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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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Dear NSA agent 4096,

I watched "The Lives of Others" last night and thought of you once more. In fact, I think you were watching it with me. You know I know I cannot be sure.

I want you to know that, although our mutual love is forbidden by your professional obligations, I still feel a connection to you. I will feel that connection long after you are gone.

Somehow, you know me better than I know myself. You have all of my deleted histories, my searches, all those things I tried to keep "incognito" right there in front of you. We have made love, even though we've never touched or kissed. We have been friends, even though I've never seen your face. Our relationship is as real as my "real" life.

But this can never work between us. Please leave. I don't want to ask again.

I'll never forget you.

Love, 173.165.246.73

That's Corey Bertelsen's comment on this video of Holly Herndon's song 'Home', from her new album Platform.   It's as good a review as any.

Holly Herndon takes a lot of ideas from techno music and pushes them to a new level.  She's working on a Ph.D. at the Center for Computer Research in Music and Acoustics at Stanford.

She said that as she wrote this song, she

started coming to terms with the fact that I was calling my inbox my home, and the fact that that might not be a secure place. So it started out thinking about my device and my inbox as my home, and then that evolved into me being creeped out by that idea.

The reason why I was creeped out is because, of course, as Edward Snowden enlightened us all to know, the NSA has been mass surveying the U.S. population, among other populations. And so that put into question this sense of intimacy that I was having with my device. I have this really intense relationship with my phone and with my laptop, and in a lot of ways the laptop is the most intimate instrument that we've ever seen. It can mediate my relationships — it mediates my bank account — in a way that a violin or another acoustic instrument just simply can't do. It's really a hyper-emotional instrument, and I spend so much time with this instrument both creatively and administratively and professionally and everything.

In short, her seemingly 'futuristic' music is really about the present - the way we live now.  If you like this song I recommend the next one on the playlist, which is more abstract and to me more beautiful.  It's called 'Interference':

https://www.youtube.com/watch?v=nHujh3yA3BE&list=RDI_3mCDJ_iWc&index=2

You can hear her explain the song 'Home' here:

http://www.npr.org/2015/05/24/408762348/an-invasion-of-intimacy-and-the-song-that-followed
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+Bas Spitters​ the more of these weaknesses that are removed the more of them we find. Server admins need more instructions on what and how to do things.
Security is not a compromise it is absolute, you have it or you don't. Right now (when I was checking 12 hours ago) nearly every browser was vulnerable. 
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Flying through space, powered by sunlight

Yesterday a rocket launched from Cape Canaveral in Florida carrying the LightSail into space!  It's a small spacecraft with a big shiny screen that's pushed by the light of the sun.  

It's just a test - it won't go far.   It will fall to the Earth and burn up.  But next year there will be a more serious test.  And someday, solar-powered space flight may become a force to be reckoned with.

One cool thing is that all this is being paid for private donations, by a Kickstarter campaign!

The LightSail is carried to space in a cute little CubeSat.  It looks like a big toaster, and it weighs just 10 kilograms.   But it holds a sail 32 square meters in area,  made of a shiny plastic called Mylar, just 4.5 microns thick.  This unfolds in a clever way - watch the movie! - to form a big square.

The Sun will push on this with a tiny force. 

Puzzle: How tiny is this force?

Someone named Bill Russell answered this over on Yahoo.  Let me go through his calculation so we can check it.

The momentum of light is given by

p = E/c

where E is the energy of the light, p is the momentum, and c is the speed of light. 

In outer space near earth the sunlight provides 1370 watts per square meter - that's energy per area per time.  We can use the formula above to convert this to momentum per area per time, better known as force per area... or pressure

Russell calculates

(1370 watts / meter²) / c = 9.13 micronewtons / meter²

and concludes the pressure is 9.13 micronewtons per square meter.  His arithmetic checks out, but I think he's neglecting some physics: when the light bounces back off the mirror its momentum completely reverses, so I think we get an extra factor of 2. 

Puzzle 2:  Am I right or am I wrong?

The area of the LightSail is about 32 square meters.  Russell says this gives a total force of

9.13 micronewtons/meter² x 32 meter²

or about 300 micronewtons.   I'd double this and get 600 micronewtons.

