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## John Baez

Occupation: I'm a mathematical physicist. (Centre for Quantum Technologies)

Location: Riverside, California

Followers: 57,606

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Views: 52,166,270

Cream of the Crop: 11/05/2011

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### Most comments: 106

2016-08-27 04:43:12 (106 comments; 27 reshares; 210 +1s; )

**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, theMilky Way is... more »

### Most reshares: 91

2016-08-08 04:51:46 (0 comments; 91 reshares; 198 +1s; )

**What's wrong with Trump?**

More and more people are wondering. Here's an insightful analysis from a psychiatric social worker. Please reshare. It's not light reading, but we need to understand what we're dealing with here.

--------------------**The Billionaire's Baffling Behavior Explained**

Recently, Mr. Trump's words and actions in various situations have become headline news. Suddenly, many people are alarmed and are questioning temperament, his emotional stability. Dementia? Campaign tactics?

No, it's not an illness that can be treated so he can return to his usual state of health. It's not like when a car's brakes don't work and the mechanic fixes them. It's more like the car came off the assembly line without them.

It's a structural problem.

We're witnessingte... more »

### Most plusones: 332

2016-08-14 02:05:13 (46 comments; 45 reshares; 332 +1s; )

**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... more »

Latest 50 posts

2016-09-24 16:14:25 (20 comments; 11 reshares; 138 +1s; )

**Solar wind**

This is the **solar wind**, the stream of particles coming from the Sun. It was photographed by **STEREO**. That's the **Solar Terrestrial Relations Observatory**, a pair of satellites we put into orbit around the Sun at the same distance as the Earth, back in 2006. One is ahead of the Earth, one is behind. Together, they can make stereo movies of the Sun!

One interesting thing is that there's no sharp boundary between the 'outer atmosphere' of the Sun, called the **corona**, and the solar wind. It's all just hot gas, after all! STEREO has been studying how this gas leaves the corona and forms the solar wind. This picture is a computer-enhanced movie of that process, taken near the Sun's edge.

What's the solar wind made of? When you take hydrogen and helium and heat them up so much that theelectrons... more »

2016-09-23 19:07:29 (19 comments; 10 reshares; 63 +1s; )

**Life on the Infinite Farm**

This is a great book about infinity - for kids. For example, there's a cow named Gracie with infinitely many legs. She likes new shoes, but she wants to keep wearing all her old shoes. What does she do?

Life on the Infinite Farm is by Richard Evan Schwartz, and it's free here:

https://www.math.brown.edu/~res/farm.pdf

Later it will be published on paper by the American Mathematical Society. I really like turning the pages when I'm reading a book to a child. Is that old-fashioned? What do modern parents think?

Gracie's tale is just a retelling of the first **Hilbert Hotel** story. There's a hotel with infinitely many rooms. Unfortunately they're all full. A guest walks in. What do you do?

You move the guest in room 1 to room 2, the guest in room 2 to room 3, andso on. Now... more »

2016-09-22 06:29:24 (14 comments; 23 reshares; 110 +1s; )

**Poncelet's Porism**

If you can fit a triangle snugly between two circles, you can always slide the triangle around. The triangle may have to change shape, but it stays snug! All 3 corners keep touching the outside circle, and all 3 sides keep touching the inside circle.

That's really cool. But even better, it also works for polygons with more than 3 sides!

This amazing fact is called **Poncelet's Porism**.

A **porism** is like a theorem, but much cooler. **Poncelet** was a French engineer and mathematician who wrote a famous book on 'projective geometry' in 1822.

What's a porism, really?

Well, Euclid is famous for his Elements, but he also wrote a more advanced book called Porisms. Unfortunately that book is lost. I hear that someone checked it out from the library of Alexandria andnever ret... more »

2016-09-21 15:17:59 (40 comments; 11 reshares; 54 +1s; )

**Black hole versus white hole**

Last time I showed you a Schwarzschild black hole... but not the whole hole.

