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A Tiny Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]
Nutters.org ^ | 13-Dec-1995 | Brett Watson

Posted on 03/05/2002 12:52:58 PM PST by Southack

There is a recurring claim among a certain group which goes along the lines of "software programs can self-form on their own if you leave enough computers on long enough" or "DNA will self-form given enough time" or even that a million monkeys typing randomly on a million keyboards for a million years will eventually produce the collected works of Shakespeare.

This mathematical proof goes a short distance toward showing in math what Nobel Prize winner Illya Prigogine first said in 1987 (see Order Out of Chaos), that the maximum possible "order" self-forming randomly in any system is the most improbable.

This particular math proof deals with the organized data in only the very first sentence of Hamlet self-forming. After one examines this proof, it should be readily apparent that even more complex forms of order, such as a short story, computer program, or DNA for a fox, are vastly more improbable.

So without further adue, here's the math:


TOPICS: Culture/Society; Miscellaneous
KEYWORDS: crevolist; sasu
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To: Ahban
Jean val Jean vs. Javier. Law and Grace. Rules and change. Sorry, this is totally off the subject.
651 posted on 12/11/2002 8:59:31 PM PST by thelastonestanding
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To: gore3000
"PER OFFSPRING. Some individuals have more offspring than others."

But we are talking about neutral mutations.

You're missing the key issue. While it's true that some individuals have more offspring because they have beneficial alleles and those alleles give a reproductive boost (by definition) to the individual, there's another possibility. That possibility is that even when individuals are on "equal footing" fitness-wise, SOME WILL PRODUCE MORE/LESS OFFSPRING SIMPLY BY PURE CHANCE. For a trivial example, one may have the bad fortune to be struck by lighting.

It should be trivially obvious that not all individuals end up having the same number of children, and that this differential is not entirely dependent upon genetic fitness. Luck, chance, other factors, call it what you will, plays a large part. Sometimes the big strong specimen gets hit by a car while the runt survives to reproduce.

This is what drives genetic drift.

An allele can reproduce faster than the general population only when it has a non-neutral effect (meaning that it has selective advantage). You look it up.

I *have* looked it up, which is why I can tell you that you're wrong. I told *you* to look it up in my previous post, you should have taken my advice.

If you had, you might have "looked up" such things as:

"If a population is finite in size (as all populations are) and if a given pair of parents have only a small number of offspring, then even in the absence of all selective forces, the frequency of a gene will not be exactly reproduced in the next generation because of sampling error. If in a population of 1000 individuals the frequency of "a" is 0.5 in one generation, then it may by chance be 0.493 or 0.505 in the next generation because of the chance production of a few more or less progeny of each genotype. In the second generation, there is another sampling error based on the new gene frequency, so the frequency of "a" may go from 0.505 to 0.510 or back to 0.498. This process of random fluctuation continues generation after generation, with no force pushing the frequency back to its initial state because the population has no "genetic memory" of its state many generations ago. Each generation is an independent event. The final result of this random change in allele frequency is that the population eventually drifts to p=1 or p=0. After this point, no further change is possible; the population has become homozygous."

(Suzuki, D.T., Griffiths, A.J.F., Miller, J.H. and Lewontin, R.C. in An Introduction to Genetic Analysis 4th ed. W.H. Freeman 1989 p.704)

Or:
"In other words, as long as the allele provides its bearer with no selective advantages or disadvantages whatsoever, its fate in the gene pool is totally indeterminate. It may disappear as soon as it arises (elimination) or it may proceed toward q = 1 (fixation) in a seemingly haphazard pattern that is aptly described as a random walk: the course taken by the allele depends entirely on how the gamete pool happens to be sampled from one generation to the next."

(Goodenough, Ursula in Genetics, 2nd ed. Harvard University 1978, p. 798-800)

For more technical treatment, see: Kimura 1968. Evolutionary rate at the molecular level. Nature 217: 624-628., or Kimura, M. 1983 The Neutral Theory of Molecular Evolution Cambridge University Press, or S. Karlin. "A first course in stochastic processes". New York, London, Academic Press. 1968.

If you want to look at the math, check out: Mathematical Methods of Population Genetics

(Sidebar: Why is it whenever anti-evolutionists challenge me to "look something up" it always supports *my* side when I do? Looks like *I'm* not the one who needs to be hitting the books harder.)

I already mentioned that it is a statistical percentage and that indeed you can get two or zero. This causes a problem for your theory because of the chance of it being none it shows that the mutation can indeed tend to dissappear in a fairly short number of generations.

That's no "problem" at all. Sure, a lot of mutations happen and then get lost in the shuffle. No one ever said they didn't. But what's important is that some *don't*, and these are the ones which become a part of the species' gene pool, available for further modification and recombination.

Just because a million people crap out on the lottery each week, that doesn't mean there aren't a bunch of lucky millionaires out there.

Therefore, again, Neutral mutations will not spread. The statistics which you keep claiming prove it show the exact opposite.

Simply repeating that doesn't make it true.

Yes, many neutral mutations occur and then are "shuffled out". But many survive and *do* spread, just on pure blind luck, in a "random walk" through the population. The ones that matter aren't the ones that die out, it's the ones which do manage to persist which provide raw material for further evolution.

I earlier urged you to run any of the simulations which are available on the net. You clearly chose not to do so, which was a mistake. If you had, you would have seen ample evidence of how neutral alleles *can* indeed spread through a population. For example:

This represent 8 "trials" of a low-frequency neutral mutation across 250 generations. Note that although 3 do quickly go to extinction (lower left), one (the grey line) drifts quite a bit up and down in frequency until it finally dies off about 200 generations later, two (turquoise and yellow lines) are still present in the population 250 generations later, and, most notably, two (the green and blue lines) have not only managed to spread through the population, they have entirely *supplanted* all competing alleles -- there is now nothing *but* the new mutation in the population.

