Posted on 03/05/2002 9:45:44 PM PST by Southack
This is part two of the famous "Million Monkeys Typing On Keyboards for a Million Years Could Produce The Works of Shakespeare" - Debunked Mathematically.
For the Thread that inadvertently kicked started these mathematical discussions, Click Here
For the Original math thread, Click Here
Wait, wait. Both of you are over-restrictive.
Here's the problem - you're changing the terms of the analogy away from what it is to something else entirely. The point of the Hamlet example is that "fitness" is defined as closeness to the actual text. Now, by that standard, "To fly or not to fly" is less fit than "To by or not to by", because it's farther from the actual text, even though it arguably "makes more sense." But "making sense" isn't part of the original analogy, and the only effect of inserting such a restiction is to artificially pump up the odds against the final text being produced.
You're inserting a restriction that doesn't exist in the original, and for which I can see no good reason to insert at all - this idea that it has to "make sense" to an imaginary audience. Further, using single-letter substitutions, there's no guarantee that you can get from a given random string to the final product at all if each intermediate step has to "make sense". Finally, if we start with a random string to see whether we can get to the final product, you've set it up in such a way that we're dead in the water right from the start - what are the odds that some random string will "make sense"? Does the semi-random string (BX@# *&uyb 37(*FDb9s (WEJKhbec x3&^@b76&@vxb3 "make sense"?
Of course not. But by the original rules, it doesn't have to "make sense" to anyone - it just has to be a string that randomly mutates in order to move closer to the actual text, passing the mutations that are more fit from one generation to the next. Really, by what standard do we judge whether a particular genome "makes sense"? It doesn't have to be pretty, or elegant, or whatever - it just has to survive and reproduce. That's all - the Shakespeare example Dawkins proposes is already far more constrained than nature is. Dawkins has to get from "A" to "B" to produce a definite, fixed final product. Nature has no such constraints - it just has to go from "A" to "somewhere".
You've overloaded the analogy in such a way as to destroy its usefulness, and the final result is that you're not really beating up Dawkins's example at all, so much as your own construct.
In Dawkins's example, "fitness" is defined as "being closer to the original text". "Fitness" in nature is a bit more slippery - essentially, we can define traits in terms of their adaptiveness to their environment. If a trait is adaptive, it is more likely to be passed on than a trait that is dysfunctional, for the simple reason that creatures who possess adaptive traits are more likely to survive than creatures burdened with dysfunctional traits.
And of course, dysfunctional traits can be a relative matter. Consider a pack of predators, some of which are slightly nearsighted, and some of which are very nearsighted. Now, in such an environment, being slightly nearsighted is probably going to be advantageous, compared to being very nearsighted, even though neither animal has what we might call "good" vision. And over time, if better eyesight leads to more successful predation, and it's not hard to imagine that it might, then the animals with "better" eyesight will be better fed, and tend to live longer and produce more offspring than their weaker-eyed counterparts, in spite of the fact that even the animals with "better" vision aren't exactly possessed of incredibly good eyesight. It's sort of like the old safari joke - if you and I are walking through the African veldt, and a lion comes upon us, I don't really have to be faster than the lion in order to get away. I just have to be faster than you ;)
So it's all relative. But what happens if we toss two completely different traits into the mix? Imagine that we have an environment where there are two large predators competing for the same food - the tigers, which have excellent eyesight, and the bears, which have an excellent sense of smell. Assuming their abilities are approximately equivalent in other ways (for the sake of argument), which trait will be "better"?
Of course, there's just no way to know that in advance. Both traits will give the respective animals the ability to detect prey over distances, but which one will be "better" is something that you'd pretty much have to wait and see. You could make an educated guess, but that's all it would be. Basically, in the natural world, "better" and "more fit" have a way of defining themselves, since they're dependent on the environment in which an organism lives. For example, if the area is particularly foggy, good eyesight won't be as helpful as a good sense of smell. But in some other environment, good eyesight might be more adaptive than a good sense of smell. And so forth...
