Happy Valentine's!!

Happy Valentine's or x^2 + (y-x^(2/3))^2 = 1

http://www.wolframalpha.com/input/?i=x^2%2B%28y-%28x^2%29^%281/3%29%29^2+%3D+1

time lapse aurora

I can never get enough!

Chinese Opera Jingle Bells

Open Durham

Want to know more about Durham, NC?

http://www.opendurham.org/about-open-durham

fun facts about taiwan

http://allenhsudesign.com/print/10-fun-facts-about-taiwan/

want to see auroras?

Here's a guide to capturing auroras:

http://www.dpreview.com/articles/8217618174/auroral-photography-a-guide-to-capturing-the-northern-lights

Hurry though! The current solar cycle peaks in 2013!

Time lapse aurora video

http://vimeo.com/flatlightfilms/aurora

awesome fantasy pictures

http://3dimpact.com/gallery_digital.html

Dragon Fight in Orion Nebula

This is a real image...very cool.

http://blogs.discovermagazine.com/badastronomy/2011/06/24/a-dragon-fight-in-the-heart-of-orion/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+BadAstronomyBlog+%28Bad+Astronomy%29

One Levitation A Day

These are nice...

http://yowayowacamera.com/

Helioviewer

Amazing! Make your own movies or screenshots of the sun.

http://helioviewer.org/

Fulfilling a childhood dream!

Physics in action! Here's an explanation for why the Northern Lights happen (http://en.wikipedia.org/wiki/Aurora_(astronomy)):

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Auroras result from emissions of photons in the Earth's upper atmosphere (thermosphere), above 80 km (50 miles), from ionizednitrogen atoms regaining an electron, and oxygen and nitrogen atoms returning from an excited state to ground state. They are ionized or excited by the collision of solar wind particles being funneled down and accelerated along the Earth's magnetic field lines; excitation energy is lost by the emission of a photon of light, or by collision with another atom or molecule:

oxygen emissions

Green or brownish-red, depending on the amount of energy absorbed.

nitrogen emissions

Blue or red. Blue if the atom regains an electron after it has been ionized. Red if returning to ground state from an excited state.

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A site that I checked for forecasts http://www.gi.alaska.edu/AuroraForecast.

I didn't get to see blue, that's rare, but I was able to see red. Green was all around. It's too bad that red happened too quickly for me to capture digitally, so it's going to have to remain in my memory.

See the full gallery on Posterous

Blue eyed islanders

Here's an interesting logic puzzle (it is quite well known, see http://en.wikipedia.org/wiki/Common_knowledge_(logic)). The version below is from Terence Tao's blog. xkcd also has a version (http://xkcd.com/blue_eyes.html).

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– The logic puzzle –

There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout, and they all know that each other is also highly logical and devout (and they all know that they all know that each other is highly logical and devout, and so forth).

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

One evening, he addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”.

What effect, if anything, does this faux pas have on the tribe?

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There are two contradictory solutions:

– Solution 1 –

The foreigner has no effect, because his comments do not tell the tribe anything that they do not already know (everyone in the tribe can already see that there are several blue-eyed people in their tribe).

– Solution 2 –

100 days after the address, all the blue eyed people commit suicide. This is proven as a special case of

Proposition. Suppose that the tribe had n blue-eyed people for some positive integer n. Then n days after the traveller’s address, all n blue-eyed people commit suicide.

Proof: We induct on n. When n=1, the single blue-eyed person realizes that the traveler is referring to him or her, and thus commits suicide on the next day. Now suppose inductively that n is larger than 1. Each blue-eyed person will reason as follows: “If I am not blue-eyed, then there will only be n-1 blue-eyed people on this island, and so they will all commit suicide n-1 days after the traveler’s address”. But when n-1 days pass, none of the blue-eyed people do so (because at that stage they have no evidence that they themselves are blue-eyed). After nobody commits suicide on the  day, each of the blue eyed people then realizes that they themselves must have blue eyes, and will then commit suicide on the  day. 

As the above two solutions give contradictory conclusions, at most one of them is correct.  Which one (if any) is the correct solution, and what is the precise reason that the other solution is invalid?