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

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It seems a lot of ultra-high-energy cosmic rays are coming from a patch of the sky near the Big Dipper!  

Cosmic rays are high-energy particles, mainly protons and atomic nuclei, which come from outer space and hit the Earth's atmosphere.  When one hits, it produces a big shower of other particles.  Most cosmic rays are believed to have picked up their energy by interacting with shock waves in the interstellar medium.  But the most energetic ones remain mysterious — nobody knows how they could have acquired such high energies.

The record is a 1994 event seen by a detector in Utah called the Fly's Eye - because that's what it looks like.   It saw a shower of particles produced by a cosmic ray with an energy of about 300 times 10¹⁸ electron volts.   That's an insane amount of energy.  It's about 50 joules: the energy of a one-kilogram mass moving at 10 meters/second, all packed into one particle!  

To put it another way: the Large Hadron Collider, our best particle accelerator, speeds up protons to an energy of 7 trillion electron volts.  The cosmic ray seen by the Fly's Eye had an energy of 300,000,000 trillion electron volts.  We're not doing so well compared to nature.  But we don't know how nature does it.

Anyway, now we've got a detector much better than the Fly's Eye: the Telescope Array.  It's also in Utah, because the air is clear and the nights are dark.  It's a jaw-dropping 760 square kilometers in size, because land is cheap.  It consists of about 500 scintillation detectors in a square grid, each 1.2 kilometers away from the next.  Each one is a solar-powered gadget containing plastic that lights up when a shower of particles hits it.  There are also three telescopes that watch the air light up.

So, we can tell where the ultra-high energy cosmic rays are coming from! 

Chart (a) shows where.  Each dot is a cosmic ray with energy more than 57 quintillion eV.  Well, the dot labelled GC is the galactic center, and the dot labelled anti-GC is the 'anti-galactic center': the direction in the sky pointing exactly away from the center of the Milky Way.  GP is the plane of the galaxy, and there's some other stuff. 

But the point is: the dots are clustered in a patch of the northern sky.

The colors in chart (b) show how many of these cosmic rays there are in a 20-degree circle around each point.  This makes it easier to see where they're coming from.  Their paths get bent by magnetic fields, so even if they all originate in one location they'd get smeared out.

What's making them?  We don't know!   That's the cool part: it's still a big mystery.  Here's what the astronomers say:

Assuming the hotspot is real, two possible interpretations are: it may be associated with the closest galaxy groups and/or the galaxy filament connecting us with the Virgo cluster; or if cosmic rays are heavy nuclei they may originate close to the supergalactic plane, and be deflected by extragalactic magnetic fields and the galactic halo field.

What the heck is the supergalactic plane?   It's the curve in chart (a) lablled SGP.  It's major structure in the local universe: nearby galaxy clusters like the Virgo cluster,  the Pisces-Perseus supercluster and the Great Attractor lie roughly in a plane!

Someday we'll figuring out what's really happening.  The paper is here:

• The Telescope Array Collaboration: R.U. Abbasi, M. Abe, T.Abu-Zayyad, M. Allen, R. Anderson, R. Azuma, E. Barcikowski, J.W. Belz, D.R. Bergman, S.A. Blake, R. Cady, M.J. Chae, B.G. Cheon, J. Chiba, M. Chikawa, W.R. Cho, T. Fujii, M. Fukushima, T. Goto, W. Hanlon, Y. Hayashi, N. Hayashida, K. Hibino, K. Honda, D. Ikeda, N. Inoue, T. Ishii, R. Ishimori, H. Ito, D. Ivanov, C.C.H. Jui, K. Kadota, F. Kakimoto, O. Kalashev, K. Kasahara, H. Kawai, S. Kawakami, S. Kawana, K. Kawata, E. Kido, H.B. Kim, J.H. Kim, J.H. Kim, S. Kitamura, Y. Kitamura, V. Kuzmin, Y.J. Kwon, J. Lan, S.I. Lim, J.P. Lundquist, K. Machida, K. Martens, T. Matsuda, T. Matsuyama, J.N. Matthews, M. Minamino, K. Mukai, I. Myers, K. Nagasawa, S. Nagataki, T. Nakamura, T. Nonaka, A. Nozato, S. Ogio, J. Ogura, M. Ohnishi, H. Ohoka, and 59 more authors, Indications of intermediate-scale anisotropy of cosmic rays with energy greater than 57 EeV in the northern sky measured with the surface detector of the Telescope Array experiment,
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+Able Lawrence - I'm not an expert on this stuff, but a quick scan reveals that:

