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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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A lynx kitten bounds forward, confident and focused.

I need this picture today, to cheer myself up.  I don't like the Brexit.  The very best possible interpretation I can put on it is that it's ordinary folks poking a stick in the eye of the elite, demanding more local control of government, more democracy.   Maybe the elite will wake up, stop trying to hog all the wealth, and realize that in the long run it pays to help the downtrodden.  

Maybe London will become less dominated by corrupt financiers.   Maybe Scotland will become independent and join the EU.   

I can imagine a wave of decentralization and localization being a good thing.... if  it's balanced by the right larger-scale structures, allowing plenty of free trade, free movement of people, and so on.   But I don't get any sense that the Brexiters have a constructive vision for the future. 

Back to the theme of youth:

The young are generally bolder, less careful, less fearful.  It's got pros and cons.

75% of British people between ages 18 and 24 said they voted for Britain to stay in the EU.   For people 25-49 it was 56%.  For people 50-64 it was 44%.  For people above 65, just 39%.

So this is an interesting case.  Perhaps the old are more fearful - of refugees, of Polish plumbers, of EU bureaucrats - but in this case they were more eager to do something rash.   It's quite amazing how little is known about what will happen next!    About all we be sure about is that it will create a big mess.

Good luck, Britain!  Good luck, EU!
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I do not concur that new either left or right was fringe. If we note the standpoint of BNF, UKIP and the euroskeptic Conservative then you are looking at a far right win.
What is almost comical is the not exclusion of Nigel Farage from the the negotiations but Nigel's reaction to not being asked. That is a whole other story.
At the end of the day we are only positing our punditry at this one the facts will be different. It would be an interesting exercise to revisit this thread a few months. What we haven't done is predict much, we have suggested a few things. What the UK will look like in 18 months is anyones guess. While hope is not a strategy perhaps those wielding political power will not forget the old unix adage for assuming superuser abilities, with great power comes great responsibility.
Perhaps all that we can hope for is that a pragmatic and reasonable creation of certainty occurs with some semblance of normality for the governed.
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Big stick insect

One of the world's largest insects lives in Australia.   It looks like a stick and it's called Ctenomorpha gargantua.   It's very hard to find, because it lives in the highest parts of the rainforests in Queensland, and it's only active at night! 

In 2014 one fell down and was found hanging on a bush.   Scientists took it to the Museum Victoria, in Melbourne.  They named it Lady Gaga-ntuan.   Now it has a daughter that's 0.56 meters long - that is, 22.2 inches long.

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Thanks, +Cytia Beata.   Pet Phasmatodea sound cool!
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By now you've probably heard: Trump said he'd given $1 million of his own money to veterans groups, but he actually hadn't.   His campaign manager, too, falsely claimed he had given this money. 

4 months later, the Washington Post and other papers started investigating.  They contacted Trump and asked what was up.  On May 24th, feeling the heat, he broke down and handed over the million bucks.

Other donors had also given money to the Donald J. Trump Foundation on the promise that Trump would then give it to veterans.  And he did - after  he was caught.  The Associated Press found that many of his checks were dated May 24, after  the Washington Post story came out.

That's bad enough, but the really interesting part is the temper tantrum that Trump threw at a press conference where he publicly announced that he'd finally given the promised money.

He blasted the media for making him “look bad” by insisting that he account for $6 million.  He called them "dishonest" and "not good people", without giving any example of dishonesty.  And he personally attacked ABC reporter Tom Llamas.

“I’m not looking for credit,” Trump insisted, contrary to all appearances. “But what I don’t want is when I raise millions of dollars have people say — like this sleazy guy over here from ABC. He’s a sleaze in my book.”

"Why am I a sleaze?" Llamas shot back.

“You’re a sleaze!” Trump shouted. “Because you know the facts and you know the facts well.”   Llamas, you see, had just asked a question about this issue.  He also had a history of asking Trump tough questions about his anti-immigrant rhetoric. 

It's shocking for a US presidential candidate to act this way.  This is what a Chicago gangster or tinpot dictator would do.

“Is this what it’s going to be like covering you if you’re president?” one reporter asked.

Trump’s reply: “Yeah, it is. I’m going to continue to attack the press.”

And indeed, Trump has said that if he becomes president, he will "open up" the libel laws to make it easier to sue people who say things he doesn't like.  This is exactly  what dictators do.

In 2005, Timothy O'Brien wrote a book TrumpNation: The Art Of Being The Donald.   He raised questions about Trump's claims of vast wealth.  Trump promptly sued O'Brien for $5 billion.  It was the largest libel lawsuit in U.S. history.  Maybe Trump was trying to gain the wealth he didn't actually have.   But the lawsuit was dismissed, because of course it's not libel to report that someone is not as rich as they claim.