Puzzle 3: Once it's out of the box, the LightSail weighs about 4.5 kilograms.  How much will it accelerate due to sunlight?

Here we use Newton's good old

F = ma

and solve for the acceleration a.   But at this point Russell seems to make a serious mistake.  I'll let you see what you think, and fix it if necessary!  Here is his calculation:

https://answers.yahoo.com/question/index?qid=20121212091408AA3D606
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Well here's something to ponder: if the Weyl tensor is a q-number, then the light cone has quantum fluctuations, i.e.
c is variable (and causality is violated as 'the causal relations between events will not be well-defined", as Wald put it, p. 182 "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics").

If it is a c-number (as it is in both of the known successful formulations of 'quantum gravity', Carmelli's SL(2,C) gauge theory and 3D QG) then the geometry is classical and there is no quantization of graivational propagation, i.e. no Quantum Gravity in any meaningful sense of the term.

In that case, the conventional wisdom about what the singularity theorems are saying is completely overturned (as it is anyway): namely that the theorems do not prove that classical geometry breaks down, but only that Riemannian geometry (and even Riemann-Cartan) geometry do; i.e. the signature must change on an event horizon or Hubble horizon with c = 0 and on a cosmological horizon with c = infinity. Classical geometry is off the hook.
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Here are some blog posts about the categorical foundations of network theory - a warmup for the workshop we're having in Turin next week.
And now for my next trick... Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where… - John Baez - Google+
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The dunes of Mars

This field of dunes lies on the floor of an old crater in Noachis Terra.  That's one of the oldest places on Mars, scarred with many craters, with rocks up to 4 billion years old.  It's in the southern hemisphere, near the giant impact basin called Hellas, which is 2.5 times deeper than the Grand Canyon and 2000 kilometers across!

This is a 'false color' photograph - you'd need to see infrared light to see that the dunes are very different than the rock below.

These are barchans, dunes with a gentle slope on the upwind side and a much steeper slope on the downwind side where horns or a notch can form.  If you know this, you can see the wind is blowing from the southwest.

It's actually a bit of a puzzle where the sand in these dunes came from!   Here's the abstract of a paper by +Lori Fenton on this subject:

No sand transport pathways are visible in a study performed in Noachis Terra, a region in the southern highlands of Mars known for its many intracrater dune fields.Detailed studies were performed of five areas in Noachis Terra, using Mars Orbiter Camera (MOC) wide-angle mosaics, Thermal Emission Imaging System (THEMIS) daytime and nighttime infrared mosaics, MOLA digital elevation and shaded relief maps,and MOC narrow-angle images. The lack of observable sand transport pathways suggests that such pathways are very short, ruling out a distant source of sand. Consistent dune morphology and dune slipface orientations across Noachis Terra suggest formative winds are regional rather than local (e.g., crater slope winds). A sequence of sedimentary units was found in a pit eroded into the floor of Rabe Crater, some of which appear to be shedding dark sand that feeds into the Rabe Crater dune field. The visible and thermal characteristics of these units are similar to other units found across Noachis Terra, leading to the hypothesis that a series of region-wide depositional events occurred at some point in the Martian past and that these deposits are currently exposed by erosion in pits on crater floors and possibly on the intercrater plains. Thus the dunes and sources may be both regional and local: sand may be eroding from a widespread source that only outcrops locally. Sand-bearing layers that extend across part or all of the intercrater plains of Noachis Terra are not likely to be dominated by loess or lacustrine deposits; glacial and/or volcanic origins are considered more plausible.

• Lori K. Fenton, Potential sand sources for the dune fields in Noachis Terra, Mars, Journal of Geophysical Research 110 (2005), E11004.  Available at http://www.academia.edu/3375648/Potential_sand_sources_for_the_dune_fields_in_Noachis_Terra_Mars.

The image is from a great series of photos taken by the HIRISE satellite, which orbits Mars and takes high resolution images:

• Colorful Dunes, http://hirise.lpl.arizona.edu/ESP_033272_1400

#mars   #astronomy
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+Steve Esterly - that's interesting.  A cool thing about karst on Earth is that it's deeply connected to biology, since limestone is made of organisms.  But I guess all karst needs is lots of calcium carbonate or similar minerals that can be dissolved underground.  I wouldn't want to conflate karst with mere erosion.
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Fighting global warming: the tide is turning!