Furthermore, note that the turquoise line came *very* close to "topping out" before it fell in frequency.

The statistical chances are the same and will even out over several generations that is why neutral drift is false.

If you say so... Feel free to "look it up" and provide me with a citation for that amazing claim. And I mean a reputable biology text or research paper, not a creationist screed, they tend to get their facts and quotes wrong a lot.

Let's remember that you only have one mutation, one single individual able to spread it.

To start with, sure -- but they have a chance to have children, maybe a bunch of them.

Let's also remember that the laws of statistics show that allele frequency will not change except with selective advantage.

There you go again...

No, the "laws of statistics" most certainly do *not* "show" this. Neutral mutations follow the "laws of statistics" in the same way as a ball bearing on a flat, level, vibrating floor -- they can go *anywhere*.

Again, you might want to "look that up" and get back to us.

Therefore in a large population, which is what you need for the many chances required for gradual evolution, the laws of statistics show that the percentage of the mutation will continue to be infinitely small and no larger than the proportion of the one individual in the original population.

Not exactly ("infinitely small" is notably incorrect), but I'll give you the obvious fact that a given mutation has a harder time "winning out" in a large population than a smaller one.

What you're forgetting, however, is that since the population *is* larger, there are more individuals who can *have* mutations.

Example: If the error rate is 0.1 per individual, then in a population of 100 there will be 10 mutations per generation (spread out across different individuals).

But in a population of 1,000,000, there will be 100,000 mutations per generation.

So yeah, while it's true that in the larger population any *given* mutation has a much smaller chance of becoming widespread, the fact remains that because there are many more *total* mutations, *one* of them still has a good chance of prospering. Again, like playing the lottery, the odds of winning suck, but enough people play that there is a frequent stream of winners.

In fact, interestingly enough, the smaller chance of a given mutation prospering in a larger population is *exactly* balanced by the fact that larger populations produce more total mutations. In other words, large populations have the same rate of "successful mutation" addition to the population as do small populations (where "successful" means "a mutation which has managed to spread through the most or all of population).

From the Introduction to Biology FAQ:

If mutations are neutral with respect to fitness, the rate of substitution (k) is equal to the rate of mutation(v). This does not mean every new mutant eventually reaches fixation. Alleles are added to the gene pool by mutation at the same rate they are lost to drift. For neutral alleles that do fix, it takes an average of 4N generations to do so. However, at equilibrium there are multiple alleles segregating in the population. In small populations, few mutations appear each generation. The ones that fix do so quickly relative to large populations. In large populations, more mutants appear over the generations. But, the ones that fix take much longer to do so. Thus, the rate of neutral evolution (in substitutions per generation) is independent of population size.

(Copyright © 1996-1997 by Chris Colby)

Because of the complexity of genes and the need to change more than one base (indeed in my view you need completely new genes for new functions) this makes evolution totally impossible since a single base mutation will remain neutral until the complete series of mutations required to make a significantly more useful function has arisen and by the laws of genetics this is absolutely impossible.

You have made a number of invalid presumptions here, including:

1. You haven't taken into account the fact that many mutations are beneficial, not *all* evolutionary steppingstones are neutral.

2. This is especially true for changes that "build upon" an existing function.

3. "Completely new functions" most certainly do *not* require "completely new genes", the literature abounds with examples of a gene serving some prior purpose mutating and gaining a whole new purpose.

4. Being "significantly more useful" is not necessary, even being "slightly more useful" is more than enough of difference for selection to do its work.

5. You (vaguely) argue that something is improbable, then make an unsupported leap to "absolutely impossible". There's a vast difference between the two.

652 posted on 12/11/2002 10:02:49 PM PST by Dan Day
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To: Dan Day
Wow, all of that and you managed to create Life in the lab, too.

You must be very proud...

Oh, did you get your Nobel Prize yet?!

< /MOCKING >

653 posted on 12/11/2002 11:10:06 PM PST by Southack
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To: Dan Day
You're missing the key issue. While it's true that some individuals have more offspring because they have beneficial alleles and those alleles give a reproductive boost (by definition) to the individual, there's another possibility. That possibility is that even when individuals are on "equal footing" fitness-wise, SOME WILL PRODUCE MORE/LESS OFFSPRING SIMPLY BY PURE CHANCE. For a trivial example, one may have the bad fortune to be struck by lighting.

So what, over several generations it will average out. Also it means that many mutations will dissappear. The laws of statistics are very strict, and we know they work. They built the casinos in Las Vegas.

If a population is finite in size (as all populations are) and if a given pair of parents have only a small number of offspring, then even in the absence of all selective forces, the frequency of a gene will not be exactly reproduced in the next generation because of sampling error.

Sampling error is way too small for it to have any effect on the matter at hand. The most you might get is that in a population of one million the sampling error will end up providing you a proportion of the allele of 1/500,000 instead of 1/1,000,000 this is not taking over the population. It also means that many mutations will die also due to 'sampling error'. As I keep saying, genetic drift is total bunk. You are starting with ONE (1) mutation you cannot get it to take over the whole population except by a miracle. Such miracles do not happen every day as evolution would require. You can postulate one or two miracles, but to postulate that not only will they happen once but numerous times to build and change one gene in one species a little bit is ludicrous. To postulate that such miracles happen all the time in all species all the time just shows that evolution is totally false.

BTW - the reason these folk have to write so much nonsense is that they are trying to obscure the truth. The truth is usually very simple, you do not need reams of nonsense to show it.

654 posted on 12/12/2002 5:25:50 AM PST by gore3000
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To: Southack
First in a series of Southack is wrong.

