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My best known work is in game theory
February 22, 2012 11:40 AM   Subscribe


 
"circle-squarer"

Just wrote that down for future use.
posted by jsavimbi at 11:50 AM on February 22, 2012 [4 favorites]


I wasn't familiar with that phrase either; I had to look it up. Now I'm going to be on pins and needles waiting for an opportunity to use it!
posted by Greg_Ace at 11:53 AM on February 22, 2012 [1 favorite]


Fantastic. I really want to read the NSA's analysis of it, as well. It's supposed to be at the exhibit.
posted by empath at 11:56 AM on February 22, 2012


I, too, have only now learned the expression and I LOVE it!

As someone who spent about 6 months in 9th grade determined to square the circle (I was taking geometry at the time and loving that, too), I filled up several notebooks of futile exercises trying to do it. Fantastic expression, and one probably earned by thousands of people throughout history "wasting" their time as I did chasing that chimaera.
posted by darkstar at 12:08 PM on February 22, 2012


Square-squaring is also a thing.
posted by zamboni at 12:31 PM on February 22, 2012


"circle-squarer"

Having seen several people (typically in mall food courts about ~10 years ago) attempting this feat, I knew exactly the type of crank he was talking about. I hope this doesn't come off as a cheap potshot, but I think most of that crowd has changed their focus to libertarianism instead these days.
posted by Challahtronix at 12:38 PM on February 22, 2012 [1 favorite]


Seriously, what kind of idiot chases fools errands like squaring the circle when there's important angle-trisection to be done?
posted by cortex at 1:18 PM on February 22, 2012 [6 favorites]


Angles can be trisected. Angles can even be trisected using simple (i.e. non-measuring) devices, like folding paper. What they can't be is trisected with a straightedge and compass.

Also, I wish I had a mall food court around here that was as intellectually rigorous as even circle-squarering.
posted by DU at 1:23 PM on February 22, 2012


NO I'M PRETTY SURE IT IS UNIVERSALLY IMPOSSIBLE TO TRISECT ANGLES
posted by cortex at 1:29 PM on February 22, 2012 [4 favorites]


There are still a lot of people on the arXiv attempting to do things like prove that the natural numbers and the real numbers have the same cardinality (and thus invalidating Cantor's rather ingenious diagonal argument.) Proofs of the (former) Poincaré conjecture, Fermat's last theorem, and the Riemann hypothesis have always been crank-bait also.
posted by TypographicalError at 1:31 PM on February 22, 2012


There are some neat circle-squaring approximations out there, though, by definite non-cranks like Ramanujan. It's often interesting (and very practical) to look at the work that's done where there are proven limitations.

So, back at the topic: Nash basically figured out modern crypto a few decades early. Not terribly surprising, I suppose.
posted by weston at 1:33 PM on February 22, 2012


Oh gawd yes...the angle trisection thing occupied me for at least a month, too.

/nerd
posted by darkstar at 1:42 PM on February 22, 2012




Would that I had more than one Favorite to give.
posted by Amanojaku at 2:46 PM on February 22, 2012 [1 favorite]


Wait a minute. I can trisect angles. Like, ninety degrees ... is three times thirty! And I can square circles too.
Proof: ☐
That was totally a circle a minute ago.
posted by Joe in Australia at 3:19 PM on February 22, 2012 [1 favorite]


The declassified public information part of the NSA website is kind of interesting to poke around in. For example, there's an article which concludes that the U.S. fired first at the Gulf of Tonkin, another which details evidence gathered by spying on Cuba, a list of cryptographer slang, and a document decoding messages from outer space.
posted by twoleftfeet at 4:03 PM on February 22, 2012 [4 favorites]


Nash wrote this letter in '55.

According to the Wikipedia article, he dates the onset of his schizophrenia to the early months of '59, just when his wife was beginning her pregnancy, interestingly.

I heard that a decompostion of a circle into a countable set of mutually exclusive sets which could then be assembled into a square was exhibited back in the '80s(?), but I haven't seen anything about it since.
posted by jamjam at 4:07 PM on February 22, 2012


Wow, the humor in that slang list is delicious. Thanks!
posted by rush at 5:19 PM on February 22, 2012 [1 favorite]


For example, there's an article which concludes that the U.S. fired first at the Gulf of Tonkin

Does the NSA mention Greedo?
posted by chavenet at 4:10 AM on February 23, 2012


It is worth pointing out the exceptionally interesting link at the bottom of that Nash article, pointing to a letter from Godel to von Neumann, written a year after Nash's letter. It is kind of the opposite of the Nash NSA letter, a direct letter between two eminent mathematicians who know each other and what each other knows. It muses about Turing's Entscheidungsproblem, one of my favorite topics.

The Godel letter instantly reminded me of my personal conjecture, I call it "The Law of Infinite Stupidity." I have postulated that the number of correct solutions to any specific problem is finite, but the number of incorrect solutions is infinite. This primarily refers to a mathematical problem on a finite state machine like a Turing Machine or any other finite state digital computer. I originally made a conjecture that number of incorrect solutions exceeds Aleph 1. However, lately I have been grading some algebra tests from high school students, and I have been musing about their infinite stupidity. I had not considered some multidimensional aspects of the domain containing correct solutions. So now I am considering the possibility that the number of incorrect solutions may be as high as Aleph to the Aleph power.
posted by charlie don't surf at 5:08 AM on February 23, 2012


It's easily provable that the number of incorrect solutions to any problem is at least alelph1, if you can exclude any region of real numbers from the correct solution, any region of the real numbers is aleph1.
posted by empath at 6:04 AM on February 23, 2012


Right, empath. But I'm mostly thinking of the Halting Problem. Any finite state machine we can practically construct has a limited amount of storage, thus the set of correct solutions it can arrive at for any one problem is much smaller than the set of real numbers. This is what the Godel letter deals with, there are computationally expensive solutions that are impractical, but not impossible.

But I'm not satisfied with your solution in general (not restricted to finite state machines), since there are problems with solutions sets that exceed the set of real numbers. My conjecture is not just that the set of incorrect solutions is equal to aleph1, but that it far exceeds it.
posted by charlie don't surf at 4:11 PM on February 23, 2012


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