It's tough to take public criticism.  Hillary Clinton knows this well.   But Clinton is not thin-skinned like Trump.   I don't want a president who throws hissy fits at press conferences, yells at reporters, and threatens writers with lawsuits.

The Washington Post article about Trump on May 24:

A video of Trump's press conference:

On Trump wanting to "open up" libel laws, and suing O'Brien:

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A mathematical mystery - part 3

Especially before the fall of the USSR, the best Russian mathematicians would often meet and discuss their work at seminars. 

Gelfand's seminar in Moscow was especially famous, since he would stop speakers any time they said something unclear.   In fact, sometimes he'd appoint an audience member to play the role of arbiter: if this guy in the audience doesn't understand it, the speaker has to explain it better!  

As a result, the seminar would often go on until late at night, even after the building was locked up.  But everyone learned a lot of math.

With such exhaustive seminars, publishing proofs sometimes became a mere afterthought.  You'll often see short papers from this era making important claims with just a tiny sketch of an argument to back them up.

That annoyed Western mathematicians.  And I've bumped into a few mysteries that I'm having trouble with, thanks to these short Russian papers without clear proofs.  Here is one.

This image by Greg Egan shows the set of points (a,b,c) for which the quintic

x^5 + ax^4 + bx^2 + c

has repeated roots... with the plane c = 0 removed.  You'll notice this surface crosses over itself in a cool way, creating lines of sharp cusps

Vladimir Arnol'd, who ran one of these famous seminars, says that one O. V. Lyashko studied this surface in 1982 with the help of a computer - a very primitive computer by our standards, I'm sure.  And he says Lyashko proved this surface looks the same as another surface defined using the icosahedron. 

Arnol'd doesn't mention removing the plane c = 0, so his claim is technically wrong.  But if you remove that plane, it looks right!   So I'd like to see a proof that these surfaces are the same (after a smooth change of coordinates).   The icosahedron and the quintic equation are connected in many ways, so there should be a nice explanation.  But I don't know it!

For more details on this surface, see my Visual Insight  blog post:

You'll also see the other surface, defined using the icosahedron.  And you can read a full explanation of that other surface here:

As I explain, the same surface shows up in yet another disguise - but again, I don't know a proof!   If you make progress on these mysteries, let me know!

The icosahedron is connected to some of the most fascinating symmetrical structures in the mathematical universe, such as E8 and the Golay code.   I'm trying to get to the bottom of this, so every clue helps.

Here is a longer description of Gelfand's seminar, as told by Simon Gindikin:

The Gelfand seminar was always an important event in the very vivid mathematical life in Moscow, and, doubtless, one of its leading centers. A considerable number of the best Moscow mathematicians participated in it at one time or another. Mathematicians from other cities used all possible pretexts to visit it. I recall how a group of Leningrad students agreed to take turns to come to Moscow on Mondays (the day of the seminar, to which other events were linked), and then would retell their friends what they had heard there. There were several excellent and very popular seminars in Moscow, but nevertheless the Gelfand seminar was always an event.

I would like to point out that, on the other hand, the seminar was very important in Gelfand's own personal mathematical life. Many of us witnessed how strongly his activities were focused on the seminar. When, in the early fifties, at the peak of antisemitism, Gelfand was chased out of Moscow University, he applied all his efforts to seminar. The absence of Gelfand at the seminar, even because of illness, was always something out of the ordinary.

One cannot avoid mentioning that the general attitude to the seminar was far from unanimous. Criticism mainly concerned its style, which was rather unusual for a scientific seminar. It was a kind of a theater with a unique stage director playing the leading role in the performance and organizing the supporting cast, most of whom had the highest qualifications. I use this metaphor with the utmost seriousness, without any intention to mean that the seminar was some sort of a spectacle. Gelfand had chosen the hardest and most dangerous genre: to demonstrate in public how he understood mathematics. It was an open lesson in the grasping of mathematics by one of the most amazing mathematicians of our time. This role could be only be played under the most favorable conditions: the genre dictates the rules of the game, which are not always very convenient for the listeners. This means, for example, that the leader follows only his own intuition in the final choice of the topics of the talks, interrupts them with comments and questions (a privilege not granted to other participants) [....] All this is done with extraordinary generosity, a true passion for mathematics.

