I’m not sure where to go with this. The initial problem was the Mount Rushmore-fifth face problem. I sketched out a possible solution to the problem, but there seems to be so much confusion about function, functional information (FI), ID, and whether cancer can produce FI, to name a few, that I don’t think anyone would follow me if I now do a more detailed examination with actual estimated values for the variables of the solution I proposed.
@T_Aquaticus took what I view to be the first correct step toward solving the original problem … proposing that we need some sort of mathematical definition and a way to measure the p-value, etc. I then provided a mathematical definition and sketched out how I would approach the problem. I could do a more detailed pass, defining variables, getting some approximate normalized numbers, the way we normally do things in science problems, but I think some confusion needs to be addressed.
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Some are under the impression that I think that new functions are impossibly improbable for natural processes to produce. That is complete rubbish and I’m mystified as to why people invent beliefs and then assign them to me. The function of an F-22 aircraft might be difficult for natural processes to achieve, but the function of producing ripples on a puddle by a dripping icicle, is easy to achieve. There are countless functions that require little or no new FI.
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Everyone is free to make up whatever mathematical definition for functional information that they like, so long as it gives meaningful results. My own definition for FSC (which in the paper I state is equivalent to FI) is published in my paper I referenced earlier. The FI required for an effect is the difference in Shannon information (∆H) between the ground/initial state of the physical system and the functional state. Simply put, it is FI = ∆H. This method can measure both FI gained (+ve) and FI lost (-ve). It also gives meaningful results when applied to the sub-molecular structure of ubiquitin.
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Since the K-L divergence always gives a +ve answer, it is not a good method to measure FI when we test it with a case where FI is lost and should yield a -ve answer. We need a measure that handles all cases, both gain and loss of FI. My method does that.
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I’m puzzled why some posters describe FI = ∆H as “arbitrary”. We all agree that H = Shannon information, and we all agree that ∆H is the change in information between two states. If the initial state represents the ground state, and the other is the functional state, then we have the amount of information required to achieve that function. This is neither arbitrary, nor rocket science. Furthermore, high FI correlates with highly constrained sub-molecular areas and binding sites, exactly as we would predict, so it is not only non-arbitrary, but it gives useful results.
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Neither Shannon information, nor mutual information, nor K-L divergence will, by itself, give us FI. It must be meaningfully associated with a defined function, or set of functions. One can find a huge value for mutual information and have zero FI. As Szostak pointed out in his nature paper, classical information should not be confused with functional information.
So there are two ways to go from here: 1) do a methodical, more detailed pass on the rock face problem originally proposed to demonstrate that my method gives meaningful results in the field or, 2) pause the problem and read Josh’s cancer paper to see why his approach to FI gives highly questionable results when it comes to cancer. Since Josh is the original poster of the problem, just let me know which option you’d prefer to see me address and I’ll proceed accordingly. I’m leaving in the morning to do some ice fishing on Lake Manitou for the weekend, so I’ll pick this up on Monday.