Oh good grief. Did I really have to specify the smallest gene to achieve replication? Well you certainly need to learn to say what you mean.
You asked:
How many DNA codons would we expect to see in the simplist known gene? Since we know that there are only four DNA codons (also called "letters" on this thread), we can calculate the precise probability / improbability of the natural, unaided self-formation of the data for a single gene once we agree upon how many codons are in a gene
You asked a reasonably clear question, I gave you the answer. If you wanted something else, you should have asked something else.
We were discussing abiogenesis and evolution weren't we?
Yes we were, but you did not clarify *which* of the two you were focusing on with that question. Furthermore, you muddled the issue by asking about *genes*. Genes, as such, most likely developed long after the first replicator -- they're a more advanced mechanism than was likely present at first.
Your question was like asking about jet engines while attempting to pose a question about the very first airplane.
No matter, consider myself to be corrected. What is the smallest possible gene size to achieve replication (i.e., to actually be germaine to this debate)?
No one knows for certain, of course, but one good candidate is a self-replicating peptide from the Ghadiri group, which is 32 amino acids long (sequence RMKQLEEKVYELLSKVACLEYEVARLKKVGE) and is an enzyme, a peptide ligase that makes a copy of itself from two 16 amino acid long subunits. It is also of a size and composition that is ideally suited to be formed by abiotic peptide synthesis. The fact that it is a self replicator is an added irony.
Oh, and the probability formula that you are going to want from me will probably end up being 1/4096^number that you give to respond to that question (4 possible valid bases ^ 2 = potential # of base pairs combinations ^ 3 base pairs per codon),
Well, there are a few problems with that..
1. It only applies to DNA sequences, and not to any of the many, many, many other possible forms of a "first replicator. I repeat, creationists like to reduce things to grade school level -- the chemistry is much more complex than that.
2. Even when applied to DNA sequences, your calculation presumes that any of the four possible bases can link up with any of the other four when making a base pair (this is obvious in your "4^2" term). However, even schoolchildren who have taken a basic Biology course know that the whole reason that the double-stranded DNA is a workable replicator is the fact that the bases *CAN'T* link up any damn way they please -- each possible base can *only* be linked to its complementary base. Nice try.
3. I *told* you that (1/4)^N wasn't going to cut it. Your equation is just a thinly disguised form of it. After correcting your erroneous "^2" term, your equation can be written as: (1/4)^(3*C), where 3*C (three times the codon count) is just another way of expressing N (the base pair count).
The reason that this is a bogus calculation is that the first replicator almost certainly wasn't DNA-based. DNA-based biology evolved from humbler beginnings, and your calculation doesn't do jack to model those other scenarios.
a probability that will decrease subtantially faster than that of the math for the monkeys typing the same length of Hamlet characters.
You have a monkey fixation, don't you? Ok, I'm going to dispose of it once and for all.
Several people, including myself, have pointed out the many things wrong with trying to use the silly "monkey typists" analogy to make any sort of conclusion about evolution (or even abiogenesis).
But hey, I'll *give* you the Shakespeare problem. Let's say that the formation of the first replicator was as hard as monkeys kicking out Shakespeare. But let's take out the science fiction aspect of it, we don't need monkeys on Mars, and various other outer space locations, as the silly author put it.
Let's move all the monkeys to just our own planet. And because we're trying to make analogies to molecular processes, let's shrink the monkeys down to molecular size.
Suddenly, you'll find something that chemists and biologists have long known, but creationists have yet to snap to: There's a *LOT* of room down there.
There are 3.3 x 10^25 molecules in a single liter of water. There are about 1 x 10^24 liters of water in the ocean. That's a total of 3.3 x 10^49 monkeys. Excuse me, molecules.
Furthermore, molecular reactions are *fast* -- typically on the order of a million per second.
And to be more realistic, let's not make every molecule be it's own typing monkey, we'll just let its current orientation represent a single "bit" of message, constantly changing as it vibrates around, jostling its neighbors.
So how long would it take a given 41 character * 5 bits/character = 205-bit sentence to be produced, like the Shakespeare example, using the oceans as a computer instead of monkeys on distant galaxies?
5.14x10^61 / (3.3x10^49 / 205) / 1,000,000 = 319303030 seconds / 3600 / 24 / 365 = 10.12 years.
Yeah, that's right, if we used water molecules instead of monkeys, we could produce the preferred Shakespeare line in about ten years, tops (5, on average). Not billions and billions of years using all available stars in the universe...
Furthermore, since 10 years would be enough time to generate a number of random sequences equal to the *total* number of 41-character strings, we would have produced, in the same 10 years, not just "to be or not to be, that is the question", but also *every* other 41-character sequence from *all* of Shakespeare's works.
And not only *that*, we would have produced *ALL* 41-character sequences from *ALL* books, newspapers, or internet postings *ever* published (including this one), or ever *to* be published.
Now that I've shown this using YOUR OWN CHOSEN NUMBERS, when you try to claim that the Earth's oceans couldn't have by chance concocted a single self-replicating molecule in a BILLION or so years, don't you feel a bit like a monkey yourself?
Class dismissed, I'm going to bed.
"So how long would it take a given 41 character * 5 bits/character = 205-bit sentence to be produced, like the Shakespeare example, using the oceans as a computer instead of monkeys on distant galaxies? 5.14x10^61 / (3.3x10^49 / 205) / 1,000,000 = 319303030 seconds / 3600 / 24 / 365 = 10.12 years.
Yeah, that's right, if we used water molecules instead of monkeys, we could produce the preferred Shakespeare line in about ten years, tops (5, on average). Not billions and billions of years using all available stars in the universe..."
You do need to go to bed, and I certainly hope that you aren't teaching poor defenseless children ANYTHING in a classroom, because you've completely botched your own feeble attempt at science.
Your equation, based upon a 5 bits per character "natural" environment, would mean that your random vibrations of molecules could ONLY vibrate in a sum total of two directions (bits being equal to on/off, a binary, two-part world).
The bigger problem, of course, is that your world presumes that every possible "movement" of a water molecule is a VALID part of a potential sequence, as well as that each movement of each water molecule is a new, valid bit of data. Each and every conceivable movement of water is equal to valid data, oh come on!
Moreover, such a world would mean that the vibrations of one molecule would not interrupt of otherwise be destructive to any other part of the system (lest our sequential chain be broken), and then
This new inanimate world of yours would actually have to "know" that it had reached the desired output.
But wait, there's more, even if your bizarre little world managed your incredulous feat, you still haven't explained how it would procede to animate itself.
After all, even when we have a valid DNA sequence from a dead organism, we still don't know how to animate it into a living, replicating, controlling process (at least not yet, and at least not without using other currently living/animated processes to provide such a jump-start or clone).
In short, you've managed to conjure up a world in which the sum total of your inanimate binary MOVEMENT would equal the number of random/natural guesses required to sequence the first sentence of Shakespeare's Hamlet, but that's a far cry from actually being a viable world in which realistic guesses were being made by currently-known natural processes.
Gee, you've shown that the sum total of all Earth's water molecules can vibrate 5.14x10^61 times in a decade, except, that has absolutely no bearing on how DNA self-formed in useful sequences of data, much less how it managed to become self-animated (a REQUIREMENT for any non-intelligent environment).
Nice try, but that sort of psuedo-science will hardly fool very many people (except perhaps those who don't want to believe anything else).