The notion that life spontaneously and naturalistically developed from non-living chemicals, also known as abiogenesis, is an absolute necessity of an atheistic worldview. When you see the material in any media by evolutionists on the topic, the impression is given that all you need is the right conditions and proof life is guaranteed to arise. In fact, this is the main idea behind the notion of the existence of alien civilizations in space. The notion is that with all the trillions of stars and planets that exist in the universe, life must have developed on another planet someplace.
Whenever efforts are made to calculate these odds, the main objection raised by evolutionists is the notion that life was simpler in the past. This is primarily a way of shutting down any calculations based on life that actually exists on Earth. Furthermore, as generally made, this claim is vague enough that can be used to attack any calculations that may be offered.
Fortunately, however, in an effort to discover what the minimum necessity for a living cell is, biologists stripped down a cell and its genome to the absolute minimum they could without killing the cell. Because of this, we have real evidence as to what the simplest possible cell, that is not a parasite, can actually be like. This effectively silences the claim that cells were simpler in the past because here we have evidence this is as simple as a cell can be without being parasitic. Jumping to the parasitic bacteria wouldn't help because they would need a host cell that is at least as complex as this minimum.
Having the glorious and highly imaginative name of JCVI-Syn3.0, this artificial species has a genome that has been reduced to the bare minimum necessary to survive. Its genome consists of just 531,490 base pairs with just 438 protein-coding genes. Now this is a sufficiently large genome for an average protein length of more than 500 amino acids, however, to give abiogenesis as good of a chance as possible we will assume that the average protein length is just 50 amino acids. Furthermore, we are going to assume a billion potentially functional proteins which are actually two orders of magnitude above the 10 million or so that are thought to be all that is used by life on Earth. This artificially raises the number of viable proteins to select from, once again to give abiogenesis the best possible chance to be shown workable.
Starting with proteins consisting of just 50 amino acids, of which there is a possibility of 20 amino acids that can be used, there are 2050 or1.259X1065 possible combinations. Given our highly exaggerated assumption of a billion functional proteins, the odds of getting a functional protein of 1 in 1.259X1056. Now by themselves these are not encouraging odds but at least theoretically within the range of being possible. However, it ignores the fact that you need to do this 438 times. This means that the odds of getting 438 functional proteins are 1 in (1.259X1056)438 or 1 in 3.6X1024550. This is where we start really start running into a problem because even if you assume the Big Bang with a 13.5-billion-year timeline there can only be 7.9X10150 possible events in the entire history of the universe which is still tens of thousands of orders of magnitude smaller than these odds. This makes the odds of getting 438 functional proteins statistically impossible. However, when you include DNA, the problem gets even worse.
Given the fact that each amino acid is encoded for by three base pairs, a 50 amino acid protein would require 150 base pairs consisting of 4 possible nucleotides resulting in 4150 or 2X1090 possible combinations, this means that the odds again getting any particular protein encoded by the DNA are 1 in 2X1090 (150/531,490) or 1 in 5.75X1086. However, you have to do this 438 times resulting in the odds of encoding all of the amino acids being 1 in 5X1038000. When this is combined with the odds of getting all functional proteins to begin with, we get odds of 1 in 5X1038000 X 3.6X1024550 or 1 in 1.8X1062551. This shows that the odds of getting just this much are statistically impossible, and it doesn't include further assembly of the various proteins into a functioning system.
Now evolutionists can always claim, without evidence, that the original life was even simpler So what would it take to actually get within it range that is theoretically possible of the 7.9X10150 possible events in the entire Big Bang history of the universe. The problem is that it would take only two proteins of a length of 50 amino acids to have more possible combinations than the total number of possible events in the universe. That is way too small to be plausible. You can extend the total number of proteins by reducing their length but the best you can do would be 14 proteins with a length of 15 amino acids, resulting in odds of 1 in 1.6455X10147, but this is still a really pushing it along with the fact that there is no evidence that such a simple cell could actually survive, and most likely would not.
Now the estimated number of planets, and the universe is 7X1020, so to make abiogenesis probable enough to occur on at least one planet would require simplifying a cell to 14 proteins with the length of just 8 amino acids, resulting in odds of 1 in 5.2X1019 of life occurring. Making it statistically possible for there to be one planet in the entire universe with life on it. There is absolutely no evidence whatsoever that this could produce a viable cell, and in fact, the evidence goes against it.
As a result, the conclusion can only be that abiogenesis is statistically impossible because bringing the odds of producing a living cell to even remotely reasonable levels of probability require reducing the cell beyond any known point possibly of actually being living. Now it is hypothetically possible that there could be some yet unknown factor out there, but that can always be claimed regardless of the facts.
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References
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5710109/
https://www.biorxiv.org/content/10.1101/2020.08.20.260398v2.full