Please forgive me. My brain often operates a 0.5x speed compared to the brains of other people. I can have somebody explain something to me multiple times, and still not understand it. Then, one day, without them adding any more explanation, I'll suddenly understand what they were trying to tell me. It just took me a while to get there.
This morning, I think I finally grasped something Paul Scott Pruett has repeated to me multiple times (see his last comment here for example). Scott has mentioned there and elsewhere that evolution has to target certain specific proteins for things to evolve. When I did my calculations on functional protein probabilities (part 1, part 2, and part 3), I was just trying to figure out what the probability was that the observable universe might, in some way, cough up a protein that could be functional, and I was assuming that whether it could be function was based solely on whether it could fold up into a stable shape.
It seemed to me to be a mistake to run these calculations as if evolution had to target specific proteins since any protein that could fold into a stable shape had the potential of being functional. If you were considering a protein with a length of 150 amino acids, the probability of getting any one specific sequence of amino acids with one random try would be 1 in 20150, which is pretty low. I thought that was cheating since the real question, as far as potentionally functional proteins were concerned, was what fraction of those 20150 possible combinations could fold up into stable shapes. It could have been, for all I knew, that half of all the possible sequences could fold into stable shapes and were therefore potentially functional. It turned out to be far less than half (Douglas Axe estimating 1 in 1077 while others estimated 1 in 1011), but I still ended up calculating that it's not unlikely at all that the universe would cough up at least one functional protein given the vast probabilistic resources in the universe due to its size and age.
Life requires more than one functional protein, though. Life requires many proteins that work together. Let me use an analogy to explain what I mean. Let's say a protein folds up into the shape of a bolt. To get a nut that fits that bolt, the nut would have to be targeted in some way. It would have to have the right size and have its threads match the threads on the bolt. You might be able to imagine a wide variety of different kinds of bolts, all with different sizes and different thread pitches, but for any particular bolt, the nut that goes with it has to be targeted in specific ways.
In the same way, if proteins are to work together in a machine, they have to somehow fit together. While you may be able to get a random protein that folds into a stable shape, you have to get a targeted protein that "fits" the original protein before you can get anything approximating a machine with different parts that work together. You can't get life just by gathering a collection of stable proteins. Some of the proteins have to be targeted in such a way that they are able to work with or fit together with other proteins.
For a nut to fit a bolt, it has to have the right sized hole and the right thread size, shape, and pitch, but there can be variation elsewhere. It can have an exterior with a hexagon shape or a square shape. It can have a different wall thickness, and it can fit bolts of different lengths. In the same way, it may be that for a given protein to function in a cell, there can be some variation in its companion proteins and still be able to work together. But there are far fewer proteins a given protein can work with than the range of all stable proteins within any given length. That means if we want to grant the existence of some random functional protein, and we want to calculate the probability of getting a simple machine that contains that given functional protein, we are going to have to calculate the probability of some targeted proteins--proteins that "fit" the original given protein.
Since the range of targeted proteins is smaller than the range of stable proteins, it's going to end up being far less probable that life could evolve significantly than it is that the universe could just cough up a stable protein. I think that's what Scott has been trying to tell me.
I don't know how I would even begin to try to run a calculation on this, though. There are too many variables and too many unknowns.
I want to say one more thing Scott said that I think I did kind of understand. The fact that evolution targets certain genes and proteins is evident in the fact that there is convergent evolution, not just on the macro scale (e.g. eyes, sonar, etc.), but also on the micro scale (genes and proteins). I'm not sure whether we should consider this sort of targeting to be unlikely, though. On the one hand, a naturalist could say that since evolution seems to favour certain outcomes, they're not that unlikely after all. We may just lack an explanation of why evolution tends toward certain outcomes. On the other hand, a supernaturalist could say that since convergent evolution is statistically improbable, the fact that it happens over and over favoures an intelligent cause. I don't know who wins that argument. Maybe my brain will eventually catch up on that in the future.
There is always the possibility that I am still misunderstanding Scott about targeted proteins.
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