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:
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.
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.
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
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.
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...
A polypeptide of length 100.... ~0.0
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.
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.
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).
"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.
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.
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.
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.
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.
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