rossum
Well-known member
Can we throw 1,000 consecutive heads on a fair coin? Yes, providing we go the right way about it. The raw chance is low, 1 in 2^1000, but it can be done.
Start with 5,000 blank cards, plus a lot more spare cards. And pens, we'll need pens to write on the cards. Plus, of course, a coin to toss.
For each of your 5,000 cards toss the coin. If it comes up tails, throw that card away. If it comes up heads, take two blank card, mark each with an 'H' for heads, and put them in a new pile. You should end up with about 5,000 cards in the new pile, each marked with an 'H'.
Now start on the new pile, which is now the old pile, if that makes sense. For each card in the (new) old pile throw the coin. If it comes up tails, throw that card away. It it comes up heads, pick two blank cards and mark them 'HH', because you now have two consecutive heads. Throw away the old card with a single 'H' on it. Again you will have about 5,000 cards with "HH".
Repeat the process. Tails means throw the card away. Heads means two more cards, each with an additional 'H', because you rolled heads.
Repeat, repeat, repeat until you end up with a tired wrist and about 5,000 cards each with 1,000 consecutive H's on them.
Looking back through the route by which every card in your final pile got there, each card is the result of 1,000 consecutive heads on the coin. Any time tails came up, that card was binned, so there are no tails on the final set of cards, only heads. One thousand consecutive heads.
How does this thought experiment relate to evolution?
Throwing tails is equivalent to not having any descendants. Throwing heads is equivalent to having descendants. In the real world, the chances are not 50/50, but there is some probability. Every one of your ancestors managed to breed successfully. If even one ancestor didn't succeed, then you wouldn't be here. You are the end of a very very long line of successful breeders, with not one single failure. Not one.
The H's on the cards are an analogue of the DNA passed from parents to offspring. That DNA is the DNA of successful breeders, and only of successful breeders—all heads with no tails. Unsuccessful breeders did not pass their DNA on to any modern descendants; if the coin came up tails that card was thrown away.
The 5,000 current cards are the breeding population. Each round of die rolls is a generation. Throwing away old cards is the previous generation dying away.
The thought experiment with cards, coin and pen is a very simple model of evolution. It shows how evolution can beat seemingly impossible odds by spreading out the odds over time. A journey of a thousand miles starts with a single step. A lot of steps will come after, but only successful breeders can take each following step on the journey.
Start with 5,000 blank cards, plus a lot more spare cards. And pens, we'll need pens to write on the cards. Plus, of course, a coin to toss.
For each of your 5,000 cards toss the coin. If it comes up tails, throw that card away. If it comes up heads, take two blank card, mark each with an 'H' for heads, and put them in a new pile. You should end up with about 5,000 cards in the new pile, each marked with an 'H'.
Now start on the new pile, which is now the old pile, if that makes sense. For each card in the (new) old pile throw the coin. If it comes up tails, throw that card away. It it comes up heads, pick two blank cards and mark them 'HH', because you now have two consecutive heads. Throw away the old card with a single 'H' on it. Again you will have about 5,000 cards with "HH".
Repeat the process. Tails means throw the card away. Heads means two more cards, each with an additional 'H', because you rolled heads.
Repeat, repeat, repeat until you end up with a tired wrist and about 5,000 cards each with 1,000 consecutive H's on them.
Looking back through the route by which every card in your final pile got there, each card is the result of 1,000 consecutive heads on the coin. Any time tails came up, that card was binned, so there are no tails on the final set of cards, only heads. One thousand consecutive heads.
How does this thought experiment relate to evolution?
Throwing tails is equivalent to not having any descendants. Throwing heads is equivalent to having descendants. In the real world, the chances are not 50/50, but there is some probability. Every one of your ancestors managed to breed successfully. If even one ancestor didn't succeed, then you wouldn't be here. You are the end of a very very long line of successful breeders, with not one single failure. Not one.
The H's on the cards are an analogue of the DNA passed from parents to offspring. That DNA is the DNA of successful breeders, and only of successful breeders—all heads with no tails. Unsuccessful breeders did not pass their DNA on to any modern descendants; if the coin came up tails that card was thrown away.
The 5,000 current cards are the breeding population. Each round of die rolls is a generation. Throwing away old cards is the previous generation dying away.
The thought experiment with cards, coin and pen is a very simple model of evolution. It shows how evolution can beat seemingly impossible odds by spreading out the odds over time. A journey of a thousand miles starts with a single step. A lot of steps will come after, but only successful breeders can take each following step on the journey.