But here's the problem - Dawkins's analogy is only useful insofar as it illustrates how quickly the process converges to a solution when "adaptive" traits are preserved from one generation to the next. But it is limited insofar as actual natural selection isn't restricted to a particular solution the way the analogy is. So if you want to qualify it by having the final product "make sense", it's a better analogy if you allow for any result that "makes sense", not just the text of Hamlet.
So if you want to give your process a knowledge of what are valid words, and a knowledge of grammar and syntax such that valid sentences are preferred, I think you could pop out perfectly grammatical sentences given a process of mutation, selection, and reproduction. It would be a rather complex evaluation of fitness, and we'd probably have to ditch criteria like "beauty" as being insufficiently objective, but I think it could be done.
True, but once you exceed the assumed (or inferred) age of the universe (by many many times) it becomes meaningless does it not?
From that perspective, the obvious answer is "yes."
However, I've never seen anything to convince me that there is a finite age for the universe. That is to say, I would submit that has always been here...
From the human perspective, though, it's easy to become fixated on a "beginning" and "end," because we're used to watching the beginnings of life (childbirth), death, creation and destruction of things... But the matter doesn't get created or destroyed, only changed in it's basic form...
Obviously, this is a philosophical question- and one which (admittedly) I'm not as well-prepared for. After all, I've always avoided philosophy classes like they were a plague!
But from a scientific perspective, we've yet to see any evidence that there was ever a ***beginning*** to the universe...
Your thoughts?
Well, that depends on what we mean by "randomly selects", doesn't it? There's no planning ahead by the evolutionary process - it doesn't "store up" traits on the theory that they might be useful someday. It's all about what's adaptive right now. If mutation is random, then adaptive/dysfunctional/neutral traits will land at random (well, not exactly - dysfunctional mutations are far more common than beneficial ones, but anyway) among creatures, and therefore the creatures that are better adapted are essentially "chosen" at random. Could be robins that inherit a mutation for slightly better eyes, or it could be blue jays just as easily. The only pattern that exists is that creatures in competitive environments that are better adapted tend to survive and flourish better than creatures that are less well adapted. Which particular creatures those are, are essentially "chosen" at random. If it's robins, it's robins, but it could have just as easily been the blue jays.
Of course, some traits will prove to be beneficial in a wide range of environments. Bears survive and flourish by being generalists - they can tolerate a wide range of environments, and can subsist on a wide range of foods, which allows them to adapt to environments as radically different as the jungles of Malaysia and the Arctic circle. But that trait isn't adaptive in all environments - there used to be bears in Africa, but not any more. The competition was too fierce, and all available niches were occupied by specialists. As generalists, that put bears as a competitive disadvantage - no matter where they turned, some more specialized creature had an advantage in that particular niche. They aren't superpredators the way the big cats of Africa are, nor are they as good at finding plant foods as the large African herbivores are. So they died out, because the traits that made them successful elsewhere left them at a disadvantage in Africa.
And not to put too fine of a point on it, but having a large brain is the sort of generally adaptive trait that leads to success in a wide range of environments ;)
So, why not say that in our literary model, some randomly generated texts are--take your pick, either more intelligible, more beautiful, more popular with theater-goers, more profound.
The reason I wanted to avoid things like "beauty" as a criterion is that beauty will tend to be in the eye of the beholder. Much as I like "Hamlet", I prefer "Richard III" or "Macbeth", personally ("Life is a tale told by an idiot, full of sound and fury, signifying nothing"). But if we can come up with some criteria where there's no question about who's a winner and who's a loser, we can make that work instead.
Isn't this the same game as going from "good" to "evil" in one-letter moves, but infinitely harder, no matter how many millions of years intervene? Is this story really believable?