Besides the **horizon**, which is the imaginary surface that light can only go in, that picture had a mysterious "antihorizon", where light can only come out. When you look at this black hole, what you actually see is the antihorizon. The simplest thing is to assume no light is coming out of the antihorizon. Then the black hole will look black.

But I didn't say what was behind the antihorizon!

In a real-world black hole there's no antihorizon, so all this is just for fun. And even in the Schwarzschild black hole, you can never actually cross the antihorizon - unless you can go faster than light. So there's no real need to say what's behind the antihorizon. And we can just decree that no light comesout of it.

2016-09-20 18:21:39 (69 comments; 25 reshares; 71 +1s; )

**Understanding black holes**

This is a diagram of a **Schwarzschild black hole** - a non-rotating, uncharged black hole that has been around forever.

Real-world black holes are different. They aren't eternal - they were formed by collapsing matter. They're also rotating. But the Schwarzschild black hole is simple: you can write down a formula for it. So this is the one to start with, when you're studying black holes.

This is a **Penrose diagram**. It shows time as going up, and just one dimension of space going across. The key to Penrose diagrams is that light moves along diagonal lines. In these diagrams the speed of light is 1. So it moves one inch across for each inch it moves up - that is, forwards in time.

The whole universe outside the black hole is squashed to a diamond. The **singularity** is the wiggly line attop. T... more »

2016-09-18 18:48:33 (57 comments; 14 reshares; 79 +1s; )

**The mystical hexagram theorem**

The picture explains this amazing result, which was discovered by Pascal in 1639, when he was only sixteen.

Take six points on an ellipse, called A,B,C,D,E,F. Connect each point to the next by a line.

The red lines intersect in a point G.

The yellow lines intersect in a point H.

The blue lines intersect in a point K.

And then the cool part:

The points G, H and K lie on a line!

I'm teaching a course on 'algebraic groups' starting on Thursday, so I need to review a bit of the history of projective geometry. This result of Pascal, called the **Hexagrammum Mysticum Theorem**, was the first exciting theorem about projective geometry after the old work of Pappus. So I'll mention it in my course! But I don't really understand why it's true. Do you know a niceexplana... more »

2016-09-17 02:15:36 (93 comments; 20 reshares; 109 +1s; )

**Exploring black holes - with cats!**

There should be a series of videos exploring black holes with cats.

So far all we have is this gif made by +Dragana Biocanin. A cat can orbit just above the photon sphere of a non-rotating black hole, moving at almost the speed of light. It's impossible for a cat to orbit below the photon sphere. As long as it's outside the event horizon it can accelerate upwards and escape the black hole's gravitational pull. But if it crosses the event horizon, it's doomed!

The **event horizon** is an imaginary surface in spacetime that's defined by this property: once a cat crosses this surface, it can't come back without going faster than light! This property involves events in the future, so there's no guaranteed way for the cat to tell when it's crossing an event horizon.

Forexample, if... more »

2016-09-16 01:13:54 (35 comments; 19 reshares; 86 +1s; )

**Light moves around a rotating black hole**

This gif by +Leo Stein shows a photon orbiting a black hole. Since the black hole is rotating, the photon traces out a complicated path. You can play around with the options here:

https://duetosymmetry.com/tool/kerr-circular-photon-orbits/

If a black hole is not rotating, light can only orbit it on circles that lie on a special sphere: the **photon sphere**.

But if the black hole is rotating, photon orbits are more complicated! They always lie on some sphere or other — but now there's a range of spheres of different radii on which photons can move!

The cool part is how a rotating massive object — a black hole, the Sun or even the Earth — warps spacetime in a way that tends to drag objects along with its rotation. This is called **frame-dragging**.

Frame-dragging... more »

2016-09-15 03:41:43 (15 comments; 18 reshares; 161 +1s; )

**Just because someone's on crutches doesn't mean they're handicapped**

Nomads kick ass. James Dator explains:

The World Nomad Games concluded on Friday in what can only be described as the greatest week-long sporting event on the planet. The games, intended to showcase ethnic sports of Central Asia, featured things you have never heard of, athletes you’ll never learn about and sports that sound absolutely terrifying.