Let me recall some of the stage director's strategems. An important feature were improvisations of various kinds. The course of the seminar could change dramatically at any moment. Another important mise en scene involved the "trial listener" game, in which one of the participants (this could be a student as well as a professor) was instructed to keep informing the seminar of his understanding of the talk, and whenever that information was negative, that part of the report would be repeated. A well-qualified trial listener could usually feel when the head of the seminar wanted an occasion for such a repetition. Also, Gelfand himself had the faculty of being "unable to understand" in situations when everyone around was sure that everything is clear. What extraordinary vistas were opened to the listeners, and sometimes even to the mathematician giving the talk, by this ability not to understand. Gelfand liked that old story of the professor complaining about his students: "Fantastically stupid students - five times I repeat proof, already I understand it myself, and still they don't get it."

It has remained beyond my understanding how Gelfand could manage all that physically for so many hours. Formally the seminar was supposed to begin at 6 pm, but usually started with an hour's delays. I am convinced that the free conversations before the actual beginning of the seminar were part of the scenario. The seminar would continue without any break until 10 or 10:30 (I have heard that before my time it was even later). The end of the seminar was in constant conflict with the rules and regulations of Moscow State University. Usually at 10 pm the cleaning woman would make her appearance, wishing to close the proceedings to do her job. After the seminar, people wishing to talk to Gelfand would hang around. The elevator would be turned off, and one would have to find the right staircase, so as not to find oneself stuck in front of a locked door, which meant walking back up to the 14th (where else but in Russia is the locking of doors so popular!). The next riddle was to find the only open exit from the building. Then the last problem (of different levels of difficulty for different participants) - how to get home on public transportation, at that time in the process of closing up. Seeing Gelfand home, the last mathematical conversations would conclude the seminar's ritual. Moscow at night was still safe and life seemed so unbelievably beautiful!

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It's fine to talk about other stuff.  I wish people would say stuff or ask more questions about the puzzle presented here, but since the details are nontrivial and described in 2 blog articles, I'm not really expecting much except to bring more attention to this puzzle, so somebody eventually solves it!
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The world's most long-winded proof

In the 1980s, the famous mathematician Ronald Graham asked if it's possible to color each positive integer either red or blue, so that no triple of integers a, b and c obeying Pythagoras’ famous equation:

a² + b² = c²

all have the same color.  He offered a prize of $100.

Now it's been solved!  The answer is no.  You can do it for numbers up to 7824, and a solution is shown in this picture.  But you can't do it for numbers up to 7825.

To prove this, you could try all the ways of coloring these numbers and show that nothing works.  Unfortunately that would require trying

3 628 407 622 680 653 855 043 364 707 128 616 108 257 615 873 380 491 654 672 530 751 098 578 199 115 261 452 571 373 352 277 580 182 512 704 196 704 700 964 418 214 007 274 963 650 268 320 833 348 358 055 727 804 748 748 967 798 143 944 388 089 113 386 055 677 702 185 975 201 206 538 492 976 737 189 116 792 750 750 283 863 541 981 894 609 646 155 018 176 099 812 920 819 928 564 304 241 881 419 294 737 371 051 103 347 331 571 936 595 489 437 811 657 956 513 586 177 418 898 046 973 204 724 260 409 472 142 274 035 658 308 994 441 030 207 341 876 595 402 406 132 471 499 889 421 272 469 466 743 202 089 120 267 254 720 539 682 163 304 267 299 158 378 822 985 523 936 240 090 542 261 895 398 063 218 866 065 556 920 106 107 895 261 677 168 544 299 103 259 221 237 129 781 775 846 127 529 160 382 322 984 799 874 720 389 723 262 131 960 763 480 055 015 082 441 821 085 319 372 482 391 253 730 679 304 024 117 656 777 104 250 811 316 994 036 885 016 048 251 200 639 797 871 184 847 323 365 327 890 924 193 402 500 160 273 667 451 747 479 728 733 677 070 215 164 678 820 411 258 921 014 893 185 210 250 670 250 411 512 184 115 164 962 089 724 089 514 186 480 233 860 912 060 039 568 930 065 326 456 428 286 693 446 250 498 886 166 303 662 106 974 996 363 841 314 102 740 092 468 317 856 149 533 746 611 128 406 657 663 556 901 416 145 644 927 496 655 933 158 468 143 482 484 006 372 447 906 612 292 829 541 260 496 970 290 197 465 492 579 693 769 880 105 128 657 628 937 735 039 288 299 048 235 836 690 797 324 513 502 829 134 531 163 352 342 497 313 541 253 617 660 116 325 236 428 177 219 201 276 485 618 928 152 536 082 354 773 892 775 152 956 930 865 700 141 446 169 861 011 718 781 238 307 958 494 122 828 500 438 409 758 341 331 326 359 243 206 743 136 842 911 727 359 310 997 123 441 791 745 020 539 221 575 643 687 646 417 117 456 946 996 365 628 976 457 655 208 423 130 822 936 961 822 716 117 367 694 165 267 852 307 626 092 080 279 836 122 376 918 659 101 107 919 099 514 855 113 769 846 184 593 342 248 535 927 407 152 514 690 465 246 338 232 121 308 958 440 135 194 441 048 499 639 516 303 692 332 532 864 631 075 547 542 841 539 848 320 583 307 785 982 596 093 517 564 724 398 774 449 380 877 817 714 717 298 596 139 689 573 570 820 356 836 562 548 742 103 826 628 952 649 445 195 215 299 968 571 218 175 989 131 452 226 726 280 771 962 970 811 426 993 797 429 280 745 007 389 078 784 134 703 325 573 686 508 850 839 302 112 856 558 329 106 490 855 990 906 295 808 952 377 118 908 425 653 871 786 066 073 831 252 442 345 238 678 271 662 351 535 236 004 206 289 778 489 301 259 384 752 840 495 042 455 478 916 057 156 112 873 606 371 350 264 102 687 648 074 992 121 706 972 612 854 704 154 657 041 404 145 923 642 777 084 367 960 280 878 796 437 947 008 894 044 010 821 287 362 106 232 574 741 311 032 906 880 293 520 619 953 280 544 651 789 897 413 312 253 724 012 410 831 696 803 510 617 000 147 747 294 278 502 175 823 823 024 255 652 077 422 574 922 776 413 427 073 317 197 412 284 579 070 292 042 084 295 513 948 442 461 828 389 757 279 712 121 164 692 705 105 851 647 684 562 196 098 398 773 163 469 604 125 793 092 370 432

