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John Baez
Works at Centre for Quantum Technologies
Attended Massachusetts Institute of Technology
Lives in Riverside, California
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John Baez

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+rasha kamel of the +Azimuth Project pointed us to a report in Science Daily which says:

Planet Earth experienced a global climate shift in the late 1980s on an unprecedented scale, fueled by anthropogenic warming and a volcanic eruption, according to new research. Scientists say that a major step change, or ‘regime shift,’ in Earth’s biophysical systems, from the upper atmosphere to the depths of the ocean and from the Arctic to Antarctica, was centered around 1987, and was sparked by the El Chichón volcanic eruption in Mexico five years earlier.

That got me curious, so I read the actual paper this rather sensationalized report is based on. For more, visit my blog!
There's no reason that the climate needs to change gradually. Recently scientists have become interested in regime shifts, which are abrupt, substantial and lasting changes in the state of a comple...
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good article.
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I've been staying at home for the last two days writing a paper about information and entropy in biological systems.  My wife is away, and I'm trying to keep distractions to a bare minimum, trying to get into that state where I'm completely absorbed, there's always something to do, and it's lots of fun.  That's what I love about writing.  At first I feel stuck, frustrated.  But gradually the ideas start falling into place - and once they do, I don't want to be anywhere else!  

This state is called flow, and it's great.  But life can't be all flow, it seems.

I like this chart.  I like any chart that takes psychology and maps it down to a few axes in a reasonably plausible way.  I don't have to 'believe in it' to enjoy a neat picture that pretends to tame the wild mess of the soul. 

Apparently this chart goes back to Mihaly Csikszentmihaly's theory of 'flow'.  According to Wikipedia:

In his seminal work, Flow: The Psychology of Optimal Experience, Csíkszentmihályi outlines his theory that people are happiest when they are in a state of flow— a state of concentration or complete absorption with the activity at hand and the situation. It is a state in which people are so involved in an activity that nothing else seems to matter.  The idea of flow is identical to the feeling of being in the zone or in the groove. The flow state is an optimal state of intrinsic motivation, where the person is fully immersed in what he is doing. This is a feeling everyone has at times, characterized by a feeling of great absorption, engagement, fulfillment, and skill—and during which temporal concerns (time, food, ego-self, etc.) are typically ignored.

In an interview with Wired magazine, Csíkszentmihályi described flow as "being completely involved in an activity for its own sake. The ego falls away. Time flies. Every action, movement, and thought follows inevitably from the previous one, like playing jazz. Your whole being is involved, and you're using your skills to the utmost."

Csikszentmihályi characterized nine component states of achieving flow including “challenge-skill balance, merging of action and awareness, clarity of goals, immediate and unambiguous feedback, concentration on the task at hand, paradox of control, transformation of time, loss of self-consciousness, and autotelic experience.”

What does autotelic mean?  It seems to mean 'internally driven', as opposed to seeking external rewards.  Csíkszentmihályi says "An autotelic person needs few material possessions and little entertainment, comfort, power, or fame because so much of what he or she does is already rewarding."  Anyway, back to the Wikipedia article:

To achieve a flow state, a balance must be struck between the challenge of the task and the skill of the performer. If the task is too easy or too difficult, flow cannot occur. Both skill level and challenge level must be matched and high; if skill and challenge are low and matched, then apathy results.

But in this chart, 'apathy' is just one of 8 options, the one diametrically opposite to 'flow'.  I like the idea of how 'relaxation' is somewhere between flow and boredom, but I'm not sure it feels next to 'control'. 

It's all very thought-provoking.  We have these different modes, or moods, and we bounce between them without very much thought about what they're for and what's the overall structure of the space of these moods.

Moods seem like the opposite of mathematics and logic, but there's probably a science of moods which we haven't fully understood yet - in part because when we're in a mood, it dominates us and prevents us from thinking about it analytically.
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+James Lamb, my experience in meditation suggests that there is a kind of unison that can be achieved, but it's not between these personae you are identifying as the various selves.   It's between the various parts of the mind that generally are all processing different stuff, so that it can filter up out of the unconscious and gain attention, and possibly get used.

Just as information filters up from the attention, it also filters down, and it's possible to get some of the various parts of your mind working together on the same problem rather than churning on different problems.   It's a fairly amazing experience.

