Mutual Algorithmic Information, Information Non-growth, and Allele Frequency

Due to popular demand I will take a quick stab at explaining the applicability of mutual algorithmic information and the information non-growth law to an allele frequency scenario.

First, I’ll outline the allele frequency scenario.

The alleles are 1s and 0s, and the gene G a bitstring of N bits.  A gene’s fitness is based on how many 1s it has, so fitness(G) = sum(G).  The population consists of a single gene, and evolution proceeds by randomly flipping one bit, and if fitness is improved, it keeps that gene, otherwise it keeps the original.  Once fitness(G) = N, the evolutionary algorithm stops and outputs G, which consists of N 1s.  The bitstring that is N 1s will be denoted Y.  We will denote the evolutionary algorithm E, and it is prefixed on an input bitstring X of length N that will be turned into the bitstring of N 1s, so executing the pair on a universal Turing machine outputs the bitstring of 1s: U(E,X) = Y.

Second, I’ll briefly state the required background knowledge on algorithmic mutual information.

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Breaking the law of information non growth

Part of my broader point that Dembski’s argument is support by standard information theory.

The article is pretty technical, though not as technical as the paper by Leonid Levin I got the ideas from.  If you skim it, you can get the basic idea.

First, I prove that randomness and computation cannot create mutual information with an independent target, essentially a dumbed down version of Levin’s proof.  Dembski’s CSI is a form of mutual information, and this proof is a more limited version of Dembski’s conservation of information.

Next, I prove that a halting oracle (intelligent agent) can violate the conservation of information and create information.

Finally, I show that there is a great deal of mutual information between the universe and mathematics.  Since mathematics is an independent target, then by the conservation of information there should be zero mutual information.  Therefore, the universe must have been created by something like a halting oracle.

I cannot promise a response to everyone’s comments, but the more technical and focussed, the more likely I will respond.