Skip to comments.A Tiny Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]
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:
"They're like Napoleon's army in Moscow. They have occupied a lot of territory, and they think they've won the war. And yet they are very exposed in a hostile climate with a population that's very much unfriendly."
"That's the case with the Darwinists in the United States. The majority of the people are skeptical of the theory. And if the theory starts to waver a bit, it could all collapse, as Napoleon's army did in a rout."
PER OFFSPRING. Some individuals have more offspring than others.
But we are talking about neutral mutations. 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.
Furthermore, it's extremely misleading to say that the 50% chance is "set in stone" -- this implies that if you have two offspring, you're guaranteed to have one with the allele and one without. This is, of course, false. Each new offspring is a "roll of the dice", and *both* could end up with the allele -- or neither. Drift happens when an allele "gets lucky", through the roll of the genetic dice.
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. Therefore, again, Neutral mutations will not spread. The statistics which you keep claiming prove it show the exact opposite.
Genetic drift comes about as an inevitable result of the fact that possessers of a given allele will happen to be more or less successful at having children (by chance) than individuals which don't have the allele.
The statistical chances are the same and will even out over several generations that is why neutral drift is false. Let's remember that you only have one mutation, one single individual able to spread it. Let's also remember that the laws of statistics show that allele frequency will not change except with selective advantage. 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.
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. Furthermore, it's extremely misleading to say that the 50% chance is "set in stone" -- this implies that if you have two offspring, you're guaranteed to have one with the allele and one without. This is, of course, false. Each new offspring is a "roll of the dice", and *both* could end up with the allele -- or neither. Drift happens when an allele "gets lucky", through the roll of the genetic dice.
Playing the body-count game does not change the argument. People are what they are, and adopt the theology or ideology that justifies what they want to do anyway. Or, in the case of truely evil people, they twist or pervert ideas to fit their ends.
On the one hand, yes that is true- some people want to love and serve God. Others want to negociate with Him. still others ignore Him. The choice one makes says a lot about the person.
OTOH, it is also false. I have seen people change. I have done a little changing myself, as the flesh dies and the Spirit renews.
The 'body count game' is not a game, but a cite of historical fact documenting my contention that Christianity has been the greatest benevolent power in human history.
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."Or:
(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)
"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."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.
(Goodenough, Ursula in Genetics, 2nd ed. Harvard University 1978, p. 798-800)
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.
You must be very proud...
Oh, did you get your Nobel Prize yet?!
< /MOCKING >
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.
"Random" simply means unaided by any intelligent bias.--Post 81
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.
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.
"Feedback" implies intelligent intervention into the process. Is that how you want to say that the first DNA came into being?
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.
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.
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).
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.