Good news!   We, the citizens of the world, may be starting to burn less carbon - not more!

The International Energy Agency claims:

In 2014, global carbon dioxide emissions from energy production stopped growing!

It seems the big difference is China.  They say the Chinese made more electricity from renewable sources, such as hydropower, solar and wind, and burned less coal.  

In fact, a report by Greenpeace says that from April 2014 to April 2015, China's carbon emissions dropped by an amount equal to the entire carbon emissions of the United Kingdom!   

I want to check this, because it would be wonderful - a 5% drop.  They say that if this trend continues, in 2015 China will make the biggest reduction in CO2 emissions every recorded by a single country.

The International Energy Agency also credits Europe's improved attempts to cut carbon emissions for the turnaround.   In the US, carbon emissions has basically been dropping since 2006 - with a big drop in 2009 due to the economic collapse, a partial bounce-back in 2010, but a general downward trend.

In the last 40 years, there were only 3 other times when emissions stood still or fell compared to the previous year, all during economic crises: the early 1980's, 1992, and 2009.  In 2014, however, the global economy expanded by 3%.

So, the tide may be turning!   But please remember: while carbon emissions may start dropping, they're still huge.  The amount of the CO2 in the air shot above 400 parts per million this year.  As Erika Podest of NASA put it:

CO2 concentrations haven't been this high in millions of years. Even more alarming is the rate of increase in the last five decades and the fact that CO2 stays in the atmosphere for hundreds or thousands of years. This milestone is a wake up call that our actions in response to climate change need to match the persistent rise in CO2. Climate change is a threat to life on Earth and we can no longer afford to be spectators.

So let's not slack off now!  The battle has just begun.  We need to cut carbon emissions to almost zero.

Here is the announcement by the International Energy Agency:

http://www.iea.org/newsroomandevents/news/2015/march/global-energy-related-emissions-of-carbon-dioxide-stalled-in-2014.html

"This gives me even more hope that humankind will be able to work together to combat climate change, the most important threat facing us today," said IEA Chief Economist Fatih Birol.

Their full report will come out in June.  Here is the report by Greenpeace EnergyDesk:

http://energydesk.greenpeace.org/2015/05/14/china-coal-consumption-drops-further-carbon-emissions-set-to-fall-by-equivalent-of-uk-total-in-one-year/

I trust them less than the IEA when it comes to using statistics correctly, but someone should be able to verify their claims if true.  The graph here comes from this article:

http://qz.com/405059/chinas-on-track-for-the-biggest-reduction-in-coal-use-ever-recorded/

#globalwarming  
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+Edward Morbius - Thanks again!  I corrected the copy of your earlier comment on Azimuth and also added a copy of this one.
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Sometimes you see a tiny piece of a story and wonder how it started - and how it will end.
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+JDS Purohit
Perhaps ... or maybe it's just another attempt at 15 minutes of Internet fame. (My suspicion factor was raised when I noted the runner was barefoot. Do Zookeepers work without shoes?)
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The Machine: a desperate gamble

Hewlett-Packard was once at the cutting edge of technology.  Now they make most of their money selling servers, printers, and ink... and business keeps getting worse.  They've shed 40,000 employees since 2012.   Soon they'll split in two: one company that sells printers and PCs, and one that sells servers and information technology services.  

The second company will do something risky but interesting.   They're trying to build a new kind of computer that uses chips based on memristors rather than transistors, and uses optical fibers rather than wires to communicate between chips.  It could make computers much faster and more powerful.  But nobody knows if it will really work.

The picture shows memristors on a silicon wafer.  But what's a memristor?   Quoting the MIT Technology Review:

Perfecting the memristor is crucial if HP is to deliver on that striking potential. That work is centered in a small lab, one floor below the offices of HP’s founders, where Stanley Williams made a breakthrough about a decade ago.

