RMKQLEEKVYELLSKVACLEYEVARLKKVGE
The probability of generating this is successive random trials is (1/20)^32 or 1 chance in 4.29x10^40. This is much ,much more probable than the 1 in 2.04x10^390 of the standard creationist generating carboxypeptidase by chance scenario, but still seems absurdly low.
Lets make it lower Ian
Ian is not correct with the 4.29x10^40 nonsense.
His figure of 1/20^32 seems a bit optimistic since he is assuming only 20 amino acids to start with, actually there is more than 500 known natural amino acids. So the first correction that needs to be made is 1/500^32. The author still does not include the odds of forming the correct configuration of those amino acids (I will not include those either); the odds would be greatly decreased if you consider it.
That IS the odds of the correct configuration.
1/
a is the probability
that a given position will hold the "correct" amino acid out of a choice of
a amino acids. Since the identity of each amino acid is (assumed to be) independent of the previous one, the probability of getting a particular string of
n amino acids is just (1/
a)[sup]
n[/sup].
It's worth noting that this is just
one peptide, which "Ian" - is calling him by his first name a "clever" attempt at disrespect? - picked because it happens to be self-replicating. Nowhere is it written in stone that there is only one such peptide, let alone organic molecule. In fact, he cites several other examples of self-replicating molecules in that very article.
Since we have no real grasp on how common self-replicating peptides, RNAs or other molecules are, we cannot put a number on the probability of self-replicators appearing - but given that there's definitely more than 1 of them, it's certainly going to be higher than the probability of the Ghadiri peptide appearing.
So the real calculation of the author must approach (1/500)^32=4.3^-87.
Still rather greater than whatever times ten to the power of 390, and well within Dembski's nonsensical universal probability bound.*
Also, how many of the hundreds of naturally occurring amino acids can form stable polypeptides? I gather some of them just break the chain if they get incorporated. Furthermore, how many of the "naturally occurring" amino acids are "naturally occurring" in the sense of "synthesised by organisms", versus "would have been there on prebiotic Earth"? If you
really want to get technical, perhaps the number 500 also needs some adjustment...
Does Ian really want to trivialize statistics?
I don't know, but you certainly seem to trivialise
him...
Fair coin toss:
Now the probability of 4 heads in a row is is (1/2)4 or 1 chance in 16: do we have to do 16 trials to get 4 heads (HHHH)? No, in successive experiments I got 11, 10, 6, 16, 1, 5, and 3 trials before HHHH turned up.
Probability predicts that over a field of possible outcomes there is a desirable outcome. Ians example seems simple enough, but here is some perspective on outcomes and universal bounds. Lets, use one white marble and 15 black marbles (same odds as Ians). What are the odds of picking that one white marble out of a bag of 16 marbles and just one being white? Of course 1/16 right? That does not mean you can not pick the white marble the first time but only it is not the most likely outcome. Simply stated that out of 16 trials you are likely to pick the white marble (on average) once every 16 tries. Now lets see the odds of picking the white marble 16 times in a row. That is (.0625)^16 or 1/5.42x10^-20 (very small). Now lets look at really small possibilities, say picking a white marble out of a bag with 10^80 marbles, one being white. According to Borel that event would never happen, why? I will not go into his justification for Borels upper limit but I will try and put some perspective on it. In the observed universe it is estimated there are only 10^80 atoms. Say you could mark one atom ant throw it into the vastness of space. Now if you could pick from anywhere in the universe what are the odds of picking that marble the first time? 1 in 10^80th right. OK say you could pick one atom every second for several billion years longer than the age of the universe. How many atoms are left? Well about 10^80. In other words you did not discard enough atoms to affect the overall amount. So the last single choice would be for a volume of about 10^80th atoms or 1 chance in ten to the 80th. Sound reasonable? Well by Borels upper limit states that choice would not produce that single marked atom (no chance at all). I would have to agree with that conclusion. Where would you pick from? Maybe a hydrogen atom in the Crab Nebula?
What is the relevance of this wall of text?
I know what the relevance of Ian Musgrave's example was, and it flew straight over your head. (Hint: the whole point was that this:
you said:
What are the odds of picking that one white marble out of a bag of 16 marbles and just one being white? Of course 1/16 right? That does not mean you can not pick the white marble the first time but only it is not the most likely outcome. Simply stated that out of 16 trials you are likely to pick the white marble (on average) once every 16 tries.
doesn't mean as much as people think it does. In fact, in the
majority of his trials, he got four heads in
less than half the expected number of trials.
You see Ians simplistic example does not consider a universal probability bound Borels or Dembskis.
You see, he doesn't consider it because it's utterly irrelevant. You, on the other hand, didn't seem to consider this:
TalkOrigins said:
Yes, one kilogram of the amino acid arginine has 2.85 x 1024 molecules in it (that's well over a billion billion); a tonne of arginine has 2.85 x 1027 molecules. If you took a semi-trailer load of each amino acid and dumped it into a medium size lake, you would have enough molecules to generate our particular replicator in a few tens of years, given that you can make 55 amino acid long proteins in 1 to 2 weeks [14,16].
and the following paragraphs. (Feel free to point out the errors. Even feel free to redo the calculations with your "adjusted" probability.)
And, of course, you completely ignored the fact that there's many more than one possible self-replicator even in the size range of "relatively small". Oh, and quite possibly many more than one habitable planet...
***
*Why nonsensical? Well, according to the Wikipedia article, it's derived from the number of "events" that could have happened over the lifetime of the universe.
So if a certain event
actually has a 10[sup]-150[/sup] chance of occurring, wouldn't that mean its chance of having occurred in the lifetime of the universe approaches
1??? Anything with that chance or higher has almost certainly occurred since the universe began. Out of Dembski and myself, one of us
really doesn't get probability...
Now, that
is a huge oversimplification, since not all events have an equal chance of occurring over the whole lifetime of the universe. Peptides, for example, can only start forming once heavy elements have dispersed into space and assembled into amino acids.
And that tells you why the magic number is completely meaningless - you're not looking at the probability of anything relevant, you're just lumping all possible subatomic level "events" under one big umbrella. You are not accounting for the way many of these events are not independent and certainly not equiprobable. For example, once hydrogen and oxygen form in a universe like ours, their probability of reacting to form water might be damn close to one. (For that matter, hydrogen and oxygen don't really form by chance, except in the sense that quantum mechanics is inherently probabilistic. But given the amount of material in the universe and the laws of physics, these elements NOT appearing is the event with the vanishingly small probability.)
(By the way, Dembski got the
Planck time wrong...)