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John Baez
I'm trying to get mathematicians and physicists to help save the planet.
Occupation: I'm a mathematical physicist.
Location: Riverside, California
His ProfilesRankThis is the rank of 'John Baez' out of all Google+ Profiles.: 1,647 (GenderRankFor the gender 'Men'.: 916)
His ProfilesRankThis is the rank of 'John Baez' out of all Google+ Profiles. in United States: 552 (GenderRankFor the gender 'Men'.: 346)
His CircleRankThis is the rank of 'John Baez' out of all indexed profiles and pages at CircleCount.com.: 4,197
Followers: 34,486
Following: 0
Cream of the Crop: 11/05/2011
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Latest postings
2013-05-18 15:35:48 (5 comments, 5 reshares, 51 +1s)
When you get bored, sometimes it's nice to take a little walk.
This is yet another photo of Eyjafjallajökull, taken by the daredevil photographer Skarphedinn Thrainsson... or Skarphéðinn Þráinsson if you can handle those runic letters "edh" (ð) and "thorn" (Þ). You can see more of his amazing photos here:
http://photos.skarpi.is/
#volcanoes
2013-05-18 02:46:29 (0 comments, 0 reshares, 1 +1s)
Another amazing shot of the Icelandic volcano Eyjafjallajökull, taken in March 2010 by Bjarni T. I would love to be one of those hikers!
For more pictures of this volcano, try:
http://www.fotopedia.com/wiki/2010_eruptions_of_Eyjafjallaj%C3%B6kull/#!/items/flickr-4480596041
#volcano
2013-05-18 02:46:10 (0 comments, 0 reshares, 0 +1s)
THE POWER OF NATURE. Remember that volcano in Iceland that erupted in the spring of 2010 and shut down air travel in parts of Europe? It's called Eyjafjallajökull, and this photo of it was taken by Marco Fulle.
As ash rises through the air from a volcano, static electricity builds up and causes lightning! But nobody is sure how it works. "What is mostly agreed upon," says geologist Brentwood Higman, "is that the process starts when particles separate, either after a collision or when a larger particle breaks in two. Then some difference in the aerodynamics of these particles causes the positively charged particles to be systematically separated from the negatively charged particles."
#volcano
2013-05-17 13:59:29 (30 comments, 0 reshares, 27 +1s)
A brief housekeeping note:
Without a fix or workaround for the Read More issue, G+ no longer does what I need it to. Accordingly, I am on hiatus until I either get it working or find another platform which works for what I'm doing. Comment threads in particular are impossible to read -- reading my last post and its comments took 31 individual clicks.
Don't take this as a personal dig at the G+ staff; it's either a problem which will be fixed or a strategic decision which excludes my use case entirely. Neither is likely catastrophic or idiotic.
EDIT: I've found that Replies and More is a reasonable workaround for the text-hostile changes to the interface. Once it autoexpands comments, I suspect it'll work great. Unfortunately, however, requiring a workaround to make G+ work well for text is probably going to make some people drop off my stream... more »
2013-05-16 05:31:31 (92 comments, 5 reshares, 103 +1s)
I hate the new G+ layout. I'm going to quit posting here until I get so lonely and bored I come crawling back with my tail between my legs...
2013-05-18 03:06:26 (10 comments, 24 reshares, 87 +1s)
Another amazing shot of the Icelandic volcano Eyjafjallajökull, taken in March 2010 by Bjarni T. I would love to be one of those hikers!
For more pictures of this volcano, try:
http://www.fotopedia.com/wiki/2010_eruptions_of_Eyjafjallaj%C3%B6kull/#!/items/flickr-4480596041
#volcanoes
2013-05-18 03:06:06 (7 comments, 23 reshares, 77 +1s)
THE POWER OF NATURE. Remember that volcano in Iceland that erupted in the spring of 2010 and shut down air travel in parts of Europe? It's called Eyjafjallajökull, and this photo of it was taken by Marco Fulle.
