O Sean Pitman, Redux

I thought it might be good to review some of Dr. Pitman's original
assertions. He's made the claim of consistency. Let's check the record. This
is one of many such specific Pitmanian claims:

> With one generation per day, this works out to
> be around 273 trillion years for just one member of our population to
> find a new meaningful 56-character sequence on average.

>From the "O Sean Pitman" thread (Spring 2004):
http://tinyurl.com/9bocd

___________


Sean Pitman wrote:
>> "Zachriel" <spam@xxxxxxxxxxxx> wrote in message
>> news:<SeqdndbhaJxEIBDd4p2dnA@xxxxxxxxxxxx>...
>>
>> http://www.zachriel.com/mutagenation/Doggerel.asp
>>
>> Consider the following phrase "evolution" as illustrated on your above
>> listed website:
>>
>> ___________
>>
>> Sean Pitman
>> pitman
>> pit, man
>> put, pan, wit
>> jut, plan, wig
>> just, plain, wing
>> just plain, wring
>> just plain, wrong
>> just plain wrong


Note: Each line in the sequence above represents a generation. The entire
sequence space is only 17 in length.


>>
>> 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.)
>> __________


Please note that it is *selection* that creates the evolutionary potential.


>
> There are just a few obvious problems with this little "evolutionary
> scenario". Certainly you did show that an evolutionary pathway exists
> between many different 3- and 4- and 5-letter words. That is how you
> got from pit to put to jut to just and from man to pan to plan to
> plain etc. But, since it gets much much harder to evolve all that
> much between longer and longer phrases by simply changing one
> character at a time, you think that you can overcome this problem by
> joining smaller sequences together once you evolve all the necessarily
> smaller sequences - right?
>
> What you don't seem to realize, despite my previous discussions of
> concerning this very point, is that in this game words don't just
> float around in neat little packages bumping into each other.
>
> For example, say that we had all of the possible meaningful 3, 4, and
> 5 character sequences already evolved in various places within a
> single genome. Say now that we want to evolve a meaningful
> 16-character sequence made up of joined 3, 4, and 5 character
> sequences. What needs to happen is not as easy as getting two
> particular words like "just" and "plain" to bump together. In fact,
> the problem is rather difficult owing to several factors. First off,
> you have to consider the odds of cutting or copying a meaningful
> sequence, such as "just" fully intact.


In a sequence space of 17, to create a snippet requires two snips, the
initial point and the end point. There are no more than L^2 = 289 possible
snippets in a sequence space of length 17. (It's actually about half that
due to symmetry.)


> For example, the copied
> sequence could have read "justa" or "ust" or "jus" or "fjust" etc.
> But, say you just happen to copy "just" just right. Now, you have to
> consider the odds that "just" will get inserted into just the right
> spot in order for a newly combined "just plain" to make sense.


There are L possible places each snippet can be inserted. For each
generation, there are no more than L^3 = 4913 possible snippet-insertions.
The number of point mutations is 17, point insertions 17+1, point deletions
17.


> What
> are the odds that "just" will get inserted right next to a sequence,
> such as "plain" so that the combination actually makes unified sense
> in English, much less beneficial sense?


If it is one of the 5000, then one in 5000. If there is no such sequence
that makes "unified sense", then zero. Nada. Zilch.


> I mean, the insertion could
> have ended up in the middle of "plain" as read, "pljustain" or "pjust
> lain" or "plaijust n" etc.


Yes, it could have, and those would be among the rejects. Stillborn.


>
> Then, just say that by some extraordinary twist of luck you just
> happened to get "just plain" stuck together just right.


Well, only if you consider one in 5000 to be lucky. But considering we can
play the game until we win, it's not so lucky after all.


> What are the
> odds that the seqeunce "wrong" would get snipped out from its other
> location and get inserted in just the right position so that the
> combination read, "just plain wrong"? I mean, even if "wrong"
> happened to get copied intact, and even if it happened to get inserted
> into the "just plain" area (out of millions of other possible
> insertion spots) what are the odd that it will get inserted right at
> the end of "just plain"?


About one in 5000.


> It could also get inserted in the middle
> somewhere to read, "just wrong plain" or "juswrong t plain" or "wrong
> just plain" or "just plwrongain" or etc.


That is exactly what has been considered. Every single possible mutation and
insertion has been counted per the original instructions. The number of
evolutionary steps (point mutations and insertions) from a given sequence
space is L^3. For a 17-character sequence, there are no more than 17^3 or
about 5000 possible evolutionary steps per generation. For a 20-character
sequence, 8000.


>
> Are you starting to see the problem? Given one mutation per
> generation per individual genome or evolving sequence, the odds that
> that mutation will result in a new meaningful sequence in a given
> individual is indeed the ratio of all meaningful sequences of a given
> length divided by the total number of possible sequences of that
> length. For 7-letter sequences, this works out to be around 1 in
> 250,000 mutations.