"Random" simply means unaided by any intelligent bias.--Post 81

From www.dictionary.com:

random

Mathematics & Statistics. Of or relating to a type of circumstance or event that is described by a probability distribution.

There are natural occurances that are non-random. Chemical reactions are non random, for example.

655 posted on 12/12/2002 6:09:33 AM PST by ThinkPlease
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To: Southack
The great thing about math is that it is scientific.

Is it? Math is just a tool. Math by itself is not scientific. It's only as good as the assumptions used to plug in the initial conditions, and the answers are the same.

656 posted on 12/12/2002 6:26:11 AM PST by ThinkPlease
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To: Southack; js1138
Another brick in the wall from post 100

"Feedback" implies intelligent intervention into the process. Is that how you want to say that the first DNA came into being?

From dictionary.com:

feedback:

The process by which a system, often biological or ecological, is modulated, controlled, or changed by the product, output, or response it produces.

Sounds like you can have natural feedback to me!

A good analogy is the climate in a given place. The climate for the following summer is affected by the climate of the previous summers. It gets feedback from the previous system in terms of the amount of water it recieved in the previous years, which affects growing and the amount of vegetation. Consecutive summers without liquid, and the feedback provided by previous years, will affect future years of vegetative development..

This leads into my next comment(post 444):

Just to be clear, a "fitness test" implies intelligent intervention.

Actually, you can have natural fitness tests. How do you get organic long chain molecules to form in the centers of giant molecular clouds in the sky? Well, first you have to succeed in getting two smaller chain molecules to bump together and molecularly bond, but the important physical test is to not have a photon of light add energy to the system to cause the molecule to disassociate. That's an good example of a netural fitness test that a molecule has to pass on its road to perpetual non-interestingness or to become something scientifically interesting. Chemically, there are other, more complex "fitness tests" that a molecule has to go through, but they probably would be too complex to go through here. One thing's for certain, the math would be a good deal more complex than that here.

I'm extremely interested in what the DNA of the bacteria that live under the earth's surface will reveal. It's not virgin DNA from the early Earth (that's all gone, I think), but it represents a completely independent evolutionary tree. It may provide links to what the early forms of DNA took, and that is important.

657 posted on 12/12/2002 6:55:58 AM PST by ThinkPlease
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To: Dan Day; Southack
The fact that the author failed to introduce *any* sort of feedback mechanism into his calculation is a fatal flaw if he's even remotely trying to model abiogenesis. And since it's *missing* any feedback whatsoever, the exact nature of any hypothetical "added" feedback is an exercise in mental masturbation.

The author doesn't address the probability of combinations, or the fact that DNA creation isn't just a sequential process, why can't you have words form simultaneously in separate locations, and then combine? I'm afraid he doesn't explain that, either.

658 posted on 12/12/2002 7:09:07 AM PST by ThinkPlease
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To: Southack
Indeed, his assumptions are speculation (of course, they are GENEROUS speculations which give huge favor to Evolution, but they are assumptions nonetheless),

Hardly. He's not addressing the real world, just a straw man that he can knock down in place of the real world. Perhaps a compilation of all of his mistaken assumptions (both spoken and nonspoken) will be in order for a later post.

but his specific math is not speculation.

Has anyone on this thread ever questioned his math? I don't think so. You've been harping on this for the entire thread, and yet I haven't seen more than one person question has math (and I don't think you actually addressed that person). When we say "errors", we do not mean strictly mathematical errors, we can mean argumentative errors, errors in assumption, etc, as well. Of course, I don't have to mention to you (for a third time) that math is just a tool, and that GIGO (garbage in, garbage out) is a big factor in any scientific analysis(also for the third time in this thread).

659 posted on 12/12/2002 7:31:36 AM PST by ThinkPlease
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To: Southack
[Crickets]

So does this mean that I can get on your case in an hour, provided you don't respond in that time? Some of us actually have a life, you know.

660 posted on 12/12/2002 7:33:35 AM PST by ThinkPlease
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To: ThinkPlease
I'm extremely interested in what the DNA of the bacteria that live under the earth's surface will reveal. It's not virgin DNA from the early Earth (that's all gone, I think), but it represents a completely independent evolutionary tree.

Are you sure about the independent tree. That would be news to me.

661 posted on 12/12/2002 7:38:39 AM PST by js1138
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To: js1138
Are you sure about the independent tree. That would be news to me.

Lemme rephrase. Independent since at least the time it was buried. I don't have the numbers in front of me, so I don't know if anyone has estimated a time of divergence, but having something that's been isolated for even several tens of millions of years is of scientific interest, I think.

662 posted on 12/12/2002 7:47:29 AM PST by ThinkPlease
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To: ThinkPlease
It would be interesting to know where the subterranian bacteria fit on the tree, assuming they do. I think there's a Nobel prize for the first person to discover an independent tree of life.
663 posted on 12/12/2002 7:55:24 AM PST by js1138
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To: ThinkPlease
Perhaps a compilation of all of his mistaken assumptions (both spoken and nonspoken) will be in order for a later post.

The assumptions are stated. You may not agree with them(you obviously don't, but then no one has come close to forming a complex molecule from scratch even using intelligent methods) but they are valid for reactions showing no preference for configurations of the constituent units.

You speak of the real world. Well, in the real world, there are no "undesigned" chemical reactions outside of life that have produced the molecules being discussed. As for your speculation about the formation of the complex molecules by accidental conjugation of parts in interstellar clouds, do you realize what a vacuum is?

I'm also certain that the numbers come out the same when parts are randomly assembled. IOW, it does not matter whether one person flips a coin 100 times or 100 people flip a coin once, the probability that all of the tosses result in heads is the same.