As ash rises through the air from a volcano, static electricity builds up and causes lightning! But nobody is sure how it works. "What is mostly agreed upon," says geologist Brentwood Higman, "is that the process starts when particles separate, either after a collision or when a larger particle breaks in two. Then some difference in the aerodynamics of these particles causes the positively charged particles to be systematically separated from the negatively charged particles."
#volcanoes
2013-05-14 14:28:13 (14 comments, 16 reshares, 53 +1s)
Check out these crazy ways planets could move! This one looks like a gravitational atom! You can run the animations on your browser:
http://www.maths.manchester.ac.uk/~jm/Choreographies/
These orbits are unlikely to ever occur, and probably most of them are unstable. So finding them is mainly a challenge in pure math... but it's a game that uses some pretty interesting ideas, not just computer simulations. These animations were created with the help of a full classification of highly symmetrical solutions of the gravitational n-body problem that lie on a plane:
• James Montaldi and Katrina Steckles, Classification of symmetry groups for planar n-body choreographies, http://arxiv.org/abs/1305.0470.
Abstract: Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body... more »
2013-05-14 05:52:52 (4 comments, 0 reshares, 11 +1s)
Busy day in analytic number theory; Harald Helfgott has complemented his previous paper http://arxiv.org/abs/1205.5252 (obtaining minor arc estimates for the odd Goldbach problem) with major arc estimates, thus finally obtaining an unconditional proof of the odd Goldbach conjecture that every odd number greater than five is the sum of three primes. (This improves upon a result of mine from last year http://terrytao.wordpress.com/2012/02/01/every-odd-integer-larger-than-1-is-the-sum-of-at-most-five-primes/ showing that such numbers are the sum of five or fewer primes, though at the cost of a significantly lengthier argument.) As with virtually all successful partial results on the Goldbach problem, the argument proceeds by the Hardy-Littlewood-Vinogradov circle method; the challenge is to make all the estimates completely effective and to optimise all parameters (which, among other things, requires a c... more »
2013-05-14 05:53:30 (0 comments, 0 reshares, 6 +1s)
Recall that the Twin Prime Conjecture states that there are infinitely many primes p and q such that | p - q | = 2.
http://en.wikipedia.org/wiki/Twin_prime
This has been, to put it mildly, EXTREMELY HARD to prove. An equivalent statement is that there are infinitely many primes p and q such that | p - q | < 3, and so one could try to arrive at a weaker statement, where 3 is replaced by some number N.
Conjecture(N): There are infinitely many primes p and q such that | p - q | < N.
Note that this is very non-obvious, because it may be that the prime numbers get more and more spaced out as they get larger, in the sense that the minimum distance between primes in [M,∞) grows as M grows. We do know that this spacing grows at most linearly, by Bertrand's posulate:
http://en.wikipedia.org/wiki/Bertrand's_postulate
which s... more »
2013-05-14 05:50:35 (4 comments, 10 reshares, 33 +1s)
Recall that the Twin Prime Conjecture states that there are infinitely many primes p and q such that | p - q | = 2.
http://en.wikipedia.org/wiki/Twin_prime
This has been, to put it mildly, EXTREMELY HARD to prove. An equivalent statement is that there are infinitely many primes p and q such that | p - q | < 3, and so one could try to arrive at a weaker statement, where 3 is replaced by some number N.
Conjecture(N): There are infinitely many primes p and q such that | p - q | < N.
Note that this is very non-obvious, because it may be that the prime numbers get more and more spaced out as they get larger, in the sense that the minimum distance between primes in [M,∞) grows as M grows. We do know that this spacing grows at most linearly, by Bertrand's posulate:
http://en.wikipedia.org/wiki/Bertrand's_postulate
which s... more »
2013-05-15 19:25:08 (25 comments, 8 reshares, 25 +1s)
Busy day in analytic number theory; Harald Helfgott has complemented his previous paper http://arxiv.org/abs/1205.5252 (obtaining minor arc estimates for the odd Goldbach problem) with major arc estimates, thus finally obtaining an unconditional proof of the odd Goldbach conjecture that every odd number greater than five is the sum of three primes. (This improves upon a result of mine from last year http://terrytao.wordpress.com/2012/02/01/every-odd-integer-larger-than-1-is-the-sum-of-at-most-five-primes/ showing that such numbers are the sum of five or fewer primes, though at the cost of a significantly lengthier argument.) As with virtually all successful partial results on the Goldbach problem, the argument proceeds by the Hardy-Littlewood-Vinogradov circle method; the challenge is to make all the estimates completely effective and to optimise all parameters (which, among other things, requires a c... more »
2013-05-11 21:57:49 (18 comments, 11 reshares, 52 +1s)
I had dinner with Gregory Benford last weekend, and he raised an interesting point. So far, radio searches for extraterrestrial life have only seen puzzling brief signals - not long transmissions. But what if this is precisely what we should expect?