And there is Pitman's fundamental error. It is *not* one in 250000 mutations
for seven-letter sequences. There are only L^3 = 343 possible evolutionary
steps for a seven-letter sequence. If the pathway exists, it will be found
fairly quickly. If such a pathway does not exist, then it will never be
found as we are not allowing simultaneous mutations.

I've shown that such a pathway exists for the 17-character sequence starting
with "Sean Pitman" and ending with "just plain wrong".


>
> On the other hand, you suggest that there are only about 8,000
> possible choices per mutation, but this does not change the odds that
> success will only be achieved once every 250,000 mutations.


This is a specific claim, and one that has been shown false.


> The odds
> that a winning sequence will be within one of the first 8,000 options
> can also be calculated and is 1 chance in 31. On average then, none
> of the first 8,000 options will be meaningful.


This is false, as has been shown.


>
> Now certainly you can find many cases where one 7-letter word can get
> mutated into another meaningful 7-letter word. That is not a problem
> for my position. There are certainly islands of 7-letter words that
> are separated from each other by no more than a single letter change.
> However, most islands of 7-letter words are separated from every other
> island by a little sea of some 250,000 meaningless sequences. The
> question is, how do you get from one island to any other? If you
> can't get from one island to another except by going through the
> neutral sea, natural selection is not going to help you since
> mutations in this sea are functionally neutral and therefore
> completely random. You could just stay on your little island, but
> then evolution would be severely limited now wouldn't it?
>
> Again, your idea of linking smaller words, which are easier to evolve,
> together to make bigger words and phrases doesn't work so well because
> of the above mention problems of proper copying and pasting of these
> words given all the millions of potentially non-meaningful
> possibilities.
>
> In short, you must take all of these possibilities into account in
> your calculation of the average number of mutational events it would
> take for mutating a new beneficial sequence of 16 characters starting
> with a bunch of 3, 4, and 5 character sequences. As far as I have
> been able to tell, you have failed to do this.
>
> Also, in your explaination of how to evolve new meaningful 7-letter
> sequences, you use a population of 10^14 or 100 trillion?! The total
> sequence space for a 7-character sequence (give 27 possible
> characters) is just over 10 billion. Within this sequence space the
> ratio is only about 1 in 250,000 meaningful vs. meaningless. Now, if
> you have a population of 100 trillion, you are going to cover the
> distance between all meaningful possibilities in very short order at
> even a fairly low mutation rate. The evolution of absolutely ANY
> beneficial 7-letter sequence could and would be achieved by such a
> population.
>
> What you evidently fail to realize is that the population expansion
> trick can only work so long because of limited ability of a given
> environment to support an growing population beyond a certain point.
> What happens when you double the sequence length to 14-characters?


Works fine, using a population of only 1000.


> Now you are at a ratio of 1 in about 62 billion. With a population of
> 100 trillion, evolution still does pretty well.


Note Dr. Pitman's implication that the evolution of 14-letter words will
take billions of evolutionary steps. In fact, it takes a population of only
a few hundred and thousands of mutations.



> Moving on to a
> sequence length of 28-characters the ratio drops to 1 in
> 3,906,250,000,000,000,000,000 or almost 4 trillion.


Works fine, using a population of only 5000 and a few million mutations.


> Still, with a
> population of 100 trillion, this distance can be covered in a
> reasonable amount of time. However, with a sequence of 56-characters
> the ratio drops to 1 in 10^43.


Still works fine, using a population of only 10000.


> Now, each and every individual in our
> population of 100 trillion is surrounded by a vast ocean of 10^29
> meaningless sequences. With one generation per day, this works out to
> be around 273 trillion years for just one member of our population to
> find a new meaningful 56-character sequence on average.


That has been falsified.


>
> See the problem?


I certainly do see the problem. You moved the goal posts from 7-letter
words, and made a claim about 14-letter words. This was falsified. Then you
moved the goal-posts to 28-letter phrases. This was falsified. As was the
56-letter challenge. Now, you've moved the goal-posts outside of what can be
directly observed with our Phrasenator.


>
> Sean
> www.naturalselection.0catch.com


You made a specific prediction based on your understanding of how evolution
works. You want to assume that evolution works by making multiple,
simultaneous point-mutations. But this is an incorrect view. Evolution mixes
and matches the tools it has on-hand. It keeps what works and discards the
rest.

You keep claiming that you have been consistent. But, in fact, you have
moved the goal-posts.

Your specific claims have been shown to be false. You have yet to admit
this, even after all this time. I didn't mind creating the Mutagenator in
order to debunk the specific claim you made concerning 14-letter words; and
afterwards, creating the Phrasenator to debunk the specific claim about
28-character phrases. I learned a lot about how language is distributed
through sequence space - and you know what that is worth! But I do mind you
not acknowledging your specific predictions have been falsified.


--
Zachriel's Phrase Mutation and Evolution Experiment
And it takes less than "zillions of years"!
http://www.zachriel.com/phrasenation/



.

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