"Many astrophysicists suspect ultrahigh-energy cosmic rays are generated by active galactic nuclei, or AGNs, in which material is sucked into a supermassive black hole at the center of galaxy, while other material is spewed away in a beam-like jet known as a blazar. Another popular possibility is that the highest-energy cosmic rays come from some supernovas (exploding stars) that emit gamma rays bursts."
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John Baez

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Warp cube

The N-Light Membrane is a cube of mirrors with fluorescent lights as edges.  3 mirrors are one-way, so you can see inside.   All you can see is reflections of the inside of the cube, extending to infinity!   

The other 3 mirrors are flexible, and the cube is connected to an air tank.  By inflating or deflating the air tank, you can make the cube convex or concave.  The reflections bend in weird ways. The effect is hypnotic.

This cube was created by an art collective called Numen/For Use, and it was displayed in St. Petersburg.   It's fun to watch videos of it shot from different angles:

What if you did a tetrahedron or octahedron?  There's no need to imagine; you can see them here:

Numen/For Use is really three Croatian and Austrian guys, Sven Jonke, Christoph Katzler and Nikola Radeljković. 

Puzzle 1: can you make a mirrored box with warped sides so the reflections make it look like you're in hyperbolic space?  You may have seen the 'hyperbolic honeycombs' in my #geometry series - that's the sort of thing I mean.

Puzzle 2: more generally, what cool effects could you get from a mirrored box? 

If we're in an ellipsoidal mirrored box and we each put one of our eyes at one of the foci of the box, all you should see is the pupil of my eye, and vice versa.

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Maybe we can't make it look like we're in hyperbolic space, but if we are skilled enough at manipulating the mirrors we could maybe make it look like somebody else is in whatever space it is:
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Open-access climate science

A recent paper says there's 75% chance of a major climate event called an El Niño by the end of 2014  This would be huge news!  So my friends and I decided to replicate this paper, criticize it, and improve it.

The paper uses a climate network, shown here.  See the little circles?   Every day, scientists measure air temperatures at each of these points.  The red ones are in the El Niño basin.   The paper calculates how temperatures in the El Niño basin are correlated to temperatures at the other points.  When the average correlation gets high enough, they predict an El Niño.

That's a very  rough summary of what the paper does!  I explain exactly what it does here:

including how they got their data.

+Graham Jones downloaded this data and wrote software that does what they do in the paper.  (At least we think so: +Nadja Kutz found a mathematical glitch, where the authors may not have said what they really meant.  Read my article for that.)  Graham's software is on GitHub, and we'll explain it soon.  

This is an experiment in open science.  Not just the final results but the software, the data, the whole process is in public view.  You can read all our discussions here:

One of our next steps will be to simplify the method used in this paper.  It's more complicated than it needs to be; Graham has already found one way to make it simpler while keeping its predictive ability just about as good.

What about after that?   Three more programmers have just joined the team - the Azimuth Code Project - but in the next couple of weeks I think we need some strategy sessions.  Personally I want to get a better feel for El Niños.  I want to read more papers, but also I'd love to watch lots of movies of Pacific air temperatures, ocean temperatures, and so on.  Some of these movies exist, but we may want to create more.  It would also be great to write software illustrating simplified models of El Niño, and one of the team wants to do that. 

We are seriously short of actual experts on climate science, but I'm afraid that's inevitable until we publish some papers: the experts are busy doing their own work, and so far there's no big reason for them to take us seriously.  And that's okay, for now: we're on a learning curve.

