geometry  
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I'm listening to a talk on the origin of life at a workshop on Biological and Bio-Inspired Information Theory.  The speaker said something like this... and I was amazed, again, at how wonderful living organisms are.

You can see videos of the talks here:

I gave a talk on "Biodiversity, entropy and thermodynamics":

but what really blew my mind was Naftali Tishby's talk on "Sensing and acting under information constraints - a principled approach to biology and intelligence":

It wasn't easy for me to follow - you should already know rate-distortion theory and the Bellman equation, and I didn't - but it's great!  It's all about how living organisms balance the cost of storing information about the past against the payoff of achieving their desired goals in the future.  It's not fluff: it's a detailed mathematical model!  And it ends by testing the model on experiments with cats listening to music and rats swimming to land.

Here's a good paper about this stuff:

• Naftali Tishby and Daniel Polani, Information theory of decisions and actions,

A conversation with Susanne Still convinced me even more that this is stuff I need to learn!  I hope to blog about it as I understand more.

In case you're wondering, rate-distortion theory is the branch of information theory that helps you find the minimum number of bits per second that must be communicated over a noisy channel so that the signal can be approximately reconstructed at the other end without exceeding a given distortion:

The Bellman equation lets you find an optimal course of action by optimizing what you do at each step:

#spnetwork doi:10.1007/978-1-4419-1452-1_19 #informationTheory #controlTheory #biology  
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Dear Google Now team, if you can make me one of these... That would be epic. Thanks, Ilya.
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Recent solar eclipse... from SPACE!

Did you miss the recent partial solar eclipse? Don't worry, the Hinode spacecraft has your back. Here's an image that Hinode took of the Moon passing completely in front of the Sun.
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This guy

Danny Macaskill: The Ridge:
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"Did The Saudis And The US Collude In Dropping Oil Prices?"
The oil price drop that has dominated the headlines in recent weeks has been framed almost exclusively in terms of oil market economics, with most media outlets blaming Saudi Arabia, through its OPEC Trojan horse, for driving down the price, thus causing serious damage to the world's major oil exporters – most notably Russia. While the market explanation is partially true, it is simplistic, and fails to address key geopolitical pressure points in...
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"60 Prominent Germans Appeal Against Another War In Europe: "It Is Not About Putin. What Is At Stake Is Europe""
Two weeks ago, as the S&P was preparing to surge on the latest round of all time high market-goosing algo trickery by the FOMC, 60 prominent German personalities from the realms of politics, economics, culture and the media were less concerned with blinking red and green stock quotes and were focused on something far more serious to the future of the world: the threat of war with Russia. In a letter published by Die Zeit, numerous famous and resp...
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Brain on psychedelic drugs shifts to a different order “...the brain does not simply become a random system after psilocybin injection, but instead retains some organizational features, albeit different from the normal state...” - according to new study.


Original article:


"Psychedelic substances can change a user’s mindset in profound ways — a fact that’s relevant even to those who’ve never touched the stuff, because such altered states of consciousness give scientists a window into how our brains give rise to our normal mental states. But neuroscientists are only beginning to understand how and why those mental changes occur.

Now some mathematicians have jumped into the fray, using a new mathematical technique to analyze the brains of people on magic mushrooms.

Psychedelic Puzzles

Scientists have known for decades that many of psychedelic drugs’ most famous effects — visual hallucinations, heightened sensory and emotional sensitivity, etc. — are linked to elevated levels of the neurotransmitter serotonin.

But increasingly neuroscience researchers are interested not just in single chemicals but also in overall brain activity, because the most complicated brain functions arise from lots of different regions working together. Over the last several years, a branch of mathematics known as network theory has been applied to study this phenomenon.

Paul Expert, a complexity researcher at the Imperial College London, and his team took this approach to analyzing fMRI data from people who’d taken psilocybin, the psychedelic chemical in magic mushrooms. The team had recently been working on a new technique for network modeling — one designed to highlight small but unusual patterns in network connectivity.