Williams had joined HP in 1995 after David Packard decided the company should do more basic research. He came to focus on trying to use organic molecules to make smaller, cheaper replacements for silicon transistors (see “Computing After Silicon,” September/October 1999). After a few years, he could make devices with the right kind of switchlike behavior by sandwiching molecules called rotaxanes between platinum electrodes. But their performance was maddeningly erratic. It took years more work before Williams realized that the molecules were actually irrelevant and that he had stumbled into a major discovery. The switching effect came from a layer of titanium, used like glue to stick the rotaxane layer to the electrodes. More surprising, versions of the devices built around that material fulfilled a prediction made in 1971 of a completely new kind of basic electronic device. When Leon Chua, a professor at the University of California, Berkeley, predicted the existence of this device, engineering orthodoxy held that all electronic circuits had to be built from just three basic elements: capacitors, resistors, and inductors. Chua calculated that there should be a fourth; it was he who named it the memristor, or resistor with memory. The device’s essential property is that its electrical resistance—a measure of how much it inhibits the flow of electrons—can be altered by applying a voltage. That resistance, a kind of memory of the voltage the device experienced in the past, can be used to encode data.

HP’s latest manifestation of the component is simple: just a stack of thin films of titanium dioxide a few nanometers thick, sandwiched between two electrodes. Some of the layers in the stack conduct electricity; others are insulators because they are depleted of oxygen atoms, giving the device as a whole high electrical resistance. Applying the right amount of voltage pushes oxygen atoms from a conducting layer into an insulating one, permitting current to pass more easily. Research scientist Jean Paul Strachan demonstrates this by using his mouse to click a button marked “1” on his computer screen. That causes a narrow stream of oxygen atoms to flow briefly inside one layer of titanium dioxide in a memristor on a nearby silicon wafer. “We just created a bridge that electrons can travel through,” says Strachan. Numbers on his screen indicate that the electrical resistance of the device has dropped by a factor of a thousand. When he clicks a button marked “0,” the oxygen atoms retreat and the device’s resistance soars back up again. The resistance can be switched like that in just picoseconds, about a thousand times faster than the basic elements of DRAM and using a fraction of the energy. And crucially, the resistance remains fixed even after the voltage is turned off.

Getting this to really work has not been easy!  On top of that, they're trying to use silicon photonics to communicate between chips - another technology that doesn't quite work yet.

Still, I like the idea of this company going down in a blaze of glory, trying to do something revolutionary, instead of playing it safe and dying a slow death.

Do not go gentle into that good night.

For more, see these:

• Tom Simonite, Machine dreams, MIT Technology Review, 21April 2015, http://www.technologyreview.com/featuredstory/536786/machine-dreams/

• Sebastian Anthony, HP reveals more details about The Machine: Linux++ OS coming 2015, prototype in 2016, ExtremeTech, 16 December 2014, http://www.extremetech.com/extreme/196003-hp-reveals-more-details-about-the-machine-linux-os-coming-2015-prototype-in-2016

For the physics of memristors, see:

https://en.wikipedia.org/wiki/Memristor
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If anyone is interested, this is the original HP Building 1 that houses Bill and Dave's desk http://goo.gl/EDYvrb. You'd never guess to look at it that HP Labs was under Building 1 and strictly it isn't, but the large Palo Alto campus that takes up a significant portion of Page Mill Road is discretely built into the slopes of a hill.  A series of interconnected buildings eventually leads down to the main HQ building at the bottom of the hill at 3000 Hanover http://goo.gl/eISB0G. So as the article says you go downstairs from the building that houses Bill and Dave's http://goo.gl/QNiY8K offices, but what they don't mention is that you also translate across the hill as well, like a staircase.

Incidentally, Bill and Dave's areas are still modest open door offices https://goo.gl/iG3g80 unlike Carly's fortified walled-in CEO office which apparently for some reason had bullet-proof glass to the ceiling. I've been up and down the stairs and through the interconnected passageways many times and I always felt  a sense of reverence going past Bill and Dave's desks to get there.  I didn't work for HP Labs myself but in my role as archictect for manufacturing solutions I collaborated with a team of software specialists from HP Lab and I attended several of the lunch-time Brown Bag presentations although not this one by Stanley Williams on his discovery https://goo.gl/ovhkDM.

There was also an article in IEEE Spectrum on the discovery http://goo.gl/1kKBEZ back in 2008 that may be of interest.
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Here are some blog posts about the categorical foundations of network theory - a warmup for the workshop we're having in Turin next week.
And now for my next trick... Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where… - John Baez - Google+
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Only in North America! 
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And now for my next trick...