Puzzle: what is the pink rectangle?

Oh, and by the way: I keep talking about "a paper".   Here it is:

• Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, Very early warning of next El Niño, PNAS, February 2014,

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+David Friedman More so, peer review journals who do not require their submissions to have their data model public or included ought not to be trusted, as a reviewer.
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Chain reaction

A domino can knock over a domino that's one and a half times taller.  Here you see a tiny domino 5 millimeters tall starting a chain reaction 13 dominos long... which eventually knocks over a domino about half a meter tall. 

The amount of energy released by the fall of that last domino is 2 billion times the amount of energy it took to knock over the first one!

And if we could do a chain reaction like this 29 dominos long, the final domino would be the size of the Empire State Building!

I got this from +W Younes, who has been posting some nice images recently, but only privately.  So, you should become friends with him.

He in turn got it from here:

I don't know where they got it from.  But it's clearly a chain reaction.  I just quoted what Younes said, and he quoted what that website said.  When you pass on information, it's good to check it.

Puzzle 1: what did I say that's not 100% correct, or at least a bit misleading?

Puzzle 2: who actually did this experiment here, so we can thank them?

Puzzle 3: where can I get a version of this animated gif that's one and a half times bigger?

This paper studies the physics of falling dominoes in detail, taking friction into account:

• J.M.J. van Leeuwen, The domino effect,

It finds an analytical solution in the "thin domino limit", but also studies the general case.
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Here's a video of a human domino chain :) Human Dominoes Prank
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John Baez

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Singapore G+ Dinner

On Friday July 4th, +Elias Mårtenson and I would like to meet any other friendly G+'ers who happen to be in Singapore.  If you want to join us, let me know!

I suggest that we meet at 6:30 pm.  Where should we meet?

Food is very important in Singapore, so let's go someplace good.  Where should we go?  I like a good hawker center better than a fancy restaurant, so I'd like to explore a new one.  A good place should at least have the four dishes shown here:

Fruit rojak - typically made of chopped-up cucumber, pineapple, benkoang (jicama), bean sprouts, taupok (puffy, deep-fried tofu) and youtiao (cut-up Chinese-style fritters), with a delicious sauce of belacan (shrimp paste), sugar, chili, and lime juice.

Grilled stingray - just what it sound like, grilled on a banana leaf and topped with sambal (chili sauce).

Satay - grilled meat on skewers, dipped in peanut chili sauce.

Carrot cake, or chai tow kway - don't be fooled, there's no carrots here!  It's made of radish cake (steamed rice flour, water, and shredded white daikon) stir fried with eggs, garlic, spring onion and sometimes dried shrimp. There are two versions.  White carrot cake does not use sweet soy sauce, and the carrot cake is fried on top of a beaten egg to form a crust.  Black carrot cake includes molasses, and the egg is simply mixed in with the carrot cake.  The picture here shows the white version, but I'm a black carrot cake man!

These photos and more are from:

• Singapore favorite food 2013, Miss Tam Chiak,

If you want to learn about Singapore foods, this blog is a great way to do it. 
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HAHAHAHA... darn, and there I was hoping to play guess the +John Baez  with you telling me what color your shirt would be and what cartoon character it had :P
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A network of networks

We have a lot to learn from nature.  Biology has its own ways of processing information, and we're just starting to figure them out.   They work differently than the digital computers built by humans.  I recently heard a great talk about this by Luca Cardelli, an expert on biological computation who works at Microsoft Research in Cambridge and Oxford.

The little gizmos in his picture here are called influence networks. They're chemical reactions built from ‘gates’ where one chemical process activates or deactivates another. 

All these influence networks actually show up in living organisms! 

The simplest one is AM, in the blue circle.  This  stands for Approximate Majority.  It's a chemical reaction where starting with molecules of two kinds, those in the majority completely take over: we get more and more of those, and less and less of the other kind.  So, it's a way for a biological system to decide among two choices!  The majority wins the vote. 

