One of the funniest abstracts to a paper on the arxiv in many moons appeared yesterday, authored by Carlos Mochon:
arXiv:0711.4114
Title: Quantum weak coin flipping with arbitrarily small bias
Authors: Carlos Mochon"God does not play dice. He flips coins instead." And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum weak coin flipping so that we too may flip coins. Instructions for the flipping of coins are contained herein. But be warned! Only those who have mastered Kitaev's formalism relating coin flipping and operator monotone functions may succeed. For those foolhardy enough to even try, a complete tutorial is included.
The paper is also excellent and well worth reading! Note that some people will consider this abstract and paper scientific fraud. Me, personally, I think that making science for Grown-Ups only is exactly the best way to stiffle scientific progress.
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After a quick reading, I guess Mochon's is a good paper. The abstract sounds more ludicrous than what we are used to but I think that this guy knows his craft. You can't compare him to Lisi.
You can't compare him to Lisi.
That's good, because I didn't :)
You did because you have made an implicit prediction, using a hyperlink and a sentence, that a well-known blogger will assign the same value to Mochon's paper as Lisi's paper. ;-)
Fantastic! Thanks!
I think by the logic of implicit link connection you might be able to connect everything everywhere, considering how connected the web graph is. I think I just called myself a scientific fraud.
Please explain, Dave. I am too stupid to understand your hyperjinks. (Is that really a word? It should be.)
I was just pointing to some comments by Lubos and another website where the rough claim was along the lines that the title of a paper constituted scientific fraud. Nothing really that interesting. But hyperjinks is an awesome word!
Even the classical case is nontrivial.
No Such Thing as a Fair Coin?
http://www.aleph.se/andart/
Diaconis, P., Holmes, S. and Montgomery, R. Dynamical Bias in the Coin Toss, SIAM Review vol 49:2, pp 211-235 analyses the process of flipping a coin. Even when vigorously flipped the coin turns out to come up more often the same way as it started. The discrepancy is small - p=0.51 for same side up, something which it would take about 250,000 trial flips to check - but it is hard to get away from.
The reason, as described in the paper, is that the fairness of a throw is dependent on the angle between the rotation axis and the normal of the coin. Imagine a coin thrown straight up, rotating around a vertical axis. Such a coin would of course land with the same face up, being 100% unfair. A coin rotating around an axis through its edge would on the other hand tend to be fair (if it rotated enough times that initial uncertainty in the flip became magnified enough). But a coin with a rotation axis inbetween would be somewhat unfair. The analysis gets a bit more complex due to precession, but it seems that averaged over all rotation axes we get a bias towards same side up. Experimental testing then seemed to confirm this dynamics.
Of course, if the original top side is hidden things become fair again.
Posted by Anders3 at 07:57 PM
Prof. Phillip V. Fellman commented to me by email: "phenomenon here, at least at the surface level. Brian Arthur nicely relieves the tension of the apparent paradox by remarking that the law of very large numbers is a basin of attraction with a lot of complex behavior around the lip of the basin but that once you climb over the lip, the attractor is so strong that you can never get out of the basin again.
The .0051 bias (seems nearly identical to the first bias against random walk theory which Farmer and Zovko found for persistence in studying 16 million odd trades over 2 3/4 years on the London Futures Exchange ["The Power of Patience", Santa Fe Institute Working Papers, 2002]) may be another one of these funny "axes of evil" on a microscale. It would be nice to go back and see if one could tie this to Yaneer Bar-Yam's question [arXiv] about a first order space-time theory."
I hyperjinked:
Really, it's worth reading the PDF of the unfair coin paper. The quotes from Joe Keller, Euler, Hopf (an important and under-rated genius), and Feynman alone. Or the graph of the hyperbolae of heads and tails initial conditions. Or the photo of their experimental apparatus. Or what to do with a half-dollar and scotch tape. Or why it is still MUCH better to flip the coin rather than to spin it on its edge. Or the air friction caveat and experiment with dropping coins of the Hoover Tower at Stanford (where Phil has been several times).
Oh, and remember that classic Twilight Zone epsiode about the coin landing on edge, and the office worker becoming telepathic?
Sorry, I accidently dropped the opening phrase of Dr. Fellman's comment:
"I think that there is a clustered volatility phenomenon here..."
Clustered volatility, for you non-economists, or non-Econophysicists, is what's missing from the Black-Scholes equation (where volatility is just hardwired in as a parameter), involves heteroskedacity (not to be confused with heteroskedasticity), and when solved, will win someone a Nobel prize in Economics (maybe someone at Santa Fe Institute).
What is the heteroskedacity of hyperjinks in a Small World Network of quantum coin-flippers?
Dave, I hope that will teach you not to generate trackbacks to a certain blog (which shall remain nameless).
Clustered volatility sounds rather like the phenomenon that clobbered some hedge funds in August...but that's another topic.