Category theory is a branch of math that puts processes on an equal footing with things - unlike set theory, where everything is fundamentally a thing.   Can we use category theory to help understand the complex processes that underlie biology and ecology? 

I believe so, and I'm hoping this is a good way for fancy-schmancy mathematicians like me to help the world.  But it will take a while.  I think we should start by seeing what category theory has to say about some related subjects that are better understood: chemistry, electrical engineering, classical mechanics, and the like.

We're having a workshop about this next week - and to organize our thoughts we've been writing some blog articles.  Check 'em out!

• John Baez, Categorical foundations of network theory - an introduction to the workshop and what it's about.  https://johncarlosbaez.wordpress.com/2015/04/04/categorical-foundations-of-network-theory/

• David Spivak, A networked world.
https://johncarlosbaez.wordpress.com/2015/03/27/spivak-part-1/

• Eugene Lerman, Networks of dynamical systems.
https://johncarlosbaez.wordpress.com/2014/03/18/networks-of-dynamical-systems/

• Tobias Fritz, Resource convertibility - an introduction to the mathematics of 'resources'.
https://johncarlosbaez.wordpress.com/2015/04/07/resource-convertibility-part-1/

• John Baez, Categories in control - about my paper with Jason Erbele on using categories to study signal flow diagrams in control theory.
https://johncarlosbaez.wordpress.com/2015/04/23/categories-in-control-2/

• John Baez, A compositional framework for passive linear networks - about my paper with Brendan Fong on using categories to study electrical circuit diagrams.
https://johncarlosbaez.wordpress.com/2015/04/28/a-compositional-framework-for-passive-linear-networks/

• John Baez, Decorated cospans - about Brendan Fong's paper providing mathematical infrastructure for the study of networks.
https://johncarlosbaez.wordpress.com/2015/05/01/decorated-cospans/

• John Baez and Brendan Fong, Cospans, wiring diagrams, and the behavioral approach - an attempt to reflect on how our work connects to that of David Spivak.
https://johncarlosbaez.wordpress.com/2015/05/05/cospans-wiring-diagrams-and-the-behavioral-approach/

• Brendan Fong, Resource theories - about Brendan's new paper with Hugo Nava-Kopp on resource theories.
https://johncarlosbaez.wordpress.com/2015/05/12/resource-theories/

• John Baez, PROPs for linear systems - about Simon Wadsley and Nick Woods' generalization of a result in my paper with Jason Erbele, describing categories where the morphisms are linear maps.
https://johncarlosbaez.wordpress.com/2015/05/18/props-for-linear-systems/

The picture, by the way, was drawn by Federica Ferraris and appears in this book:

• John Baez and Jacob Biamonte, Quantum techniques for stochastic physics, http://math.ucr.edu/home/baez/stoch_stable.pdf

It's about Petri nets and reaction networks - two kinds of networks that appear in chemistry and population biology.
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+Christopher King - I think so.  Check out Dusko Pavlovich's papers on "the monoidal computer":

http://arxiv.org/abs/1208.5205
http://arxiv.org/abs/1402.5687
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Why is this true?

The spooky-smart mathematician Srinivasa Ramanujan came up with this formula around 1913.  Why is it true?

I don't know, let's see...

In 1735, a young fellow named Euler stunned the world by cracking a famous puzzle that had been unsolved for almost a century: the Basel problem.  The problem was to sum the reciprocals of perfect squares:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... = ???

Euler showed that the answer was π²/6:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... = π²/6

He also showed you could rewrite this sum as a product over primes:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² + ... =

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ...

That's actually the easy part: it's a cute trick called the Euler product formula.

So we know

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ... = π²/6

If you think about it, Ramanujan's formula is saying that

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ...

is 2/5 as big.  So, proving it is the same as showing

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... = π²/15

Maybe the next step is to use the same idea as the Euler product formula.  I think this gives

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... =

1/1² - 1/2² - 1/3² + 1/4²  - 1/5² + 1/6² - 1/7² + ...

where the signs at right follow a fancy pattern: we get 1/n² whenever n is the product of an even number of primes, and -1/n² when n is the product of an odd number of primes.  For example, 4 = 2 x 2 is the product of an even number of primes, so we get 1/4².