possibilities.  But recently, three mathematicians cleverly figured out how to eliminate most of the options.  That left fewer than a trillion to check!  

So they spent 2 days on a supercomputer, running 800 processors in parallel, and checked all the options.  None worked.   They verified their solution on another computer.

This is the world's biggest proof: it's 200 terabytes long!  That's about equal to all the digitized text held by the US Library of Congress.  There's also a 68-gigabyte digital signature - sort of a proof that a proof exists - if you want to skim it.

It's interesting that these 200 terabytes were used to solve a yes-or-no question, whose answer takes a single bit to state: no.

I'm not sure breaking the world's record for the longest proof is something to be proud of.  Mathematicians prize short, elegant proofs.   I bet a shorter proof of this result will eventually be found.

Still, it's fun that we can do such things.   Here's a story about the proof:

and here's the actual paper:

• Marijn J. H. Heule, Oliver Kullmann and Victor W. Marek, Solving and verifying the Boolean Pythagorean triples problem via cube-and-conquer,

The cube-and-conquer paradigm is a "hybrid SAT method for hard problems, employing both look-ahead and CDCL solvers"... whatever that means.  It would be interesting to learn about this.  But it's time for breakfast!

Anyone who makes a joke about Fermat's remark:

"I have discovered a truly marvellous proof of this, which this margin is too narrow to contain."

loses 10 points, for not reading my whole post.

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Good to hear some details about Stampede!
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This is the small stellated dodecahedron.   It's like a star made of stars.   It has 12 pentagrams, 5-pointed stars, as faces.  These stars cross over each other.  Five meet at each sharp corner.

But here's the really cool part: you should think of each pentagram as a pentagon that's been mapped into space in a very distorted way, with a 'branch point of order 2' at its center.

What does that mean?  

Stand at the center of a pentagon!   Measure the angle you see between two corners that are connected by an edge.  You'll get 2π/5.   But now stand at the center of a pentagram.   Measure the angle you see between two corners that are connected by an edge.  You get 4π/5.  Twice as big! 

So, to map a pentagon into space in a way that makes it look like a pentagram, you need to wrap it twice around its central point.   That's what a branch point of order 2 is all about.

That's the cool way to think of this shape you see spinning before you.  It's a surface made of 12 pentagons, each wrapped twice around its center, with 5 meeting at each sharp corner. 

There's another way to think about this surface!   Any equation of this sort

z⁵ + pz + q = 0

has 5 solutions, or roots.   To make this true we need to bend the rules a bit.  First, we let the solutions be complex numbers...  so let p and q be complex too.  Second, we must allow for the possibility of repeated roots: when you factor z⁵ + pz + q, the same root may show up twice.