There were 16 sports with medals up for grabs. These are the ones that are the absolute wildest.**Cirit**

This Turkish equestrian sport involves teams of riders chasing each other and throwing javelins at each other while on horseback. Yes, seriously.**Er Enish**

It’s wrestling, except you’re on a horse. You win by pulling your opponent off their horse.**Kok-boru**

more »

2016-09-13 00:41:47 (75 comments; 19 reshares; 103 +1s; )

**An even bigger particle accelerator?**

This is Chen-Ning Yang. He helped create **Yang-Mills theory** - the wonderful theory that describes all the forces in nature except gravity. He helped find the **Yang-Baxter equations**, which describe what particles do when they move around on a thin sheet of matter, tracing out braids.

He's one of China's top particle physicists... and he's come out against building a new, bigger particle accelerator! This is a big deal, because only China has the will to pay for the next machine.

In 2012, two months after the Large Hadron Collider (near Geneva) found the Higgs boson, a Chinese institute called for a bigger machine: the **Circular Electron Positron Collider** or **CEPC**.

This machine would be a ring 80 kilometers around. It would collide electrons and positrons at an energy of250 GeV... more »

2016-09-11 06:38:13 (25 comments; 20 reshares; 116 +1s; )

**Just above the photon sphere**

This gif shows what it's like to orbit a non-rotating black hole just above its **photon sphere**.

That's the imaginary sphere where you'd need to move at the speed of light to maintain a circular orbit. At the photon sphere, the horizon of the black hole looks like a perfectly straight line!

But since you can't move at the speed of light, this gif shows you orbiting slightly above the photon sphere, a bit slower than light.

We cannot go to such a place - not yet, anyway. The gravity would rip us to shreds if we tried. But thanks to physics, we can figure out what it would be like to be there! And that is a wonderful thing.

The red stuff drawn on the black hole is just to help you imagine your motion. You would not really see that stuff.

The light above the blackhole is st... more »

2016-09-09 06:43:28 (50 comments; 5 reshares; 47 +1s; )

**The Ultimate Question, and its Answer**

+David Madore has a lot of great stuff on his website - videos of black holes, a discussion of infinities, and more. He has an interesting story that claims to tell you the Ultimate Question, and its Answer.

(No, it's not 42.)

I like it, but I can't tell how much sense it makes.

Here's the key part:**What is the Ultimate Question, and what is its Answer? The answer to that is, of course: “The Ultimate Question is ‘What is the Ultimate Question, and what is its Answer?’ and its answer is what has just been given.”. This is completely obvious: there is no difference between the question “What color was Alexander's white horse?” and the question “What is the answer to the question ‘What color was Alexander's white horse?’?”. Consequently, the Ultimate Questionis “What is the Answer t... more »**

**
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2016-09-08 08:39:04 (36 comments; 14 reshares; 75 +1s; )

**Cosmic censorship**

Einstein's theory of gravity predicts **singularities**: places where you can fall off the edge of spacetime. In reality, these may be places where Einstein's theory breaks down! We don't really know.

Why not just go look? Unfortunately, most singularities are hidden. You can't see them and come back and tell us what you saw.

One singularity that's not hidden, according to Einstein's theory, is the Big Bang.

Look into the sky in any direction and you are really looking back in time, because it takes time for light to travel. If you look far enough - with the right kind of equipment - you can see a faint glow of microwaves left over from the Big Bang. Actually this glow is from hot gas that cooled down enough to become transparent 380,000 years after the Big Bang. It's harder to seebeyond that... more »

2016-09-06 02:19:14 (35 comments; 9 reshares; 79 +1s; )

**Singularities - when spacetime goes bad**

Physicists don't like it when things become infinite, but for Einstein's theory of gravity, infinities are deeply connected to its most dramatic successful predictions: black holes and the Big Bang!

In this theory, the density of the Universe approaches infinity as we go back in time to the Big Bang. The density of a star approaches infinity when it collapses to form a black hole. The curvature of spacetime approaches infinity, too! These situations where spacetime goes bad are called **singularities**.

