Today I looked up at the night sky and there was this wonderfully full moon, but it was sitting in the middle of a huge perfectly round disk opening into the heavens amidst the clouds. I wondered what the heck it was, thinking it might be the result of Earth-shadow.

It turns out this was a moon halo. The page says that the phenomenon is “familiar,” but I’ve never seen it in my life, and had I not looked up for no reason, I would have missed this one, too! By my hand measurement, it spanned 45° in diameter, which is a pretty big portion of the sky. Jupiter was also visible within the ring of the halo. Quite amazing.

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Because this article is spamming the internet today, I decided to read Li’s paper and learn what the heck is this Gaussian copula.

For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.

And anyway, here is the paper referenced in the article.
(Read the article)

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In my undergraduate EM class, I didn’t particularly pay attention to this part of the course, because it wasn’t on the test. I ended up never knowing what the heck the Smith chart is supposed to be — always thought it was some kind of polar to rectangular complex number conversion chart. Today through random browsing I found this simply excellent explanation:

http://www.maxim-ic.com/appnotes.cfm/an_pk/742/

Turns out it is not quite what I thought, and it is pretty neat. It does convert between two complex numbers, but the relationship has nothing to do with rectangular to polar. It’s the real and imaginary grid lines of normalized load impedance (the circles) layered on top of the real and imaginary grid lines of normalized reflection coefficient (the straight lines). Normalized load impedance and normalized reflection coefficient are functions of each other, so the Smith chart is used to convert between them. Very nice!

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