A provocative example is Sullivan, et al. (1997). This survey lasted about 2.5 hours, with 190 1.2 minute integrations. With many repeat observations, they saw nothing that did not seem manmade. However, they “recorded intriguing, non-repeatable, narrowband signals, apparently not of manmade origin and with some degree of concentration toward the galactic plane…” Similar searches also saw one-time signals, not repeated (Shostak & Tarter, 1985; Gray & Marvel, Gray, 1994; 199 Tarter, 2001). These searches had slow times to revisit or reconfirm, often days (Tarter, 2001). Overall, few searches lasted more than hour, with lagging confirma... more »
2013-05-11 14:19:19 (0 comments, 0 reshares, 2 +1s)
+John Cook 's post on Perrin pseudoprimes got me messing around with them some more. Initially I was just messing around with Sage, trying to write a faster algorithm for finding them as a way of teaching myself about Sage programming and its limits. But in trying to understand what I was doing, I eventually got some interesting and probably very basic facts about number theory into my thick head.
To review, the Perrin numbers are a lot like the famous Fibonacci numbers, only you don't add the two most recent numbers to get the next one; you add the second and third most recent numbers, skipping over the most recent one. And you start with 3, 0, 2 as the seed. So they go 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17... It's http://oeis.org/A001608.
They initially jump around a bit, but once they get going they start increasing monotonically. Instead of the golden ratio, the ratio be... more »
2013-05-11 03:38:43 (23 comments, 108 reshares, 135 +1s)
Check out Anselm Levskaya's program called polyHédronisme, which lets you draw strange and beautiful polyhedra on your web browser!
http://levskaya.github.io/polyhedronisme/
You start with a Platonic solid and then do things to it. I got this one by typing "aaaaD", which starts with a dodecahedron and then does "ambo" 4 times. If you want to figure out what "ambo" means, try "D", then "aD", then "aaD".
Thanks to +William Rutiser for pointing this out!
2013-05-09 16:38:19 (23 comments, 3 reshares, 21 +1s)
Here in southern California, people make the drug 'crystal meth' from medicines like Sudafed at home - and sometimes they set their homes on fire. Here's why:
A guy loads NaOH dry solid pellets, about 1 inch high, into a plastic bottle, and adds about 2-3 inch thick layer of dry ammonium nitrate granules. Then he fills the bottle with ethyl ether and adds a good chunk of lithium metal foil. He screws the cap on and swirls the mix around. God have mercy.
This man is not building a home-made ANFO for roadside bombing. It is not going to be a Molotov cocktail enhanced with a metal/oxidizer, or perhaps a crude rocket. He is making a batch of meth by the Shake and Bake method. As he ads a pack of ground pseudoephedrine pills, he squirts in a small amount of water, caps the bottle and starts shaking real fast. The water initiates a vigorous and pretty much ... more »
2013-05-08 17:26:48 (56 comments, 140 reshares, 406 +1s)
Yay! You can now search Gmail by size and/or age, which lets you delete big old useless mails! It goes like this:
size:5m older_than:1y
So, now I can delete emails like this one, which came with over 10 megabytes of attachments:
THE ATTACHED QUANTUM WORLD EXISTS INSIDE OF A BRAIN NEURON, DIRECTLY BEHIND THE RODS AND CONES OF THE EYE, AND EVOLVES AND COMMUNICATES WITH ALL OTHER NEURONS IN THE BRAIN OF ALL CARBON BASED FORMS OF LIFE ON THIS PLANET, AND PROBABLY EXISTS IN ALL OF OTHER PLANETS OF THE UNIVERSE.