Einstein didn't like singularities. They could mean that his theory - general relativity - breaks down under extreme conditions. But so far, they fit what we see very well.

In the 1960's, two guys named Roger Penrose and Stephen Hawking became famous by proving **singularitytheorems... more »**

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**2016-09-05 04:37:57 (31 comments; 11 reshares; 65 +1s; )

**The photon sphere**

A nonrotating black hole is surrounded by an imaginary sphere called the **event horizon**. If you cross this sphere, you are doomed to fall in.

If you carry a flashlight and try to shine light straight out, light emitted at the instant you cross the event horizon will basically stay there! Why? Because to stay on the horizon you must move outwards at the speed of light. As the Red Queen said in Alice in Wonderland:

"Now, here, you see, it takes all the running you can do, to keep in the same place."

But there's another imaginary sphere outside the event horizon, called the **photon sphere**. This is where light can go in circles around the black hole!

This picture by +David Madore shows the view from the photon sphere. The black hole occupies exactly half the sky! As he says:

This ... more »

2016-09-04 03:52:21 (4 comments; 6 reshares; 53 +1s; )

**Kummer surface**

This picture by +Abdelaziz Nait Merzouk almost completes my series on surfaces with the maximum number of **nodes** - those places where the tips of two cones meet. This surface has 16 nodes, the most possible for a surface described by a **quartic** equation: a polynomial equation of degree 4.

Unlike other surfaces in this series, it's connected to some pretty deep math. Take a complex curve of genus 2, form its Jacobian variety, mod out by the Kummer involution, and you get a surface like this! Whee! Where's my "mad scientist" emoji? 😃

For an explanation of all that, go here:

http://blogs.ams.org/visualinsight/2016/09/01/kummers-quartic-surface/

As usual, mathematicians seem to have a perverse desire to make things complicated. For example, a "complex curve of genus 2" isbasically j... more »

2016-09-02 00:37:26 (94 comments; 18 reshares; 199 +1s; )

**Black Saturns**

Imagine a black hole with a black ring. Physicists call such a thing a **black Saturn**.

Nobody has ever seen one. But we can still study them.

You see, we know the equation that describes black holes. It's called **Einstein's equation**, the basic formula in Einstein's theory of gravity.

We know this equation has solutions with a round **event horizon** - a surface that you can't escape if you fall through it. These are black holes. And we've seen plenty of black holes - or at least the hot gas falling into black holes.

Could there be a **black ring** - an event horizon shaped like a ring? It would need to spin so it wouldn't collapse.

Nobody has ever seen a black ring... and there's a reason why! They're mathematically impossible. There's nosolution of... more »

2016-09-01 06:06:53 (47 comments; 29 reshares; 83 +1s; )

**Waiting for the motivation fairy**

Go ahead! Procrastinate! If you wait long enough, a fairy princess may suddenly appear and cast a spell motivating you to get work done.

Here's what Hugh Kearns and Maria Gardiner have to say about this approach. It contains good advice:**If you were trying to set up ideal conditions for procrastination, conducting a research project would provide them. Such projects tend to be large and time-consuming: completing a doctoral research project, for example, often takes three years or more. Deadlines and endpoints are often fuzzy and ill-defined. Then there’s the reward structure: you can put in a lot of effort with little to no positive feedback along the way, and the rewards, if there are any, take a long time to come.****Add to this the fact that scientists are often perfectionists with demanding, ifnot id... more »**

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**2016-08-31 05:17:00 (40 comments; 6 reshares; 72 +1s; )

**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 firstto give ... more »

2016-08-27 04:43:12 (106 comments; 27 reshares; 210 +1s; )

**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, theMilky Way is... more »

2016-08-26 05:35:36 (30 comments; 23 reshares; 102 +1s; )

**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 anaut... more »**

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**2016-08-25 10:03:24 (40 comments; 3 reshares; 46 +1s; )

**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 ... more »

2016-08-24 11:38:23 (28 comments; 22 reshares; 138 +1s; )

