ℝolliℵg M∀th Thr∑a∂

Indeed.

so if he has three coins, then he has

⅔ of a foreign gold coin
⅓ of a foreign nongold coin
⅔ of a domestic nongold coin
4/3 of a domestic gold coin

but this is impossible! he can only have 0, 1 or 2 of each of those types of coin

you lost me a bit here. if you are choosing 3 coins from the same guy then you need to consider that you are picking the coins without replacement and the probabilities should be different - the prior should change each time. if you are choosing 3 coins from different guys then you could absolutely get 3 coins of the same type!

i majored in quantum mechanics!

sorry I was calculating expectation values for # of each type of coin

ok my flight just got cancelled so i have far too much time on my hands. i am thinking abt what happens if we simply take all 3 coins from a single guys pocket (without placement) where the coins in his pocket satisfy the rules of the initial problem (2 gold, 1 foreign). there are 4 possible states for each of the coins in his pocket. writing a coin's state as:

(0,0) = not gold, not foreign
(0,1) = not gold, foreign
(1,0) = gold, not foreign
(1,1) = gold, foreign

then the 3 coins in his pocket have 3 possible states:

state 1: (1,0),(1,0),(0,1) - prob: 1/3 (uniform prior)
state 2: (1,0),(1,1),(0,0) - prob: 1/3
state 3: (1,1),(1,0),(0,0) - prob: 1/3

then after we take all 3 coins from the guys pocket the probability that we have at least one coin of one of the 4 states is:

Pr(we have at least 1 (0,0) coin) = 2/3
Pr(we have at least 1 (0,1) coin) = 1/3
Pr(we have at least 1 (1,0) coin) = 1
Pr(we have at least 1 (1,1) coin) = 2/3

state 2 and state 3 are equivalent, no?

oh i see why you did that, nm

i majored in quantum mechanics!

― the late great, Thursday, October 9, 2014 1:32 PM (1 hour ago) Bookmark Flag Post Permalink

sheepish emoji face

‘I do not even know what a matrix is’, Heisenberg had lamented when told of the origins of the strange multiplication rule that lay at the heart of his new physics. It was a reaction widely shared among physicists when they were presented with his matrix mechanics.

The question reminds me of Bertrand’s paradox from Calcul des probabilités. If you’re unfamiliar with Kolmogorov axioms, don’t read the Wikipedia article until you’ve worked it:

There’re three boxes.

• contains two gold coins
• contains two silver coins
• contains one gold coin and one silver coin

I love this problem. While it’s similar to Monty Hall, the geometric, probabilistic, and statistical solutions are far more elegant.

Scott Aaronson likes to describe quantum information thy as the extension of the concept of "probability" to allow negative values/amplitudes.

Interesting, but this interoperation marginalizes probability theory—whose usefulness is due to its simplicity and few dependencies. Information theory, on the other hand, requires a vast and complex framework. Fundamental objects in probability, e.g events and random variables, are easily reducible into the simplest mathematical objects. Hell, this includes continuous interpretations, whose fundamental theorem is simply proved with characteristic functions. While Shannon entropy is formally expressed using expected values and random variables, they aren’t equivalent. It’s far more nuanced than just the addition of negative values. Oh, and Aaronson is an asshole. So that’s probably motivating my nitpicking.

2/3, right?

Aaronson is an asshole? Tell me more! This is the kind of scuttlebutt I'm really looking for here.

no wait! tell us more about information theory's vast and complex framework

Aaronson is an asshole? Tell me more! This is the kind of scuttlebutt I'm really looking for here.

He wrongly threw my former advisor under the bus. It still pisses me off.

no wait! tell us more about information theory's vast and complex framework

LOL. This is what happens when I drink a bottle of wine before posting.

i am serious!

ok good to know! I really like his work (& er know someone who has to write about it) so I like to know about who I'm going to laud

i've heard a few explanations of how you can look at quantum stuff not just as a generalization of probability, but even more basically of logic. you just do the right sort of algebraic setup and let your variables "vary" over a different, weirder domain.

Anyone read any of this guy's stuff? http://www.newyorker.com/magazine/2008/03/03/numbers-guy

it's great. i know some of his work with his students on the munduruku (sp?) re their grasp of small numbers and then another category for "bigger than small" rather than more different numbers. So like 1 2 3 4 5 6 7 big

Also the tribe people get a diff number concept just from learning in schools taught in European languages.

Thanks. Wonder if it's worth reading his number sense book, or any of the others.

Number Sense is the famous one. could just look for articles on the net if you want a sample before buying

http://webmuseum.mit.edu/detail.php?t=exhibitions&type=exh&f=&s=3&record=6

Grothendieck is dead.

RIP :(

Thought revive would be for tomorrow's anniversary of Euler's formula V - E + F = 2.

RIP BIG G

Grothendiecks to watch out for

http://inference-review.com/article/a-country-known-only-by-name

http://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Icosian_grid_small_with_labels2.svg/500px-Icosian_grid_small_with_labels2.svg.png

Been reading Four Colors Suffice: How the Map Problem was Solved, by Robin J. Wilson, which is very well done, informative and entertaining. If you don't believe me, there is a rave review by John H. Conway on the back.

Here is a related cheat sheet: http://www.mei.org.uk/files/conference07/A2.pdf

Here is review in the AMS: http://www.ams.org/notices/200402/rev-toft.pdf

Also dipping into related book: Euler's Gem: The Polyhedron Formula and the Birth of Topology
By David S. Richeson

Related article:
The Truth about Königsberg, by Brian Hopkins and Robin J. Wilson
http://www.maa.org/programs/maa-awards/writing-awards/the-truth-about-konigsberg
http://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/hopkins.pdf

Kuratowski's original paper, in French, on a Polish website: http://matwbn.icm.edu.pl/ksiazki/fm/fm15/fm15126.pdf

A translation and helpful introduction can be found in Graph Theory 1736-1936, by Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson.

In which they explain that "gauche" translates to "non-planar."

OK, found a good Dover book on graph theory, if anyone is interested. Has a lot of nice biographical background stuff in addition to the mathematical content, which historical material also includes some relevant graphs with names of mathematicians and scientists in them. Just learned Einstein's Erdös number from one of these latter.

http://math.oregonstate.edu/bridge/papers/

http://education.lms.ac.uk/2014/12/alexander-grothendieck-some-recollections/

attn euler in particular: are you familiar with rodin and with "axiomatic method and category theory" (http://arxiv.org/abs/1210.1478) and do you have any opinions w/r/t such?

hah I know rodin extremely well! both as a person and as a scholar. he's a category theory partisan, but he knows lots of other math too, and some philo as well. I haven't read the book though. I think it just appeared with springer?

Enigma:The Movie means Enigma:The Book is back in print. It seems to have been out of since the first run, thirty some odd years ago.

u guys ever watch those Geometry Center videos? i was introduced to them during my self-ban. easily the best thing ever created

https://www.youtube.com/watch?v=AGLPbSMxSUM

https://www.youtube.com/watch?v=-gLNlC_hQ3M

https://www.youtube.com/watch?v=wO61D9x6lNY

Guess it actually came out again in 2012 for Turing centennary. (xp to self)

flopson otm

Will check those out, thx

need part 2 of knot not

ya wtf fuck you bbc worldwide

you could hit this guy up i guess http://www.geom.uiuc.edu/video/AKPeters.html

http://www.crcpress.com/product/isbn/9781568814537

$1/minute