In your cells, this chemical reaction gets used in an epigenetic switch - a gizmo that turns a gene on or off.  That's important, because somehow a cell has to decide if it's going to be a kidney cell or a liver cell, and so on.

The blue arrows show how a bigger, more complicated influence network can simulate a smaller one.  Cardelli has worked out a mathematical theory of this.  So, he can tell you exactly what the blue arrows in his picture are.  They're called morphisms.

Here's my summary of Cardelli's talk, including links to his work, and a lot more:

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"There's a lot left to understand here, and I wish I had another grad student just to help work out my ideas on this stuff." .... good luck :)
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Now you can apply to attend a workshop on Entropy and Information in Biological Systems.  This is going to be fun!

I'm running it with John Harte at Berkeley, who uses maximum entropy methods to study ecosystems, and +Marc Harper at UCLA, who uses information theory to study evolutionary games.  It's happening on April 8-10, 2015 at the National Institute for Mathematical and Biological Synthesis in Knoxville Tennesee.  There will be financial support for workshop attendees who need it.  We will choose among the best applicants and invite 10-15 of them. 

To apply, go here:

The idea

Information theory and entropy methods are becoming powerful tools in biology, from the level of individual cells, to whole ecosystems, to experimental design, model-building, and the measurement of biodiversity. The aim of this investigative workshop is to synthesize different ways of applying these concepts to help systematize and unify work in biological systems.  Early attempts at “grand syntheses” often misfired, but applications of information theory and entropy to specific highly focused topics in biology have been increasingly successful.  In ecology, entropy maximization methods have proven successful in predicting the distribution and abundance of species.  Entropy is also widely used as a measure of biodiversity.  Work on the role of information in game theory has shed new light on evolution. As a population evolves, it can be seen as gaining information about its environment.  The principle of maximum entropy production has emerged as a fascinating yet controversial approach to predicting the behavior of biological systems, from individual organisms to whole ecosystems.  This investigative workshop will bring together top researchers from these diverse fields to share insights and methods and address some long-standing conceptual problems.

Our goals

• To study the validity of the principle of Maximum Entropy Production (MEP), which states that biological systems – and indeed all open, non-equilibrium systems – act to produce entropy at the maximum rate.

• To familiarize all the participants with applications to ecology of the MaxEnt method: choosing the probabilistic hypothesis with the highest entropy subject to the constraints of our data. We will compare MaxEnt with competing approaches and examine whether MaxEnt provides a sufficient justification for the principle of MEP.

• To clarify relations between known characterizations of entropy, the use of entropy as a measure of biodiversity, and the use of MaxEnt methods in ecology.

• To develop the concept of evolutionary games as “learning” processes in which information is gained over time.

• To study the interplay between information theory and the thermodynamics of individual cells and organelles.

For more details including a list of invited speakers, go here:
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Applied!  Sounds like a blast.
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What if famous paintings were photoshopped like models today?

Lauren Wade writes: Whether it’s tucking tummies, contouring jaw lines, enlarging eyes and lips, brushing out cellulite, or full-out head swapping, I’ve seen it all as a photo editor. While the conversation about the media’s portrayal and obsession with an unrealistic and unattainable beauty standard is not a new one, I think it’s crazy how much retouching people don’t notice. Over the last five years, having done many of the quick, subtle fixes that are the industry standard myself, I know that even an image considered to look “natural” is anything but.

So, she changed a bunch of famous paintings.  This is Titian's Danaë With Eros.  You can see the rest here:
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+Harald Hanche-Olsen - I don't know why you missed those; I saw 'em.  Worse is when comments wrongly get marked as spam by G+.  Then nobody sees them until I remember to check and restore them... and I believe then they look as if they've always been there.
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Water world

Here is weather simulated on an aqua planet: a world like our Earth, but with only ocean!  With no land, the weather becomes simpler.  Here's what happens when you add land:

The aqua planet simulation was done in 2004, in Japan.   The planet's surface was divided into an icosahedron!   Then each triangle was chopped into smaller triangles with sides 3.5 kilometers long.  These are just barely small enough to simulate clouds, but nobody had simulated the whole planet's atmosphere in such a fine-grained way before.  It required a supercomputer.

