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:
1
Shakespeare wasn't a random process...
For the ones who say "but it is an INFINITE amount of monkies" I say, but you do not have an INFINITE amount of time to work with, nor an infinite amount of matter. The universe, as incrediably vast as it is, is FAR to brief and tiny for life to have arisen by chance. You DO NOT have an infinite number to work with. The numbers you have are huge, but are as nothing compared to the scope of the problem.
As for the crowd who insists "but it is not random, their are rules", I say this- If rules, then a Rulemaker. And if the Rules say that new Phylums, classes, orders and families can arise by chance, then we should be able to create new versions of these things BY generating those chances (inducing mutations under (intelligent in this case) selection pressure). We can't, so if there are rules, one of them seems to be that their are limits to the amount of change that can be produced by chance mutations and selctions pressures.
That's how it works in this example. It's not a perfect evolutionary analogy, because our example here is working towards a specific goal - a particular sentence - whereas evolution via natural selection doesn't really have a goal in mind.
If order is derived by chance from nothing then mustn?t we assume that each try is completely unique and in no way connected with any other attempt? Isn?t this very meaning of randomness?
Let's walk through it. First, we need an environment. And to experience some sort of evolutionary process, our environment has to have selective pressures - that is, some traits will be more helpful for survival, and some will be less helpful, and some will be downright dangerous for creatures that have them. Imagine a dysfunctional creature that drowns every time it rains, and you'll see what I mean.
So, for this little thought experiment, we want an environment consisting of a chains of letters, 41 letters long. And we further want an environment where chains that are more like the final product have an advantage over chains that don't. And the chains that aren't much like the final product will have a disadvantage, and will die and go away.
So, we start with a random string of letters created by spinning the big genetics wheel. Now, as this is a random process, the odds that we'll get the final product right at the start are pretty damn long, as this article rushes to assure us. But the odds are, that we'll get a string of letters out that has at least one or two letters in the right place.
Now we have a chain that has a slight resemblance to the final product. These few letters in the right place are an adaptive trait - they are preferentially replicated in the next generation. What that means is that those letters are (almost) automatically replicated in the next generation - after all, if they weren't, the offspring would die, right?
So, come the next generation, we have a chain where a few letters are already in place, and since that's an adaptive trait, those letters get passed on to the offspring - the next chain. And then we spin the big genetics wheel yet again, but not for all letters - some letters are passed on from the parents. So we spin and generate random letters in place of the non-adaptive letters. And we find that one or two of the new letters are in the right place, in addition to the one or two that we had from the last generation.
Keep this up, and after a few generations. you'll have the final sentence. And it won't take trillions and trilions of years, either. If you programmed a computer to do it for you, you'd have the final product in probably less than 60 generations, and almost certainly less than 100.
It is a random process, but some random products are more successfull than others. That's what I'm talking about, and that's why this article is dead wrong. Period.
How can a random process accrue 'data' to achieve some eventual state when said state is supposed to be an unknown?
Well, that's where the "million monkeys" analogy breaks down ;)
There's no selective pressure in monkeys typing randomly, so there's no reason for them to eventually produce "Hamlet." If we imagine a selective pressure - e.g., we reward monkeys that can produce things a little bit like "Hamlet", and shoot the monkeys that type gibberish, we'd have a selective pressure. And then we up the bar a little bit by rewarding the few monkeys that can produce something somewhat like "Hamlet," and shooting the monkeys that only produce stuff a little bit like "Hamlet." And then we up the bar again by rewarding monkeys that produce stuff that's a lot like "Hamlet" and shooting all the lesser monkeys.
Keep that up for a while, and you'll get "Hamlet" out of a monkey soon enough ;)
Seen on a bulletin board at Arizona State University back in the 60's-
The monthly meeting of the Flat Earth Society will present the movie "Around the World in 80 Days"
Your comment is irrelevent. At the very least, the math shows an event that couldn't happen, ever. The final resulting statistical probability is even greater number than the total number of electrons in the universe.
Well, then you believe in predestination and all in encompasses. Shakespeare was born of a man and a woman who produced a son with talent (on loan from God! :-)), the son didn't get run over by a dung wagon at six years old, but might have. He didn't get bubonic plague at nine years old, but might have. He didn't break his leg on the playing field and miss his first day of writing class, but he might have. He didn't etc. ad nauseum.
Either we're all random processes with chance and free will shaping our lives and works, or we're all automatons of the universal God. Which is it? FR threads accumulate posts in the six figure range debating this issue.
Glad to know that your mind is so vast and all encompassing that you actually know what random is with regard to the whole of creation.
Precisely! Neither is evolution.
And it is a completely meaningless number. It has nothing to do with evolution or the origin of DNA.
I see no mathematical proof of either of your assertations.
Which is?
Hey, this is a math thread. If you don't like the numbers in the article, then feel free to post your own calculations for the self-formation of the first DNA.
It isn't a question of having different numbers. Your premise is wrong. You are calculating the odds of a random process and infering a meaning relating to DNA, but DNA formation isn't a random process. It's a meaningless excercise.
I see no mathematical proof in your mathematical proof. My math didn't go beyond fourth semester calculus and linear algebra, but I'm pretty sure that not even (17^9)*(17^9)*(17^9)... quite qualifies as infinity or even the known number of cell divisions since the beginning of creation.
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