FORMERLY, I WAS DIRECTOR OF RESEARCH AT THE VETERANS ADMINISTRATION, WEST LOS ANGELES LOCATED IN WEST LOS ANGELES. I WAS CONTACTED BY THE FORMER DIRECTOR TO TAKE OVER THE RESEARCH DEPARTMENT, AND ALL THE VARIOUS LABORATORIES, WHICH I AGREED TO DO.
IN THAT REGARD, I WAS ABLE TO DEVELOPMENT A LABORATORY PROCEEDURE, ENABLING ONE MICRON OF TISS... more »
2013-05-08 00:23:21 (16 comments, 13 reshares, 89 +1s)
You know you've written too many math papers in your life when you try to do physics and your fingers keep making this typo: theoremodynamics.
2013-05-07 17:23:29 (6 comments, 3 reshares, 32 +1s)
Even a camel can get tired crossing the Taklamakan Desert! This photo was taken by Richard Desomme in a flat barren area west of the Keriya River:
http://www.panoramio.com/photo/4663632
There's a story to be told here, but I don't know it. The precise location is 37° 51' 27.03" N, 81° 13' 58.48" E.
#silkroad
2013-05-06 19:42:26 (19 comments, 10 reshares, 43 +1s)
The Green Belt Along The World’s Longest Desert Highway ... National Geographic - "The Tarim Desert Highway across the Taklamakan desert, in China, links the cities of Luntai and Minfeng on the northern and southern edges of the Tarim basin. The total length of the highway is 552 km, of which approximately 446 km is built across uninhabited areas covered by shifting sand dunes, 20 metes tall, that frequently bury the highway. To prevent the highway from getting buried by the encroaching sand dunes, rows of vegetation were planted on both sides of the road to anchor the sand with their roots. A massive irrigation system was constructed that pump water from underground reservoirs to sustain the artificial ecosystem. ..." http://bit.ly/ZL9cth
2013-05-06 04:18:14 (42 comments, 39 reshares, 97 +1s)
At the Category-Theoretic Foundations of Mathematics Workshop at U.C. Irvine this weekend, I met Olivia Caramello, who is a powerful advocate of topos theory as an approach to unifying mathematics. She was a student of one of the best topos theorists in the world, now she's a research fellow at Cambridge University, and she lives and breathes math. I always enjoy meeting brilliant young mathematicians who are eager to explore mind-blowing new realms and confident in their power to do it. They can be scary, but they're fun to see - sort of like a lion or tiger.
I'm not going to tell you what a topos is; I'll just say some stuff about them. They were invented by Grothendieck in the 1960's as part of his quest to prove some conjectures in number theory. The solutions of a bunch of polynomial equations give, indirectly, a topos, and he thought of this topos as a gen... more »
2013-05-03 06:11:25 (54 comments, 28 reshares, 64 +1s)
Senior US government officials will be briefed at the White House this week on the danger that the Arctic will be ice-free in summer very soon. The meeting will include NASA's acting chief scientist, Gale Allen, the director of the NSF, Cora Marett, representatives from the US Department of Homeland Security and the Pentagon, and 10 Arctic specialists, including marine scientist Carlos Duarte, director of the Oceans Institute at the University of Western Australia.
Duarte recently said the melting of the Arctic is accelerating faster than any models had predicted, and the situation would be as hard to slow down as a runaway train. He claimed the Arctic Ocean could be ice-free in summer by 2015!
(In 2007, the IPCC predicted that that quite a bit of summertime Arctic ice would last until 2100. It's been melting much faster than they expected. I've read recent claims that... more »
2013-05-02 18:35:20 (9 comments, 0 reshares, 8 +1s)
Puzzle: Which mathematician called infinitesimals "the cholera bacillus of mathematics?"
If you look up the answer online, please don't give it away here!
2013-05-02 18:55:51 (13 comments, 18 reshares, 82 +1s)
Puzzle: What's the 13th root of
8800844344048929957521901577223641785941172005261565487280650870412023307854274990144578442271602817 ?