664 posted on 12/12/2002 8:21:17 AM PST by AndrewC
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To: AndrewC
You speak of the real world. Well, in the real world, there are no "undesigned" chemical reactions outside of life that have produced the molecules being discussed. As for your speculation about the formation of the complex molecules by accidental conjugation of parts in interstellar clouds, do you realize what a vacuum is?

First, given an assumption of a naturalistic origin of life, there has to be a chemical reaction that created life. Life exists, after all. Just because we haven't found that sequence doesn't mean that it isn't there.

Secondly, the formation of complex molecules (including some complex peptides) in the interstellar medium is a known quantity. Deep within the heart of Giant molecular clouds, molecular lines indicating significant quantities of organic molecules of a variety of types (including one with a significant amount of Ethanol). In 2002, the smallest amino acid, Glycine was discovered in Sagittarius B2 (18 Jul 2002 edition of New Scientist). It appears that a vacuum is not a problem in this matter.

To merge the two comments, I refer you to this paper by David Woon, "Pathways to Glycine and Other Amino Acids in Ultraviolet-irradiated Astrophysical Ices Determined via Quantum Chemical Modeling", Astrophysical Journal Letters, 2002, 571, pg L177-L180

The abstract can be read here, Abstract

665 posted on 12/12/2002 8:41:09 AM PST by ThinkPlease
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To: ThinkPlease
Placemarker of the Beast.
666 posted on 12/12/2002 8:55:04 AM PST by Junior
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To: ThinkPlease
First, given an assumption of a naturalistic origin of life,

That is known as begging the question, "proving" what you have assumed. Secondly, I know that there is evidence of the formation of "complex" chemicals in gaseous clouds, but your "known quantity" of complex peptides, I do not believe. Glycine is an amino acid --- here is its structure

Let me see, 2 carbon, 2 Oxygen, 1 nitrogen, and 5 hydrogen, looks like a complex peptide to me.

667 posted on 12/12/2002 9:25:08 AM PST by AndrewC
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To: AndrewC
Perhaps ypu'd like to bless us with a calculation of the probability of complex peptides forming spontaneously.
668 posted on 12/12/2002 9:35:11 AM PST by js1138
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To: AndrewC
"proving" what you have assumed.

I didn't prove that, though. I have stated nothing about "proving" anything. I simply state my assumptions. Brett Watson is not clear about his assumptions. There is much hidden behind the scenes that he doesn't mention.

"known quantity" of complex peptides..

Perhaps my wording was confusing. How about this: We know that complex peptides can be formed in detectable quantities in gaseous clouds. Molecular rotational and vibration spectral lines indicating these molecules have been detected in giant molecular clouds...

669 posted on 12/12/2002 9:36:11 AM PST by ThinkPlease
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To: js1138
Perhaps ypu'd like to bless us with a calculation of the probability of complex peptides forming spontaneously.

A polypeptide of length 100.... ~0.0

670 posted on 12/12/2002 9:37:36 AM PST by AndrewC
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To: Southack
Bump
671 posted on 12/12/2002 9:40:17 AM PST by Fiddlstix
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To: ThinkPlease
We know that complex peptides can be formed in detectable quantities in gaseous clouds. Molecular rotational and vibration spectral lines indicating these molecules have been detected in giant molecular clouds...

Well, might and could are simply might and could. Please provide the evidence that someone believable is willing to state as unequivocal evidence of the hypothetical complex peptide.

672 posted on 12/12/2002 9:48:43 AM PST by AndrewC
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To: AndrewC
A polypeptide of length 100.... ~0.0

Never say never. I'm still looking up the detection strength of the Glycine lines, and the density estimates. It's quite possible that there is more out there, we just can't detect it because there isn't enough of them to firmly detect.

673 posted on 12/12/2002 9:50:48 AM PST by ThinkPlease
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To: ThinkPlease
Never say never. I'm still looking up the detection strength of the Glycine lines, and the density estimates. It's quite possible that there is more out there, we just can't detect it because there isn't enough of them to firmly detect.

Well, we can't detect bridge trolls so they must be hard to find.

Now the density of gaseous clouds is estimated to be 10,000 atoms(molecules)/cm3. Interstellar space is 0.1-1 atom/cm3.

674 posted on 12/12/2002 10:07:04 AM PST by AndrewC
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To: ThinkPlease
"The author doesn't address the probability of combinations, or the fact that DNA creation isn't just a sequential process, why can't you have words form simultaneously in separate locations, and then combine? I'm afraid he doesn't explain that, either."

On the contrary, the author's math does take into account "groupings" from other locations recombining, simply because the mathematical odds of obtaining a given sequence are identical whether you are talking about groups of size 1 character after another combining or groups of 50 after another combining (presuming that all such groups themselves are formed without intelligent intervention or intelligent feedback, and further presuming that no intelligence is injected into which groups are "kept" for recombining with other groups).

To wit: the monkeys don't "know" when they have a valid English word, so they wouldn't know to share such valid words with each other to make a longer sentence of valid words. They are just mindlessly banging on their keyboards (which might actually resemble some of the behavior by a few posters on this thread, grin).

675 posted on 12/12/2002 10:47:41 AM PST by Southack
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To: ThinkPlease
Just to be clear, a "fitness test" implies intelligent intervention. - Southack

"Actually, you can have natural fitness tests." - ThinkPlease

Yes, you are correct that natural feedback is quite possible.

However, you are incorrect to assume that what small snippet of conversation that you quoted above from me was somehow meant to imply otherwise.

That comment was directed at another poster, not at you, and it was covering a different angle of this debate.

Specificly, it goes all of the way back to Post #12, where the poster in question wanted the monkeys to be forced to use an English Dictionary so that they would "know" when they had managed to bang out a valid word.