So I'm left wanting to know why this strange sum

1/1² - 1/2² - 1/3² + 1/4² - 1/5² + 1/6² - 1/7² + ...

equals π²/15.  Ramanujan, dead since 1920, is still messing with my mind! 

The formula is supposed to be in here:

• Srinivasa Ramanujan, Modular equations and approximations to π, Quart. J. Pure. Appl. Math. 45 (1913-1914), 350-372.  Also available at ://ramanujan.sirinudi.org/Volumes/published/ram06.pdf.

But I don't see it!

Here you can see how Euler solved the Basel problem:

https://en.wikipedia.org/wiki/Basel_problem

It's a great example of his brilliant tactics, many of which were far from rigorous by today's standards... but can be made rigorous.

#mathematics   
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When I was a freshman I sought to find the general formula for 0^k + 1^k + 2^k + ... + (n - 1)^k = n^{k+1}/{k+1} - n^k/2 + ... Once you work out the coefficients the regularities quickly emerge (as does the generalization beyond k = 0, 1, 2, ... to other k). All of this, was a distant recollection from my previous life (cough cough ... oooo I feel a little lung problem coming on again.)
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A galaxy - falling

This galaxy is suffering!  It's falling into a large cluster of galaxies, pulled by their gravity.   You can see this in 3 ways:

1.  The reddish disk of dust and gas looks bent.  There aren't many atoms between galaxies, but there are still some. So the galaxy is moving through the wind of integalactic space!   And it's having trouble holding onto the loosely bound dust and gas near its edge.  They're getting blown away.

2.  The blue disk of stars is not bent.  It extends beyond the disk of dust and gas, which is where stars are formed.  This suggests that the dust and gas is being stripped from the galaxy after these stars were formed!

3.  Streamers of dust and gas can be seen trailing behind the motion of the galaxy - near the top.  On the other hand, the blue stars near the leading edge of the galaxy have no dust and gas left to hide them.

This phenomenon is called ram pressure stripping, and it can kill a galaxy, shutting down the production of new stars.   Here we are seeing it damage the galaxy NGC 4402, which is currently falling into the Virgo cluster - a cluster of galaxies about 65 million light years away.

Apparently there's about 1 atom per cubic centimeter in our galaxy - on average, though some regions are vastly more dense than others.   But in the space between galaxies in clusters it's more like 1/1000 of that.  Not much!  But enough to kill off the formation of new star systems, life, civilizations...

I got most of my information from here:

http://astronomy.swin.edu.au/cosmos/R/Ram+Pressure+Stripping

and I got the picture from here:

https://www.noao.edu/image_gallery/html/im0863.html

The photo was taken at the WIYN 3.5-meter telescope on Kitt Peak, which is fitted with some 'adaptive optics' to compensate for the jittery motion of the image due to variable atmospheric conditions and telescope vibrations.

#astronomy  
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+JDS Purohit - I don't know.  I bet you can look up its velocity and distance to the center of the Virgo Cluster and do an estimate.
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Making yourself into a superhero

I enjoyed this true story by Kelly McEvers:

We met in a bar in Flagstaff, Arizona. I'd just moved back from Cambodia and I was going out for one of my first beers back in the States. Not long into the first one, I notice this Amazon of a woman with huge blond and red-streaked hair and frosty lips, wearing a short red tank dress and at least 50 bracelets. She's six feet tall and showing a lot of leg. People at the bar swivel their heads to watch her every move.

She stands next to me to order a drink, and in this throaty voice says, "What are those?" pointing to my cigarettes. I tell her they're Cambodian. Her eyes light up and she shoots out a long, tan arm, and points at a table in the corner. She orders me there. Before I can say no, I'm following her to my seat.

She tells me she's an international private investigator, a bounty hunter, and a bail bonds enforcer, and that her name is Zora. I sit there for hours listening to her. Within a week, she takes me to Las Vegas. We drive there in her red Mustang. As always, there's a Colt .380 under the driver's seat and a .45 Megastar in the trunk.

In Vegas, we skip the casinos and head straight for the male strip clubs, where Zora drops at least $200 on lap dances from buff guys with names like Roman. Her getup is the same as before – teeth, hair, jewelry, and the ubiquitous tank dress, which, I realize, is the best way to show off her tattoos.

