Lifelong debunker takes on arbiter of neutral choices
news.stanford.edu
news.stanford.edu
"Lifelong debunker": Persi Diaconis, an interesting chap who used to be a professional magician but turned to mathematics and is now a professor at Stanford. (His best-known work is on the statistics of riffle-shuffles: how many such shuffles do you need to do to make your pack of cards "random enough"?)
"Arbiter of neutral choices": a coin-toss.
What the title actually means: Diaconis is doing some work on the behaviour of coin-tosses; he has a simplified model of coin-tossing that suggests that there should be a small bias in favour of having the coin land the same way up as it started; he's doing (or, rather, getting some other people to do) some experimental work aimed at tuning the model on the basis of high-speed video footage of real coin tosses.
And, er, the story ends there: he isn't finished yet. But supposedly it's looking as if there might be a 51:49 bias. That would be large enough to be of some practical interest -- though maybe not very much since, as the article mentions, a skilled coin tosser can make them come up quite reliably whichever way s/he chooses.
The first thing that popped in my head was that if the coin tossed was to hit a "rough" surface on the ground, all bets are off again. The article doesn't specify is the experiment was tossing a coin and catching it (which I myself can reliably toss and bias it to the side i want, catching it in my hand, w/o using stats to prove it), or if the coin was to land on a surface of some sort.
To bet strategically, one had to calculate the odds that a die with one-hundredth of an inch shaved off an edge would tumble out of the box on any given side.
..."Barely six to nine months after he struggled with my advanced calculus course, he was applying to the finest graduate schools to continue his study," says D'Aristotile, who has taught probability courses at Stanford the past four summers.
...A recommendation letter from Martin Gardner was enough to lure Fred Mosteller -- a statistician on the selection committee who had dabbled with magic -- into taking Diaconis as one of his graduate students.
...To make his point, Diaconis commissioned a team of Harvard technicians to build a mechanical coin tosser -- a 3-pound, 15-inch-wide contraption that, when bolted to a table, launches a coin into the air such that it lands the same way every single time. ... But what he really wanted to know was whether unrehearsed tosses -- by ordinary folk who flip coins with unpredictable speeds and heights and catch them at different angles -- would show that the outcome of the act was, in fact, random.
...Diaconis first approached statistics Associate Professor Susan Holmes, who is also his wife, and asked if he could try her computer's camera.
..."What that means is, when I'm stuck on a problem, I feel free to call somebody who's an expert and try to talk them into helping."
While he and Holmes were analyzing the coin toss images, for instance, coffee-shop conversations with physics professors Kapitulnik and Stephen Shenker spurred them to consider the effects of air resistance, an important factor they had neglected in previous analyses.
...Several months ago, Diaconis recognized that Andersen's work in the statistical mechanics of fluids sounded similar to a mathematical theory being developed by of one of his colleagues, mathematics Professor Horng-Tzer Yau, who came to Stanford last fall.
...Mathematics doctoral student Joe Blitzstein agrees, noting that the most important thing he's learned from Diaconis, his thesis adviser, is "how to recognize that one problem is really the same as another, in a different guise."
...Though Diaconis had made a key conceptual leap by connecting falling cats and flipped coins, he still hadn't found a camera that could adequately capture the complex motion of a split-second coin toss. Without these images, it would be impossible to derive the quantitative model needed to calculate the size of a coin flip's predicted bias. ... Over a latte at Bytes Café in the Packard Electrical Engineering Building a year ago, Diaconis asked Wandell, an expert in human vision and color perception, if he knew anything about slow-motion photography. ... Two years earlier, a team led by Wandell and electrical engineering Professor Abbas El Gamal had built a speedy digital camera that shoots 10,000 frames per second -- 400 times faster than a typical camcorder.