But it has nothing to do with integrating those personae.   They are quite useful, and since they share the same substrate, there's no need to unify one, any more than you need to unify all the clothes in your closet into a single outfit.

There's some evidence that they are useful, for example, in learning new languages: each language becomes a persona, and when you wear the persona of a particular language, you just naturally speak as well as you can in that language.   If you try to learn the language without giving it a new persona, then it's very difficult to make progress, because everything has to be translated--nothing is spontaneous.

I don't know if this particular theory has been rigorously studied, so it may be total hogwash, but it matches my own experience of language.
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Miniature atoms

In The Incredible Shrinking Man, a guy exposed to radiation becomes smaller and smaller.   Eventually he realizes he'll shrink forever - even down to subatomic size.  Of course that's impossible.  But guess what: we can now make miniature atoms!

In fact we can make atoms almost like hydrogen, but 1/186 times as big across.  Unfortunately they only last 2 microseconds.  But that's still long enough for them to form molecules, and for us to do chemical experiments with them.  Chemists have gotten really good at this stuff.

The trick is to take the electron in a hydrogen atom and replace it with a muon.  This is a particle 207 times heavier than an electron, but otherwise very similar.  Unfortunately a muon has a half-life of just 2 microseconds: then it decays into an electron and some other crud.  

Why is an ordinary hydrogen atom the size it is, anyway?  It's the uncertainty principle.  The atom is making its energy as small as possible while remaining consistent with the uncertainty principle.  

A hydrogen atom is made of an electron and a proton.  If it were bigger, its potential energy would increase, because the electron would be further from the proton.  So, the atom "wants to be small".  And without quantum mechanics to save it, it would collapse down to a point: The Incredible Shrinking Atom.

But if the atom were smaller, you'd know the position of its particles more precisely - so the uncertainty principle says you'd know their momentum less precisely.  They'd be wiggling around more wildly and unpredictably  So the kinetic energy would, on average, be higher.  

So there's a tradeoff!  Too big means lots of potential energy.  Too small means lots of kinetic energy.  Somewhere in the middle is the best - and you can use this to actually calculate how big a hydrogen atom is!   

But what if you could change the mass of the electron?  This would change the calculation.  It turns out that making electrons heavier would make atoms smaller!  

While we can't make electrons heavier, we can do the next best thing: use muons.

Muonic hydrogen is a muon orbiting a proton.  It's like an atom, but much smaller than usual, so it does weirdly different things when it meets an ordinary atom.  It's a whole new exotic playground for chemists.  

And, you can do nuclear fusion more easily if you start with smaller atoms!  It's called muon-catalyzed fusion, and people have really done it.  The only problem is that it takes a whole lot of energy to make muons, and they don't last long.  So, it's not practical - it doesn't pay off.  At least not yet.  Maybe we just need a few more brilliant ideas:

By the way: a while ago I talked about making a version of hydrogen where we keep the electron and replace the proton by a positively charged antimuon.  That's called muonium.  Muonium is lighter than ordinary hydrogen but almost the same size, just a tiny bit bigger.  It's chemically almost the same as hydrogen, except that it decays in 2 microseconds.  

With muonic hydrogen it's the reverse: it's a lot smaller, but it's just a bit heavier.  It's chemically very different from ordinary hydrogen.

Finally, for the übernerds:

If you do the calculation, you can show that the radius of a hydrogen-like atom is proportional to


where m is the mass of the lighter particle and M is the mass of the heavier one.  If we say an electron has mass 1, then a muon has mass 207 and a proton has mass 1836.  You can use this formula to see that muonic hydrogen has a radius 1/186 as big as ordinary hydrogen, while muonium has a radius 1.004 times as big.  
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+قا بهنام‬‎‎ - Those are good papers; you can find newer papers on Dirac structures on the arXiv:

so you should look at all of them and see what you like.

I like this one because I'm interested in "higher structures":
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Last night I saw a UFO

My wife and I were walking to a friend's house shortly after sunset when we saw something amazing.

It started out as a yellow-orange dot in the sky, too bright to be an ordinary plane, moving very slowly.  I thought it might be a helicopter, but no - it was perfectly silent.  

Then it seemed to shine a green beam of light to its left.  Then it grew bright white, and then it expanded.  I was scared for a second, but after expanding to roughly twice the size of a full moon it stopped growing.  It looked like a searchlight shining through the mist had just turned towards us!  This was very confusing, because the sky was not misty.

