Where Grey Matter meets Dark Matter

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Episode 23 - 6 February 2010

Persi Diaconis.

Picture this: You're playing a card game with your family. Let's say you're playing Snap. You get a fresh pack out, and begin to shuffle the cards. You shuffle for a while, everyone starts getting impatient, but you want to be thorough. You eventually stop, and deal the cards out. Your sister, to your left, plays a card. 5 of clubs. Then it's your mother's turn. 6 of clubs. There's a bit of laughter, and 'that's a coincidence!'. Play passes on to your aunt. 7 of clubs. She looks at you accusingly. You cast your eyes downward and play your turn. 8 of clubs. Everyone groans. 'But I was shuffling for ages!' you protest.

Situations like this can often lead to accusations of cheating brought against the dealer, although the chastised cheater is usually so busy trying to figure out why the shuffle went so poorly that he doesn't think to defend his integrity. Pretty soon there's a saloon-style gunfight, whiskey glasses are broken and somebody ends up fleeing on his filly into the sunset chased by those immortal words, 'This town ain't big enough for the both of us'.

Source: http://www.countyseatsaloon.com/

Maybe this illustration is getting out of hand. The point is, what went wrong with the shuffling?

Source: Flickr

Persi Diaconis is a magician-turned-mathematician who concerns himself with just this question. It turns out that it takes seven (7) riffle shuffles (also called dovetail shuffles by some) to randomise a deck good 'enough' for good play. What is 'enough' you ask? Well, 'random enough' means that the deck is 'most of the way' to being completely smoothly distributed. Sounds technical? It requires technical definitions; see Persi's paper for the real deal.

Of course if you use the ex-official CTP shuffling method, that most commonly employed in family card games, which Persi calls the 'clump-clump' method, 2500 shuffles are in order for the same level of randomisation.

It also turns out that if you riffle-shuffle 'perfectly' (where you interleave the cards exactly) it's possible to not randomize the deck at all, but to bring it back to its original order. At this point, the ears of the disreputable will audibly prick up. Yes, this is the source of some great magic and great swindles.

A diagrammatic representation of what happens during a perfect riffle shuffle, with a 98-card deck.
Source: http://www.cs.cmu.edu/~cdm/bilder.html

But underneath all of this, lies the venerable art of mathematics. From group theory to good old fashioned probability and statistics, Persi takes us on a rollercoaster ride of reputable roguishness. Roughly.


  • Bayer, Dave & Diaconis, Persi (1992), Trailing the dovetail shuffle to its lair, The Annals of Applied Probability, Vol.2, No.2, pp. 294-313.
  • Persi's website, including this bio.


Who doesn't love bees? Sure, they sting you sometimes, but usually (unless you're allergic) this does more harm to them than you. Plus, they make that sweet, sweet snack which, like a certain chocolate spread, forms a nutrituous breakfast food.

This is no doubt why Jerry Seinfeld decided to devote an entire movie to them. It's a good movie, with something for everyone to love and hate. So if you're one of those people who love hating things, you'll love/hate the hell out of this movie.

The sort of movie you can take home to your folks.

We use this movie as an excuse to talk about our favourite insect -- the bee (the favourite was dung beetles, until we realised they're bullshit). Well, family of insects that it is, let it not be said that there is only one type of bee. There are over 20,000 species in the world, and over 1,500 of them are native to Australia. So it's easy to see they've been busy little bee-vers.

This guy got a bee in his bonnet or what?

Bees have a number of interesting habits, including honey making, pollination, and making the hexagons they're so famous for. There's also the dancing, and the fact that they can fly at all - thanks aerodynamics! (Listen to the episode for an explanation of why the urban myth that science says bees can't fly is exactly that.)

Slow-motion bee flight. Notice how far he gets with each wing stroke..

We also talk about threats to the poor little blighters, including the feared Colony Collapse Disorder. There has been a whole bunch of research done into this in recent years, and while the jury's still out on a definite cause, there are some likely suspects lined up - including the Varroa destructor mite, a truly horrible little bug. Here at Cosmic Tea Party we strive to remain objective and unbiased when it comes to the good- and evil-ness of different creatures. But this guy's pretty mean.



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