Does this help anything?
http://math.ucr.edu/home/baez/bio_info/bio_info_web.pdf
Biodiversity, Entropy and Thermodynamics
John Baez
http://math.ucr.edu/home/baez/bio info/
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In this particular thread I am showing @swamidass conditional MI I(C1:C2|G) increase example does not contradict my argument, since it requires prior absolute MI I(C1:C2) due to the fact I(C1:C2|G) = I(C1:C2) - I(C1:C2:G). My argument is that natural processes cannot create I(C1:C2), so the possibility that natural processes can increase I(C1:C2|G) has no bearing on my argument.
What it shows is that all your theoretical statements can be true and have absolutely zero grounding for ID arguments against evolution. I’ve never disagree with the proofs that MI isn’t supposed to grow in a narrow theoretical construct. I’ve argued instead that it has nothing to do with the real world of evolutionary biology.
Nothing to do with evolutionary biology is a stretch. DNA and proteins are organized in a relevant sequence as is mutual information as Eric has been arguing.
Your statement here seems to be in agreement with the one you just responded to. The prior MI I(C1:C2) is produced by common ancestry of C1 and C2 from G. Are you really arguing that replication of DNA requires intelligence?
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My point is that since I(C1:C2|G) is upper limited by I(C1:C2) then when evolutionary biologists measure I(C1:C2|G) as you seem to say they are, they are also measuring a lower bound on I(C1:C2). And if I(C1:C2) cannot come about through naturalistic processes, so any I(C1:C2) > 0 is an indication of intelligent design, then likewise any measurement of I(C1:C2|G) > 0 is an indication of intelligent design. So, I do not understand why your claim that I(C1:C2|G) > 0 can be produced by natural causes undermines ID, if you at the same time agree I(C1:C2) cannot be produced by natural causes. I am very confused.
This is what the argument boils down to.
Since in other threads, Eric has adamantly held that any sort of consistency or order in nature is against methodological naturalism and thus an argument for ID, I wonder if all that he is arguing is that the existence of any regular biological phenomena (such as DNA replication) points to a a Designer.
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Exactly. Replication of DNA produces MI, lots of it, by an apparently natural process. The objection to this is that it is not new FI, in that there is no new commonalities produced by replication. That is where the cancer example is great. It shows that there are new FI produced independent of common descent too.
So common descent produces MI, and common selective pressures can produce MI too. The argument is, by demonstration, false. Yes, @EricMH, I’m giving necessary caveats. The theoretical and uncomputable MI of your proofs never increases, but that has nothing to do with this.
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@colewd maybe God did need to intervene in evolution. Fine. That might be possible.
However, we can be certain that the ID information arguments do not demonstrate this to be the case. That is what is established here.
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This claim is not established in my opinion unless you define function in very loose terms.
How do you know that the remaining FI after subtracting out common ancestry (i.e. (C1 \cap C2) \setminus G) is the result of common selection as opposed to say, neutral evolution? What experiments or reasoning is done to establish that?
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As I understand it, the main thrust of the mathematical argument you made is that Durston wildly overestimates the amount of MI that needs to be explained. If he properly subtracts out the common ancestry, then natural causes are sufficient to explain the small amount of MI remaining. So, they can no longer complain that evolution fails to explain function.
Why can’t I(C1:C2) came through naturalistic processes? Isn’t DNA replication a naturalistic process?
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Very good point!
If the sequences are short enough and the mutation rate high enough then some of the similarity can be due to neutral evolution. This arises because mutations are not uniformly distributed. Great point.
We can actually compute how much of this we expect based on known distributions. In cancer, it is not normally very much. Let us imagine we are looking for point mutations that are in common between two cancers, and assume they are uniformly randomly distributed across one haplotype, somewhere in 3 billion bases, and will need to be changed into one of three alternate bases. If each cancer has only one mutations. We can compute the probability of them having the same mutation: 1/ (3 billion) * 1/3, or not very high at all.
What if there are 100 mutations in one cancer line, and 200 in another? The math is a bit more complex. The easiest way to show overlaps are not common is this. Essentially, we know that on average there is a (100 mutations / 3 billion * 1/3) chance of picking the same mutation as is already found in one cancer, or basically (100 mutations / 3 billion * 1/3) * 200 mutations expected in common by chance (zero mutations). So we do not expect there to be any mutations in common in this case by neutral evolution.
As we increase the mutation rate, the number of cell lines and the mutational bias, we do expect to see some overlap by neutral evolution. Usually not much. That, however, is where a lot of research is being done, to make sense of the ambiguous cases.
That is half the argument.
The other half is that the amount of FI demonstrably created is far greater than they think is possible by natural processes.
All the various notations employed in these related fields make my head spin. I’ll try to catch up!
Also, @dga471, we will verify this with experiments too in the case of cancer. That independently confirms it.
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We define function in highly precise terms: the cancer phenotype. There are clear guidelines for determining which cells have attained this function and which ones have not. There may be no phenotypic function more studied than cancer. If this does not qualify as a well defined function, than nothing in biology does.
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I have followed your argument so far, and I think it makes sense.
I have a couple of questions:
In the case of cancer, what is this FI (overlapping MI of two cancers) doing precisely?
Does Behe’s argument about existing functional controls breaking apply here, or is there truly new novel function being gained (something allowed for, but normally only operated under certain regulation)?
Thanks,
Eli
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