Originally posted by midnight Target
It did happen and the math is wrong.
Ahh yes, mr midnight, biology professor, mathematician and BB poster extraordinere. What is wrong with the math then?
From the book:
In the list of concessions, it was assumed that all of the appropriate atoms on earth’s surface, including air, water, and crust of the earth, were made into amino acids and arranged conveniently in sets to make it easier for chance to come up
with a usable protein. It can be estimated that there would be about 10^41 such sets available.
With each of these sets making a total of 10^24 different chains per year as assumed in concession 11, that gives a total of 10^24 x 10^41 chains produced on earth in a year’s time, which is 10^65. Under concession 14, the total chains made since the earth began would be 5 x 10^74, which we will round off to 10^75.
We have just seen that chance could have made 10^75 different protein-length chains at the speed assumed during the entire time the earth has existed. Using the formula from the alphabet, we can now estimate how many of those might be considered usable protein molecules. First, we should allow for one substitution per chain. This would have the effect of changing that 1/10^240 formula to around 1/10^236. The probability, then, for usable protein molecules in this total of 10^75 produced since the world began is 10^75 / 10^236.
Simplifying the fraction, we get 1 in 10^161 as the probability that even one would be usable, on the average.
Therefore, the odds are 10^161 to 1 that not one usable protein would have been produced by chance in all the history of the earth, using all the appropriate atoms on earth at the fantastic rate described. This is a figure containing 161 zeroes.
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Note that here he is talking about one protein, but a cell contains more than one protein, therefore he made another calculation, namely this one:
It has just been calculated that the probability of a single protein molecule being arranged by chance is 1 in 10^161, using all atoms on earth and allowing all the time since the world began. What is the probability of getting an entire set of proteins for the smallest theoretical living entity?
The second protein molecule will be far more difficult than the first, because it has to be part of a matching set. The protein molecules of a cell are quite specifically adapted to work together as a team. We assumed that the first protein could be any usable protein that might be good somewhere. Once that first one is specified, the rest of the set has to match it exactly. It is like assembling a car from a crate of automobile parts. Once the kind of automobile is determined by the first component used, then all the other items must be of that same matching group. Nothing else on earth will fit, in most cases, except the part made for that particular purpose.
After the first protein molecule is obtained by chance (if it ever happens), then the others must be quite specific in the same way as the automobile components.
The probability of getting the first protein molecule was influenced by the formula taken from the alphabet analogy. The second one is more difficult to obtain, we have just seen, because it has to be more exact to match the first one, instead of being just any protein.
The total number of possible orders in a chain of 400 amino acids of 20 kinds is 20^400. (The formula is: the number of kinds to the power of the number of units in the chain.) As stated above, 20^400 is the same as 10^520.
Considering the first one as already obtained, we need 238 more. The second one could be any one of those 238. The probability is therefore 238/10^520. The third one could be any of the 237 still needed, so its probability would be 237 /10^520. Calculating all of these, and allowing for one substitution per chain, we arrive at a probability of 1 in 10^122470. Even if almost a trillion different sequences might work in each protein, the probability resulting is 1 in 10^119614.
This figure represents the second through the 239th protein molecules. Multiplying in the first one, which was at a probability of 1 / 10236, we arrive at the final figure for the minimum set needed for the simplest theoretical living entity, namely. 1 chance in 10^119850.
Earlier, we obtained the figure of 10^75 which was the total number of chains made since the earth began. In order to allow for overlapping sets of 239 each, we will use that same figure to represent the total protein sets formed. Dividing into the big figure just calculated, we learn that the odds against one minimum set of proteins happening in the entire history of the earth are 10^119775 to 1.
Even if such a set could be obtained, we would not have life. It would simply be a helpless group of nonliving molecules alone in a sterile world, uncaring and uncared for, the end of the line.
