Contradictory Points in ID and Information Theory Arguments?

On exactly this issue, I have a question about Eric’s use of Levin’s results on Kolgomorov mutual information. I believe he continues to see this result as a key part of his arguments.

Early in the discussion. Eric said that the two things of interest were the DNA code and the environment. It seems to me that these are indeed the two entities of interest if we want to talk about evolution and not just mutation of genomes.

I recognize that mutual information with the environment is difficult to define. That diffculty can lead to introducing proxies like functional information in the genome and then arguing that this is still mutual information where Levin’s result applies. But that approach has been hashed out from many viewpoints in the discussions. It is not what I want to ask about.

Instead, my question is this. As I understand it, Levin’s result says that if I(X, Y) is the Kolmogorov mutual information between X and Y and E(X) is some function of X comprising only “algorithmic processing and randomness” transformations, then I(E(X), Y)<=I(X, Y).

Now Eric has said that X is the genetic code and Y is the environment. Then E(X) is taking to refer to the process of evolution.

My question is why E(X) is limited to be a function of only X. It seems that any evolutionary process must involve the environment Y as well. So we should be considering functions E(X, Y). Does Levin’s result still apply if we do so?

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This quote is one of the earliest one’s I could find where Eric introduces oracles:

I believe Eric admits mutual information can be created during the process we call evolution. But he also believes that his theoretical math arguments must apply to any natural biological process. He claims these arguments show mutual information cannot be generated by any process which is Turing computable (ie any algorithmic or stochastic process). Hence some super-Turing machine processes must be involved. These are called ‘oracles’.

Turing himself invented the term ‘oracle’ to help him “explore the mathematics of the uncomputable”. See this article in SEP for details of why he did so.

I have seen posts in the forum claiming that oracles are logically impossible. But this is not true. Oracles are logically possible. They can be implemented by supertasks or by encoding information in real numbers, for example.

However, logical possibility does not imply that oracles are physically possible, if physically possible refers to something implementable under the physics of our universe. Whether oracles are physically possible remains an open possibility. One approach would involve “Malament-Hogarth spacetime, which is physically possible in the sense of constituting a solution to Einstein’s field equations for General Relativity.” But whether our spacetime has even local regions of Malament-Hogarth spacetime is unknown.

See this link plato.stanford.edu/entries/computation-physicalsystems/#Hyp for more details on physical computation, supertasks, and Malament-Hogarth spacetime.

Sorry for the incomplete link, but as a new user I can only have two links per message. So you have to add https:// to front of above to get link. Or go to Stanford Encyclopedia of Philosophy and search for Physical Computation. The subtopic is Hypercomputation.

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I have not had time to follow the details of the exchange between @colewd and the others, but it seems that we have drifted from the OP, which is really about how LoING interacts with ID arguments. I was hoping that someone could straighten me out on any of my misunderstandings of what ID people were trying to argue, but I guess everyone is equally confused, sometimes in different ways.

My meta-conclusion from this right now is that even if there is a way to interpret ID statements in the OP charitably enough such that they do not blatantly contradict each other, the ID argumentative framework has a clear lack of rigor and clarity. It does not help when its leading proponents are making basic mathematical mistakes that confuse the main argument (even if they insist that it doesn’t undermine it.) I have often talked with people working in sub-fields of physics or science outside of mine, and while I have not always understood everything they said, usually I would ask a few basic probing questions and things would never blatantly contradict each other like the above.

A great example even in this forum is Halting Oracles And Law of information Non Growth - #22 by swamidass, where I tried to poke holes in your argument for halting oracles but you were able to immediately give very clear answers to all of my concerns. There was no fudging or evasiveness. To me it’s a great example of what distinguishes theories with strong foundations and those which seem to be built on a mound of sand.

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Great final post @dga471 . I’ll move some of the off topic dialogue to a separate thread.

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I had a message from @EricMH that I am basically correct in my understanding of his arguments/objections. If anything new comes of that I will start a new thread.

Otherwise, I still have two promised responses, them I’m done here too.

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