In 1981, Wim Klein figured out the answer using just his mind in 1 minute and 28 seconds.
That sounds impressive. But more recent lightning calculators have gotten much faster! For example, in 2004 Gert Mittring took just 11.8 seconds to compute the 13th root of
7066437381674286102234008830240157375704233170702632731269721516000395709065419973141914549389684111
People actually have contests to compute 13th roots of hundred-digit numbers. It's not magic; it's a skill that can be learned, and Ron Doerfler explains some of the tricks here:
http://myreckonings.com/wordpress/2011/10/05/the-13th-root-of-a-100-digit-number-part-i/
But the people who do really well have great pow... more »
2013-05-01 20:56:32 (15 comments, 5 reshares, 15 +1s)
Suppose we take "applied mathematics" in an extremely broad sense that includes math developed for use in electrical engineering, population biology, epidemiology, chemistry, and many other fields. Suppose we look for mathematical structures that repeatedly appear in these diverse contexts — especially structures that aren't familiar to pure mathematicians. What do we find? The answers may give us some clues about how to improve the foundations of mathematics!
This is what I'm talking about at the Category-Theoretic Foundations of Mathematics Workshop at U.C. Irvine this weekend. You can see my talk slides here!
2013-05-01 20:10:18 (23 comments, 36 reshares, 87 +1s)
Suppose we take "applied mathematics" in an extremely broad sense that includes math developed for use in electrical engineering, population biology, epidemiology, chemistry, and many other fields. Suppose we look for mathematical structures that repeatedly appear in these diverse contexts — especially structures that aren't familiar to pure mathematicians. What do we find? The answers may give us some clues about how to improve the foundations of mathematics!
This is what I'm talking about at the Category-Theoretic Foundations of Mathematics Workshop at U.C. Irvine this weekend. You can see my talk slides here!
2013-04-30 21:17:54 (7 comments, 4 reshares, 25 +1s)
The Real
seeing the real in things
really seeing the real
describing the exact actuality
of what it is you see
or what it is you seem to see
you really seem to see the real
the exact and actual reality
of the real in things you seem to see
what you see is what seems
2013-04-30 05:12:40 (15 comments, 2 reshares, 46 +1s)
Spock versus Columbo. Not quite, but this 1973 episode of Columbo featuring Leonard Nimoy as a murderous doctor is the next best thing. It's called "A Stitch in Crime", and it's a fun, elegantly constructed battle of wits. Columbo wins at the very last second. And doesn't Nimoy's ear look a bit pointy here?
2013-04-29 21:34:50 (11 comments, 6 reshares, 42 +1s)
Here's another Enneper surface, drawn by Paul Nylander. It's been cut off before it intersects itself, and it has a nice metal frame.
This one has 5-fold symmetry: you can see a kind of pentagon on top. But in fact it has more symmetry! Indeed, it has the same symmetries as a pentagonal antiprism.
That's the shape you get by taking two regular pentagons, holding one directly above the other, and then turning the top one 1/10th of a turn, like this:
http://en.wikipedia.org/wiki/Pentagonal_antiprism
So, the top is a regular pentagon, and so is the bottom, but there are 10 triangles around the sides. If you hold a light directly above a pentagonal antiprism, the shadow is a regular 10-sided shape: a regular decagon.
And in fact, the pentagonal antiprism has the same symmetry group as a regular decagon. Checking... more »
2013-04-30 17:34:26 (32 comments, 60 reshares, 108 +1s)
These are 20 different women: the top contestants in a Korean beauty contest called Miss Daegu 2013. They're clearly approximating a specific ideal face... and +Jia-Bin Huang has computed their average to estimate what this ideal face looks like:
http://jbhuang0604.blogspot.se/2013/04/miss-korea-2013-contestants-face.html
The different faces form a cluster in a high-dimensional space, and using a robust version of a 'principal component analysis' he works out the longest axes of this cluster - that is, the main ways the faces differ from the average.
I find the conformity built into this beauty contest somewhat horrifying... but the math is fascinating. Thanks to +Wayne Radinsky for pointing this out!
(For more information, see Jia-Bin Huang's comment below!)