And yes, injecting feedback from an English dictionary does indeed add intelligence to the proposed math process for this thread, and that would imply intelligent intervention.

Moreover, as I've already explained at least twice on this very thread, feeling the "need" to add "intelligent feedback" into the process is PRECISELY the intellectual trap that the author wishes Evolutionists to fall for.

It seems to be a rather effective (if somewhat obvious) trap, too.

676 posted on 12/12/2002 10:59:50 AM PST by Southack
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To: ThinkPlease
Has anyone on this thread ever questioned his math?

So why don't you question it? Why do you reject it without evidence against it? Why do you attempt a snow job when you do not know of anything wrong with what the author of the article says? Clearly your beliefs are not based on science but on your emotional predilections.

677 posted on 12/12/2002 8:55:51 PM PST by gore3000
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To: ThinkPlease
Life exists, after all. Just because we haven't found that sequence doesn't mean that it isn't there.

No one here, on either side, has denied that there is life on earth. The discussion, in case you came in late, is about how it arose, whether by intelligent design or by some totally materialistic occurrence which no one can even imagine.

678 posted on 12/12/2002 9:00:13 PM PST by gore3000
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To: gore3000
First, I'd like to say that unlike a lot of anti-evolutionists I've discussed things with over the years, you manifestly have a very good intuition for math. You make quite a few correct conclusions, even on things that most people would not find obvious, apparently by intuition alone (since I don't see any sign that you've cranked through the actual numbers or equations, or rely on any pre-discovered laws -- in fact, you seem quite distrustful of them).

However, intuition alone can often be a risky thing. Many things in math and science work in counterintuitive ways -- subtle effects can have larger consequences than seems obvious at first look, or can combine in completely unexpected ways, which can only be discerned if you take a much closer look and work through full rigorous proofs, or carefully simulate thousands of trials on a computer, or run experiments to check how things really work instead of the way you'd presume they work.

Intuition can take you far, but it's absolutely no substitute for actually checking your presumptions against reality.

This is especially the case when your intuition takes you to a conclusion which seems to prove a point you'd like to support... The temptation is very strong to declare victory and examine it no further, rather than truly dig as deep as possible to make certain that you haven't overlooked something which makes the case not as simple as you'd first presumed.

And now, back to the discussion.

So what, over several generations it will average out.

No, actually, it doesn't. Random walks aren't like running tallies of coin flips. Because each new step picks up where the last one left off, any deviation from the "average" at any step permanently offsets the "baseline" and becomes the new "center". Any initial (or subsequent) deviation permanently biases all future results, making it impossible even in theory for an "average" position to be maintained or returned to or "averaged out". Once a random walk wanders "off" its initial position, which it generally does very soon, it has no more "incentive" to wander back to its original position than it does to wander off in the other direction entirely. This is *not* a process that "evens out over time". You can get a good feel for this property of random walks by playing with this Java applet.

This leads to very counterintuitive results, but a careful examination of actual random walk behavior (either by rigorously derived math, or by carefully conducted computer simulations) reveals that while the results are hardly "obvious", they are nonetheless true.

For example, let's consider the simplest possible type of random walk. Mark a spot on the ground and call it "zero". Stand on the spot. Now flip a coin. If you get heads, take one step to the right. If you get tails, take one step to the left. Now that you're at your new spot, flip the coin again and repeat. Then keep repeating, following where the coin leads you.

Now let's examine the actual properties of such a walk.

1. At the end of, say, 1000 flips/steps, what do you think your *single* most likely position is? Intuition says, "on point zero", which happens to be correct. But that's about the *only* intuitive answer that is correct for random walks.

2. After 1000 random steps, what's your most likely *distance* from point zero? Intuition says the most likely distance is zero, or close to it. Actual analysis shows that your most likely distance is actually square-root(1000), or 32 feet away. Quite counterintuitive.

3. As you perform more and more random steps, are you more and more likely to end up near point zero, or not? Intuition says you should more likely "average out" to someplace near point zero. Actual analysis shows that your position becomes more and more likely to be farther and farther from point zero. The longer you do the random walk, the farther afield you are likely to end up. The reason is that the distribution curve, although centered on point zero, becomes flatter and flatter and wider and wider -- after a large number of random steps, the vast middle of the distribution curve becomes so flat that you're just about as likely to end up anywhere at all as opposed to point zero itself. Although point zero itself always has a somewhat greater probability than any other single spot, the odds of actually being *at* point zero (or even close to it) continue to shrink the more random steps you take. A really nice "look-see" Java demonstration of this can be found here.

4. How many times are you likely to cross over point zero? That is, how often will you randomly wander from the left of point zero to the right of it, or vice versa? Intuition says that you'll cross over it many, many times if you do the random walk a long time. Actual analysis shows that the most likely number of crossings is *zero*, the next most likely number of crossings is one, then two, and so on.

Don't try to rely on intuition alone when doing analysis on random processes, it too often leads to seemingly reasonable, but wrong, results.

For good introductions to random walks, see:

Random Walks - 1-dimensional
Random Walks - 2-dimensional
The One-Dimensional Random Walk
Chemistry 531 The One-dimensional Random Walk

Also it means that many mutations will dissappear.

Yes, of course they will. But it matters not how many vanish, it matters how many manage to persist. There's no harm in "losing" mutations if enough do survive to drive evolution.

As I previously showed, small populations retain a larger percentage of mutations but produce fewer to work with, while large populations retain fewer mutations (as a percentage) but produce more overall. The net effect is that although many mutations are lost in either case, the population as a whole will acquire mutations at a rate equal to the mutation rate in a single individual.

Note that this is for neutral mutations -- beneficial mutations are accumulated in the population at large at a faster rate.

