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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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  • Massachusetts Institute of Technology
    Mathematics, 1982 - 1986
  • Princeton University
    Mathematics, 1979 - 1982
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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.
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I'm a mathematical physicist.
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    Visiting Researcher, 2011 - present
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John Baez

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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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Xah Lee's profile photoSteve Wenner's profile photoJohn Baez's profile photo
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+Steve Wenner - "I still don't see how to draw three orthogonal axes through a tetrahedron such that permutations of the axes yield symmetries of the tetrahedron."

Good.  That's impossible, so I'm glad you can't see how to do it. 

Here we are taking four orthogonal axes in 4d space and projecting them down to four non-orthogonal axes in 3d space.  Each axis then goes through the center of a regular tetrahedron and one of its 4 vertices.
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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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The self-driving cars technology is almost ready for mainstream deployment..
https://medium.com/@UNU.ai/will-we-bow-down-to-robot-overlords-bdf180e9847#.7b9a8d1yv
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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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+David Washington wrote: "Also I wonder what happens if one were to put a receiver between the sat and ground station."

The virtue of quantum entanglement is that if someone spies on one of the photons and measures its spin along some axis, that breaks the entanglement and the two parties trying to use the entanglement can detect this.
This is the basis of quantum cryptography.

I haven't thought much about what could happen if the evil third party intercepts both photons and broadcasts their own pair.  I'm sure someone must have analyzed this.  Luckily, this is fairly hard to do if the photons are being broadcast from a satellite to Beijing and Austria.

It would be easier for the evil third party to just shoot down the satellite and prevent the use of quantum cryptography.

"Something bothers me about all this, I am going to assume its my own ignorance :)"

Quantum theory is utterly mind-blowing.  I'm only blase after having spent most of my time thinking about it from the summer of my junior year in high school (when I started reading the third volume of The Feynman Lectures on Physics, the part about quantum mechanics) to the end of grad school (when I finished a thesis on quantum field theory).  You have to change your whole attitude toward reality to understand it.  So yes, it should bother you!
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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
Rare crypto implementation in ShadowBrokers dump connects it to Equation Group.
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So true
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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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Abid Ullah's profile photoGodhave Mercyonme's profile photoJohn Baez's profile photo
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The news is out:

http://www.nytimes.com/2016/08/25/science/earth-planet-proxima-centauri.html

From the journal article:

"Here we report observations that reveal the presence of a small planet with a minimum mass of about 1.3 Earth masses orbiting Proxima with a period of approximately 11.2 days at a semi-major-axis distance of around 0.05 astronomical units."

A year that's just 11 Earth days long!
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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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+John Baez 'After 2 microseconds, it turns into an electron, a muon neutrino and an electron antineutrino'
also
'and that is a long time for this kind of experiment'
'Eyes wide shut' those
eyelidss are now wide open,

fascinatig.
Of course i will tell the kids.
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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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+David Washington - I think if it were everywhere I'd be glad at the triumph of intelligent life throughout the cosmos.  Then I could stop worrying so much about our stupid little civilization and what it's doing to our planet.  I could relax knowing that at least not everyone is so fucked up.
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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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"This is undoubtedly less fun to read than to listen to.." ... excellent tune.. would use this as the title. Tasty. Very tasty. Thank you.
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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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OY
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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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David Washington's profile photoDavid “goo.gl/LuFkzX” Tweed's profile photoJohn Baez's profile photo
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Heh.  Don't tell the women Yu Jianchun is trying to date.  

(I was hoping it would be a complicated pun involving the number-theoretic properties of the number 14.)
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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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Interestingly, now that I see this post via the bell button rather than on the main g+ page, and that I've seen the clip in YouTube video form, the animation has loaded just fine
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John Baez

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And even in defeat... victory!

This shows great presence of mind, and a sense of humor.
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+Shantha Hulme I am glad to hear that.

Thank you for sharing with me. This sounds like: “Life is like a piano; the white keys represent happiness and the black show sadness. But as you go through life's journey, remember that the black keys also create music.”(Ehssan)
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