Now here's the cool part: the small stellated dodecahedron is the set of all lists of 5 numbers that are roots of some equation of this form:

z⁵+ pz + q = 0

So it's not just a pretty star-shaped thing.  It's a serious mathematical entity!    It's actually a Riemann surface, the most symmetrical Riemann surface with 4 holes!   You can build it starting from a tiling of the hyperbolic plane by pentagons.  In this tiling 5 pentagons meet at each corner - just like 4 squares meet at each corner in a square tiling of the ordinary plane.

It's all about the number 5, which has a lot of star power.  To understand more, read my blog article:

Most of this was discovered by Felix Klein in 1877.   He discovered lots of cool facts like this.  It's almost annoying.  I keep learning cool things about Riemann surfaces and the hyperbolic plane... and it keeps turning out they were discovered by Klein.    He found more than his fair share. 

By the way, this post and many others are now part of my "geometry" collection.   If you want to binge on beauty, go there now:

But beware: next morning you may wake up in a gutter with a headache, seeing stars.

This image was created by someone named 'Cyp' and placed on Wikicommons.

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We had one of these made from metal and shell as a lampshade in the hall at Auntie Jo's...
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Broke — but self-funding

During the primaries, Trump claimed he was rich and couldn't be bought.  He said he wouldn't have a super-PAC.   Now he has a lot of super-PACs - all fighting each other.   But his campaign has very little cash!  

In May he tweeted:

Good news is that my campaign has perhaps more cash than any campaign in the history of politics.

But this was a lie.   By the end of May his campaign had less than $1.3 million.  At least, that's what he reported to the Federal Election Commission.  

That may sound like a lot if you don't know US politics.  But Clinton, by comparison, had $42 million.   Even Ben Carson - remember that guy, the nutty candidate who claimed the pyramids were built for storing grain? - had $1.7 million when he quit back in March.

So, by US standards, Trump's campaign is broke.  

And he keeps putting campaign money back into his own pocket!

Throughout his campaign, up to the end of May, he has given $6.2 million of campaign funds to companies he owns.  That's roughly 10% of his campaign spending so far.    And in May this rose to almost 20%: he spent $6.7 million on his campaign, but over $1 million of that went to his own companies.

According to the Huffington Post:

The most striking expenditure in the new filings was $423,372, paid by the Trump campaign for rentals and catering at Trump’s 126-room Palm Beach, Florida, mansion, Mar-A-Lago, which Trump operates as a private club.

Other Trump-owned recipients of campaign funds include Trump Restaurants, which raked in $125,080 in rent and utilities; Trump Tower Commercial, which charged $72,800 in rent and utilities in the building that houses Trump’s campaign headquarters; the Trump National Golf Club, in Jupiter, Florida, which collected $35,845 for facilities rental and catering; and the Trump International Golf Club in West Palm Beach, Florida, which billed the campaign for $29,715, for facilities rentals and catering.

So, Trump has given a whole new meaning to the term "self-funding".  In 2000, he said:

It's very possible that I could be the first presidential candidate to run and make money on it.

It seems that Trump plans to let the Republican National Committee pay for most of his campaign.  They've got some money: they started June with $20 million in cash.  But four years ago at this time, they had more than $60 million.  Their big donors are shying away from Trump.
I would love to get money out of US politics.  I hadn't expected Trump to take the lead. 

Here is his May report to the Federal Election Commission:

Here is the Huffington Post article:

Here is an article on Trump's super-PACs:

Trump's boast that his might be the first presidential campaign to make

More figures from here:

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Silly sounding elements

Forget Trump. We have until November to prevent scientists from naming an element oganesson

I don't have anything against Yuri Oganessian, a pioneer in the study of  highly radioactive, short-lived elements.   I just think the word "oganesson" stumbles off the tongue like a dazed, jet-lagged passenger staggering off a plane and falling down the stairway. 

And it's a noble gas!   A noble gas should sound noble.  

Neon.  Argon.  Krypton.  Xenon.  Oganesson.  

Which one does not belong?  Which name was created by somebody without a shred of poetry in their soul?

The International Union of Pure and Applied Chemistry, or IUPAC, has begun a five-month public review, ending 8 November 2016, before it names these elements:

Element 113: Nihonium (Nh)
Element 115, Moscovium (Mc)
Element 117, Tennessine (Ts)
Element 118, Oganesson (Og)

I have no opinions except about how the names sound and look.  Nihonium and Moscovium sound okay to me.   The word "Tennessine" is awkward.   I like the state of Tennessee.  I have nothing against it having its own highly radioactive element.   I just don't like this word.  This element is a halogen, and again it's the least pretty of the bunch:

Fluorine.  Chlorine.   Bromine.   Iodine.   Astatine.   Tennessine.

