"So, you simple cannot get from "O" to "Beware a war of words, Sean Pitman, ere you err" without crossing significant gaps of neutral or even detrimental meaning/function."

Sean Pitman discusses his "significant gaps".
http://tinyurl.com/2vv73

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A POND of DOGGEREL

Using our original rules of point-mutation and concatenation, we will evolve a simple line of verse. The original rules are a subset of the extended rules.

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The BLIND PIG and the ACORN

In a space of a thousand letters, we have evolved a phrase with significant meaning. In addition, we have evolved a large number of words that can be used to evolve many other phrases with significantly different meanings, e.g "a bee and a bear".

There are two types of selection criteria involved in our discussion; selection for phrases with *specific* meaning, that is, goals analogous to animal husbandry; and undirected evolution for phrases with *any* meaning whatsoever. So, if we want to find a phrase with a specific meaning, we select from our available mutations words that are hopeful. For instance, if we want to create a phrase meaning "contemplating suicide", we might select the word "be", which means to exist. On the other hand, if we don't care about specific meaning, but any meaning will do, then evolution can meander about. We might select "a bee and a bear", rather than "a steer and a lyre", or visa versa; while tossing out other viable candidates. The important point is that selection occurs to narrow our future options.

Sean Pitman claims, "The lower the density, the harder it is to evolve new stuff." This is somewhat misleading. We can assume he means that the connections between valid phrases, instead of being wide avenues, are actually thin tendrils, and that these tendrils become stretched as we increase the number of letters, until they finally snap and there is no way to get from "a blind pig" to "the acorn". However, we have shown that such a path exists all the way from "O" to "O Sean Pitman". So in fact, if a particular path exists, then the fewer the choices, the *easier* it is to find the specific path.

You can find the entire poem "Beware a War of Words", and the story of the "Sea of Beneficence", earlier in this essay, here:

At each generation, selections must be made for evolution to work. The choices must be reduced to a few after each generation. The key is the selection criteria, but as Sean Pitman has repeatedly pointed out, the vast majority of mutations are not even valid words or phrases, claiming a ratio for seven-letter words of 250,000 junk sequences for each meaningful one, and an astronomical ratio for 14-letter words. This reduces the problem by many orders of magnitude. We can select artificially, like the horticulturalist, or we can allow the process to occur based upon some rule of meaningfulness, such as assigning higher meaning-quotients to more complex phrases.

In any case, as long as a path exists, evolution can continue. So if we don't care about finding a phrase with a specific meaning, then evolution can meander about, finding longer and longer phrases, just as meaningful in their own way as "O Sean Pitman". For example, from our existing population of words, we can easily see the evolution of a phrase such as this one,

A bee and a bear kiss by a fire
While Sean Pitman plays the lyre.

or a multitude of others much like it. It is important to note that our evolutionary process won't find every possible combination of words, or even any specific combination of words. But it will find some of them.

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WHAT CAN I SAY

Well, we have not actually shown that we can evolve ANY possible string of text. Some words and phrases may be out-of-reach of our methods, even when using the Patented Pitman Slicer-Dicer. With the original rules, there do appear to be problems finding routes to specific words, but there always seems to be another word or phrase that will do just as well. On the other hand, we do know that the poem "Beware a War of Words" can be evolved, and this clearly indicates the power of mutation and selection in regards to our game.

The biological Theory of Evolution does not claim that every imaginable creature can be evolved, and certainly not that every imaginable creature must evolve and co-exist. Rather, like our game, evolution is opportunistic; and though every conceivable creature may not be evolvable, the diversity of life on Earth clearly indicates that the range of evolvable organic forms is vast.

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ZILLIONS OF SEAN PITMAN'S

Perhaps we can't evolve, for instance, from "painter" to "eternal", but does that necessarily mean that we can't evolve from "Sean Pitman" to "just plain wrong"?

According to Sean Pitman's calculation, we would have to consider each and every possible combination of letters and spaces for the 16 letters that make up "just plain wrong", 26^16 or 10^22, a very large number indeed. But we don't have to look at every single combination, but only at those that are available in each generation. In addition, we can immediately discard invalid words and phrases, and need consider only the ones that appear to get us closer to our goal (which for a breeder might be a slightly stronger horse, or a dog with its nose a bit closer to the ground).

Let L = total length of all extant string species
Let M = total possible mutations
Let G = number of generations

We have shown that the number of possible mutations under the extended rules is M < L^3 per generation. Including spaces and commas, the largest L is 17 in length, so M < 5000 for each generation (most of which are not even valid words or phrases). The selection criterion is obvious in this case; pit, put, jut, just. The total choices we must make are not 5000^G as Sean Pitman would suggest, but on the order of 5000*G. It is the process of selecting that makes it a mathematical product rather than an exponent. (And the choosing is obvious in this case.)

In a Sea swimming with trillions of Sean Pitman's, some just might evolve into new and different forms.