This is all about an experiment Richard Dawkins did with an audience of young people to demonstrate improbable events happen all the time and the inclination to see the supernatural is in fact illogical.. Ref: [https://www.youtube.com/watch?v=H1TxH0zf07w]..
So lets see what this same experiment reveals when analysed as to conformance with the second law.. the basis of my falsification.. First I must say I agree the outcome is in no way supernatural.. and you do end up with an apparently remarkable result.. in the case given guessing 8 times in a row the outcome of the toss of a coin. But what does this actually demonstrate..?
Lets take the number of people participating as = N
the number of correct guesses in a row = n
The total number of guess 'events' = N + N/2 + N/4 + ... +N/2^(n-1) = (lets call this) E
(n)
E = N . \ 1 {ie N x (sum of the series 1/2^(n-1) (n) times)}
/ 2^(m-1)
m=1
Assuming half sit down after each toss of the coin.. because they got it wrong.
Now my falsification is based on the observation that the number of random changes (events or tosses of coin) required on average to get a certain improbable outcome is how the process balances the entropy decrease of that outcome (state) with an entropy increase in the surroundings. Its the entropy cost of the low entropy state which by the second law must be paid by that process.
So now we have the end result being the low entropy state of 8 correct guesses in a row which is equivalent to tossing 8 heads in a row or tossing 8 coins and ending up with 8 heads.
The probability of this outcome = 1/2^8 (or 1/2^n for 'n' correct guesses in a row)
So the question is, what is the audience size N to give enough events to pay the cost..?
Now let's do the same with replication and selection, because these are things that happen in reality.
ReplyDeleteLet's take our audience. Ask them to guess the outcome of a coin flip.
Anyone who gets it right, lives. The rest die. We have an audience of half the size, roughly.
The survivors breed to fill up the audience.
Next generation: our audience is now comprised entirely from descendants of people who guessed the first coin toss correctly. Get this audience to guess a coin flip. Kill those that get it wrong, breed those that get it right.
Next generation: our audience is now comprised entirely from descendants of people who guessed the first two coin tosses correctly. Get this audience to guess a coin flip. Kill those that get it wrong, breed those that get it right.
Next generation: our audience is now comprised entirely from descendants of people who guessed the first three coin tosses correctly. Get this audience to guess a coin flip. Kill those that get it wrong, breed those that get it right.
MILLIONS OF YEARS PASS
Next generation: our audience is now comprised entirely from descendants of people who have never, ever, gotten a coinflip call wrong, despite millions of coinflips occurring.
This is not fantastically unlikely, it is in fact completely inevitable given selection and replication.
So you see: replication and selection are VERY VERY IMPORTANT.
Apologies for the 9 year delay in answering you Dr J. A lot has happened in those years and I trust you are well and in good fighting spirits. Ah your modified Dawkins model looks impressive, but I am sorry to be the bearer of bad news but it's wrong! This is why:
DeleteLet me quote your concluding statement:
"MILLIONS OF YEARS PASS
Next generation: our audience is now comprised entirely from descendants of people who have never, ever, gotten a coinflip call wrong, despite millions of coinflips occurring."
Actually after the second generation only one quarter have guessed two heads in a row. After the third generation only one eighth remain who guessed three heads in a row. And after 7 generations only one in 128 have guessed 7 heads in a row.
The fact that each new generation is filled up with descendants of successful guessers has nothing to do with their future success.
The end result after millions of years is just a repeating cycle of 50% dying and regeneration with no greater decrease in entropy than is accounted for by the original size of the audience. Which is what actually pays the entropy cost up front.
Thank you so much for your thoughtful response..