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Kurt Godel sent in a 1972 letter to Hao Wang, here what Godel wrote: here

I believe that mechanism in biology is a prejudice of our time which will be disproved. In this case, one disproof, in my opinion, will consist in a mathematical theorem to the effect that the formation within geological time of a human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of the elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.

I want someone to explain it in modern times. For example, it looks that Godel doesn't believe in evolution, so he states that the reason may come from logical argument and moreover if there exist a counterexample that evolution is wrong, then he states the following which I don't understand: "the effect that the formation within geological time of a human body by the laws of physics is as unlikely as the separation by chance of the atmosphere into its components".

Does "geological time of a human body" mean "average age of human"?

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    Geological time means the period involved with the processes that forms geological features. The maximum geological time is the age of the Earth. Godel is saying that, based on probability, he thinks there were not enough time on Earth for Evolution to have produced the result we see.
    – christo183
    Nov 27, 2019 at 6:53
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    Godel is not 'disbelieving' in evolution but is making a point that evolutionary theory needs to address. I share his view that the current mechanistic model does not seem plausible given the limited time life has been evolving on this planet, but nobody has come up with the sort of neat mathematical theorem Godel mentions as yet.
    – user20253
    Nov 27, 2019 at 13:51
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    – J D
    Nov 27, 2019 at 14:54

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It's a property of English grammar that a phrase like "the baking of a cake within an hour" can be rewritten as "the baking within an hour of a cake" without changing the meaning, although the latter phrasing is apt to sound more old-fashioned to modern ears. Similarly, Godel's phrasing there is equivalent to "the formation of a human body by the laws of physics within geological time", i.e. he doesn't think humans could evolve spontaneously from prebiotic chemicals within geological time. It sounds like he may have been thinking about a calculation similar to Fred Hoyle's argument about a tornado sweeping through a junkyard and creating a 747 jet, though this argument ignores the fact that evolution by random mutation and natural selection is a lawlike process that is not akin to throwing components together at random (even the formation of some simple structure like a spherical star would be tremendously unlikely if you just assigned positions to its component atoms at random).

BTW, on the grammatical point, "within geological time" in Godel's comment (or 'within an hour' in my example) would function as an "adverb prepositional phrase", and as mentioned here, "Adverb prepositional phrases can come anywhere in the sentence and can be moved within the sentence without changing the meaning."

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    What is lawlike about the random mutations required by evolution? There are no underlying biological laws that make certain mutations happen, or if there are we don't yet know them. I'm curious about this point.
    – user4894
    Nov 27, 2019 at 8:28
  • Lawlike could be defended as a description of the regularity of particular kinds of mutations such as errors in replication, damage from radiation, damage from chemical interactions, and interactions with extracellular sources such as viral insertion. The particular occurences of any one mutation are random, but the processes are highly regular and well understood. en.wikipedia.org/wiki/Mutation
    – J D
    Nov 27, 2019 at 14:52
  • @user4894 - Different people may use the word differently, but I would say a theory like quantum mechanics that says probability distributions depend mathematically on laws of physics and past conditions is a "lawlike" one even if non-deterministic. Also note that if you don't count this as lawlike, then my other example of a diffuse nebula contracting to a spherical star under gravity couldn't be lawlike either, since in quantum physics there would be a random element to the motions of the particles.
    – Hypnosifl
    Nov 27, 2019 at 17:02
  • @Hypnosifl You said evolution is lawlike. Your examples don't support your point.
    – user4894
    Nov 27, 2019 at 21:50
  • @user4894 - Why do you think they don't? Can you address the point about whether you consider statistical theories like quantum mechanics to be lawlike? If so I don't see why mutation wouldn't be, since it obeys regular statistics and ultimately is just a consequence of molecules and other basic particles obeying quantum mechanics.
    – Hypnosifl
    Nov 27, 2019 at 23:43

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