Then it gradually dimmed, and a blue streak formed to its left.  At this point we were standing in front of our friends' house, and I kept wanting to call them out, but not wanting to miss what would happen next.  When it had almost faded out, we called them and they saw it.

We went inside, and then some other friends came in - very excited about the amazing UFO they had seen!   We discussed it for a while, and I gradually realized that none of my explanations of this phenomenon made sense.  I was excited, but annoyed that I might never understand what I had seen.

Luckily, thousands of other people saw it too.  It was much higher up than I thought. 

Puzzle: what was it?  Watch the video here and try to guess!

If you give up, read this:

I'm very happy that I saw this strange event and found out what it was. 
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+JDS Purohit - if the sighting was inexplicable, I probably wouldn't have written about it.  I was thinking about that on Saturday night, after I saw the "UFO" and before I learned that thousands of people had seen it.  Maybe I should have written about it, but I probably wouldn't have.
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Pulsar planets

When a big star runs out of fuel, its core collapses and its outer layers explode into space.  If it's not too big, its core becomes a big ball of neutrons.  And if the resulting neutron star is spinning fast and emitting lots of radiation from its north and south magnetic poles, we call it a pulsar.  It's called that because you see a pulse of radiation as it spins.

A pulsar is an amazing thing.  Imagine something twice as heavy as our Sun, only 20 kilometers across, spinning around 1000 times a second, shooting out beams of radiation!  

Now, imagine a planet near a pulsar: a dead world raked by intense radiation.  It would be a strange, intensely alien place.

But in fact, the first planets to be discovered outside our solar system were pulsar planets!  The reason is that pulsars keep time very accurately: the pulses are like the ticks of a clock.  By detecting slight irregularities, we can tell if a pulsar is getting pulled back and forth by an orbiting planet.
In 1992, Aleksander Wolszczan and Dale Frail found the first planets outside our solar system: two planets orbiting a pulsar named PSR B1257+12.  One is 4 times as heavy as the Earth, and it orbits the pulsar every 66 days.  The other is just a bit heavier than the Earth, and it orbits every 99 days.

It seems these planets were formed from the debris of a companion star that used to orbit the pulsar.  This star would have been destroyed by the huge explosion that formed the pulsar, called a supernova.

There's another pulsar planet that's very different.  It's very close to a pulsar named PSR J1719-1438.  It's so close that its orbit would fit inside our Sun, and it orbits the pulsar once every two hours.  

It seems to have the mass of Jupiter, but a diameter just 4 times that of our Earth.  If so, it must be extremely dense: a bit more dense than platinum!   

What could it be?  People think it's the remains of a white dwarf star whose outer layers were blasted away by the supernova that formed the pulsar.  If so, it could be made mostly of carbon and oxygen - leftover elements that the white dwarf wasn't able to burn.

In fact, it might even be similar to an enormous high-density diamond, so it's been nicknamed The Diamond Planet.  But nobody is sure.

The picture here is from NASA, and it's an artist's impression of the planets orbiting PSR 1257+12.  For more, see:

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+John Baez, +Manuel Schneider, of course, powerful though radiating pulsars are, they're nowhere near as terrifying as newborn pulsars (particularly the  are hypothesised to be for the first few seconds to minutes of their lives. We're talking a magnetic field so intense it polarizes spacetime and a rotation rate just under that at which the thing would fly apart (!)... it loses this rotation very fast: the rotation and insane magnetic field are coupled together by the (rotation-induced) motion of stellar masses of material about once a millisecond from deep within the pulsar to fairly near its surface.

Obviously this sort of thing, more or less accelerating and decelerating stars to great velocities every millisecond or so, saps the rotation fast: it cools and solidifies (or solidifies more than that, anyway) within seconds, and the crazy magnetic field dissipates. (As for what form this circulating material is in, one paper describes it as being in "an unclear state", which I thought was turning "we haven't worked this out" and making a nice pun out of it.)

(The papers were talking about the formation of magnetars, and hypothesising that all pulsars start that way: it's just that some are lucky enough to keep more of the field than others.)
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The Balaban 11-cage

An n-cage is a graph - a bunch of dots connected by edges - where:

1) every dot has 3 neighbors,

2) the shortest cycle of edges that gets you back where you started has length n,


3) the graph has as few dots as possible while meeting conditions 1) and 2).