**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 SpaceScale.<... more »

2016-08-23 14:32:26 (52 comments; 12 reshares; 100 +1s; )

**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, inthis w... more »**

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**2016-08-21 02:02:52 (45 comments; 12 reshares; 114 +1s; )

**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, butthey'... more »

2016-08-18 07:02:26 (62 comments; 53 reshares; 103 +1s; )

**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 ongovernment ... more »

2016-08-16 05:31:43 (16 comments; 15 reshares; 69 +1s; )

**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 bythe 1800s. Th... more »

2016-08-14 02:05:13 (46 comments; 45 reshares; 332 +1s; )

**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... more »

2016-08-13 06:32:47 (27 comments; 30 reshares; 157 +1s; )

**And even in defeat... victory!**

This shows great presence of mind, and a sense of humor.

2016-08-12 05:18:30 (93 comments; 41 reshares; 257 +1s; )

**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, weshould be abl... more »

2016-08-09 12:26:55 (16 comments; 10 reshares; 63 +1s; )

**WWW: the Wood Wide Web**

The world wide web was not the first powerful communication network! Long before came the **wood wide web**, underground in every forest.

This picture was produced by a program called **Mycelium**, which takes a picture and evolves it using the rules by which fungi send out tiny threads... sort of like roots... that absorb nutrients.

A **mycelium** is the name for this network of threads formed by a fungus - or a bunch of fungi. A mycelium can be huge! In his book Mycelium Running, Paul Stamets writes:

"Is this the largest organism in the world? This 2,400-acre [970-hectare] site in eastern Oregon had a contiguous growth of mycelium before logging roads cut through it. Estimated at 1,665 football fields in size and 2,200 years old, this one fungus has killed the forest above it several times over, and in sodoing ... more »

2016-08-08 04:51:46 (0 comments; 91 reshares; 198 +1s; )

**What's wrong with Trump?**

More and more people are wondering. Here's an insightful analysis from a psychiatric social worker. Please reshare. It's not light reading, but we need to understand what we're dealing with here.

--------------------**The Billionaire's Baffling Behavior Explained**

Recently, Mr. Trump's words and actions in various situations have become headline news. Suddenly, many people are alarmed and are questioning temperament, his emotional stability. Dementia? Campaign tactics?

No, it's not an illness that can be treated so he can return to his usual state of health. It's not like when a car's brakes don't work and the mechanic fixes them. It's more like the car came off the assembly line without them.

It's a structural problem.

We're witnessingte... more »

2016-08-05 15:24:03 (30 comments; 12 reshares; 87 +1s; )

**The quest for beauty**

This is a nice interview of Miranda Cheng, an assistant professor at the University of Amsterdam working on the math of string theory. She's on a quest to understand the connection between strings and some mysterious functions in Ramanujan's lost notebook.

It's sort of spooky how much of Ramanujan's work makes more sense with the help of string theory. But perhaps it shouldn't be surprising. String theory hasn't really done anything to predict the results of experiments - it's mainly attractive because of its mathematical beauty. Ramanujan, too, was motivated by the quest for beauty. He got there sooner... but he only saw the tip of the vast iceberg we're exploring now.

What's "mathematical beauty"? Here's what Cheng says:**It’s kind of hard to say why it isbeautiful. I... more »**

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**2016-08-04 05:25:21 (16 comments; 10 reshares; 65 +1s; )

**Endrass octic**

This surface looks cute - but it's also the best known solution to a hard math problem. It's called the **Endrass octic**.

Why 'Endrass'? Because was discovered in 1995 by Stephan Endrass while he was writing his Ph.D. thesis.

Why 'octic'? Because it's described by a polynomial equation of degree 8.

You'll notice it has lots of points where the tips of two cones meet. It has 168 of them, though not all are visible here. And this is, so far, the largest number of such points that people have gotten for an octic.

It may not be the best possible. But it's the best so far. In 1984, a guy named Miyaoka showed that you can't get get more than 174 of these conical points in an octic. So, there's a gap between what we know is possible and what might be possible. (If you're... more »

2016-08-03 05:12:57 (29 comments; 72 reshares; 147 +1s; )

**Primes with no sevens**

This is a prime number whose decimal digits are all ones. It has 317 ones. It's not the world record. The number with 1031 ones is also known to be prime!