Brains on Drugs

The team used fMRI data from a previous study, in which 15 healthy people rested inside an fMRI scanner for 12 minutes on two separate occasions. The volunteers received a placebo in one of those sessions, and a mild dose of psilocybin during the other, but they weren’t told which was which.

The investigators crunched the data, specifically studying the brain’s functional connectivity — the amount of active communication among different brain areas.

They found two main effects of the psilocybin. First, most brain connections were fleeting. New connectivity patterns tended to disperse more quickly under the influence of psilocybin than under placebo. But, intriguingly, the second effect was in the opposite direction: a few select connectivity patterns were surprisingly stable, and very different from the normal brain’s stable connections.

This indicates “that the brain does not simply become a random system after psilocybin injection, but instead retains some organizational features, albeit different from the normal state,” the authors write in their paper in the Journal of the Royal Society Interface.

Far Out

The findings seem to explain some of the psychological experiences of a psilocybin trip. Linear thinking and planning become extremely difficult, but nonlinear “out of the box” thinking explodes in all directions. By the same token, it can become difficult to tell fantasy apart from reality during a psilocybin trip; but focusing on a certain thought or image — real or imagined — often greatly amplifies that thought’s intensity and vividness.

The authors suggest that effects like these may be rooted in the two connectivity traits they spotted, since the connectivity patterns that rapidly disperse may reflect unorganized thinking, while the stable inter-regional connections may reflect information from one sensory domain “bleeding” into other areas of sensory experience. In fact, the researchers also suggest that synesthesia — the sensory blurring that causes users of psychedelics to experience sounds as colors, for example — may be a result of these connectivity changes too.

The researchers hope that the patterns they’ve found will provide neuroscientists with new approaches for studying the brain on psychedelic drugs, and therefore better understand the strange psychological effects their users report."

 #drug #Psychedelic #brain #hallucination 
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Looping Lorentzian lattice

A rapidly moving observer will see time (the vertical axis) and space (the horizontal axis) in a different way than you do at rest.  As their speed increases  the warping increases. 

Each black dot is a point in spacetime.  As viewed by faster and faster observers, it moves along a hyperbola.  But after a while, the whole lattice of black dots gets back to the same pattern it started with!

The warpings of spacetime shown here are called Lorentz transformations.  Greg Egan made this movie to illustrate how we can do a Lorentz transformation to a lattice in spacetime and get back the same lattice.  This is the one of the symmetries that you get in what I was calling a 'spacetime crystal' - technically, a lattice coming from a hyperbolic Dynkin diagram:

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Patek Philippe 175th Anniversary 5175R Grandmaster Chime

Engineering Their Most Complicated Wristwatch Yet
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Is there a way to pocket Google+ post?
M-theory and octonions

My former student +John Huerta (at left) has just finished an amazing paper that I've got to tell you about!

You've probably heard rumors that superstring theory lives in 10 dimensions and something more mysterious called M-theory lives in 11.  You may have wondered why.  

In fact, there's a nice way to define superstrings in dimensions 3, 4, 6, and 10 - at least before you take quantum mechanics into account.  Of these theories, you can only consistently quantize the 10-dimensional version.   But never mind that.  What's so great about the numbers 3, 4, 6 and 10?

What's so great is that they're 2 more than 1, 2, 4, and 8.

If you try to set up a nice number system where you can add, multiply, subtract and divide, it only works in dimensions 1, 2, 4, and 8.  The real numbers form a line, and that's 1-dimensional.  The complex numbers form a plane, and that's 2-dimensional.  There are also more esoteric options: the quaternions are 4-dimensional, and the octonions are 8-dimensional.  When you try to go beyond these, you lose the law that

|xy| = |x| |y|

and things aren't so nice.

I've spent decades studying the quaternions and octonions, just because they're weird and interesting.  Why do the dimensions double each time in this game?  I've learned the answer, and I could tell you - but it might shatter your brain.  What happens if you go further, to dimension 16?  I've learned a bit about that too, though I bet there are big mysteries still lurking here. 

I also learned that being an expert on this stuff does not make you popular at parties.