By the way, simulating weather is different than simulating climate. When people try to predict the climate 50 years from now, they don't do it by simulating each day's weather for the next 50 years.

This weather simulation project was called NICAM, the Nonhydrostatic ICosahedral Atmospheric Model.  Later, in 2008, they added land.  You can see how much more interesting it gets!  

I imagine people can do much better now, but I'm not an expert in this subject.  For example, I don't know why the aqua planet doesn't have cyclones!  Is this just a deficiency of the model... or would a world without land really not have cyclones?

You can read more about NICAM here:

and the details of the aqua planet are here:

• H. Tomita et al, A global cloud-resolving simulation: Preliminary results from an aqua planet experiment, Geophysical Research Letters 32 (2005),

The paper is free!

The NICAM project is still underway.  They're very interested in the Madden-Julian oscillation, the largest form of variability in the tropical atmosphere on time scales of 30-90 days. It’s a pulse that moves east across the Indian Ocean and Pacific Ocean at 4-8 meters/second.  It gives patches of anomalously high rainfall... and also patches of anomalously low rainfall.

I want to learn more about the Madden-Julian oscillation, since strong Madden-Julian oscillations often hint that 6-12 months later there will be an El Niño.

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Cyclones? I was dreaming they could be vortices trailing a continent or other protuberance through the water into the air? 
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Puzzle 1: Suppose you have 10 white balls and 10 black balls.  You can distribute them any way between two urns, as long as you put at least one ball in each urn.   Your friend selects an urn at random and randomly selects a ball from that urn.  How can you maximize the chance that your friend picks a white ball?  

This is from Paul Nahin's new book Will You Be Alive 10 Years From Now?   It's a great introduction to probability based on puzzles and history.   I like it because it's fun at many levels.   You need to know some probability theory to follow it.   But it should be okay for beginners - it uses some calculus near the end - and it was also fun for me.  

The use of history is key here.  Some books use 'human interest stories' as a way to placate the reader who is getting bored with the science.  For example, while talking about Schrödinger's equation, they might digress and tell us how the married Erwin Schrödinger invented his equation during a two-and-a-half-week romantic getaway with a mysterious girlfriend in the Swiss Alps.   But this book uses stories to propel the explanations forward.

For example: I know how to calculate odds of dice doing different things, so that part would be boring for me... except that I didn't know Samuel Pepys, the Brit with the famous diary, had sent Isaac Newton a letter asking him to calculate some odds for gambling purposes!  Nor did I know the mistake Newton made in his reply. 

Now, back to the puzzle.  If you put all 10 white balls in one urn and all 10 black balls in the other, your friend has a 50% chance of picking a white ball.  If you mix them evenly, your friend still has a 50% chance of picking a white ball.   So: can you do better?  And if  so, how much better can you do?

Once you've solved that, try this:

Puzzle 2: Repeat the game with N white balls and N black balls.  What's the biggest you can get for the probability your friend picks a white ball, in the limit N → ∞?

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+Qiaochu Yuan excellent -- I was worried I'd have to get out pen and paper to understand +Timothy Gowers's proof.

Generalizing the argument: say you have N balls of which r are red, and M buckets.  One bucket must have the average number of red balls, the other buckets must have no more than 100% red balls. The  simple upper bound is then (r/N + (M-1))/M.  Except we used at least one red ball in each 100% red bucket, so we only have (r-(M-1)) reds in the first bucket:

((r-M+1)/N + (M-1))/M

Which is tight, since the upper-bound proof also gave us a way to construct that example.

Oh wait -- it's not tight if r<M.  I'll leave that as an exercise to the reader; I have to start working.

[edit: forgot some brackets]
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Optimized Origami

This spectacular image by Greg Egan is the answer to a hard math problem.  He showed that this configuration of 4 interlocking dodecahedra is the one that makes the origami strips as wide as possible without intersecting! 