Even larger guys like this are suspected to be prime. Are there infinitely many? Mathematicians believe so, but they can't prove it.

Why do they believe it? The main reason is that they have an estimate of the "probability" that a number with some number of digits is prime. We can use this to guess the answer to this puzzle.

Of course the whole idea of "probability" is a bit weird here. A number is either prime or not: the math gods do not flip coins to decide which numbers are prime!

Nonetheless, treating primes as if they were random turns out to be useful. Mathematicians have made many guesses using this idea, andthen proved ... more »

2016-08-01 02:27:09 (8 comments; 12 reshares; 108 +1s; )

**Single-minded determination meets gentle courtesy**

2016-07-31 02:44:02 (37 comments; 18 reshares; 103 +1s; )

**The search for dark matter**

In South Dakota, in a town named Lead, there was a gold mine. Now it's abandoned. But at the bottom of this mine, more than a mile underground, there sits a one-meter-tall, 12-sided container. It contains 370 kilograms of a noble gas chilled to liquid form. Liquid xenon!

It's called the **Large Underground Xenon** experiment, or **LUX**. It's been looking for particles that could explain dark matter. If such a particle interacts with a xenon atom, LUX can detect it.

Of course, we also need to distinguish these particles from other things. Xenon, a gas at room temperatures, chilled to liquid form, is a great choice here. For one thing, it's self-shielding! Xenon is so dense that most gamma rays and neutrons don't get through more than a few centimeters of the stuff. But it's perfectlytransparent t... more »

2016-07-30 05:17:01 (33 comments; 9 reshares; 73 +1s; )

**Death of the diphoton bump**

In June 2015, after a two-year upgrade, the Large Hadron Collider turned on again. In its first run it had discovered the Higgs boson, a particle 133 times heavier than the proton — and the main missing piece of the Standard Model. When the collider restarted, with a lot more energy, everyone was hoping to see something new.

In December 2015, two separate detectors saw something: pairs of photons, seemingly emitted by the decay of a brand new particle 6 times heavier than the Higgs boson.

But was it for real? Maybe it was just a random fluctuation — noise, rather than a true signal.

It seemed unlikely to be just chance. Combining the data from both detectors, the chance of coincidentally seeing a bump this big at this location in the photon spectrum was one in 100 thousand.

But in particle physicsthat's n... more »

2016-07-29 04:16:41 (0 comments; 28 reshares; 107 +1s; )

**Melania Trump has disappeared**

Her website was deleted on Wednesday. Check it out:

http://www.melaniatrump.com

But it's not so easy to make things disappear on the internet! You can still see what it looked like ten days ago:

https://web.archive.org/web/20160719142534/http://www.melaniatrump.com/

Why was it deleted? Melania Trump didn't really get a degree of architecture. Her website said:**After obtaining a degree in design and architecture at University in Slovenia, Melania was jetting between photo shoots in Paris and Milan, finally settling in New York in 1996.**

But in fact she dropped out before getting a degree. She attended the University of Ljubljana’s architecture school... but quit after her freshman year!

I don't think this lie - or her plagiarized speech - is a bigdeal com... more »

2016-07-27 04:02:07 (59 comments; 12 reshares; 96 +1s; )

**Satanic crystal found in ancient meteorite**

Just kidding! There's nothing devilish about the pentagram here. It's what scientists saw when they shot X-rays through a tiny piece of a meteorite found in the far northeast of Russia.

No ordinary crystal can produce this pattern - it takes a **quasicrystal**, where the atoms are packed in a way that never quite repeats. Scientists have made lots of quasicrystals in the lab, but only two have been found in nature, both in meteorites!

This is the second one. It contains a mineral called **icosahedrite**, made of aluminum, copper and iron. It's only stable at high temperatures and pressures, so it must have formed in a collision. It's been slowly decaying ever since, but very slowly. It could be billions of years old.

