The Current Condition of Darwin's Hypothesis II

One of my readers generated a very good discussion about my last blog post on my Facebook wall (I encourage all of you to like my page ;-).   He had several criticisms, some of which may be valid, about the underlying assumptions in the math that led me to the astronomically small probabilities for Darwin's Hypothesis.  While I think that correcting for the assumptions will likely not lead to any less ridiculous probability calculation, he is correct that I can not mathematically prove that for all of them.  There are too many variables in a problem that size.  So, let's try this from a slightly smaller scale angle, and making all assumptions and approximations on the side of the evolutionary hypothesis.  If I leave an unaccounted for assumption without realizing it, please feel free to point it out either in the comments below or on my Facebook page (which I encourage you to like).  Throughout the post, and through all my future blog posts, I will place hyperlinks that will bring you to Wikipedia or other article pages that will explain the terms that are highlighted, or show where I get my numbers.

Let’s begin with a very generous estimate.  Even if we involve all of the carbon atoms in the world (about 2*10^47) and allow them all to be only involved in DNA, that would require about 20 carbon atoms per base-pair including the backbones.  That means we have enough carbon atoms available on earth for about 10^46 base-pairs with about one quarter of them representing each possible coding letter that is used on the genetic code.  There are 3.1 billion base-pairs necessary for the recipe of one correctly formed human being, but again being conservative, for the sake of argument let’s say that since only two percent of those are in coding regions and most amino acid codons can be coded in more than one way that we are looking at only about 30 million that must eventually be brought to a certain order.  Now, having likely grossly overstated the number of base-pairs available and grossly understated the number of them that must find a specific order, let’s begin building a human by random, but iterative evolutionary processes.  

The first thing that will need to happen is that a set of DNA large enough to be the code for a living thing will have to be assembled by random processes without the benefit of the DNA replication or natural selection that goes on in a cell since this will be the first cell.  The living thing with the least number of base-pairs in its genome that has been discovered so far is the Carsonella bacterium which has 160,000 base-pairs in its genome, coding for 182 different proteins.  The Carsonella bacterium is a very useful case for this discussion in that not only is it the smallest living thing in the world from a genomics perspective, but it is only half the size of the next smallest living thing to be discovered so far.  Also, bacteria genomes are 98% coding regions, which leave us a lot less room for error, so to speak, in the ordering of the base-pairs.

So, before we begin assembling a human, let's begin assembling a Carsonella bacterium sized organism for the human to eventually evolve from.  There are 10^96329 ways in which 160,000 base-pairs, with four possibilities at each site, can be assembled.  Our earth allows us enough carbon for, at most, as stated, about 10^46 base-pairs.  That gives us enough base-pairs to assemble about 7*10^40 Carsonella Bacterium length genome possibilities at a time.  It is believed by evolutionists that about one billion years passed between the birth of the earth and the first life upon it.  The average chemical reaction takes about 200 femtoseconds.  If we count the number of 200 femtosecond reaction intervals in the one billion years that allegedly passed between the birth of the earth and the first life upon it, and multiply that 7*10^40 as the top end maximum number of 160,000 base-pair genomes could be brought into existence at one time, that billion years allows for, at most, about 5*10^74 Carsonella Bacterium sized genome combinations attempts, which means that in that time period, it is physically impossible for more than one in 2*10^96254 of the possible assemblies for 160,000 base-pairs to have been attempted.  

The question then arises, what fraction of the possible 10^96329 ways in which 160,000 base-pairs can be assembled would lead to a living thing that could code for the necessary proteins to sustain reproducible life and get the natural selection ball rolling?  Is the 5*10^74 arrangements we allow time for enough to expect a living Carsonella Bacterium sized living thing to emerge?  At this point I am a bit stuck mathematically, because I can not find a spreadsheet program or an online calculator that will calculate a probability using the hypergeometric distribution on numbers this large. I have worked out some of the math as best I could in the picture below.

Where P is the probability of generating a life sustaining combination of 160,000 base-pairs using the time and population parameters above and K is the total number of life sustaining combinations possible.  When K is a small number on the order of one, this probability approaches 1 in about 10^96400.  As K gets larger, the probability will get more manageable, but considering that only one species of a bacteria with this small a number of base pairs has ever been discovered, and that the next simplest known bacteria is twice as complex, there are likely not a very large number of life sustaining possibilities on bacteria that small.  If someone can give us reason to suggest that K might be larger than a few million, and than find a calculating program that can handle numbers this size and plug them in and find a reasonable probability for generating even the smallest life form in the billion years suggested by evolution, please let me know either here or on my Facebook wall.  I will also keep looking for online calculators that can handle this workload.  If/when we can finish this calculation I will update this blog with a part three of this post.  In the meantime, I think this calculation demonstrates the extreme unlikeliness of the evolutionary hypothesis in the light of the amount of genetic information that would have to be generated from complete disorganization.