I recently posted on Irreducible Complexity in Mathematics, Physics and Biology. That thread generated interest in a well-written article by ID proponents in Italy. The article touches on the work of Turing, Chaitin, von Neumann and relates it to ID-sympathetic literature by Dembski, Behe, Voie, Trevors and Abel. The article was so well written and informative, that I felt it deserved its own thread. Our readers can learn much about ID through this article!
Mathematics and the origin-of-life problem
Here are some excerpts:
The works of Gödel, Turing, Chaitin and Von Neumann even from different points of view, show basic limits of the reasoning power. Someone said that these results got the fall of the platonistic conceptions about mathematics. This conclusion is fully wrong. The truth is exactly the inverse of that. Plato never said the total truth could be derived from few axioms. Instead what was fallen on 1931 is the positivistic utopia that reason may get more from less! In nuce reason cannot get Infinity from finite. In short that is the moral we can learn from the theorems about information irreducibility. These are particular cases only of a more general ascertainment: total truth cannot be axiomatizable. We cannot close the Unlimited into a limited system. The Total Possibility, i.e. the Infinite, is not reducible to a system. In all fields one can find the effects of this universal truth. Gödel found them in metamathematics, Turing found them in informatics, Chaitin found them in AIT. In the following we will show as also the fundamental problem of biology – the origin of life – is unsolvable without an intelligent source indeed due to the same reasons.
To say it in few words, Gödel’s works in metamathematics, Turing’s ideas in computability theory, Chaintin’s results in algorithmic information theory (AIT) and Von Neumann’s researches in informatics are friend to ID because all are different expressions of a unique universal truth: “more” doesn’t come from “less”; a lower thing cannot cause a higher thing; causes are more than effects; intelligence stays above and its results below.
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Chaitin saw relations between the Gödel’s results and Turing’s ones. Gödel’s incompleteness and Turing’s incomputability are two aspects of the same problem.Moreover the information incompressibility of [Chatin’s Algorithmic Information Theory] AIT is related to the “irreducible complexity” concept (IC).
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Those are just some excerpts. The readers are encouraged to read the whole article as it is so well written. It is inspiring to see there are ID proponents doing good work in other countries!
Let me add this quote by Godel himself (from End of Materialist Science):
“The formation within geological time of a human body,” Kurt Godel remarked to the logician Hao Wang, “by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components.”
(Hat Tip: Dr. Albert Voie and others who alerted me to this article)