To see how this mineral could have formed, scientistssimulate... more »

2016-07-26 06:47:27 (0 comments; 9 reshares; 72 +1s; )

**What Sanders thinks about Clinton and Trump**

I've never lived through an election where the choice is so stark - where the consequences of our vote will be so huge. Bernie Sanders laid it out clearly at the Democratic National Convention yesterday:**This election is about which candidate understands the real problems facing this country and has offered real solutions – not just bombast, fear-mongering, name-calling and divisiveness.****We need leadership in this country which will improve the lives of working families, the children, the elderly, the sick and the poor. We need leadership which brings our people together and makes us stronger – not leadership which insults Latinos, Muslims, women, African-Americans and veterans – and divides us up.****By these measures, any objective observer will conclude that – based on her ideas andher lead... more »**

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**2016-07-25 15:39:23 (0 comments; 20 reshares; 82 +1s; )

**Endorsed by Putin**

Putin, eager to weaken the EU and NATO, has been backing right-wing demagogues throughout Europe. So it came as no surprise when he started complimenting Trump. Not only is Trump would-be strongman of Putin's ilk (only less clever), he's also been threatening to break US commitments to NATO.

In December, Putin called Trump "an outstanding and talented personality". Trump, in a rare moment of sweetness, replied:**"It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond."**

Putin? Respected?

Putin now appears to be backing Trump even more strongly, with Russian operatives hacking into Democratic National Committee (DNC) computers and trying to embarrass them shortly before the convention.

On June 14th, thecybe... more »

2016-07-24 04:19:04 (13 comments; 10 reshares; 77 +1s; )

**New kinds of quasiparticles**

You can get electrons to behave in many strange ways in different materials. They act like various kinds of particles... but they're not truly fundamental particles, so they're called **quasiparticles**.

For example, the spin, charge and position of electrons can move in completely independent ways.

Imagine an audience at a football game holding up signs, and then creating a wave by wiggling their signs. This wave can move even even if the people stand still!

Similarly, we can have electrons more or less standing still, with their spins lined up. Then their spins can wiggle a bit, and this wiggle can move through the material, even though the electrons don't move. This wave of altered spin can act like a particle! It's called a **spinon**.

You can also imagine a hole in a densecrowd of... more »

2016-07-23 02:54:41 (22 comments; 4 reshares; 43 +1s; )

**The quest for larger infinities**

There are different kinds of bigness. But they're connected.

There's a fascinating contest where you try to write the computer program of a certain length that would print out the largest possible integer. This contest was actually carried out on the xkcd blog, and Eliezer Yudkowsky won. Unless you know more about logic than he does, you won't be able to beat him.

There's another contest where you try to name the largest "computable ordinal", and that's what my post is about:

https://johncarlosbaez.wordpress.com/2016/07/07/large-countable-ordinals-part-3/

And there's another contest where you try to name the largest "cardinal". Here we get into inaccessible cardinals, indescribable cardinals, huge cardinals, superhuge cardinals and the like.

But th... more »

2016-07-21 23:28:18 (0 comments; 18 reshares; 102 +1s; )

**Republicans for Trump**

Cruz caused a stir at the Republican convention by not endorsing Trump. But here's what other Republicans say:

“He’s a race-baiting, xenophobic religious bigot. He doesn’t represent my party. He doesn’t represent the values that the men and women who wear the uniform are fighting for.” — Senator Lindsey Graham, Republican of South Carolina

“I don’t think this guy has any more core principles than a Kardashian marriage.” — Senator Ben Sasse, Republican of Nebraska

“We saw and looked at true hate in the eyes last year in Charleston. I will not stop until we fight a man that chooses not to disavow the K.K.K. That is not a part of our party.” — Nikki Haley, Republican governor of South Carolina

“Donald Trump is a madman who must be stopped,” — Bobby Jindal, former Republican governor ofLouisiana

“I won’t vo... more »

2016-07-19 02:19:16 (13 comments; 11 reshares; 70 +1s; )

