Because you’re worse at that than you are at maths.
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All math is an estimate of reality as you appear to know. The calculation N^L can represent the total sequence space. The functional sequence space needs to be sufficiently large that a search is possible. The empirical data does not support it being sufficiently large across the domain of protein families to make the current theory viable. The empirical data is as follows:
The current data shows an average of 6 out of 20 amino acids are equally substitutable. This appears to vary and in cases where we see a few to no changes in consensus sequences over 100 million generations it appears to be substantially less. In other cases it appears to be more.
The current data shows many proteins are highly preserved.
Protein families sequences are not often close to each other showing that very different sequences with similar function exist that the theory attributes to a common ancestor. How did a search find these different sequences given the chance of collection of deleterious mutations of which some generate a null mutation is so high?
Proteins in multicellular eukaryotes are often part of complex biological functions that contain many proteins. The proteins often perform multiple functions. Therefor they are not the result of a single search.
Please, somebody, make it stop!
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Does it? How much of sequence space has been used by evolutionary searches and/or the Intelligent Designer, Bill?
Note that no assumptions go into this assessment. However, the ID hypothesis makes a clear prediction from the “I” part.
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It does, you’re just refusing to admit it.
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No, it is not!
That’s not a calculation.
Can it?
Prove it. Prove that the possibility of a search is contingent upon functional sequence space size. While you’re at it, please, specify what “sufficiently large” means, exactly. How large? Let’s see a calculation.
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The old quote about stupidity, by Friedrich Schiller.
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Let’s talk about proof beyond a reasonable doubt.
This is a program that will allow you to test the time it takes to search through a sequence and find an original set of letters you type in. In the top go to simulation then type in 2 letters which represents a sequence space of 26^2. The two letters will be found in minutes with the random search program. When you add a letter it with lengthen the average time by 26X.
The mutation rate here is seconds and you will visualize genetic entropy as the rapid changes will turn a coherent sentence into gibberish.
Hopefully this empirical exercise will help you see the N^L is a useful calculation for the sequence space you are trying to measure.
No, thank you. Just respond to the challenge, that’s all I ask.
So, in other words, it’s not a demonstration of your claim.
So, in other words, it’s working backwards, the exact thing you have been told repeatedly is not what happens in nature. Why are you wasting anyone’s time with this garbage?
Oh, so it’s a garbage search program to boot, then? Finding a sequence of two letters should take nanoseconds, not minutes.
Will it? Proof, please. Mathematical proof. The sort you are oh-so-qualified to present. Come on, pretend like us lowly plebeians could comprehend it, and just write it up.
An “empirical exercise” toying around with an inaccurate simulation is not a mathematical proof. Please, present one.
That’s not a calculation.
Until you can consistently articulate what on earth you are even trying to measure without stumbling over such basics as confusing 50% with 2, I don’t think I’ll take your advice on what is an appropriate measure for what ever it is you are talking about. You were talking about how on average every other item in a sequence is being randomly substituted, and set N=2 as the ratio of total sequence items to the average number of substituted ones. The space of all sequences after half are substituted (counted such that the elements are distinguished only by whether or not they have been substituted) can for large values of sequence length L be approximated by 2^L. I granted that. This does not hold if N\neq2. At all. On the other hand, N^L is the number of sequences of length L with elements each freely chosen out of a set of size N. What on earth this has to do with the substitution choice problem we were discussing just a message ago is beyond me, but I’m not asking for an explanation. All I’m asking you quoted. Still, somehow, you need a reminder of that very passage, so here it is again:
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Yes. Of course, someone with your vast mathematical expertise easily understands that, when the numerator of a fraction is kept at 1, the value of the fraction decreases as the denominator increases.
What that has to do with @Gisteron’s question shall forever remain a mystery, I suspect.
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So a blind random guess for a single target sequence. But evolution isn’t random guessing. And you yourself have agreed evolution doesn’t have targets.
So a completely irrelevant and incredibly stupid response.
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Also a description of Bill trying to answer a question.
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An empirical exercise shows you the math is reliable in the real world. How did you determine the simulation is inaccurate?
A simple proof for us plebeians 
is not going to be rigorous.
If you assume the number of combinations of N elements to the L length is NxNxN… counting the number of Ns where N =L then it is easy to show if N=10 and L =10 that 10x10x10x10x10x10x10x10x10x10=10^10= 10 billion
All this being said you will get a much better feel for this problem playing with the simulator then trying to generate a rigorous mathematical proof.
Wow Bill we’re so glad you’re here to tell us what an exponent is.
I must, however, repeat myself:
Telling us that “it’s a ginormous space” is neither here nor there. It’s the distance between useful sequence, and the fraction of the space that is useful, that is important.
That the space is big doesn’t matter if a sufficiently large percentage of the space is occupied by useful sequence (which it is), or if most useful sequences are near each other (as they are), or if the search strategy is intrinsically biased towards the parts of the space that has useful sequences (which it is).
When will you understand this? You’ve had the data spoon-fed to you, together with intense elaborations of these explanations now a hundred times at least. By this stage I think you still couldn’t see it if it was surgically installed in your visual cortex. You don’t want to see it.
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No, it does not.
Simulations are not experiments. They can reveal whether your calculations are internally consistent, or even help render quantitative predictions from a given model. But no amount of playing with simulations can show you the applicability of the simulated model to nature. Only experimental data can show that, and, needless to say, you have none. And that’s ignoring how what you so cutely call “an empirical exercise” is simulating a clearly inaccurate model of something unrelated to the question at hand.
I asked you to present a proof of your claim. You’re not going to have me forget all about it like a six-year-old by giving me some irrelevant toy to distract myself with.
By the way you described it as neither simulating anything we were talking about, nor anything that happens in nature.
I did not ask for “a simple proof for us plebeians”. I asked for a proof. Make it a rigorous one. Anything more than the mere hot gas you’ve been expelling so far would be a blessing.
Sorry, you must have overlooked the question. Here, let me present it to you again:
I’m not trying to generate a rigorous mathematical proof. I’m challenging you to present one. And you keep not doing it, and responding with irrelevancies instead. By rights I should take offense to the condescension implicit when ever you try to explain what potentiation is like the rest of us have not graduated from elementary school, but getting emotional over such insults will do nothing to advance the discussion, so instead I just keep asking you get back on topic and busy with the proof. Please, go on.
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If we’ve learned nothing else, it should be that asking Bill to do math is like asking a cat to not knock something off the counter.
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What insight do think this will bring us?
Only one way to find out, I say. Go on.
And remember, it’s not about what exponentiation means, nor that exponentiation is a thing, nor about the size of the space of L digit long sequences in a system of N digits. The challenge was:
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From basic statistics assume that the probability of “a” occurring and “b” occurring is p of a x p of b?
If each position in a sequence has 10 equally probable numbers in each position then the total equally probable positions of both a and b is a x b.
From this core you can build your proof.
Mentioned above is that if all letters contain the same elements as a sequence then the total number of equally probable positions in abcd is a x b x c x d =a^4 since a=b=c=d.
From the simulation however you can visualize how fast a sequence breaks down when randomly changed. You cannot visualize this from generating a proof.
Swing and a miss
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