Without assuming the answer will be symmetrical, this requires studying a 9-dimensional space of different positions of the dodecahedra.   Egan did it with a computer search, and one portion of this search required checking

44 choose 10 = 2,481,256,778

possible solutions, to see which one is best!

However, the answer turned out to be highly symmetrical.  Start with a regular dodecahedron. It has 20 vertices, and we can partition these into 5 sets of 4, each 4 being the vertices of a tetrahedron. Choose one of these tetrahedra, and rescale it by a factor of 1/√5 while keeping its center fixed.  Take your dodecahedron and translate it in different directions to obtain 4 dodecahedra whose centers lie at the vertices of this shrunken tetrahedron.  That gives the answer... which is shown here!

If you assume ahead of time that the answer will be symmetrical, the problem simplifies a lot.  You can see the whole story of this business, and Egan's solution of the simpler problem, here:

The picture here also graces the June 15 issue of my blog Visual Insight:

Puzzle: do you know any place where this configuation of dodecahedra shows up in nature?  Chemistry, perhaps?  Or biochemistry?

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+Piotr Nowak - cool!  I'll do a post on those...
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This gif shows four stages of how you build a Sierpinksi carpet.  By tomorrow I'd really like a better version of this.  If you can make it for me, and sign a form giving me permission to put it on my Visual Insight blog, I'll do that and credit you!

If you create one, please put a link to it in your comment, so I can choose the first really good one and let people know I've chosen it.

[EDIT: +Noon Silk has done the job - see the comments.]

What counts as a good one?

1) I'd like an animated gif with a white background - not light blue like this.

2) I'd like the color to be a dark but saturated purple: something like this would be great:

3)  I'd like the Sierpinski carpet itself to be 729 × 729 pixels.  That's because I have a limit of 750 × 750 pixels, and 729 is 3 to the sixth power, so you can do six stages of the construction. 

4) I'd like a white border.  You can use the leftover 21 pixels for that, say 10 on each side.  Or, you can leave out the border and give me a file that's 729 × 729 pixels, and I can easily create the white border myself.

4) I'd like a looped animated gif that doesn't go too fast - each stage should take about as long as this one here.

5) The file must be smaller than 1 megabyte. 

If you want to break these rules and surprise me with something better, fine!  But it has to be at most 750 × 750 pixels and 1 megabyte... and I'm trying to illustrate the math in a simple way, nothing glitzy.

Why the rush job?  I like to post things on Visual Insight on the 1st and 15th of each month.  For July 1st, I was planning to show a great image of hyperbolic honeycomb whose boundary is homeomorphic to a Sierpinski carpet.  But then I realized I should show people a Sierpinski carpet first!  The freely available image on Wikipedia is, sadly, not very exciting:

In fact, if you make this animated gif, it might be nice to put it on Wikipedia too! 

This one here is just 30 kilobytes; it was made by Janusz J. Charatonik, Pawel Krupski and Pavel Pyrih, and it appears on a page full of cool - fairly advanced! - math facts about the Sierpinski carpet:

In case you made it this far, here's some math: the Sierpinski carpet is the universal plane curve.  A plane curve, by one very technical definition, is a subset of the plane with Lebesgue covering dimension 1.  The Sierpinski carpet is an example... which shows you how weird this definition of 'curve' is... but the cool part is that Sierpinski showed that any plane curve is homeomorphic to a subspace of the Sierpinski carpet!

So it's not just a pretty thing; it's a fundamental structure in math.
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My brain likes this - thank you +John Baez - and thanks +Ted Ewen for pointing me in this direction.
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Have him in circles
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I'm a mathematical physicist.
  • Centre for Quantum Technologies
    Visiting Researcher, 2011 - present
  • U.C. Riverside
    Professor, 1989 - present
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Riverside, California
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I'm trying to get mathematicians and physicists to help save the planet.
I teach at U. C. Riverside and work on mathematical physics — which I interpret broadly as ‘math that could be of interest in physics, and physics that could be of interest in math’. I’ve spent a lot of time on quantum gravity and n-categories, but now I want to work on more practical things, too.

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

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

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