The last condition makes cages rather special, and the small ones tend to be connected to other pieces of beautiful mathematics.

In 1973, the Romanian graph theorist Balaban discovered the 11-cage shown here.   It has 112 edges and 168 edges.

Puzzle 1: Why is the number 168 important in mathematics?  And no, it's not because 168 = 24 x 7 is the number of hours in a week.

Puzzle 2: Does the mathematical significance of the number 168 shed some light on the Balaban 11-cage?

In 2003, McKay and Myrvold proved that the Balaban 11-cage is the only 11-cage. By contrast, there are three different 10-cages.  One was discovered by Balaban, and then two others were found by Harries and Wong.  Those two are shown here:

and the cool part is that they're similar.

You can define a spectrum of a graph, which is a bit like the spectrum of an atom: it says at what frequencies the graph would vibrate if it were elastic.  The two 10-cages found by Harries and Wong have the same spectrum!  This is one of several nice examples of different things that have the same spectrum. 

I think the Balaban 11-cage would make a very nice pattern for a tribal rug like the ones made in Central Asia.  But this picture was not created by a weaver in Afghanistan; it was created by 'Koko90' and put on Wikicommons under a Creative Commons Attribution-Share Alike 3.0 Unported license.
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It's a good design 
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What does ISIS want?

Why did ISIS make these seemingly absurd attacks on Paris and a Russan plane? How can it possibly help them to have both Europe and Russia motivated to annihilate them?

To find out, we can start by reading what they say. They could be lying, but still....

They say they want to destroy the "gray zone" of tolerance where Muslims and "infidels" can peacefully coexist. They want to bring about a war against Muslims worldwide, to force Muslims into their arms. And they want conditions in predominantly Muslim nations to deteriorate, to create lawless zones that they can occupy.

Shortly after the Charlie Hebdo attacks in Paris, ISIS put out this statement:

“The world today is divided into two camps. Bush spoke the truth when he said, ‘either you are with us or you are with the terrorists.’ Meaning either you are with the crusade or you are with Islam.

In their English-language magazine Dabiq, they went further and predicted the "extinction" of the "gray zone":

The Muslims in the West will quickly find themselves between one of two choices, they either apostatize and adopt the kufrī [infidel] religion propagated by Bush, Obama, Blair, Cameron, Sarkozy, and Hollande in the name of Islam so as to live amongst the kuffār [infidels] without hardship, or they perform hijrah [emigrate] to the Islamic State and thereby escape persecution from the crusader governments and citizens... Muslims in the crusader countries will find themselves driven to abandon their homes for a place to live in the Khilāfah [caliphate], as the crusaders increase persecution against Muslims living in Western lands so as to force them into a tolerable sect of apostasy in the name of 'Islam' before forcing them into blatant Christianity and democracy.

In 2004, an Al Qaeda strategist named Abu Bakr Naji put out a book called Management of Savagery. I haven't read this book - it may not be translated into English - but here's what Wikipedia says about it:

Management of Savagery discusses the need to create and manage nationalist and religious resentment and violence in order to create long-term propaganda opportunities for jihadist groups. Notably, Naji discusses the value of provoking military responses from superpowers in order to recruit and train guerilla fighters and to create martyrs. Naji suggests that a long-lasting strategy of attrition will reveal fundamental weaknesses in the ability of superpowers to defeat committed jihadists.

Management of Savagery argues that carrying out a campaign of constant violent attacks in Muslim states will eventually exhaust their ability and will to enforce their authority, and that as the writ of the state withers away, chaos—or "savagery"—will ensue. Jihadists can take advantage of this savagery to win popular support, or at least acquiescence, by implementing security, providing social services, and imposing Sharia. As these territories increase, they can become the nucleus of a new caliphate. Naji nominated Jordan, Saudi Arabia, Yemen, North Africa, Nigeria and Pakistan as potential targets, due to their geography, weak military presence in remote areas, existing jihadist presence, and easy accessibility of weapons.

Naji professes to have been inspired by Ibn Taymiyya, the influential 14th century Islamic scholar and theologian.