**Into the clouds**

Frigatebirds are amazing:**Ornithologist Henri Weimerskirch put satellite tags on a couple of dozen frigatebirds, as well as instruments that measured body functions such as heart rate. When the data started to come in, he could hardly believe how high the birds flew.****“First, we found, ‘Whoa, 1,500 meters. Wow. Excellent, fantastique,’ ” says Weimerskirch, who is with the National Center for Scientific Research in Paris. “And after 2,000, after 3,000, after 4,000 meters — OK, at this altitude they are in freezing conditions, especially surprising for a tropical bird.”****Four thousand meters is more than 12,000 feet, or as high as parts of the Rocky Mountains. “There is no other bird flying so high relative to the sea surface,” he says.****Weimerskirch says that kind of flying should take a hugeamount of energy.... more »**

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**2016-07-16 00:51:06 (25 comments; 4 reshares; 72 +1s; )

**A winning septic**

A septic tank is a system for disposing of sewage. A **septic surface** is a surface described by a polynomial equation of degree 7.

This picture by +Abdelaziz Nait Merzouk shows a septic surface discovered by Oliver Labs when he was working on his PhD thesis.

It looks like a beautiful flower of some strange sort. But it's famous because it's the septic with the largest known number of points that look like two cones meeting tip to tip.

How many? Ninety-nine! We know that no septic can have more than 104 of these **ordinary double points**, as they're called. But we don't know any with more than 99. So this is currently one of the winners. There are others, too, also discovered by Labs.

This surface is called the **Labs septic**, which reminds me of yet another meaning of the word'sep... more »

2016-07-12 04:25:39 (24 comments; 26 reshares; 92 +1s; )

**Global warming: demand the truth**

After announcements that 2015 was the hottest year on record and February 2016 was the hottest month, the news station CNN aired five times more fossil fuel advertising than actual climate reporting!

So, please sign this petition to CNN. Tell them: **start reporting on climate change**. And please reshare this message.

A study by the group Media Matters showed that the American Petroleum Institute is getting more coverage than actual news about global warming. This doesn't even include the ads from individual fossil fuel companies and the Koch brothers.

Here's some actual news, in case you hadn't heard:

1) The extent of Arctic sea ice in June was the lowest in recorded history for that month of the year: 260,000 square kilometers less than ever before! It's on track to break allrecor... more »

2016-07-10 15:13:26 (49 comments; 23 reshares; 128 +1s; )

**Gimbal lock**

Here you see 3 rotating rings called **gimbals**. Gimbals are used in gyroscopes and inertial measurement units, which are gadgets that measure an object's orientation - like a drone, or a spacecraft. Gimbals are also used to orient thrusters on rockets.

With 3 gimbals, you can rotate the inner one to whatever orientation you want. The basic reason is that it takes 3 numbers to describe a rotation in 3 dimensional space. This is a special lucky property of the number 3.

But when two of the gimbal's axes happen to be lined up, you get **gimbal lock**. In other words: you lose the ability to rotate the inner gimbal a tiny bit in any way you want. The reason is that in this situation, rotating one of the two aligned gimbals has the same effect on the inner gimbal as rotating the other!

I've always foundgimbal lock... more »

2016-07-08 08:08:55 (11 comments; 1 reshares; 43 +1s; )

**Adventures in Asia**

I'm back in Singapore, the land of explosive cuisine. This is the menu from our favorite Chinese restaurant. It's on Southbridge Road across from the Sri Mariamman Temple - a popular Hindu temple where they do firewalking on the holiday called Theemithi. Maybe they do it to cool down after eating here.

I hadn't known it was called **The Explosion Pot Barbecue**. They sell excellent barbecued fish, roast skewers of lamb with cumin, roast chives, dumplings, and other Szechuan delights. The food is a bit spicy, but I haven't seen any exploding pots, so this may be a mistranslation of something that makes more sense in Chinese.

As usual I'm working at the +Centre for Quantum Technologies and my wife +Lisa Raphals is teaching at the philosophy department at NUS. You can see her in the background ordering ourfood.

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