[math && computing] // SHARING: Set of All Sets Paradox in Portal 2

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I was playing through Portal 2 some weeks ago and came across this awesome little math-related Easter egg. Close to the end of the game you run across this sign about paradoxes and the last statement about sets in the box of quotations is part of the paradox surrounding the universal set.

Let me make my Foundations of Mathematics professor proud and try to explain this contradiction. Firstly, a set is a collection of things called elements, anything you like, actual things like books, or concepts like numbers, and those collections usually contain things that are related like the set of My Favorite Books, or the set of whole numbers, but they don't necessarily have to have a relationship. Sets can even be comprised of other sets, for example I could compose a set of My Favorite books, My Favorite Movies, My Favorite Shapes, etc. Secondly, the universal set, as the name suggests, is the set that contains everything, all the elements individually, and all the possible sets of elements (similarly, if I recall correctly, the term can be applied to a limited point of view, perhaps just all books if that is what you're interested in looking at). The paradox comes from the universal set being the 'set of all sets.' If the universal set contains everything then it must contain itself because the universal set is part of everything that exists. However, if it did contain itself then there would be a bigger set containing everything and the universal set and hence that would be the universal set and the set we just included couldn't be the universal set. With this new universal set, we could once again included itself, making an even bigger set, then that would have to be the universal set, etc. etc. ad infinitum. A similar effect can be seen with the liar paradox--the first statement in the box. I hope this explanation is correct. In any case, there is a ton of literature about these concepts online if you're looking for more info :D

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[music] // PLAYLIST: "Months" by The Middle East

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I feel like I make the comparison to Iron and Wine a lot--perhaps it's a thing I have, a complex I'm developing... But for this new track from The Middle East, from their first full-length album I Want That You Are Always Happy, the comparison is apt. "Months" is sad- and southern-sounding, winding through unpredictable acoustic plucking, incorporating a simple bass drum and maraca midway through, and adding some breathy vocals and whistling, straight from The Book of Beam. It's a lovely track though. With each release The Middle East seem to put out a track that really captures you. With their EP, The Recordings of The Middle East, it was "Blood" and with their newest installment, with songs like "Months, there's sure to be something to get you. I Want That You Are Always Happy is out in their native Australia already, and will be available in the US in July.

Listen to "Months":

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[music] // PLAYLIST: "Don't Gotta Work It Out" by Fits & the Tantrums

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Fitz and the Tantrums have recently been making the rounds on the late night talk show circuit with their song "Moneygrabber" from their latest album Pickin' up the Pieces (available on Dangerbird Records). The soul/rhythm and bass sextet (five of which are Tantrums) is speared by Michael Fitzpatrick (the Fitz!) and the group have an old school sound that has been re-realized in the last few years with acts like Amy Winehouse, Duffy, Mark Ronson, et cetera, and "Don't Gotta Work It Out" definitely falls squarely within those boundaries. The song funks along with a bouncing piano, soulful brass hits, and disparate lyrics about break-up building through a sing-along choruses (chorii?) to an awesome instrumental end (around 3:30). Pretty cool.

Listen to "Don't Gotta Work It Out":

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