A number of media outlets have compared the attempts by the Islamic State of Iraq and the Levant to establish territorial control in Iraq and Syria with the strategy outlined in Management of Savagery. The premier issue of the Islamic State's online magazine, Dabiq, contained discussion of guerrilla warfare and tactics that closely resembled the writings and terminology used in Management of Savagery, although the book was not mentioned directly. Journalist Hassan Hassan, writing in The Guardian, reported an ISIL-affiliated cleric as saying that Management of Savagery is widely read among the group’s commanders and some of its rank-and-file fighters. It was also mentioned by another member of ISIL in a list of books and ideologues that influence the group.

You can read issues of Dabiq at the Clarion Project website:

It pays to know your enemy.

The Wikipedia article on Management of Savagery:

I found the quotes from Dabiq here:
All of the issues of the Islamic State's glossy propaganda magazine 'Dabiq,' named after a key site in Muslim apocalypse mythology can be found here.
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+Andrew Miloradovsky - On the radio I heard about a recent book about the "business model" of ISIS and other terrorist organizations.  Unfortunately I haven't been able to recall or find the title.  A business perspective might be interesting.
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Elliptic functions

You probably know about the sine and cosine.  These are the most basic functions that are periodic:

sin(x + 2π) = sin(x)

Elliptic functions are functions of two variables, x and y, that are periodic in two directions:

f(x + 2π,y) = f(x,y)


f(x,y + 2π) = f(x,y)

This movie is a way of illustrating an elliptic function.

What makes elliptic functions so special is that you can think of them as functions of a single complex variable:

z = x + iy

and then they have a derivative in the special sense you learn about in a course on complex functions!

It's a lot harder for a complex function to have a derivative than an ordinary real function.  A function like

f(x,y) = sin(x) sin(y)

is periodic in two directions, but it doesn't have a derivative df/dz.  Mysterious as this may sound, this is the reason elliptic functions are so special.

In the late 1800s, all the best mathematicians thought about elliptic functions, so there are 'Jacobi elliptic functions' and 'Weierstrass elliptic functions' and many more.  Now they're less popular, but they're still incredibly important.  You need to think about them if you want to deeply understand how long the perimeter of an ellipse is.  They're also important in physics, and fundamental to the proof of Fermat's Last Theorem.

+Gerard Westendorp has been making mathematical illustrations for a long time, so if you like such things, circle him!

An elliptic function actually has a derivative everywhere except at certain points where the function 'blows up' - that is, becomes infinite.  These points are called poles.   You can prove an elliptic function has to have poles unless it is constant (and thus too boring to talk about). 

Because an elliptic function is periodic in two directions, its poles make a repeating pattern in the plane, which you can see in this movie.  The poles are the points from which checkerboard pattern keeps expanding outward.  The zeros of the elliptic function - the points where it's zero - are the points where the checkerboard keeps shrinking inward.

For more on elliptic functions, you could try this:

It's a bit scary: for example, instead of saying a function has a derivative except at points where it blows up, they say it's meromorphic.    It means the same thing, but it's shorter and it makes you sound more educated.
A Jacobi elliptic function. This time The checkerboard pattern is animated only over magnitude, not phase, so that the squares appear to originate from… - Gerard Westendorp - Google+
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Thanks +John Baez . I've been studying these for a couple of years to help understand image forces in particle accelerators. They haven't helped as each solution seems to contain an expression more complex than what I started with... Will keep at it however! Lovely illustrations.
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Which do you like best?

+Jacob Biamonte and I wrote a book, and now we have an artist designing the cover.  Which one do you like best, and how could it be improved? 

The wolf-rabbit theme is important in the book, since we show how interactions between predators and prey can be modeled using ideas from quantum physics.  Tracks of rabbits and wolves in the snow look a bit like particle tracks in a cloud chamber. 

You can read the book here:

Quantum Techniques for Stochastic Mechanics

and you can see rabbit and wolf tracks forming a Feynman diagram on page 13.
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The cover with the wolf and bunny reminds me of a standard high school / undergrad textbook.  This may not be a bad thing though, because you could potentially lure some readers in to a more challenging book than they may have expected based on the friendly-looking cover.  So my answer is that it depends on who you want your audience to be.  I think you would reach out to a wider audience with wolf/bunny cover. If you are mainly reaching out to experts in this field, then I'd choose the dark colored one.  
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Superionic ice

There are over 15 kinds of ice.  Different kinds are stable at different pressures and temperatures.  Some of the weirdest may exist inside ice giants: planets like Uranus and Neptune, which have also been found orbiting other stars.  Most of what we know about these kinds of ice comes from computer simulations, since they only exist at very high pressures.

