I was listening to Star Talk with Neil Degrasse Tyson (Listen to the Podcast, Subscribe via iTunes), the other day, and I came across an episode entitled Pseudoscience. Neil Degrasse Tyson is an agnostic, and I’m a believer in Jesus, yet I couldn’t agree more with what he said. If you get one thing from the broadcast, it would be this:
Imagine a game with 1000 people. The goal is to complete a fair coin toss multiple times until only one person is left standing. If your coin lands on heads, you get to remain standing. Everyone that gets tails has to sit down.
A fair coin toss is 50/50. So there’s a 50% chance you land on heads, and a 50% chance you land on tails. If you’re familiar with probability and statistics, you know that the random distribution of outcomes will not quite be 50/50 on a small number of flips. For example, out of 100 tosses of the coin, it might be 47/53 or 66/34 but we know that as we increase the amount of flips to approach infinity, the distribution approaches exactly 50/50. So let’s begin!
We start with 1000 people.
Coin Toss 1: Roughly 50% of the people land on tails and have to sit down. There are 500 still standing.
Coin Toss 2: 50% of the people land on tails. There are 250 standing.
Coin Toss 3: 50% of the people land on tails. There are 125 standing.
Coin Toss 4: 50% of the people land on tails. There are 64 1 standing.
Coin Toss 5: 50% of the people land on tails. There are 32 standing.
Coin Toss 6: 50% of the people land on tails. There are 16 standing.
Coin Toss 7: 50% of the people land on tails. There are 8 standing.
Coin Toss 8: 50% of the people land on tails. There are 4 standing.
Coin Toss 9: 50% of the people land on tails. There are 2 standing.
Coin Toss 10: 50% of the people land on tails. There is one person standing.
Out of the 1000 people we started with, we’re now down to 1 person who tossed the coin 10 times and got heads every time. There’s a 1/2n chance you flip any sequence of heads vs tails, that’s why there’s a 1/1024 chance that you flip ten heads in a row.
The thing about human nature is we don’t care about the 999 losers. The news reporter doesn’t interview them. We interview the one guy that won. He says something like this:
At about the 6th coin toss, I just felt like I was on a roll! Somehow deep inside, I knew I was going to roll 10 heads in a row and win the game. I can’t explain it, I just had this lucky feeling!
The news reporters don’t interview the other 15 people who got that exact same “lucky” feeling at Coin Toss #6. We want to see the winner and say, “That could be me!” So all that guy has to do is write a book, that says, “I won, and you can too!” and people will buy it, because they don’t understand how the natural world works.
We interview the winner, because we as humans have a craving to be special or find meaningful patterns where there are none. This is a universal human weakness, and it’s why con artists will never go hungry.
Obviously, half of 125 is 62.5, but we choose to round to 64 instead of 62 because it’s easier to continue to divide 64 by 2 for the purposes of our mental exercise.↩