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Ramon Pla
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The ones you're not looking at turn clockwise

Look at either the red dot or the yellow dot.  The circles near that dot will turn counterclockwise.  The ones you're not looking at turn clockwise!

Or: let your eyes bounce back and forth between the two.

Or: look away from both of them.

Puzzle: how does it work?

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Ten kinds of matter

A cool discovery: substances can be divided into 10 kinds.

The basic idea is pretty simple.  Some substances have time-reversal symmetry: they would look the same, even on the atomic level, if you made a movie of them and ran it backwards.  Some don't - these are more rare, like certain superconductors made of yttrium barium copper oxide!   The substances that do have time reversal symmetry have a symmetry operator T that can square to 1 or to -1: please take my word for this, it's a quantum thing.  So, we get 3 choices, which are listed in the chart under T as 1, -1, or 0 (no time reversal symmetry).

Similarly, some substances have charge conjugation symmetry, meaning a symmetry where we switch particles and holes: places where a particle is missing.  The 'particles' here can be rather abstract things, like phonons - little vibrations of sound in a substance, which act like particles - or spinons - little wiggles in the spin of electrons.  Basically any sort of wave can, thanks to quantum mechanics, also act like a particle.  And sometimes we can switch particles and holes, and a substance will act the same way!

The substances that do have charge conjugation symmetry have a symmetry operator C that can square to 1 or to -1.  So again we get 3 choices, listed in the chart under C as 1, -1, or 0 (no charge conjugation symmetry).

So far we have 3 × 3 = 9 kinds of matter.  What is the tenth kind? 

Some kinds of matter don't have time reversal or charge conjugation symmetry, but they're symmetrical under the combination of time reversal and charge conjugation!  You switch particles and holes and run the movie backwards, and things look the same! 

This chart shows a 1 under the S when your matter has this combined symmetry, and 0 when it doesn't.  So, 0 0 1 is the tenth kind of matter (the second row in the chart).

This stuff was first discovered around 1997 by Altland and Zirnbauer.  But it's just the beginning of an amazing story.  Since then people have found substances called topological insulators that act like insulators in their interior but conduct electricity on their surface.   We can make 3-dimensional topological insulators, but also 2-dimensional ones (that is, thin films) and even 1-dimensional ones (wires).  And we can theorize about higher-dimensional ones, though this is mainly a mathematical game.

So we can ask which of the 10 kinds of substance can arise as topological insulators in various dimensions. And the answer is: in any particular dimension, only 5 kinds can show up. This chart shows how it works for dimensions 1 through 8.  The kinds that can't show up are labelled 0. 

(There's more information in this chart, which I'm too lazy to explain now.)

If you look at the chart, you'll see it has some nice patterns.  And it repeats after dimension 8.  In other words, dimension 9 works just like dimension 1, and so on.

There is a huge amount of cool math lurking here, and you can see some more in my blog article:

This math is called the ten-fold way.

The chart here comes from the paper that showed only 5 kinds of topological insulator are possible in each dimension:

• Shinsei Ryu, Andreas P Schnyder, Akira Furusaki, and Andreas W. W. Ludwig,  Topological insulators and superconductors: tenfold way and dimensional hierarchy, New J. Phys. 12 (2010) 065010,

#spnetwork arXiv:0912.2157 #must_read #condensed_matter #topology

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I really enjoy posting fun stuff here.  But this is serious.

Steve Easterbrook just finished writing a series of important posts on Azimuth, summarizing part of the IPCC report on climate change.  Here's a short version of his last post.  Pay attention!


To stay below 2°C of warming, most fossil fuels must stay buried in the ground.

Perhaps the most profound advance since the previous IPCC report is a characterization of our global carbon budget. This is based on a finding that has emerged strongly from a number of studies in the last few years: the expected temperature change has a simple linear relationship with cumulative CO2 emissions since the beginning of the industrial era.

The chart is hard to follow, but the main idea is this: whatever we do, the results tend to lie on a straight line on this graph. You do get a slightly different slope in one case, “1% percent CO2 increase per year", where only CO2 rises - and much more slowly than it has over the last few decades.  But all the more realistic scenarios lie in the orange band, and all have about the same slope.

This is a useful insight, because it means that for any target ceiling for temperature rise - like the UN’s commitment to not allow warming to rise more than 2°C above pre-industrial levels - we can easily estimate the total amount of carbon we can spew into the atmosphere:

• To give us a one third (33%) chance of staying below 2°C of warming over pre-industrial levels, we cannot ever emit more than 880 gigatonnes of carbon.

• To give us a 50% chance, we cannot ever emit more than 840 gigatonnes of carbon.

• To give us a 66% chance, we cannot ever emit more than 800 gigatonnes of carbon.

Since the beginning of industrialization, we have already emitted a little more than 500 gigatonnes. So, our remaining budget is somewhere between 300 and 400 gigatonnes of carbon.

Existing known fossil fuel reserves are enough to release at least 1000 gigatonnes. New discoveries and unconventional sources will likely more than double this.

That leads to one conclusion:

Most of our remaining carbon reserves must never reach the atmosphere.

We’ve never done that before. There is no political or economic system anywhere in the world currently that can persuade an energy company to leave a valuable fossil fuel resource untapped. There is no government in the world that has demonstrated the ability to forgo the economic wealth from natural resource extraction, for the good of the planet as a whole. We’re lacking both the political will and the political institutions to achieve this. Finding a way to achieve this presents us with a challenge far bigger than we ever imagined.


Red Steve's whole series of posts starting here:

Each post summarizes a key finding of the IPCC Working Group 1 report on climate change, released last year.  These findings are:

1. The warming is unequivocal.

2. Humans caused the majority of it.

3. The warming is largely irreversible.

4. Most of the heat is going into the oceans.

5. Current rates of ocean acidification are unprecedented.

6. We have to choose which future we want very soon.

7.  To stay below 2°C of warming, the world must become carbon negative.

8.  To stay below 2°C of warming, most fossil fuels must stay buried in the ground.

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