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Recursion for Turing Machines is old concept for them to write own description. Its definitely true the brain is more than genes(experience.) so maybe you could consider experience as input to turing machine, but then the model is not better than just a human. Maybe true that genes=string encoding = TMs but nothing say about complexity since machine change on input advice.
Main idea is genes can be string encoding for TM, which let you believe if brain = singularity, TM + advice can be too.