They're called superionic ices, because while the oxygen atoms get locked in a crystal structure, the hydrogen atoms become ionized, breaking apart into protons and electrons.  The protons can then move around like a liquid between the oxygen atoms!  

The first phase of superionic ice was predicted in 1999 by a group of Italian scientists.   They predicted that this ice exists at pressures 500,000 times the atmospheric pressure here on Earth, and temperatures of a few thousand Kelvin.  In this kind of ice, the oxygen atoms form a crystal called a body centered cubic.

In 2012, Hugh F. Wilson, Michael L. Wong, and Burkhard Militzer predicted the new phase shown here.  This may show up above 1,000,000 times atmospheric pressure.  The oxygen atoms, shown as blue spheres, form a pattern called a face centered cubic.  The protons are likely to be found in the orange regions.

Hugh Wilson said:

Superionic water is a fairly exotic sort of substance.  The phases of water we're familiar with all consist of water molecules in various arrangements, but superionic water is a non-molecular form of ice, where hydrogen atoms are shared between oxygens. It's somewhere between a solid and a liquid—the hydrogen atoms move around freely like in a liquid, while the oxygens stay rigidly fixed in place. It would probably flow more like a liquid, though, since the planes of oxygen atoms can slide quite freely against one another, lubricated by the hydrogens.

These simulations are hard, and newer papers are reporting different results.  You can also try to make superionic ice in the lab, but that's even harder!   In 2005 Laurence Fried tried to make it at the Lawrence Livermore National Laboratory in California.  He smashed water molecules between diamond anvils while simultaneously zapping it with lasers.  He seemed to find evidence for superionic ice.

Eventually theory and experiment will converge on the truth.  Only then will we understand the hearts of the ice giants.

You can read more here:

and for some even newer results, try this:

Here's the paper on the first kind of superionic ice:

• C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, M. Bernasconi, and M. Parrinello, Superionic and metallic states of water and ammonia at giant planet conditions, Science 283 (1999), 44-46.  Available free with registration at

and here's the second kind:

• Hugh F. Wilson, Michael L. Wong, Burkhard and Militzer, Superionic to superionic phase change in water: consequences for the interiors of Uranus and Neptune.  Available free at

#spnetwork arXiv:1211.6482 #ice
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That's just beautiful, thank you, so many thoughts here :)
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Cakes, Custard, Categories and Colbert

Today, my friend Eugenia Cheng will appear on The Late Show with Stephen Colbert.   She'll be one of three guests, including that guy who starred in some recent James Bond movies.

Eugenia recently wrote a book called Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, which has gotten a lot of publicity.   This must be why she's on the show.

In the US, this book appeared under the title How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, presumably because Americans are less familiar with category theory and custard (not to mention the peculiar British concept of “pudding”).

Eugenia learned category theory as a grad student at Cambridge, mainly from Peter Johnstone and her advisor Martin Hyland.  But around that time Hyland became interested in some mathematical structures called n-categories, which are even better than categories.  Eugenia wound up doing her thesis on an approach to n-categories that James Dolan and I had dreamt up. 

I visited Cambridge for the first time around then, for purely coincidental reasons - my wife was visiting a research institute there. I started hanging out in the mathematics department, and Eugenia and I wound up becoming friends.  So, it makes me really happy to see she’s bringing math and even category theory to a large audience.

Here’s my review of Eugenia’s book for the London Mathematical Society Newsletter:

    Eugenia Cheng has written a delightfully clear and down-to-earth explanation of the spirit of mathematics, and in particular category theory, based on their similarities to cooking. Sometimes people complain about a math textbook that it’s “just a cookbook”, offering recipes but no insight. Cheng shows the flip side of this analogy, providing plenty of insight into mathematics by exploring its resemblance to the culinary arts. Her book has recipes, but it’s no mere cookbook.

    Among all forms of cooking, it seems Cheng’s favorite is the baking of desserts—and among all forms of mathematics, category theory. This is no coincidence: like category theory, the art of the pastry chef is one of the most exacting, but also one of the most delightful, thanks to the elegance of its results. Cheng gives an example: “Making puff pastry is a long and precise process, involving repeated steps of chilling, rolling and foldking to create the deliciously delicate and buttery layers that makes puff pastery different from other kinds of pastery.”

