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Narendra Bharathi
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Narendra Bharathi

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All of us are familiar with overflow bugs. However, sometimes you write code that counts on overflow. This is a story where overflow was supposed to happen but didn't, hence the name underflow bug. Round-robin In our Java implementation of the…
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Narendra Bharathi

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Thanks to +Steven Vaughan-Nichols, I have successfully recovered another koan of Master Foo.  Enjoy.
On one otherwise tranquil morning Master Foo's meditations were disturbed by cries of distress. Finding that they came from one of the novices, he inquired "What is the difficulty here?" The novice replied, "I am frustrated by my tools. Every day I must use many different editors because neither ...
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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., http://www.pnas.org/content/early/2015/01/07/1413024112.full.pdf

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:

https://golem.ph.utexas.edu/category/2014/11/integral_octonions_part_7.html

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, http://arxiv.org/abs/hep-th/0501168.

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, http://arxiv.org/abs/hep-th/0206125.

• Axel Kleinschmidt, Hermann Nicolai, Jakob Palmkvist, Hyperbolic Weyl groups and the four normed division algebras, http://arxiv.org/abs/0805.3018.

#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:

http://www.birs.ca/videos/2014

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

http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410291038-Baez.mp4

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":

http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281032-Tishby.mp4

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, http://www.cs.huji.ac.il/labs/learning/Papers/IT-PAC.pdf

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:

 https://en.wikipedia.org/wiki/Rate-distortion_theory

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

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

#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.

http://www.cfa.harvard.edu/news/2014-27
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"Did The Saudis And The US Collude In Dropping Oil Prices?" http://www.zerohedge.com/news/2014-12-24/did-saudis-and-us-collude-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"" http://www.zerohedge.com/news/2014-12-26/60-prominent-germans-appeal-against-another-war-europe-it-not-about-putin-what-stake
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.

SOURCES:

Original article:
http://rsif.royalsocietypublishing.org/content/11/101/20140873.full

Popular:
http://blogs.discovermagazine.com/d-brief/2014/10/29/brain-psychedelic-drugs

"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:

https://plus.google.com/u/0/117663015413546257905/posts/6MEi2TAvPaS

#geometry  
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