But "oganesson" is worse.  IUPAC could have done better hiring that unemployed guy who used to make up names for elements on Star Trek.  The only good thing about "oganesson" is that it has such a short half-life that we'll hardly ever need to say that word. 

I would gladly accept tennessine if it would stop "oganesson" from lurching onto the periodic table.  In fact, I'd volunteer to eat the world's entire supply of tennessine.

If you agree with me, or have other opinions, write a polite letter to Dr. Lynn M. Soby, the Executive Director of IUPAC, at

PS - yes, I know helium is also a noble gas.  People gave it a name suitable for a metal, not a noble gas, before they knew better.  It's too late to call it helion.
Provisional recommendations - for public review: IUPAC is naming the four new elements nihonium, moscovium, tennessine, and oganesson
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+David Washington That's how ents talk and it takes them forever to discuss anything.
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Does dark matter have dark hair?

By now there's a lot of evidence that dark matter exists, but not so much about what it is.  The most popular theories say it's some kind of particles that don't interact much with ordinary matter, except through gravity.  These particles would need to be fairly massive - as elementary particles go - so that despite having been hot and energetic shortly after the Big  Bang, they'd move slow enough to bunch up thanks to gravity.  Indeed, the bunching up of dark matter seems necessary to explain the formation of the visible galaxies!  

Searches for dark matter particles have not found much.  The DAMA experiment, a kilometer underground in Italy, seemed to detect them.  Even better, it saw more of them in the summer, when the Earth is moving faster relative to the Milky Way, than in the winter.  That's just what you'd expect!  But other similar experiments haven't seen anything.  So most physicists doubt the DAMA results.  

Maybe dark matter is not made of massive weakly interacting particles.  Maybe it's a superfluid made of light but strongly interacting particles.  Maybe there are lot more 25-solar-mass black holes than most people think!  There are lots of theories, and I don't have time to talk about them all.  

I just want to tell you about a cool idea which assumes that dark matter is made of massive weakly interacting particles.  It's still the most popular theory, so we should take it seriously and ask: if they exist, what would these particles do?

In the early Universe they'd attract each other by gravity.  They'd bunch up, helping seed the formation of galaxies.  But after stars and planets formed, they'd pull at the dark matter, making it thicker in some places, thinner in others.  

And this is something we can simulate using computers!  After all, the relevant physics is well-understood: just Newton's law of gravity, applied to stars, planets and zillions of tiny dark matter particles.  

Gary Prezeau of NASA's Jet Propulsion Laboratory did these simulations and discovered something amazing. 

When dark matter flows past the Earth, it gets deflected and focused by the Earth's gravity.  Like light passing through a lens, it gets intensely concentrated at certain locations!

This creates long thin 'hairs' where the density of dark matter is enhanced by a factor of 10 million.   Each hair is densest at its 'root'.   At the root, the density of dark matter is about a billion times greater than average!

The hairs in this picture are not to scale: the Earth is drawn too big.   The roots of the hairs would be about a million kilometers from Earth, while the Earth's radius is only 6,400 kilometers.  

Of course we don't know dark matter particles exist.  What's cool is that if they exist, it forms such beautiful structures!  And if we could do a dark matter search in space, near one of these possible roots, we might have a better chance of finding something.   

Let me paraphrase Prezeau, because the real beauty is in the details.  From his abstract:

It is shown that compact bodies form strands of concentrated dark matter filaments henceforth simply called 'hairs'. These hairs are a consequence of the fine-grained stream structure of dark matter halos surrounding galaxies, and as such they constitute a new physical prediction of the standard model of cosmology. Using both an analytical model of planetary density and numerical simulations (a fast way of computing geodesics) with realistic planetary density inputs, dark matter streams moving through a compact body are shown to produce hugely magnified dark matter densities along the stream velocity axis going through the center of the body. Typical hair density enhancements are 10^7 for Earth and 10^8 for Jupiter. The largest enhancements occur for particles streaming through the core of the body that mostly focus at a single point called the root of the hair. For the Earth, the root is located at about 10^6 kilometers from the planetary center with a density enhancement of around 10^9 while for a gas giant like Jupiter, the root is located at around 10^5 kilometes with a enhancement of around 10^11. Beyond the root, the hair density precisely reflects the density layers of the body providing a direct probe of planetary interiors.

The mathematicians and physicists among you may enjoy even more detail.  Again, I'll paraphrase:

According to the standard model of cosmology, the velocity dispersion of cold dark matter (CDM) is expected to be greatly suppressed as the universe expands and the CDM collisionless gas cools.  In particular, for a weakly interacting mass particle with mass of 100 GeV that decoupled from normal matter when the Universe cooled to an energy of 10 MeV per particle, the velocity dispersion is only about 0.0003 meters per second.