    However, she does not scorn the humbler branches of mathematics and cooking, and there’s nothing effete or snobby about this book. No special background is needed to follow it, so if you’re a mathematician who wants your relatives and friends to understand what you are doing and why you love it, this is the perfect gift to inflict on them.

    On the other hand, experts may be disappointed unless they pay close attention. There is a fashionable sort of book that lauds the achievements of mathematical geniuses, explaining them in just enough detail to give the reader a sense of awe: typical titles are A Beautiful Mind and The Man Who Knew Infinity. Cheng avoids this sort of hagiography, which may intimidate as often as it inspires. Instead, her book uses examples to show that mathematics is close to everyday experience, not to be feared.

    While the book is written in bite-sized pieces suitable for the hasty pace of modern life, it has a coherent architecture and tells an overall story. It does this so winningly and divertingly that one might not even notice. The book’s first part tackles the question “what is mathematics?” The second asks “what is category theory?” Unlike timid people who raise big questions, play with them a while, and move on, Cheng actually proposes answers! I will not attempt to explain them, but the short version is that mathematics exists to make difficult things easy, and category theory exists to make difficult mathematics easy. Thus, what mathematics does for the rest of life, category theory does for mathematics.

    Of course, mathematics only succeeds in making a tiny part of life easy, and Cheng admits this freely, saying quite a bit about the limitations of mathematics, and rationality in general. Similarly, category theory only succeeds in making small portions of mathematics easy—but those portions lie close to the glowing core of the subject, the part that illuminates the rest.

    And as Cheng explains, illumination is what we most need today. Mere information, once hard to come by, is now cheap as water, pouring through the pipes of the internet in an unrelenting torrent. Your cell phone is probably better at taking square roots or listing finite simple groups than you will ever be. But there is much more to mathematics than that—just as cooking is much more than merely following a cookbook.
@DrEugeniaCheng Hi Dr! We loved you cream tea video! We'd love to see a another video to feature on our C4 show · Dr Eugenia Cheng – @DrEugeniaCheng. Carve a Möbius strip out of a bagel, cover with Möbius salmon, and eat it.
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Awesome! I added this book to my to-read list thanks to +William Rutiser's recommendation -- thanks, William!
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John Baez

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The ice pits of Pluto

You are trapped on Pluto.  Your only hope of survival is traveling a long distance to an old base where there is still a working rocket.

Your rover is insulated against the amazingly cold temperatures, and its huge corrugated metal wheels have no trouble driving over the ice - which is mostly made of frozen nitrogen.  

But then you come to a large pit.  It's about 10 meters deep and 100 meters across.  Its walls are not very steep, so you can cross it, but it's a bit annoying.

Then you come to another pit.  And another, and another.

You have entered Sputnik Planum, a huge field of ice pits in a plain named after the old Russian satellite Sputnik.  

We don't know how these pit formed.  They may be caused by sublimation where ice turns directly into gas as it warms up in the chilly Plutonian summer.  They may start small and grow over time.  But why are they here, and not all over Pluto?  

Many of these pits are connected, forming troughs that line up.  Why?  We don't know.

Good luck.  Maybe you will find out.  If you survive, maybe you can tell us.

For more, see:

#astronomy #pluto
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Fun! This would make a nice compact video game.
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Have him in circles
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I'm a mathematical physicist.
  • Centre for Quantum Technologies
    Visiting Researcher, 2011 - present
  • U.C. Riverside
    Professor, 1989 - present
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Riverside, California
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I'm trying to get mathematicians and physicists to help save the planet.
I teach at U. C. Riverside and work on mathematical physics — which I interpret broadly as ‘math that could be of interest in physics, and physics that could be of interest in math’. I’ve spent a lot of time on quantum gravity and n-categories, but now I want to work on more practical things, too.

Why? I keep realizing more and more that our little planet is in deep trouble! The deep secrets of math and physics are endlessly engrossing — but they can wait, and other things can’t.

So, I’ve cooked up a plan to get scientists and engineers interested in saving the planet: it's called the Azimuth Project.  It includes a wiki, a blog, and a discussion forum.  I also have an Azimuth page here on Google+, where you can keep track of news related to energy, the environment and sustainability.

Check them out, and join the team!  Or drop me a line here.
  • Massachusetts Institute of Technology
    Mathematics, 1982 - 1986
  • Princeton University
    Mathematics, 1979 - 1982
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