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START with a MEANINGFUL ENGLISH WORD

"Start with a meaningful English word and then add to or change that word so that it makes both meaningful and beneficial sense in a given situation/environment. At first such a game is fairly easy to do. But, very quickly you get to a point where any more additions or changes become very difficult without there being significant changes happening that are 'just right'. . . The same thing happens with genes and proteins."

Sean Pitman's "meaningful words".
http://tinyurl.com/ysfka

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SERENDIPITY

We have calculated every single possible mutation in every single generation, but is this really necessary? Perhaps, we could just try half the number, or 1% of the number, or 1% of 1% of the number.

Consider L=1000 such that M=10^9. If the rate of mutation in a population of 10^14 is just one in a million, we will see 10^8 mutations per generation. Assuming we are looking for one very particular and fortuitous mutation, and all others are to be discarded as useless, we can still expect to find that one mutation occurring once every ten generations or so. We are bound to have beneficial mutations after enough generations; indeed, in a population of 10^14 we will see a myriad of interesting mutations in every generation. And perhaps that one singular mutation isn't required. Perhaps, it may never be considered as there are many synonyms and phrases (or genes) which may have the same meaning.

* Consequently, we have overstated the computational difficulty by many, many orders of magnitude.

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ELEMENTARY ARITHMETIC, MY DEAR PITMAN

"It all works much like the English language system or any other language system. . . . In the English language system there are around 23,109 meaningful 7-letter words. This seems like a lot until one realizes that there are 8,031,810,176 potential 7-letter words out there in 7-letter sequence space. This ratio of meaningful vs. potential 7-letter words gives us 1 meaningful 7-letter word for every 347,561 meaningless 7-letter words. What this means is that on average each meaningful 7-letter word is surrounded like an island by well over 300,000 meaningless words."
http://tinyurl.com/2p3hr

The root of our Creationist friend's argument is this:
 

From this he calculates the chance of 'evolving' a word with L letters is N/M (famously known as the Sean Ratio or simply the Pitman Number of L), which for seven-letter words is about 1 in 300,000. Of note, he hasn't included seven-letter phrases, e.g. "the cat", but no matter.

Let's try a slightly different problem. Consider a dictionary of 100,000 words. How many possible thousand-word essays or poems or lists can we form from this dictionary? Well, the answer is 100,000^1000 or 10^5000. This is a number larger than all the particles in the universe.

* This is very excellent news for those in the language-arts, indeed!

But is this how evolution works? Of course not. Evolution works by tinkering with what is already there. We only need to count the number of mutations available at any one time, make a selection or a limited number of selections, then repeat the procedure. This will not result in a complete search of the available options. We may never be able to evolve from one particular seven-letter word to another particular seven-letter word. However, that does not mean that all available pathways are unavailable, as we have shown repeatedly.

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A BIG FISH in a LITTLE POND

The Sea of Beneficence

We have successfully shown that the number of possible mutations is very low compared to the population of our little pond, so much so, that we can expect virtually every single beneficial and non-valid mutation to be tried in each and every generation.

We purposefully chose a very, very small pond, on the order of the number of prokaryotes in the human gut (10^14). We didn't even count the number of base-pairs for those prokaryotes (10^20), or count the base-pairs in the bigger pond of the prokaryote oceans (10^36), or allow our computations to extend over a billion years (10^12 generations), for a total computational capacity on the order of 10^48; and considering all our simplifying assumptions, this is counting way, way above the number of computations actually required.

In any case, we can always have the Grim Reaper drop by with a huge extinction event, a Malthusian Catastrophe, and wipe out huge numbers of unneeded words and phrases. Then we can create a whole new poem or essay—like the extinction of dinosaurs making room for mammals. In fact, we can constantly evolve new ecosystems as long as they fit within our pond. And, of course, there may be more than one pond in the world. Indeed, each self-reproducing species is a genetic world unto itself. (And perhaps our analogy illustrates why speciation, that is, the segregation of gene-pools, is so prevalent in nature.)

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MEANING

We have shown that random mutation with selection allows the 'evolution' of a bit of doggerel -- a verse in iambic pentameter, complete with allusions, imagery and syntax, contributing to a unified whole, communicating a specific message. This contradicts the claim made by Sean Pitman that there exist "walls of non-beneficial function", that is, "significant gaps of neutral or even detrimental meaning/function", and that it would take "zillions of years" to sort through all the non-beneficial possibilities.

Sean Pitman's use of the word "zillions" had immediately indicated to me that he had not bothered to calculate the number of permutations involved, and that he probably had conceptual problems with very large numbers —

— a classic argument from incredulity founded on ignorance.

Now, does any of this really mean anything to the study of biology? Heck no! Are you kidding? Though both genetics and our word-game display features of information networks, we must be careful about extrapolating between the systems. But to those who would assert that complex order can't arise from random mutation (with selection), let this be a warning.

"Beware a war of words, ere you err."

O Sean Pitman
http://tinyurl.com/yqhb3