I just read a mathematical treatment of this issue by a geophysist from Los Alamos:
Taking 10^80 as a generous estimate for the total number of atoms in the cosmos, 10^12 for a generous upper bound for the average number of interatomic interactions per second per atom, and 10^18 seconds (roughly 30 billion years) as an upper bound for the age of the universe, we get 10^110 as a very generous upper limit on the total number of ineratomic interactions which could have ever occured during the long cosmic history the evolutionist imagines. Now if we make the extremely generous assumption that each interatomic interaction always produces a unique molecule, then we conclude that no more than 10^110 unique molecules could have ever existed in the universe during it's entire history.
Now let's contemplate what is involved in demanding that a purely random process find a minimal set of about 1,000 protein molecules needed for the most primitive form of life. To simplify the problem dramatically, suppose somehow we already have found 999 of the 1,000 different proteins required and we need only to search for that final magic sequence of amino acids which gives us that last special protein. Let's restrict our consideration to the specific set of 20 amino acids found in living systems and ignore the hundred or so that are not. Let's also ignore the fact that only those with left-handed symmetry appear in life proteins. Let's also igonre the incredibly unfavorable chemical reaction kinetics involved in forming long peptide chains in any sort of plausible non-living chemical environment.
Let's merely focus on the task of obtaining a suitable sequence of amino acids that yields a 3D protein structure with some minmal degree of essential functionality. Various theoretical and experimental evidence indicates that in some average sense about half of the amino sites must be specified exactly. For a relatively short protein consisting of a chain of 200 amino acids, the number of random trials needed for a reasonable likelihood of hitting a useful sequence is then in the order of 20^100 (100 amino acid sites with 20 possible candidates at each site), or about 10^130 trials. This is a hundred billion times the upper bound we computed for the total number of molecules ever to exist in the history of the cosmos!!. No random process could ever hope to find even one such protein structure, much less the full set of roughly 1,000 needed in the simplest forms of life. It is therefore sheer irrationality for a person to believe random chemical interactions could ever identify a viable set of functional proteins out of the truly staggering number of candidate possibilities.
In the face of such stunningly unfavorable odds, how could any scientist with any sense of honesty appeal to chance interactions as the explanation for the complexity we observe in living system? To do so, with conscious awareness of these numbers, in my opinion represents a serious breach of scientific integrity. This line of argument applies, of course, not only to biogenesis but also to the issue of how a new gene/protein might arise in any sort of macroevolution process.
Taking 10^80 as a generous estimate for the total number of atoms in the cosmos, 10^12 for a generous upper bound for the average number of interatomic interactions per second per atom, and 10^18 seconds (roughly 30 billion years) as an upper bound for the age of the universe, we get 10^110 as a very generous upper limit on the total number of ineratomic interactions which could have ever occured during the long cosmic history the evolutionist imagines. Now if we make the extremely generous assumption that each interatomic interaction always produces a unique molecule, then we conclude that no more than 10^110 unique molecules could have ever existed in the universe during it's entire history.
Now let's contemplate what is involved in demanding that a purely random process find a minimal set of about 1,000 protein molecules needed for the most primitive form of life. To simplify the problem dramatically, suppose somehow we already have found 999 of the 1,000 different proteins required and we need only to search for that final magic sequence of amino acids which gives us that last special protein. Let's restrict our consideration to the specific set of 20 amino acids found in living systems and ignore the hundred or so that are not. Let's also ignore the fact that only those with left-handed symmetry appear in life proteins. Let's also igonre the incredibly unfavorable chemical reaction kinetics involved in forming long peptide chains in any sort of plausible non-living chemical environment.
Let's merely focus on the task of obtaining a suitable sequence of amino acids that yields a 3D protein structure with some minmal degree of essential functionality. Various theoretical and experimental evidence indicates that in some average sense about half of the amino sites must be specified exactly. For a relatively short protein consisting of a chain of 200 amino acids, the number of random trials needed for a reasonable likelihood of hitting a useful sequence is then in the order of 20^100 (100 amino acid sites with 20 possible candidates at each site), or about 10^130 trials. This is a hundred billion times the upper bound we computed for the total number of molecules ever to exist in the history of the cosmos!!. No random process could ever hope to find even one such protein structure, much less the full set of roughly 1,000 needed in the simplest forms of life. It is therefore sheer irrationality for a person to believe random chemical interactions could ever identify a viable set of functional proteins out of the truly staggering number of candidate possibilities.
In the face of such stunningly unfavorable odds, how could any scientist with any sense of honesty appeal to chance interactions as the explanation for the complexity we observe in living system? To do so, with conscious awareness of these numbers, in my opinion represents a serious breach of scientific integrity. This line of argument applies, of course, not only to biogenesis but also to the issue of how a new gene/protein might arise in any sort of macroevolution process.
& or arranged for that sequence of amino acids to line up just right...
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