As the Universe cools and the nonlinear effects of gravity become more prominent and galactic halos grow, the dispersion of velocities will increase somewhat, but 10 kilometers per second is an upper limit on the velocity dispersion of the resulting dark matter streams.

Dark matter starts out having a very low spread in velocities, but its location can be anywhere.  So, it forms a 3-dimensional sheet in the 6-dimensional space of position-velocity pairs, called phase space

As time passes this sheets gets bent, but it can never be broken.   When this sheet gets folded enough, we get a 'caustic where lots of different dark matter particles have almost the same position, though different velocities.  You can see a caustic by shining light into a reflective coffee cup, or shining light through a magnifying glass.  The same math applies here:

A phase-space perspective sheds additional light on the processes affecting the CDM under the influence of gravity.  When the CDM decouples from normal matter, the CDM occupies a 3-dimensional sheet in the 6-dimensional phase space since it has a tiny velocity dispersions. The process of galactic halo formation cannot tear this hypersurface, thanks to generalization of Liouville’s theorem.  Under the influence of gravity, a particular phase space volume of the hypersurface is stretched and folded with each orbit of the CDM creating layers of fine-grained dark matter streams, each with a vanishingly small velocity dispersion. These stretches and folds also produce caustics: regions with very high CDM densities that are inversely proportional to the square root of the velocity dispersion.

Here are some more pictures:

and here's the paper:

• Gary Prezeau, Dense dark matter hairs spreading out from Earth, Jupiter and other compact bodies,

#spnetwork arXiv:1507.07009 #astronomy  
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+Able Lawrence - okay, I'm doing it.  Thanks for suggesting it.
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Let us read what we paid for

Imagine a business like this: you get highly trained experts to give you their research for free... and then you sell it back to them.  Of course these experts need equipment, and they need to earn a living... so you get taxpayers to foot the bill.  

And if the taxpayers want to actually read the papers they paid for?   Then you charge them a big fee!

It's not surprising that with this business model, big publishers are getting rich while libraries go broke.  Reed-Elsevier has a 37% profit margin!

But people are starting to fight back — from governments to energetic students like ‎Alexandra Elbakyan here.

On Friday, the Competitiveness Council —a gathering of European ministers of science, innovation, trade, and industry—said that by 2020, all publicly funded scientific papers published in Europe should be made immediately free for everyone to read

This will start a big fight, and it may take longer than 2020.   But Alexandra Elbakyan isn't waiting around.

In 2011, as a computer science grad student in Kazakhstan, she got sick of paying big fees to read science papers.  She set up SciHub, a pirate website that steals papers from the publishers and sets them free.

SciHub now has 51,000,000 papers in its database.  In October 2015, Elsevier sued them.  In November, their domain name was shut down.  But they popped up somewhere else.  By February, people were downloading 200,000 papers per day.   Even scientists with paid access to the publisher's databases are starting to use SciHub, because it's easier to use.

Clearly piracy is the not the ultimate solution. Elbakyan now lives in an undisclosed location, to avoid being extradited.  But she gave the world a much-needed kick in the butt.   The old business model of get smart people to work for free and sell the product back to them is on its way out.

For more, read:

John Bohannon, Who's downloading pirated papers? Everyone, Science, 28 April 2016,

and especially the SciHub Twitter feed:

Also read this:

Martin Enserink, In dramatic statement, European leaders call for ‘immediate’ open access to all scientific papers by 2020, Science,
27 May 2016,

The key word here is immediate - right now the US lets the journals sit on publicly funded papers for a year.  The Dutch government is really pushing this!  Congratulations to them!

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+Matthew Rapaport - yes, when there's a mass exodus of good authors from journal, its impact factor drops.  Since the Elsevier boycott began, a number of Elsevier journals had their whole board of editors resign, start a new journal, and tell everyone to publish in the new journal.  That's a good step. 
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I don't like posting about politics.  I prefer math.  Math is the beautiful game of truth.  Politics is the ugly game of lies. 

But I woke up in the middle of the night and realized that if I didn't say the obvious, I might regret it:

We've got to fight Trump with everything we've got.

The US is dangerously close to electing a buffoon and would-be dictator: our very own Berlusconi, our very own Putin.  Elizabeth Warren explains it clearly, so please reshare this video:

Unfortunately, if you’ve been watching the presidential race, you know that we need to stand up now more than ever. Just yesterday, it came out that Donald Trump had said back in 2007 that he was “excited” for the real estate market to crash because, quote, “I’ve always made more money in bad markets than in good markets.” That’s right. The rest of us were horrified by the 2008 financial crisis, by what happened to the millions of families like Mr. Estrada’s that were forced out of their homes. But Donald Trump was drooling over the idea of a housing meltdown — because it meant he could buy up a bunch more property on the cheap.