2013-04-28 22:35:19 (37 comments, 2 reshares, 35 +1s)
Time to harvest the kumquats! Our tree is packed with them. It's great to eat the whole fruit, since the peel is sweet yet packed with flavorful oil, mostly limonene.
Limonene is also what gives orange and lemon peels their special smell. It's one of a group of hydrocarbon molecules called terpenes, which are found in pine needles, cinnamon, cloves, ginger, camphor, mints, and the sap of many trees. Plants produce terpenes to repel insects! Trees also release more terpenes in warmer weather, creating a haze that acts as a natural form of cloud seeding. The clouds reflect sunlight, letting the forest regulate its temperature.
Limonene is one of the simplest terpenes. It's a hexagonal ring of carbons with a single extra carbon attached to one corner and a Y-shaped group of three carbons attached to the opposite corner... all decorated by hydro... more »
2013-04-28 15:53:11 (11 comments, 14 reshares, 60 +1s)
The Enneper surface we've been looking at is just the first of an infinite family of highly symmetrical minimal surfaces. Here's the next, drawn by Greg Egan. It has a little triangle on top instead of a little 'bigon' (a 2-sided shape). After this comes one with a little square on top, and so on.
What's cool is that all these fancy shapes are just different ways of mapping a disc into 3-dimensional space!
He writes:
Here's the next-higher-order Enneper surface, with threefold symmetry, that comes from putting f=1, g=z^2 in the Weierstrass–Enneper parameterisation.
I've used a polar coordinate mesh in the (u,v) plane (as you suggested Blinking Spirit had probably done for the lowest-order case). This has the advantage that the mesh, as well as the surface, is invariant under rotations of 2pi/3, so the animation only n... more »
2013-04-27 16:31:45 (10 comments, 9 reshares, 64 +1s)
This is the Falcon's Perch Treehouse in Long Island, New York. The photograph was taken by Pete Nelson. His book New Treehouses of the World is full of great photos like this. Sometimes I'm too sleepy to read right before bedtime, but I still want to do something, and I still have the energy to look at pictures. There's something deeply appealing about a good treehouse.
2013-04-27 03:18:37 (14 comments, 4 reshares, 79 +1s)
My aunt died. No need for sympathies... she was 100 years old, and had a great life!
2013-04-26 14:05:49 (1 comments, 1 reshares, 7 +1s)
Last week I gave a talk at the Perimeter Institute on global warming and what physicists can do about it. You can see a video of the talk here!
I gave the talk yesterday at a nearby college and a student asked if any US universities were doing research on thorium reactors. I didn't know the answer, so now I should look it up. Some people at the Perimeter Institute work on quantum computation... so for them, I said quantum dot solar cells would be a good thing to work on. (See my talk to learn why.)
2013-04-26 14:03:09 (15 comments, 4 reshares, 25 +1s)
Last week I gave a talk at the Perimeter Institute on global warming and what physicists can do about it. You can see a video of the talk here!
I gave the talk yesterday at a nearby college and a student asked if any US universities were doing research on thorium reactors. I didn't know the answer, so now I should look it up. Some people at the Perimeter Institute work on quantum computation... so for them, I said quantum dot solar cells would be a good thing to work on. (See my talk to learn why.)
2013-04-25 14:48:28 (14 comments, 1 reshares, 13 +1s)
This passage from the Stanford Encyclopedia of Philosophy pisses me off. Is there any way to fix it?
"Eilenberg & Mac Lane (1945) introduced categories in a purely auxiliary fashion, only as a formal ground for what they called functors and natural transformations, recognizing from the outset that categories are wholly dispensable in practice."
Eilenberg and Mac Lane certainly did not believe categories were 'dispensable', 'purely auxiliary' and 'only formal'. The author may believe this, but he's projecting his views on these authors.
2013-04-25 14:17:04 (6 comments, 19 reshares, 53 +1s)
Dark lightning. You've heard of dark matter and dark energy, but how about dark lightning? This is a cute name for gamma ray flashes created shortly before visible lightning.