Also, interesting things happen when a large population is split up into separate breeding subpopulations, called "demes".

The laws of statistics are very strict, and we know they work. They built the casinos in Las Vegas.

Certainly, but you must take care to apply them properly. Many people have gone broke in Vegas through their misapplication of statistics to a given game. Check out the book "Scarne on Gambling" for a long list of gambler's fallacies and "betting systems".

Sampling error is way too small for it to have any effect on the matter at hand. The most you might get is that in a population of one million the sampling error will end up providing you a proportion of the allele of 1/500,000 instead of 1/1,000,000 this is not taking over the population.

Intuitively, yes, that makes sense and seems reasonable. In actual practice, it doesn't work that way.

It also means that many mutations will die also due to 'sampling error'.

Yes it does. But this is of no consequence as long as enough mutations persist to drive evolution. And studies of how many mutations have actually entered the gene pool for various populations indicates that the real-world mutation acquisition rate is indeed sufficiently high to account for evolution.

Intuition is a fine thing, but eventually it needs to reality-checked.

As I keep saying, genetic drift is total bunk.

As Galilleo replied when faced with similar obstinance, "and yet it still moves".

You can declare it bunk as much as you like, but countless different sorts of studies (mathematical analysis, simulation, examinations of real-world genetics, etc.) show that no matter how much you may disbelieve it, it still works.

You need to pause and actually test your intuition from time to time.

You are starting with ONE (1) mutation you cannot get it to take over the whole population except by a miracle.

Intuition says that. Intuition is wrong in this case. The actual dynamics are more interesting than intuition would lead you to believe.

Such miracles do not happen every day as evolution would require.

This misstates the issue. Evolution does not require it to happen "every day". Nor is the introduction of new mutations into the population a "miracle".

Actual measurements of non-fatal mutation rates are on the order of 1 per 1000 alleles per generation, or 4 per each human birth (1.6 deleterious). This means that each human generation introduces *fourteen billion* new neutral-or-beneficial mutations into the population. True, most of the neutral ones will sputter out, but surely you can see that there are so bloody many that *some* will hit the mutation lottery and become established. And the beneficial ones will (statistically) grow in frequency through selection.

That makes for a *lot* of raw material for evolution to sift and select and build on.

Let's do some quick estimates. Let's be conservative and say that all of the non-deleterious mutations are merely neutral, and not beneficial. Using the statistics from our last post, we find that 2.4 neutral mutations per generation will become "fixed" in the human gene pool eventually. It has been roughly 5 million years since we shared a common ancestor with chimpanzees. For most of human history, a generation has been no more than 15 years or so long. That means we've had 333,000 generations since our kinship with the chimps, and at 2.4 "successful" mutations per generation (out of billions lost through chance) we've accumulated 800,000 mutations to separate us from the chimps (and the chimps have accumulated about the same number in *another* direction).

Is it reasonable to presume that 1.6 million acquired mutations would be enough to turn a man into a chimp or vice versa? I think it is. More likely, we're separated by far *fewer* genetic differences. In fact, actual comparison between human DNA and chimp DNA turns up less than 0.5% differences, or 150,000 allele base pairs. So the *actual*, *measured* neutral mutation acquisition rate is *ten times* greater than that necessary to split humans and chimps from their presumed common ancestor.

You were saying?

You can postulate one or two miracles, but to postulate that not only will they happen once but numerous times to build and change one gene in one species a little bit is ludicrous.

So says intuition. But see above.

To postulate that such miracles happen all the time in all species all the time just shows that evolution is totally false.

Again, you're working way too much on intuition here. You jump from "rare and unlikely per single event" to "impossible" or "totally false", which is not a valid transition. Unlikely things still do happen, and over enough time or a large enough population, they happen at a pretty steady rate.

Again, please do a reality-check every once in a while.

BTW - the reason these folk have to write so much nonsense is that they are trying to obscure the truth. The truth is usually very simple, you do not need reams of nonsense to show it.

Now this is just beneath you. I have more respect for your intelligence than that.

It's just intellectually dishonest to try to dismiss reams of evidence and study as being merely attempts to "obscure the truth".

That's just an excuse to avoid having to examine it, and deal with what it reveals.

As for the "truth is usually very simple", I think you know better than that. Things only seem simple to simple minds. The more we actually examine something, especially things in nature, the more wondrous and intricate we discover them to be.

679 posted on 12/13/2002 1:14:22 AM PST by Dan Day
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To: gore3000
Life exists, after all. Just because we haven't found that sequence doesn't mean that it isn't there.

No one here, on either side, has denied that there is life on earth. The discussion, in case you came in late, is about how it arose, whether by intelligent design or by some totally materialistic occurrence which no one can even imagine.

Poor Gore. Like his namesake, he misses the point of my post early, and often. Please come back when you've figured it out. I'll give you a hint. Read that line in context to the rest of the post, and it might avail you a clue.

680 posted on 12/13/2002 8:35:09 AM PST by ThinkPlease
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To: Dan Day
;^)
681 posted on 12/13/2002 8:45:25 AM PST by js1138
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To: Dan Day
For example, let's consider the simplest possible type of random walk. Mark a spot on the ground and call it "zero". Stand on the spot. Now flip a coin. If you get heads, take one step to the right. If you get tails, take one step to the left. Now that you're at your new spot, flip the coin again and repeat. Then keep repeating, following where the coin leads you.

A random walk is no good as a simulation of what happens in genetics. This is the problem - you never lose. In the case of a single mutation for example with a 50% chance of getting it passed on and the individual having two children the possible outcomes are both, one or none. When you get none, the walk is finished. Your simulation does not account for the walk ever ending, therefore it gives false results.