One cool thing is this.  A string is a curve, so it's 1-dimensional, but as time passes it traces out a 2-dimensional surface.  So, if we have a string floating around in some spacetime, we've got a 2-dimensional surface together with some extra dimensions of spacetime.   

But for the string to be 'super' - for it to have supersymmetry, a symmetry between bosons and fermions - we need a certain special equation to be true.  And it's true precisely when we can take the extra dimensions and think of them as one of our nice number systems.  

So, we need 1, 2, 4 or 8 extra dimensions.  So the total dimension of spacetime needs to be 3, 4, 6, or 10.

(That's a very rough sketch of a complicated argument, of course.  I'm leaving out the details, but later I'll show you where to find them.)

We can also look at theories of 'branes', which are like strings but higher-dimensional.  Instead of a curve, a 2-brane is a 2-dimensional surface.  As time passes, it traces out a 3-dimensional surface.  So, if we have a 2-brane floating around in some spacetime, we've got a 3-dimensional surface together with some extra dimensions of spacetime.   And it turns out that 2-branes can also have supersymmetry when the extra  dimensions can be seen as one of our nice numbers systems!

So now the total dimension of spacetime needs to be 3 more than 1, 2, 4, and 8.  It needs to be 4, 5, 7 or 11.

When we take quantum mechanics into account it seems that the 11-dimensional theory works best... but the quantum aspects are still mysterious, murky and messy compared to superstring theory, so it's called M-theory.

There's stuff we don't understand, and stuff we do.  In his new paper, John Huerta has pushed forward the line separating the two.  He's shown that using the octonions we can build a 'super-3-group', an algebraic structure that seems just right for understanding the symmetries of supersymmetric 2-branes in 11 dimensions.  

I could say a lot more, but it's better if you read this:

• John Baez and John Huerta, The strangest numbers in string theory,

This is a fun and easy article about this stuff, which we wrote for Scientific American.  

Then, if that's too easy, try this:

• John Baez and John Huerta, Division algebras and supersymmetry I,

Here we get into the details, and explain the special equation that makes superstrings work nicely in 3, 4, 6, and 10 dimensions - and how it follows from having a nice number system in dimensions 1, 2, 4 and 8.  This stuff was known before, but not explained all in one place.

Next, try this:

• John Baez and John Huerta, Division algebras and supersymmetry II,

Here we explain the special equation that makes supersymmetric 2-branes work in dimension 4, 5, 7 and 11.  More importantly, we start studying how the symmetries of superstrings and super-2-branes come out of the nice number systems.  Physicists use gadgets called 'Lie algebras' to study symmetry... so they should like these generalizations, called 'Lie 2-superalgebras' and 'Lie 3-superalgebras'.

Next, try this:

• John Huerta, Division algebras and supersymmetry III,

At this point John Huerta sailed off on his own!  

Physicists like Lie algebras, but what they really love are 'Lie groups'.  Lie algebras are just a trick for studying Lie groups: it's the groups that directly describe symmetry.  In this paper John cooked up the 'Lie 2-supergroups' that govern classical superstrings in dimensions 3, 4, 6 and 10.  Just as a group is a special sort of category, a 2-group is a special sort of 2-category.  So at this point John got into 'higher category theory' - one of my favorite subjects.

And here's his new paper, the last of the series:

• John Huerta, Division algebras and supersymmetry IV,

Here John built the 'Lie 3-supergroups' that govern classical super-2-branes in dimensions 3, 4, 6 and 10.  A 3-group is a special sort of 3-category.  

I really love how the math of superstrings and M-theory emerge nicely from combining the octonions with higher category theory. In case you're wondering: I have no strong opinion about whether these ideas apply to our physical universe.  I see no convincing experimental evidence in favor of string theory or M-theory.  All I know is that they're beautiful.  

Maybe they apply to some other universes that are less messed-up than ours.  Maybe we're in some sort of purgatory for species who still need to learn basic math.  If so, John Huerta just placed out.  :-)

#spnetwork arxiv:1409.4361 #octonions #superstrings #Mtheory
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