Lightning happens in stages. First, a streamer of electricity travels from one charged area to another, say, from a cloud to the ground, or from one layer within a cloud to another. This prompts a return stroke with the reverse charge to go in the opposite direction. The initial streamer electrified the air it moved through, creating a path of least resistance that allows the return stroke to carry a much greater current.
Scientists analyzed 56 terrestrial gamma-ray flashes with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite from 2004 to 2009 and compared them with bursts of radio waves that happened at the same time.
The large majority of ter... more »
2013-04-25 03:45:00 (9 comments, 9 reshares, 39 +1s)
I've been talking a lot about Silk Road towns in the Taklamakan Desert, their history and architecture. But this desert might also play an important role in the world's weather! Check out this amazing Sudden Stratospheric Warming event. See where it starts? For more, read this:
http://neven1.typepad.com/blog/2013/04/sudden-stratospheric-warmings-causes-effects.html
These events are not rare. They're so dramatic that at first scientists thought they were caused by volcanic eruptions! They're still mysterious.
#silkroad
2013-04-24 17:25:21 (42 comments, 16 reshares, 59 +1s)
Puzzle: what are the symmetries of this shape? How many symmetries does it have? And if you know some group theory: what is its symmetry group?
This is an image of Enneper's surface, created by Greg Egan. You can describe it using these equations:
x = u - u^3/3 + uv^2 y = -v + v^3/3 - vu^2 z = u^2 - v^2
and the curves on the surface are curves where u or v are constant. You can use these equations to help see the symmetries of Enneper's surface, or you can figure them out by just looking at it.
#minimalsurface
2013-04-23 19:35:46 (32 comments, 39 reshares, 72 +1s)
All beautiful ideas are connected. Engineers know and love this chart of analogies, and now I'm explaining it in a bunch of articles on my blog. Start here:
http://johncarlosbaez.wordpress.com/2013/04/23/network-theory-part-29/
and work back as needed. As the series continues, we'll see that category theory can help make these analogies very precise.
2013-04-23 18:20:09 (4 comments, 12 reshares, 52 +1s)
This is the Beauty of Xiaohe, one of the mummies found in the Small River Cemetery near the eastern end of the Tarim River in the Taklamakan Desert.
This cemetery dates back to 1970 BC. It was rediscovered in 1934 AD by the Swedish archaeologist Folke Bergman... and then forgotten until a Chinese expedition found it again with the help of a GPS system. Archaeologists began excavating it in 2003.
When they dug into it, they found five layers of burials. They found almost 200 poles, each standing 4 meters tall. Many had flat blades, painted black and red, like oars. At the foot of each pole there was a boat, laid upside down and covered with cowhide. Inside the boats were bodies. Mummies!
The mummies were wearing large woolen capes with tassels and leather boots. They had felt caps with feathers tucked in the brim. And next to them were grave good... more »
2013-04-22 20:39:46 (7 comments, 10 reshares, 25 +1s)
This is +Ron Avitzur's image of the Enneper surface. It's a minimal surface, meaning one that necessarily gets more area if you warp any small patch of it. A soap film will make a minimal surface if it doesn't enclose any air. But the Enneper surface intersects itself: in math jargon, we say it's immersed in 3d space, but not embedded. So, you can't make it with soapy water!
You can describe the Enneper surface using these equations:
x = u - u^3/3 + uv^2 y = -v + v^3/3 - vu^2 z = u^2 - v^2
As u and v range over all real numbers, the point (x,y,z) hits every point of the
Enneper surface.
Greg Egan has also made a nice animated gif of the Enneper surface, and I'll show you that soon. Then I'll talk about generalizations of the Enneper surface - fancier minimal surfaces that can be defined using... more »
2013-04-22 20:40:20 (27 comments, 27 reshares, 68 +1s)
This is +Ron Avitzur's image of the Enneper surface. It's a minimal surface, meaning one that necessarily gets more area if you warp any small patch of it. A soap film will make a minimal surface if it doesn't enclose any air. But the Enneper surface intersects itself: in math jargon, we say it's immersed in 3d space, but not embedded. So, you can't make it with soapy water!