This leads to very counterintuitive results

It gives counterintuitive results because it does not reflect reality. If you are betting on outcomes and you have one quarter to play with and keep playing indefinitely with that quarter, you may get ahead for a while but eventually you will lose your quarter and that is what happens with mutations. In fact, statistical analysis shows that the mutation will be lost in less than 10 generations.

Yes, of course they will. But it matters not how many vanish, it matters how many manage to persist.

It does matter that many will be lost. This is the basis of Haldane's dilemma. Evolutionists talk as if there is an almost infinite amount of time and an almost infinite amount of tries. However, both are finite and it is not a matter of some 4 billion years either. Taking evolutionary assumptions for example for the evolution of all mammals you have just about some 100 million years and the generations of mammals are fairly long (not like those of bacteria and insects) so you have quite a limited number of chances. You also need quite a few mutations to occur when you consider the number of species involved and the fact that to achieve the differences you need different mutations in each.

As I previously showed, small populations retain a larger percentage of mutations but produce fewer to work with, while large populations retain fewer mutations (as a percentage) but produce more overall. The net effect is that although many mutations are lost in either case, the population as a whole will acquire mutations at a rate equal to the mutation rate in a single individual.

Mutations will spread more easily in small populations because there is a greater chance of their being 'fixed'. This happens because individuals in small populations procreate with closer relatives than those in large populations. In short they are more inbred. The scientific facts show that inbreeding is bad and in fact 'inbred' is often use as an insult because of the deleterious effects it has.

That neutral mutations may persist in a population does not help evolution, because mutations are not additive amongst individuals as genetics shows. Because as I have shown a particular mutation will likely remain in only a single individual, additions to that mutation, which are required for neutral drift to accomplish any sort of evolutionary change, must rely on that single individual currently carrying the mutation to have another favorable mutation to add to it. Here is why that has an infinitely small chance of happening - the amount of unfavorable mutations far exceeds the possible neutral or favorable mutations possible and the original mutation will die due to the overwhelming chances of unfavorable mutations.

Actual measurements of non-fatal mutation rates are on the order of 1 per 1000 alleles per generation, or 4 per each human birth (1.6 deleterious).

The above is totally false. To determine that you would require the sequencing of the entire genome of both parents and the child for a large sample of the human population. No such sequencing has been done. This is an example of evolutionists just totally making up evidence for their theory.

It's just intellectually dishonest to try to dismiss reams of evidence and study as being merely attempts to "obscure the truth".

I am not dismissing reams of evidence, on the contrary. It is evolutionists who are trying to dismiss reams of evidence, in this case the certified fact that mutations are harmful to an organism, the certified fact that genetics tells us that a new allele will not spread in a population. As I showed above the random walk is a fraudulent model for what happens in genetics. It is not intuition alone that tells us that a single mutation will not spread through a population, it is verified facts. It is like saying that a person can go into a casino with one dollar and end up owning the casino. Yes it can happen - ONCE. However evolution requires that it happen all the time. Unlike gambling casinos though, where the odds are usually not too bad, with mutations there is a big joker in the deck working against the gambling mutation. That joker is called bad mutations which are even by the phony statistics of evolutionists, overwhelmingly against even a neutral mutation (you gave the phony chance of 1.6 against a neutral mutation just above). So you are not working with even odds but with massively unfavorable odds against both a mutation surviving and a mutation ever spreading. This is why evolutionists who talk about neutral drift never mention that mutations will dissappear due to unfavorable mutations intervening and destroying the 'line' which carries them.

That this occurs with mutations is not to be doubted. The facts of inbreeding show quite well that it is the non-inbreed individuals that are more successful. The facts of inbreeding show that severely inbred populations are subject to much more genetic disease than non-inbred populations. The facts of inbreeding show that inbred populations are less viable than non-inbred ones. These facts show the falsity of both neutral drift and Gould's punk-eek.

682 posted on 12/14/2002 1:47:01 AM PST by gore3000
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To: gore3000
"...the amount of unfavorable mutations far exceeds the possible neutral or favorable mutations possible..."

Very true. The amount of unfavorable random data mutations which occur while downloading programs over the internet will greatly outnumber the quantity of data mutations that yield new, favorable programming functionality from noisy downloads.

Likewise, most genetic programming mutations are unfavorable.

683 posted on 12/14/2002 9:45:32 PM PST by Southack
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To: The Shootist
You can deny god all you want, but science cannot save you from dying. You will know the truth then.
684 posted on 03/11/2003 4:00:18 PM PST by The ark
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To: Southack
"I hypothesize 17 billion galaxies, each containing 17 billion habitable planets, each planet with 17 billion monkeys each typing away and producing one line per second for 17 billion years. What are the chances of the phrase "TO BE OR NOT TO BE, THAT IS THE QUESTION." not being included in the output?

0.999999999999946575937950778196079485682838665648264132188104299326596142975867879656916416973433628

I'd bet money on that. It's about 99.999999999995% sure that they would fail to produce the sentence."

17 billion galaxies x 17 billion habitable planets x 17 billion monkeys at one line per second x 17 billion years (or 365.25 * 24 * 60 * 60) = 2.6357223096 x 10^48.

If the failure rate is 99.999999999995%, then the success rate is 0.000000000005%.

In those 17 billion years, the line will be created (2.6357223096 x 10^48)(0.000000000005) = 1.3178611548 x 10^37 times = 13,178,611,548,000,000,000,000,000,000,000,000,000 times = umpteen gazillion times.

I think that either I or the author of this thread has made a mistake, because I do not understand how the laws of probability would allow that many successful lines of text, if "... they have still only produced 1/18,718,157,355,362 of the possible..." lines of text.

