What are the odds of turning this sentence:
We hold these bruths to be self evident
into
We hold these truths to be self evident
provided we can turn one letter in the sentence into any of the 26 characters (space included)? We can choose any of the 39 characters and for each of the 39 we have a one in 26 chance of getting the right one (It is not 27 because we can choose any character except the one already presented). We have to keep in mind that a random process does not know that any of these words are spelled differently. The odds are 26^39, which is one in 10^55. According to Sean Carroll, author of the Darwinists text the Making of the Fittest, the odds are exactly one. Here is why he thinks that: Let us add another condition. Let's imagine that you only get to make an attempt to get the right letter one in a hundred periods? Now what are the odds of getting the right answer in one period? You just multiply 10^2 by 10^55, which is 10^57. Sean Carroll looks at the first condition assumes that the odds are one, and calculates the odds of the second condition.
To calculate the odds of getting a precise mutation in the genome it must be kept in mind that any of the letters in the entire genome can change, and that any of those letters can change to any of the three other letters. Therefore, if a genome is 3 billion letters long and we needed a single precise letter, let's say letter 2,777,000,000 to turn into C then the odds of that happening would be 3^3,000,000,000, which is 10^10^11. (The genome is slightly more complicated because the DNA is grouped into words of 3 letters each, which gives 64 combinations and these 64 different words ultimately code for 20 different amino acids, so there are some repetitions that must be taken into account.) However, the principle remains that if an exact mutation is needed then chance cannot find it.
DNA is remarkably faithful. In humans one mutation occurrs only one in every 100,000 DNA, though in some animals it is five times more faithful. Thus in one offspring there will be 30,000 letters that are incorrectly transcribed in its genome (3 billion divided by 100,000). So if a very precise mutation is needed the offspring will make 30,000 attempts. In any case the odds of hitting one in 10^10^11 are impossible with only 30,000 attempts. It is estimated that DNA has been split about 10^40 times in the history of our Earth. 30,000 times 10^48 is a mere 10^453, which is not enough probalistic resources to hit one in 10^10^11 odds. What Sean Carroll does is he looks at the second condition which is one attempt per 500,000 and asssumes that the odds of the first condition is one. Thus he says that the odds of a particular organism getting a precise mutation are one in 500,000.
We know however that there are numerous beneficial mutations in any of the the 3.2 billion letters of the human genome or any genome. There are many more point mutations that result deleterious affects. It is theoretically possible to do a survey of all the known mutations and calculate the ratio of good mutations to bad or neutral but this has not been done. However, even that would be deceptive since many bad mutations result in immediate death of the organism. To calculate the odds of scoring a magic mutation we would have to know all of them, which we cannot know. Nevertheless, Sean Carroll is not attempting to do this, he is merely attempting to calculate the odds of one precise mutation. The bizarre part is that the zebra finch, herring gull, rhea, and budgerigar all acquired the exact same mutation (A to T at position 268 on the Opsin gene) after they split from their common ancestor. These four mutations could not have arose at random, rather some intelligent source must have purposely mutated them. The odds that it happened by chance are simply too large to be overcome. Click on the below image to see Carroll's actual words.
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