What kind of a man does that? Root for people to get thrown out on the street? Root for people to lose their jobs? Root for people to lose their pensions? Root for two little girls in Clark County, Nevada, to end up living in a van? What kind of a man does that? I’ll tell you exactly what kind — a man who cares about no one but himself. A small, insecure moneygrubber who doesn’t care who gets hurt, so long as he makes some money off it. What kind of man does that? A man who will NEVER be President of the United States.

Sometimes Trump claims he is tough on Wall Street – tough on the guys who cheated people like Mr. Estrada. I’m sure you’ve heard him say that. But now he’s singing a very different song. Last week, he said that the new Dodd-Frank financial regulations have, and I’m quoting here, “made it impossible for bankers to function” and he will put out a new plan soon that “will be close to dismantling Dodd-Frank.” Donald Trump is worried about helping poor little Wall Street? Let me find the world’s smallest violin to play a sad, sad song.

Can Donald Trump even name three things that Dodd-Frank does? Seriously, someone ask him. But this much he should know: If he’s so tough on Wall Street, he should be cheering on Dodd-Frank’s capital and leverage requirements that have made big banks less likely to fail. If he’s so tough on Wall Street, he should be cheering on Dodd-Frank’s living wills process, which is helping push big banks to become safer. If he’s so tough on Wall Street, he should be cheering on the Consumer Financial Protection Bureau, which has already returned over $11 billion to families who were cheated.

He SHOULD be, but he’s not. Now that he’s sewn up the Republican nomination, Donald Trump is dropping the pretense. Now he’s kissing the fannies of poor, misunderstood Wall Street bankers. But the American people are a whole lot smarter than Donald Trump thinks they are. The American people are NOT looking for a bait and switch. They are NOT looking for a man so desperate for power he will say and do anything to get elected. Take the hint, Donald: the time for letting big banks call all the shots in Washington is coming to an end.

And I want to make just one last point about Donald Trump that won’t fit into a Twitter war. One last point that sums up what Donald Trump is all about – his taxes.

We don’t know what Trump pays in taxes because he is the first Presidential nominee in 40 years to refuse to disclose his tax returns. Maybe he’s just a lousy businessman who doesn’t want you to find out that he’s worth a lot less money than he claims.

But we know one thing: the last time his taxes were made public, Donald Trump paid nothing — zero. Zero taxes before, and for all we know he’s paying zero taxes today. And he’s proud of it. Two weeks ago he said he’s more than happy to dodge taxes because he doesn’t want to throw his money “down the drain.”

Trump likes being a billionaire, and doesn’t think the rules that apply to everyone else should apply to him. But let’s be clear: Donald Trump didn’t get rich on his own. His businesses rely on the roads and bridges the rest of us paid for. His businesses rely on workers the rest of us paid to educate and on police-forces and fire fighters who protect all of us and the rest of us pay to support. Donald Trump and his businesses are protected by a world-class military that defends us abroad and keeps us safe at home and that the rest of us pay to support. When anyone builds something terrific, they should get to keep a big hunk of it. But they should also pay a fair share forward so the next kid and the next kid and the next kid who come along gets their chance to build something too. That’s how we build a future that works for everyone.

And that goes double for Donald Trump, because he didn’t even get rich by building something terrific. He inherited a fortune from his father, and kept it going by scamming people, declaring bankruptcy, and skipping out on what he owed.

Nurses, teachers, and dockworkers pay their fair share for all the services that keep Trump’s businesses going. Programmers and engineers and small business owners pay their fair share to support our military who show courage and sacrifice every single day. Donald Trump thinks supporting them is throwing money “down the drain.”

I say we just throw Donald Trump down the drain.

Let’s face it: Donald Trump cares about exactly one thing — Donald Trump. It’s time for some accountability because these statements disqualify Donald Trump from ever becoming President. The free ride is over.

I am going to disable comments because I don't see a need for discussion.  +Elizabeth Hahn gets the last word.
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I think you just made me realize why I've always loved math so much. :) but I agree, this is very important. 

John Baez

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A windy day

This is a tornado that occurred in south-central Oklahoma on May 9th.   It's impressive what moist air can do when it's not in thermal equilibrium.

At first I couldn't remember where I found this video.  But Chris Greene found it:

Watch the whole thing!  At the end you'll see a car driving dangerously close to an oncoming tornado.  I wonder how that worked out.
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fair enough :)
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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 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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