685 posted on 08/31/2003 11:53:20 AM PDT by Voice in your head ("The secret of Happiness is Freedom, and the secret of Freedom, Courage." - Thucydides)
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To: mykej

You are confusing correlations. The concern here is about an individual cell’s entropy. The individual code information per cell, or per codon, does not increase—it can only decrease as the plant or baby ages.


686 posted on 05/09/2008 7:37:39 AM PDT by Target Zero
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To: Target Zero

Hi everybody,

This thread is fascinating. There is so much in it. But there is at least one thing missing or at the very least not discussed enough. Why there is no more evidence of the evolution? Before I start, I want to say that I would want to be an evolutionist because it seems so logical! But the theory of evolution have to stand on his own legs. Even if there is no other good scientific solutions doesn’t make it valid by default!

So my point is that there is not enough intermediate species in the fossil records that we’ve found so far. My main argument is that I suppose that for every species that did appear in our fossil records we should have at the very least one intermediate specie or more. In some case it should be a lot more than one! Just take the example of the whale, the elephant, the giraffe or the man. In each case it could be argued that a lot of iteration had been needed to arrive at what we have today. Some of these iterations will have produced new species. Even in the case where those iteration will not have produced new species, a lot of variability will have been seen. Take the neck’s giraffe, how many intermediate “mutant” would have been needed to arrive at this point. The elephant trunk is an other example of a large number of intermediate “mutant” to arrive at this very complex organ. The blue whale is an other example of an extreme number of intermediate “mutant” to arrive at such an extraordinary animal. I write mutant because I don’t want to define all of those intermediate creature as new species as I don’t really know if it is the case or not. An other example is there is no link between Eohippus (a small dog-like animal that existed 50 million years ago) and its descendent Mesohippus (a sheep-sized animal that lived 30 million years ago).

The fossil records is mostly constituted of species that are not intermediate, or precursor for other species. Of course, it could be argued that we don’t know that yet. I agree with that. Where I diverge is if we do believe in evolution, we should found a greater diversity of fossil that we have found up to now. In fact, we should find mostly intermediate species, or at the very least a lot more diversity in what we’ve found. It seems based on articles that I’ve read that they are at least 5 millions species and maybe up to 100 millions species on our planet today. If for every specie that we have we have at least one intermediate or more, where are they?

Most of the time, specialist argue of the relative rarity of fossils. The special conditions needed to have fossils are few and far between, so that explain the relative dearth of fossils and especially the absence of missing links between them. I propose the exact opposite, if we need an intermediate specie or more for each one that we have today. It should be easier to find intermediate species. A corollary finding could be why today we do not observe more of these intermediate species. In fact, it could be argued that every living creature are intermediate species. But if it is so, the fossils records are not there to prove it and our day to day observation are short of concrete examples. So how can you prove evolution, when you can’t prove it based on fossil records or actual observation. I don’t like math that much, but lets say that 10 millions species exist today, and let’s say that the earth had 3.5 billions years to produce them. It means that we should produce a new specie every 350 years. Of course if we have 50 millions species it means a new species every 70 years. But since we need at least one intermediate specie to produce a new specie, because an intermediate specie will maybe have no practical use of the new mutation (an half trunk for an elephant or an half neck for a giraffe) we need an intermediate form or a new specie every 35 to 175 years. Of course, since very few of the mutation are beneficial. Maybe less than 1 in 1000 are beneficial if you believe what the the article below says

http://74.125.47.132/search?q=cache:z7g_arS600QJ:www.detectingdesign.com/Presentations/Mutations.ppt+benefical+mutation+versus+bad+mutation&hl=en&ct=clnk&cd=1&gl=ca)

It means that we should observe a lot more mutation that we observe today. Since those mutation would produce some exterior change, as the trunk of the elephant, we should observe mutation every 12 to 60 days or so. Of course, it will be very difficult to observe those because there is just too much data. But for the casual observer the fact seem to contradict the observation. I have read a lot on this subject and so far I have see no proof of an actual new specie under the sun. More to the point we have a lot of extinct species in the fossil records that would prove that we need more new species from evolution than less. An other way of saying that is we should observe more variation in mutation and more creation of new species as we have seen up to date.

An other strange fact is some species does not seem to evolute at all. The Coelacanth did not change a lot for 410 millions years (Wikipedia). Shark are an other example of a species that did not evolute for a great period of time. So it is putting a greater pressure on the rest of the biosphere to produce more new species and thus mutate more rapidly. This problem of actual observation of evolution is not new. Even Darwin admitted it in 1859, when On the Origin of Species was first published, he described the lack of transitional fossils as “the most obvious and gravest objection which can be urged against my theory”. Some have tried to explain this with some new theories about evolution to explain this absence of observable fact. They call it punctuated equilibrium and even some preeminent evolutionist are critical of it

http://en.wikipedia.org/wiki/Punctuated_equilibrium

That theory have been created in part to explain the absence of transitional form of life in the fossil records. But it my opinion, it does not matter if new species are formed rapidly or not as they’re should be always more transitional form of life as definite one. And for those of you who don’t like my English, forgive me as I am french .

Cheers!


687 posted on 12/30/2008 9:13:42 PM PST by Djut
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To: gfactor

17 Billion galaxies, each with 17 Billion planets, each with 17 Billion monkeys typing a line a second for 17 Billion years and still the odds are basically impossible that such a result would occur. And that is a very simple result when compared to even the most basic organism. Not to mention the fact that he threw in the monkeys, typewriter, planets and paper... It is pretty conclusive that the complexity required for our system to exist rules out the possibility of it occurring randomly.


688 posted on 02/17/2009 2:38:37 PM PST by tinbud
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To: Southack

ping


689 posted on 02/12/2010 4:35:44 PM PST by BrandtMichaels
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