Creationists and Darwinian skeptics often claim that natural selection could not produce the sort of improbability (often, for reasons that nobody is quite sure of, below 1 in 10 to the 500th power) that we see around us.
So it comes as a pleasant surprise to find that UK skeptic and magician Derren Brown (his homepage is here) has effectively explained it. Brown follows the fortunes, rather literally, of a woman who he tells 24 hours in advance the name of the winner of a horserace. After 3 successful predictions, he tells her to bet, and she wins several hundred pounds; Brown calls this "The System". After 5 successful predictions, he tells her that she should get all the cash she can to bet on a final race prediction. She borrows £4000 and gives him the money to bet on that horse. It loses, of course.
Ethics notwithstanding, Brown explains the system - several thousand people were approached and arranged into 6 groups, and each race had six horses. After round 1, one sixth remain. They are organised into six groups and so forth until one woman remains. Incidentally, Brown didn't bet her money on the losing horse, but I reckon he bet on all six horses and handed her the winning ticket. All losers were offered reimbursement.
Similarly, Brown throws ten heads in a row. It looks magical, until he shows the thirteen hours of throwing coins until he gets that sequence. This is, of course, how natural selection is responsible for low probability outcomes. I think it was Fisher who said that natural selection is a probability engine. With a large enough population, you can expect to get most sorts of low probability outcomes.
Watch the video - it's on Youtube:
The System Part 2
The System Part 3
The System Part 4
The System Part 6 (5 repeats this without the last bit)
I hope this doesn't breach copyright. If it does, let me know Channel 4...
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This very same scheme was the subject of a kid's show on public television many years ago. The show was Square One TV and the segment was called "MathNet" (Based on the old crime show DragNet)
If this show exists on DVD it is well worth the time to watch. My older kids still the sing the mathy songs (they're 25 and 27)
I once heard of another demonstration of this. A big shot Business prof was speaking to a large group of brokers and investment advisors about investment strategies. He asked everyone to stand up and take out a quarter and flip it. He then told everyone who got a heads to sit down, so half of the audience did and he instructed those standing to flip the coin again and all those who got tails to sit down. This went on seven or eight more times until there was only one person standing. The prof then told the audience to say hello to Warren Buffett.
How to get an improbable outcome - have Republicans manage your tabulation process.
Derren Brown's horse racing exercise is a variant of survivor bias in mutual fund and hedge fund evaluation. I once gave a speech to a Chamber of Commerce group in which I set up a similar hypothetical situation, calling the direction of movement of the stock market from week to week. According to the proportion of hands that were raised signifying that people in the audience would pay me for subsequent forecasts (after having been unknowingly in the group that by chance got 8 correct calls in a row), I could have made out quite well. For a while, at least. :)
Oops. I see natural cynic has a similar story.
After 5 successful predictions ... Ethics notwithstanding, Brown explains the system - several thousand people were approached and arranged into 6 groups, and each race had six horses. After round 1, one sixth remain.
Since 6^5 is 7776, they must've contacted 7,776 people.
Daniel Dennet has a better example, one that doesn't rely on trickery.
I bet you that by this time t/row I can produce someone who has just tossed 10 heads in a row from 10 tosses.
To do this, I invite 1024 of my friends along and pair them off with a coin for each pair, which they then call.
Those who toss tails are eliminated while those who call heads are paired off.
Continue in 10 rounds until there is only one person left.
That person has tossed 10 heads in a row from 10 tosses.
Guaranteed.
You even have 1024 friends? I might be able to scrape up fifteen people if I impose on workmates...
I watched this a few weeks ago and had the "trick" figured out quite early on. It's a very simple phenomenon, but one that is easily misinterpreted by people on a regular basis. It also should provide a bit of perspective for people who believe that fine-tuning implies design.
What does the presenter do in the 25%-chance situation that the final pair of coin-tossers are both eliminated?
{ahem!} Above question pertains to individual flipping scenario posited in comment # 2, not shared-coin scenario of # 7.
This system is described en "Adam Had Three Brothers".
A 1960 short story by R.A. Lafferty
Umm...no. There's no guarantee that you'll get any heads at any step in the process. You could hypothetically end up with 512 tails in the first round and end up eliminating everybody straight off. What you ought to be doing is eliminating those who are wrong at each stage, whether they call heads or tails. That guarantees you one person at the end who has made 10 correct consecutive calls, but there's no way of knowing beforehand what those 10 calls will have been.
I really enjoy this guys work, and wish his show were broadcast here in the states (there are many more of his episodes on YouTube).
But John, you really took away what makes watching him so much fun. I would have enjoyed it a whole lot more if your post didn't spoil it by revealing the technique he used in advance. Maybe its just me, but a large part of the fun of watching him work is trying to figure out how he does it. It takes all the fun and drama out of it if you know what he's doing. A spoiler alert would have been appropriate (IMO).
TinyFrog: "Since 6^5 is 7776, they must've contacted 7,776 people."
They did.
"You even have 1024 friends?" In *My Space*, you can have thousands of friends, personal contact not required.
You might, Susan. I have six friends on Facebook and I'm way too old for MySpace.
Forbes Magazine has been tracking mutual fund results for decades and eventually came to the conclusion that the only worthwhile piece of information you need about a mutual fund is the cost of operations (the lower the costs and fees, the better the customer will do). Even though some funds do very well for a very long time, there is no way to be certain that the fund is going to have above average results for the future. All you can know is that there was a fund that had the best results over the historical period in question.
This is a problem for folks who don't understand probability. Someone has to win the NCAA championship or a horse race. The system is rigged to force a winner. The same thing with natural selection. Life continues and it changes as it continues, but there is nothing that we can say about what the winning form of life will be based on what we know about life today. Humans are a very unusual result. Our success is an anomaly, but the fact that there are successful organisms is not. We can say with strong likelihood that humans will eventually disappear from earth and that other groups will take a dominant role -- not necessarily as dominant as humans today.
Prior performance is no predictor of future results, but the cost of operations of humans is pretty high.
#13: I don't see how you can guarantee that either. Maybe everyone will call it wrong the first time. Or at some later stage, everyone of those you've kept alive will call it wrong. And then?
As I understand #7's scenario, there are two people to each coin, one of whom calls heads, and the other tails. So there's exactly one winner for each pair, guaranteed.
RBH writes:
I've heard of a stock market scam based on this. Man sends out spam to 16,000 people in business, picking the fate (up or down) of a stock. To the 8,000 folks he guessed right, he sends another pick. To the 4,000 people he got 2 in a row, he sends another. Until he gets a pool of 500 folks where he guessed right 5 times in a row. Then he asks for money for the sure fired system that allowed him to pick stocks with such accuracy.
Say, that reminds me: I've heard of a similar scam. It involves writing letters to parents claiming that they can pull some strings to get their kid into an Ivy League school. They only have to pay if their kid makes it in. When a certain percentage of kids gets in, the scammer gets paid.
Whoops. I said that before I watched the video (and they mentioned the number). I was actually commenting on Wilkin's comment that "several thousand people were approached".
Also, at 5:50 into the video Derren Brown says he asked her to keep a video-diary after the first round. I wonder if they passed out cameras to all remaining 1,296 people, or if it was just lucky that she had her own camera.