To help confirm a major step in the LUCA hypothesis. I have looked at this problem and do not see any promising steps toward a model.
This is about the number of ALLELES that signal evolvability for this gene. A group of ALLELES all with less than several mutations each show less variation than required to evolve a new (non myosin) gene.
You didnāt show any maths.
No, not necessary. Obviously and straightforwardly false.
Iāll never understand how you are able to say things this wrong this confidently. Itās shocking.
I showed the numbers. You can simply divide to understand the amount of exploration to find a solution. To divide exponents subtract the exponents. In this case 30000-28850=250 or 10^250.
Bill, you are getting some fair criticism, and throwing out a few numbers is not adequate. You need to show your method, your assumptions, and maybe your calculations too. We canāt read your mind to know what you are thinking, so you need to explain what you mean with mathematical precision. Take it back a few steps and explain your reasoning, work back until you find a point of understanding, then build forward. 
Demonstrate that any of those numbers are relevant to anything.
You showed some numbers that you clearly have not thought about in any depth. Why did you falsely claim to have shown the math?
Do your numbers have any basis in reality?
So how many alleles are there?
Once you figure that out, we can address that word salad.
Here is a very simple toy model using people with cell phones with functions and the number of digits in a phone as the total search space.
If I have 100 million or people in the US with cell phones and 10 digit numbers on each phone my chances of dialing a working number is one over 10^10 (number of possible phone numbers) minus 10^8 total people with phones.
My chance of reaching someone on the first dial is 1/100.
if I have a 13 digit number the odds decrease to 1/100000. As I now have 10^13 possible phone numbers. Exponent 13-8=5 or 10^5 or 100000
The math formula with exponents in the first case is 10^10 over exponent 10-8 or 10^2.
I hope this helps.
Not really. You havenāt made a connection between your toy model and the situation at hand, and with out no amount of arithmetic will help.
Start with your assumptions.
The assumption is the N^P is the equation for total search space. The functional space is to be estimated based on empirical evidence.
Why?
How?
Why canāt you actually answer questions?
Basic statistics. The total search space is equal to the number of possible position in the sequence to the power of the length of the sequence.
By doing research on the subject like the Szostak experiment and the Hayashi experiment, estimating and figuring out the range of measured function in sequence space and adjusting those numbers to account up or down based on the length of the sequence.
Also estimating on preservation of sequences in the data base that indicates the substitutability of amino acids.
This is the reason there is no detailed model for the arrival of new unique protein sequences.
Not an answer to the question, as it says absolutely nothing about your assumptions. Why do you think that equation is applicable to the question at hand?
Again, you havenāt explained the assumptions you would be using, so this isnāt even in the same direction as an answer to the question.
Word salad.
This isnāt even wrong.
But if functional phone numbers are connected to each other and clustered together, and if the sampling process is intrinsically biased towards similar phone numbers, it doesnāt really matter whether there are only very few functional 15-digit phone numbers, as you could have 123 connected to 1234 to 12345 to 123456 etc.
You donāt need to test all possible 15 digit phone numbers, you just need to sample into the vicinity of already functional phone numbers. 4 digit numbers have very similar functional 5 digit numbers, which have very similar 6 digit numbers nearby, and so on. Thus you can randomly walk around in the space of phone numbers from high probability to low probability phone numbers, guided only by purifying selection. Even if the frequency of functional phone numbers drops off with length(which is physically an unrealistic assumption, since the longer the sequence is the more potential binding spots it has), there being traversable pathways connecting them means selection can keep you on a path of functional phone numbers and you can blindly wander to increased complexity. Of course, if longer phone numbers are also situationally beneficial compared to shorter phone numbers, you might even some times get selection towards more unlikely phone numbers.
And then thereās the fact that mutations like duplication, large-scale insertions and deletions, rearrangement, fusion, and recombination of phone numbers are possible so you donāt have to navigate around exclusively by point substitutions or single digit insertions/deletions.
So even with your physically unrealistic assumption that longer sequences have fewer functions the mere size of the sequence space does nothing to show that longer sequences canāt be reached by a process of blind sampling combined with selection.
All your analogies and arguments about sequence space are bad and have been debunked innumerable times. You always end up having assumed what you are trying to prove. You have it as an unsupported axiom that functional sequences are both rare and isolated in sequence space, and that there are no pathways connecting them, and you always fail to include the effect of selection and the effect of sampling being biased to the vicinity of already functional things, in wandering around in sequence space.
I have explained all this to you something like twenty times over the last three years in excruciating detail, with references, pictures, figures, and analogies.
What is wrong with you?
Numbers are not maths.
Congratulations, Bill. You are now in the set of creationism advocates who claim superior mathematical ability but are unable to cope with junior school arithmetic.
30000 - 28850 = 1150.
You can check this on a calculator if you wish. (You should probably have done that before posting).
I already donāt take any notice of what you say, but perhaps thisāll show a fence-sitter or two why you are only suitable for entertainment.
It shows you how much function you must demonstrate exists in order to make the LUCA hypothesis viable given current proposed mechanisms of variation.
Define ānewā and āuniqueā?
There are no toys involved.
The point I keep making (and you keep running away from) is that human MYH7 gives you some idea of the numbers of different sequences that work.
The numerator of your ratio is many orders of magnitude more than 1. This is what I mean about deliberate misrepresentation of the actual, objective data.
No, it only shows what you assume the search space to be, which we already knew. The question is WHY? Do try to actually answer the question.
Look, Iāll help you out: When is the equation you gave earlier appropriate to use, and are those conditions met for the systems in question?