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Calculations of Bradley and Thaxton for random production of a single protein.

Walter L. Bradley and Charles B. Thaxton calculated the probability of a random formation of amino acids into a protein to be 4.9 x 10-191. They began with the assumption that the probability of starting with an L-amino acid was .5, and the probability of starting with an L-amino acid was .5, and the probability of two L-amino acids joining with a peptide bond was also .5. They assumed that the twenty necessary amino acids existed in equal concentration in the prebiotic soup so that the probability of the right amino acid in the required position was .05.
Bradley and Thaxton were also generous towards the proponents of random processes when they also assumed that all of the chemical reactions would be with amino acids, ignoring the high probability of reactions with non-amino acid chemicals. They calculated the probability of the necessary placement of one amino acid to be .5 x .5 x .05 or .125. This, of coarse, meant that the probability of assembling N such amino acids would be .0125 x .0125 for N terms. Assuming a protein with 100 amino acids (.0125 x .0125 for 100 terms ), the mathematically impossible probability would be 4.9 x 10-191.
Bradley and Thaxton noted their agreement with Hubert P. Yockey and concluded that even assuming that all the carbon on earth existed in the form of amino acids and reacted at the greatest possible rate of 1012/s for one billion years (when actually only 130 million years were available), the mathematically impossible probability for the formation of one functional protein would be 10-65.

Walter L. Bradley and Charles B. Thaxton, “Information and the Origin of Life” in The Creation Hypothesis, ed. J. P. Moreland (Downers Grove, Il : InterVarsity Press, 1994), p. 190

Calculations of Bernd-Olaf Kuppers for the random generation of the sequence of a bacterium.

Proceeding from the realistic assumption that all sequence alternatives of a nucleic-acid molecule are physically equivalent, Bernd-Olaf Kuppers concluded that the unguided, random formation of a predefined sequence ( such as the specific sequence of the nucleotides in the DNA molecule ) is reciprocally proportional to the number of all possible combinations of possible sequences. Kuppers noted that Michael Polanyi correctly emphasized that if the reverse assumption were true and the sequence of a nucleic-acid acid molecule would not have the capability to store information necessary to replicate living matter.

In calculating the expectation probability for the nucleotide sequence of a bacterium, Kuppers demonstrated the reason mathematicians have severe problems in accepting the assumptions of random origins:

“The human genome consists of about 109 nucleotides, and the number of combinatorially possible sequences attains the unimaginable size of 41000 million = 10 600 million. Even in the simple case of a bacterium, the genome consists of some 4.106 nucleotides, and the number of combinatorially possible sequences is 4 4million = 10 2.4 million. The expectation probability for the nucleotide sequence of a bacterium is thus so slight that not even the entire space of the universe would be enough to make the random synthesis of a bacterial genome probable. For example, the entire mass of the universe, expressed as a multiple of the mass of the hydrogen atom, amounts to about 1080 units. Even if all the matter in space consisted of DNA molecules of the structural complexity of the bacterial genome, with random sequence, then the chances of finding among them a bacterial genome or something resembling one would still be completely negligible.”
Brand-Olaf Kuppers, Information and the Origin of Life ( Cambridge, Mass:: The MIT Press, 1990 ), pp 59-60.

Calculations of Sir Fred Hoyle and Chandra Wickramasinghe for random generation of a simple enzyme and calculations for a single celled bacterium.

Although he is an evolutionist, and an atheist, Hoyle sees the mathematical statistical difficulty in producing a single bacterium like E. coli. In his calculations of the probability of life emerging from chance interactions with chemicals, Hoyle assumed that the first living cell was much simpler than today’s bacteria. However, his calculation for the likelihood of even one very simple enzyme arising at the right time in the right place was only chance in 1020. Because there are thousands of different enzymes with different functions, to produce the simplest living cell, Hoyle calculated that about 2,000 enzymes were needed with each one performing a specific task to form a single bacterium lie E coli.

No matter how large the environment one considers, life cannot have a random beginning….there are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in (1020)2000 = 1040,000, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup. If one is not prejudiced either by social beliefs or by a scientific training into the conviction that life originated on the Earth, this simple calculation wipes the idea entirely out of court….the enormous information content of even the simplest living systems….cannot in out view be generated by what are often called “natural” processes, …For life to have originated on the Earth it would be necessary that quite explicit instruction should have been provided for its assembly…There is no way in which we can expect to avoid the need for information, no way in which we can simply get by with a bigger and better organic soup, as we ourselves hoped might be possible a year or two ago.
-Hoyle & Wickramasinghe, Evolution from Space (London: J.M. Dent & Sons, 1981).