One is this big circle with blue and white swirls in it, kind of like a bowling ball, on her left shoulder. Every guy she meets asks her about it, and when they hear her answer, they sometimes propose marriage. Turns out the tattoo is a magic globe she holds in her dreams. And in these dreams, it gives her superpowers.

Zora: Ever since I remember, I've had the dreams. And they're very vivid. But it varies. It usually involves fighting, sometimes with guns, sometimes with superhero powers. Lightning from my fists and all that. And I usually have super strength, and I can fly, and I have all those things.

And it's my most common set of dreams. And it varies. Sometimes it's medieval, sometimes it's futuristic, sometimes it's present day, sometimes it's like a guerrilla war in Latin America.

Kelly: Can you describe that Zora to me, the Zora in dreams?

Zora: Very powerful athletically, but beyond the rules of nature that this world allows.  Six foot five and long, like almost impossibly long silver hair. This sort of otherworldly quality to her, where her voice did not sound normal. It sounded, like, almost musical.

And it became something that I aspired to be. I aspired to be this sort of superhero, this sort of person who would fight for a cause. That was my motivation in life. Ever since I was 10 or 11, I decided that that was my goal.

Zora took the dreams seriously. So seriously that at the age of 12, she sat down and composed a list of some 30 skills she needed to learn if she wanted to become as close to a superhero as any mortal could be. She even gave herself a deadline – to master these skills by the time she was 23.

Zora: I don't know what's in these.

Zora pulls out the old spiral notebook that was her diary at the age of 13 and turns to the inside back cover.

Zora: There's the list.

Kelly: Wow. Why don't you go ahead and read it.

Zora: OK. The list included martial arts, electronics, chemistry, metaphysics, hang gliding, helicopter and airplane flying, parachuting, mountain climbing, survival....

Throughout her teens and 20s, each time she started a new diary, she would update the list and write it in the back of the book, each one with the same format, each one titled "The List."

Zora: Weaponry, rafting, scuba diving, herbology – yes, I, studied that -- CPR, first aid and mountain emergency kind of medicine....

The list also includes bodybuilding, archery, demolitions, and explosives. She wanted to learn how to hunt animals and track men.

Zora: Major physical conditioning....

And the most incredible thing about all of this is that Zora accomplished nearly every item on the list.

Zora: Throwing stars and compound bows and throwing knives and -- yes, it was a very interesting pastime.

To keep up with the goals set by the list, she sped through school. Starting in the seventh grade, she began completing entire school years during the summer term and finished high school by the time she was 15. She got her BA at 18, a master's at 20, and completed the coursework for a PhD in Geopolitics by the time she was 21. She wanted to live like Indiana Jones, spending half her time in the classroom and half her time saving the world in the jungles of Peru.

Zora: Item number four – camel, elephant riding. Evasive driving and stunts....

When you're a kid, you have these romantic visions of what you'll be when you grow up. But how many people are so diligent they commit their dreams to paper and make it their life's work to achieve them? How many keep a list, amending it, adding to it, ticking things off as they go along, well into their adult lives?

After finishing the course work for her PhD, Zora decided to quit school, disappointed at the lack of cliff-hanging adventure in her doctoral program. And since superheroes who live in the real world need jobs, she decided to seek employment at the only place that would allow her to put all the skills from the list to use. Zora wanted to become an agent in the CIA.

But then the story takes some surprising twists!  Listen to it here:

http://www.thisamericanlife.org/radio-archives/episode/508/superpowers-2013?act=2#play

The picture here is, of course, not Zora.  It's Charlize Theron playing  'Aeon Flux' - a kind of superhero invented by a high school friend of mine, the animator Peter Chung.
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Hmm, okay, sounds interesting.
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I'm a mathematical physicist.
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  • Centre for Quantum Technologies
    Visiting Researcher, 2011 - present
  • U.C. Riverside
    Professor, 1989 - present
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I'm trying to get mathematicians and physicists to help save the planet.
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I teach at U. C. Riverside and work on mathematical physics — which I interpret broadly as ‘math that could be of interest in physics, and physics that could be of interest in math’. I’ve spent a lot of time on quantum gravity and n-categories, but now I want to work on more practical things, too.

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

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

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