I recently read "Darwin's Doubt" by Dr. Stephen Meyer. In his book he has a calculation about the probability of building a single protein necessary for life. I'd like to thank Dr. Meyer for the calculation and his wonderful book.
I have audaciously changed some of his assumptions and expanded the calculation to a simplified global calculation of the probability for all proteins in life to have arrived by chance. The basis of my calculation is that some undirected process of protein assembly has been active on earth and all biomass on earth is taking part in the process. This is a gracious assumption. There is currently around 560 billion tons of biomass on earth (both living and dead biomass, this number excludes the weight of water in the biomass). A protein is made up of 350 amino acid base pairs on average. A protein that size weighs 40,000 atomic units x 1.66x10^-27 kg per atomic unit = 66.4x10^-24 kg/protein. Therefore there are around (5.6x10^14 tons x 907 kg/ton) / 66.4x10^-24 kg/protein = 7.64x10^36 proteins on earth and 7.64x10^36 proteins x 350 amino acids/protein = 2.68x10^39 amino acid molecules on earth. Quite an impressive number.
Suppose each amino acid was involved in a process that made proteins at a rate of 1000 amino acids per second. Currently, the fastest known protein assembly operates at 1000 amino acids per second and is directed by cellular processes for creating proteins from existing DNA. This would be a random process, but I've assumed the same rate. Therefore there are 365 x 24 x 60 x 60 x 1000 = 31.5 billion amino acid assemblies per year per molecule. This would total 2.68x10^39 x 3.15x10^10 = 8.44x10^49 amino acid assemblies on earth per year if all biomass was participating in the process.
There are 4 possible pairs in DNA, with an 350 base pair protein, the possibilities number 4^350 which is much too big for a calculator. I'll rewrite as (4^50)^7. That's (1.27x10^30)^7 = 5.33x10^210. Let's further say the protein accuracy necessary is only 80% (i.e. say only 275 of the pairs out of 350 have to be exact to form a functional protein). That reduces the search space to 4^275 = (4^25)^11 = (1.23x10^15)^11 = 9.75x10^165. There are 10 million estimated proteins involved in biology. I'm going to assume that number is low by a factor of 10. Therefore, I'll assume there are 100 million proteins that are useful out of the 9.75x10^165 possible.
So, assuming an aggressive process of protein formation, the amount of time to arrive at the proteins we know exist would be 9.75x10^165 / 10^8 / 8.44x10^49 = 1.16x10^108 years. The universe is thought to be 13 billion years old. If the entire history of the universe was conducive to the assumed process then the number of life sustaining worlds the process would have to be executed on to arrive at life on one planet would need to be 1.16x10^108 / 13x10^9 = 8.9x10^97.
The current estimate of stars in the observable universe is 70 billion trillion or 7x10^22. That means, if there was a life sustaining planet around each star, where this process was occurring with similar biomass amounts as earth, then there would need to be 8.9x10^97 / 7x10^22 = 1.3x10^75 observable universes (each conducive to the process, i.e. livable universes) for one planet to have arrived at life by chance. This number is unfathomably larger than the number of stars in the observable universe.
My friends, something other than chance or a blind process like evolution was involved in life's arrival. And that something is capable of the creative powers and foresight to create all of life as we know it...to tip the scales in favor of life by influencing the material world. I would conclude that the something is necessarily non-material. I would also conclude that it would be dominant over the material world, perhaps even the cause of our universe. In short, I'd conjecture a non-material, creative, intelligent being as the first cause of our universe and of the life we and all creatures on the planet share.