The problem I have is that you're still inserting this requirement that every intermediate step be as "sensible" as the starting and ending products. Unless you can persuade me that this requirement is somehow analogous to how natural selection operates in populations, I don't see the necessity of putting it in there at all. There is no similarly analogous requirement in nature, only that the intermediate form be more fit than its predecessor - "fitness", again, being defined as distance from the end product in this case. If that's how we define fitness as our criteria for selection, what does it give us to add some other criterion, particularly when it appears to me to be completely artificial?
What do get when you run the expansion of the universe backward?
Hell, we don't even know (given the astronomical limitations faced by observers of stellar phenomena) that the universe is expanding. The data suggests this, but suggestions and fact are often two distinct things...
Simply put, we don't have enough data to point to a beginning, any more than we have data to say there was a God, or "creation" in the biblical sense. Nothing there to comment on...
Seriously, there are few concepts in astronomy more thoroughly established the the expansion of the universe.
What part of "It might infer a central tendancy to matter... But that does not point to a "beginning" for the universe or matter or time..." do you NOT understand?
What he understands is that it's not as speculative as you make it out. We aren't talking about infering tendencies. We are talking about observations and measurements, and the principles of physics.
I defy you to find a respectable physicist other than Hoyle who would agree with this statement. I know nothing of beginnings and would agree that science knows nothing of beginnings -- but expansion is as established as any observed fact in nature.
Because we're already assuming from the beginning that survival is a matter of fitness, right? Fitter creatures will tend to survive and flourish better than less fit creatures. And here, we've defined fitness as the distance from the original text. So, it then follows that as creatures become more fit from generation to generation, their survival becomes more likely from generation to generation. If our original random starting string "survived" long enough to produce some superior offspring, there's no reason to believe that those superior offspring won't also survive - after all, they're more fit than the parent was.
I hope this is not too opaque - what I want to get at is that, in this example, "survival" and "fitness" travel hand in hand already. In effect, they are two sides of the same coin - if descendants are more fit than their ancestors, then by definition, they are more likely to survive than their ancestors. Once you define "fitness", you've effectively taken care of "survival" as well. That's why I don't see the necessity of inserting further restrictions about making sense.
As for a general intelligence have superior survival value--nah, not necessarily. Some of the most successful life forms (bacteria) have little intelligence.
Oh, it's not the only way, to be sure. There are archaebacteria that are essentially unchanged in billions of years. But I can't help but look around me and think that a certain large-brained species has been remarkably successful ;)
But genomes aren't like that. The actual number of functional genes in the human genome is not definitively known, but the best estimates are that it consists of around 30,000 genes, some consisting of a few dozen base pairs, and some consisting of thousands and thousands of base pairs, with the rest falling somewhere in that range. But the full human genome consists of about 4 billion base pairs. So it turns out that, IIRC, around 95% of the human genome is not functional - it exists in the form of introns. But these introns are more than just random genetic noise - they are bits and pieces of old genes from precursor organisms that have been retained, which isn't a surprise, I think. Nature is parsimonious, and there's no penalty for retaining them, so why not? And the way that functional genes (extrons) are differentiated from introns is that they have special genetic markers at the beginning and end - "START" and "STOP" codes, essentially.
So there's a critical difference right off the bat - while a bit flip in software is almost uniformly disastrous, it turns out that changes can accumulate within introns with no effect at all, positive or negative. Since the vast majority of the genome is non-functional, changes in those non-functional portions don't harm or help the organism. And mutations can accumulate within those introns without harming the host organism.
So, if you can picture mutations occurring within those introns, and gradually accumulating, then you can have a fully functional gene spring forth after a while by simply mutating the start and stop codes - what was junk becomes a (hopefully) working gene if the markers change to indicate it as a working gene.
