There are ways to estimate it and the number of possibilities is so large.
What do think the conditions would have to be to make a positive claim that it was the result of RMNS and neutral mutations? 500 Bits is around 4^250.
Heh. Bill sure loves his Sharpshooter fallacious argument, doesn’t he? 
Where are those calculations, and the estimates of what the ancestral genomes looked like?
The problem is that you use equations for measuring mutual information, not functional information.
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This FI nonsense is and remains gibberish for reasons elucidated now fifty times. You don’t know how to determine the FI for any known protein, because you don’t actually know the prevalence of functional sequences in sequence space.
Even if you could sort of ballpark it, you’d still not know whether it simply evolved from a nearby sequence incrementally by natural selection.
Further still, you’re stuck in this meaningless “target” thinking where you do after-the-fact probability calculations as if what evolves is something that had to be found and nothing else could have possibly evolved. So it’s the texas sharpshooter fallacy all over again.
Evolution isn’t searching for specific sequences, rather sequences incrementally change into other sequences under the influence of both positive and negative selection. The cumulative results of this kind of transgenerational, iterative process aren’t targets. Pick any specific genome sequence after multiple generations of random mutation and you can calculate some infinitesimal probability that exact sequence should have evolved. But it did. Obviously, since mutations do in fact happen, and they accumulate over generations, it’s going to look very unlikely what it results in even after a few iterations.
The only thing that matters to evolution is fitness. What results from the cumulative mutational and selectional process evolved because in part because of it’s effect on fitness, not because it was some target protein that had to evolve. Solution space is blindly sampled by huge mutating populations, and some times a useful mutation sticks around. They accumulate, and some times after many thousands of generations they have resulted in a de novo protein, or changed protein substantially into another, or moved some genes around, or duplicated others, or deleted something.
The whole thing with FI is technobabble nonsense of no real-world value or consequence. And the method used to try to estimate it is compeltely fatuous.
Take an example like the BSC4 gene in yeast. It’s a novel protein coding gene that exist in no other species, and it evolved from non-coding DNA. We know of almost no sequence variation in this protein since it is so young. There are a handful of variants of this sequence known. It is about 132 amino acids long, so it has, using the same method as you and Gpuccio suggests(which doens’t work, but lets just go with it), at least 552 bits of FI. There you go, a protein with >500 bits that evolved. And it has your most-favorite function of all: It participates in DNA repair.
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Here’s another cool paper on BSC4 that has consequences for arguments put forward by ID folks:
https://www.cell.com/structure/fulltext/S0969-2126(17)30297-6
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I know this is your claim and I know you believe evolution could take any direction. I disagree with this hypothesis because of the interdependence of proteins. In the case of the flagellum all 30 need to bind together to form a single functional protein complex. The function of the flagellum is very precise.
Your claim about functional information is just an assertion that Gpuccio’s and Kirks estimates are so far off that you can’t make a conclusion. I believe this has to be your position or evolution by natural selection and neutral mutations is false. So, I respect your effort to hold on to this position I just disagree with it and believe functional information is an immature science but one the has tremendous future potential.
I find particularly interesting the points of evolutionary history where functional information contents spike.
There are none. If @gpuccio actually knew what BLAST did, and what the output meant, this error would not be repeated over and over again.
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Gee, Bill’s posting the Sharpshooter fallacy again. The idea that the complex functional sequences we see now are the only possible ones which can exist and that it’s impossible they were co-opted and/or evolved from simpler functional precursors .
What a novel idea Bill. I wonder why no other ID-Creationist ever offered it. 
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I just ran an alignment of 2335 AA prp8 between Rhesus Macaque, mouse and human proteins.
The results were
Identical 2333
similar positions 2
Identity 99.914%
What do you think this data means?
That prp8 is highly conserved in mammalian species.
What does this data mean Bill?
Prp8, the pivotal protein of the spliceosomal catalytic center, evolved from a retroelement-encoded reverse transcriptase
Dlakić, Mushegian
RNA, 2011 May; 17(5): 799–808.Abstract: Prp8 is the largest and most highly conserved protein of the spliceosome, encoded by all sequenced eukaryotic genomes but missing from prokaryotes and viruses. Despite all evidence that Prp8 is an integral part of the spliceosomal catalytic center, much remains to be learned about its molecular functions and evolutionary origin. By analyzing sequence and structure similarities between Prp8 and other protein domains, we show that its N-terminal region contains a putative bromodomain. The central conserved domain of Prp8 is related to the catalytic domain of reverse transcriptases (RTs) and is most similar to homologous enzymes encoded by prokaryotic retroelements. However, putative catalytic residues in this RT domain are only partially conserved and may not be sufficient for the nucleotidyltransferase activity. The RT domain is followed by an uncharacterized sequence region with relatives found in fungal RT-like proteins. This part of Prp8 is predicted to adopt an α-helical structure and may be functionally equivalent to diverse maturase/X domains of retroelements and to the thumb domain of retroviral RTs. Together with a previously identified C-terminal domain that has an RNaseH-like fold, our results suggest evolutionary connections between Prp8 and ancient mobile elements. Prp8 may have evolved by acquiring nucleic acid–binding domains from inactivated retroelements, and their present-day role may be in maintaining proper conformation of the bound RNA cofactors and substrates of the splicing reaction. This is only the second example—the other one being telomerase—of the RT recruitment from a genomic parasite to serve an essential cellular function.
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He’s being polite and not personalizing it. You’re personalizing it in an entirely false way, refusing to acknowledge his politeness.
The whole FI hypothesis has no basis in biology, biochemistry, or reality.
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Again, you are trying to personalize everything instead of analyzing a scientific hypothesis. Such personalization is not a productive thing to do if what you are doing has any relationship to science specifically, or truth-seeking in general.
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I think you’re avoiding most of the evidence and desperately trying to personalize the disagreement.
Which bacterial flagellum?
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What I am not accepting is evolutionary paradigms such as the evolution could take any direction or we can explain biology from the origin of life based on the simple becoming complex.
I am challenging Rum on these concepts that are not necessarily grounded in facts but were made up to support the current paradigm.
That reference corroborates nothing about you or Gpuccio’s argument. It provides a means to calculate the FI for a sequence(it provides the equation), but it does not provide a means of gaining the knowledge required to get the numbers to plug in to the equation.
Having an equation is useless if you have no way of obtaining the numbers required to plug in to it.
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I guess that’s all that’s left for you to do, after that guy who wrote the very article you are citing has said in no uncertain terms that you have no clue what his article actually said.
Well, I suppose there is also the option of being an honest individual and admitting that you were wrong. What about that one?
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This is where the disagreement is. I agree we cannot come up with precise numbers but disagree that we cannot make a tentative conclusion base on the conservation data given the large gap between evolvability and the measurement.
Why are you assuming that I am wrong? If Art convinces my that I am wrong then I will admit it. Asserting is not convincing. At this point my belief is that Art has no choice but to take the position he is taking and I do not have a problem with that. I have tremendous respect for @Art"s willingness to litigate tough issues although I don’t always agree with his conclusions. On this one I would prefer to get @gpuccio involved in the discussion.