So all the rest I wrote in my post.
remember that we only need few of the rare examples to challenge unguided process
You can challenge things all you like, what matters here is whether those challenges make sense. In your case, they don’t.
. and there are probably much more than just few rare examples in nature.
Is that so? How do you know? You don’t know it for cytochrome C. Even if you could show cytochrome c as we know it is relatively rare in sequence space, that wouldn’t tell you that it couldn’t evolve from some other more abundant function.
The problem is when you are claiming that X could not have evolved, you are taking on an enormous burden of proof. You now have the burden of demonstrating that no conceivable scenario for X’s evolution could work.
I know, I explained why. But that reason also undermines your meaningless calculation, since you don’t actually know the relationship between protein length and frequency of function in sequences space.
It could be that most of those 10^93 functions cluster densely in the L=80 range, just to pick an example, and then they grown increasingly rare as you go shorter or longer. But that could also imply, in turn, that there are selectable paths to shorter or longer sequences from sequences of L=80.
We simply don’t know. But for your claim that X could not evolve to work, you would need to actually show what this relationship is like. To make matters even worse for your claim, you would also need to show that there are no other functions nearby that overlap anywhere in sequence space from which cytochrome c could have evolved.
I’m sorry for you that you have taken on this massive burden, but that is really what you have done.
remember that about third of the cytochrome c protein is crucial for its function. so only about 30 aa are needed theoretically. thus the chance is 20^30
A chance can’t be 20^30. It can be between 0 and 1. You must mean 1 in 20^30, but that would imply only one sequence in L=30 space is a functional cytochrome c.
very close to 10^37
No that doesn’t make sense you are getting your numbers mixed up. 10^37 isn’t a size of the space, it’s a probability, or a frequency. The frequency is actually ~10^-38. Notice the minus.
That is:
\frac{\displaystyle10^{93}}{\displaystyle20^{100}} \simeq7.9\times10^{-38}.
You are saying that, if hypothetically there was a 30 amino acid long but functional cytochrome c, then the total sequence space for 30 amino acid proteins is approximately 10^39. So far so good.
But then you say that is “very close to 10^37”. But that number isn’t the size of sequence space.
That number is supposed to be ~10^-38, which is the the ratio of functional cytochromes c to all possible sequences 100 amino acids in length, if all 10^93 cytochromes c are 100 amino acids long. But they aren’t. There are many shorter, and many longer. And we don’t know how the lenght correlates to frequency functional ones in that space.
If that was the same density of function in L=30 sequence space in absolute terms, that would basically mean that out of all sequences in that space of proteins 30 amino acids in length, only one of them would be a functional cytochrome c. We just have no reason to believe any such thing.