And it turns out that this is mostly how new traits are added. Every once in a while, a mutation to an existing, functional gene will result in some improvement, but like software, such changes turn out to be disastrous far more often than not. But changes can accumulate within the introns far more readily, because there's no penalty for mutations within introns. And then the right mutation flips the switch, so to speak, and a new gene (or a non-functioning old gene, of course) is turned on. Of course, it's also likely that this new gene could be dysfunctional itself, and hence will not be an advantage. In which case, if it proves to be a serious disability to the organism, survival becomes less likely in competitive environments, and the new gene is selected against. But every once in a while, such a new gene, or recycled old gene, will prove to be advantageous, and that trait will be selected for, and propagated throughout descendant organisms.
So, that's the first key difference that springs to mind - software doesn't have an analogous genetic "junkyard" from which to draw new parts, and recycle old ones. Virtually all hits to software are fatal, whereas the majority of mutations to genomes make no difference at all, because they land in unused parts anyway.
Let's pick up human intelligence, which somehow got into your/our posts. So far as we can tell, there is not a photomorph increase in human intelligence--our ancestors of 200,000 years ago are thought to have the same brains as us, and therefore the same raw intelligence as us. What the heck did they need that potential brainpower for? How was that intelligence "evolved" by the exigencies of the environment? Put another way, why did 1%, or .01%, of cavemen have the potential for understanding number theory?
Go back further. "Cro magnon" man is thought to have arisen about 120,000 years ago, and is anatomically identical to modern man - it is modern man, essentially. And if you had a time machine, and brought back a representative from back then, and you cleaned him up and gave him a shave and haircut, probably the only thing that might be unusual about him would be his height.
But, if you go back further, to about 1.6 million years ago, you find the first remains of Homo erectus (the so-called "Java man"). And H. erectus had a noticeably smaller cranial capacity. The current average cranial capacity is about 1350 cc worldwide (with a wide range of capacities considered "normal"), as compared to about 1150 cc on average for early Cro magnon specimens, and about 900 cc for early specimens of H. erectus, and around 1150 cc for later specimens.
So now, take one more step back, to the first known specimen of the genus Homo, and you find Homo habilis. Dated to approximately 2 million years ago, H. habilis had an average cranial capacity of around 750 cc.
So what's the point? Well, there's a well-established lineage, in terms of brain size, and thus intellectual capacity. But there's no reason to think that early hominids had the capacity to understand particle physics or number theory. Indeed, the earliest Australopithecines (A. afarensis and A. africanus) had cranial capacities in the 400-500 cc range, only slightly larger than a modern chimpanzee, at around 390 cc.
But the ultimate question is, why intelligence at all? The thing is, though, asking that question is like asking "why wings?" or "why lungs?" There's no metaphysical "why" that science can satisfactorily answer, but the mundane answer is that basic reasoning capacities must have conferred an advantage to creatures that possessed them, versus creatures that didn't. And even the most limited of problem-solving skills is still better than nothing, I think. So as small improvements in intelligence propagated and were selected for, small improvements to the small improvements would also have proven advantageous. And so forth, and so on. If you look at the very earliest hominid specimens, and then compare them to modern humans, it looks like a quantum leap. But when you see the progression, it looks much less miraculous. This is the hominid answer to the creationists argument of "what good is a partially formed trait?" Well, the "half a brain" of H. habilis is better than the comparative nothing of A. afarensis, even though it's not as "good" as what we have today.
So that's a long-winded answer to both hominid intelligence and transitional forms, with the single added point that every organism, unless it goes extinct, is a transitional form. It doesn't make any sense to think of evolution as having an "end", so thinking of what's out there today as the "end product" is misleading, and thinking of everything that came before as "transitional" is equally misleading. Any step in an evolutionary process is an illustration of a transition - no matter what you are right now, natural selection is operating right now to transform your species into something else in the distant future. We are transitional forms, put simply.
So, without too much work, it ought not to be too difficult to imagine a process similar to hominid brain development also operating in the transition from land mammals to whales. And somewhere on this thread (or other threads, I know for sure - if you can't locate it, you can ping him back and I'm sure he'll be happy to point you to it), VadeRetro has posted what evidence there is for whale evolution, and the process and steps present therein.
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