You can describe the Enneper surface using these equations:
x = u - u^3/3 + uv^2 y = -v + v^3/3 - vu^2 z = u^2 - v^2
As u and v range over all real numbers, the point (x,y,z) hits every point of the
Enneper surface.
Greg Egan has also made a nice animated gif of the Enneper surface, and I'll show you that soon. Then I'll talk about generalizations of the Enneper surface - fancier minimal surfaces that can be defined using... more »
2013-04-21 21:27:53 (0 comments, 1 reshares, 11 +1s)
David Tanzer has a great elementary intro to the three main approaches to equations: the formula-based approach, the theoretical approach and the computational approach.
2013-04-21 19:58:30 (1 comments, 10 reshares, 30 +1s)
David Tanzer has a great elementary intro to the three main approaches to equations: the formula-based approach, the theoretical approach and the computational approach.
2013-04-21 20:25:48 (6 comments, 3 reshares, 16 +1s)
I met the young and adventurous mathematician David Farris when I was living in Shanghai. Now he's visiting Singapore. Unfortunately I'm not there now - I'm going back in June. He went up to Johor Bahru, a big city in Malaysia just north of Singapore which I've never yet explored, and he found - among other things - a little shop that sells fermented coconut juice. I love these little places. He writes:
So, here's how to find the toddy (delicious, lightly fermented coconut sap) shop right next to the bus station in Johor Bahru. I've attached a picture. The location is 1.464102,103.761612 in Google Maps. It's on the south side of Jalan Suleiman. It's a tiny street, just one block, so you can just walk down it and look for it. It's extremely near to the Kotaraya Bus terminal, where there are buses to and from Singapore; you go out from the south(eas... more »
2013-04-21 14:55:37 (17 comments, 9 reshares, 54 +1s)
Enneper's surface is a minimal surface described by a rather simple equation... but it's hard to visualize, because of how it intersects itself!
Alfred Enneper and Karl Weierstrass were thinking about minimal surfaces back around 1863, and they discovered every such surface that's simply a disk mapped into 3d space could be described in a clever way using complex numbers. This is called the Enneper-Weierstrass parametrization:
http://en.wikipedia.org/wiki/Weierstrass%E2%80%93Enneper_parameterization
I don't understand this yet... if you do, please explain it! Enneper's surface is very simple in these terms, but you can also describe it using cubic functions:
http://en.wikipedia.org/wiki/Enneper_surface
This image from Wikicommons was created by someone with the charming username 'Blinking Spirit'. You can ... more »
2013-04-20 01:37:53 (40 comments, 16 reshares, 80 +1s)
An Indian couple both teach in the same computer science department, but they use different last names - let's call them Prof. Rama and Prof. Sita. They get lots of students wanting jobs as postdocs. Some aren't used to the idea of women professors.
One of these students knocks on Prof. Sita's door and walks in. She's grading papers. The student assumes she must be Prof. Sita's secretary. He says "I'd like to speak to Prof. Sita."
"Okay," she says. "What do you want?"
"I'm interested in a postdoc position."
"Hmm," she says. "What are your qualifications?"
"I'd rather wait and talk to Prof. Sita," he says.
"You can talk to me right now!"
"No, really - I'd rather wait."
&quo... more »
2013-04-19 15:16:16 (22 comments, 10 reshares, 42 +1s)
We need to cut CO2 emissions by about 12 gigatonnes/year by 2020 to hold global warming to 2 °C. After the UN climate conference in Copenhagen, many countries made pledges to reduce CO2 emissions... but by 2020 these pledges will cut emissions by at most 6 gigatonnes/year. Even worse, the confirmed value of all these pledges is only 3 gigatonnes/year.
How can we bridge the gap? That's what this paper is about:
• Kornelis Blok, Niklas Höhne, Kees van der Leun and Nicholas Harrison, Bridging the greenhouse-gas emissions gap, Nature Climate Change 2 (2012), 471-474, http://www.readcube.com/articles/10.1038/nclimate1602.
The authors list 21 things that cities, large companies and individual citizens could do to cut greenhouse gas emisssions by the equivalent of 10 gigatonnes/year of CO2 by 2020. For each thing on the list, they claim:<... more »
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