A Second Mathematical Proof Against Evolution [AKA - Million Monkeys Can't Type Shakespeare]

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

So now you must argue that evolution occurs in introns. Two points: (1) since introns are nonfunctional, how can they be selected for? Lots of bit flips can happen in the noise parts of the DNA, but if they are noise, the odds that by chance something useful will turn up and become activated are rather long; and (2) it is not true that software has no equivalent to introns. Programmers frequently insert English-language comments in non-functional parts of the code to help future programmers understand how the code is supposed to work--from the compiler's point of view, that is pure noise--what are the odds that bit flips in the notes section of a program will create functional code that, because a IGNORE WHAT FOLLOWS flag accidentally gets deleted, becomes functional. Stop to think about the consequences of arguing from introns: you have now abandoned evolutionary theory, because by definition natural selection cannot be the engine that shoves incremental intron changes along a path of somatic change.

Do now you must argue that evolution occurs in introns. Two points: (1) since introns are nonfunctional, how can they be selected for? Lots of bit flips can happen in the noise parts of the DNA, but if they are noise, the odds that by chance something useful will turn up and become activated are rather long...

I don't argue that all evolution occurs in introns, only that introns form a ready source of new genes. Remember that I also said that mutations can occur in fully functional genes as well, but as with all mutations, the odds are that they will be harmful, rather than beneficial. But still, that's probably how much of evolution takes place - changes to functional genes, rather than introns, despite the costs. Most mutations to functional genes are harmful, but a few are beneficial. In re-reading my previous post, I am probably guilty of overstating how much occurs in introns, but it does happen.

Anyway, it's not until those introns are activated that natural selection operates on them. That's why they can accumulate changes over time with no effect at all - until they become activated, they are neither functional nor dysfunctional, and thus confer no benefits or penalties to the organism carrying them until such time. And when they are activated, and begin functioning in some manner, that's when they are subject to selection pressures - not before. And if they never get activated, then they are never selected for or against.

And remember, I never said introns were "noise" - they aren't random, they're leftovers, genetic flotsam, junk parts, remainders of your ancestors. Now, some of it has become noise over time due to accumulated mutations (so-called "genetic drift"), but much of it is readily identifiable.

(2) it is not true that software has no equivalent to introns. Programmers frequently insert English-language comments in non-functional parts of the code to help future programmers understand how the code is supposed to work--from the compiler's point of view, that is pure noise--what are the odds that bit flips in the notes section of a program will create functional code that, because a IGNORE WHAT FOLLOWS flag accidentally gets deleted, becomes functional.

Except that I seem to recall that preprocessors and compilers routinely strip comments out and replace then with whitespace before compiling. CPP does it - most do it unless explicitly told not to, IIRC ;)

Anyway, point taken. But, I went and looked it up - it's actually about 97% of the human genome that is non-functional, not 95%. Even if you call cpp with the "-C" option, 97% of your executable is not going to be comments, unless you compile "Hello, world" with your life story in the comments. And it probably won't run anyway, since cpp treats preserved comments as tokens - it'll give you some wacky behavior, anyway ;)

It's also a little more flexible in the genome - DNA encoding is not a purely binary language. Instead of "on" and "off" for a single bit, the functional part of a gene is a three-letter "word" (where the "letters" are nucleotides represented by A G, C, and T), and there are many redundant codes. TATA, CAAT, and GGGCGG are all codes for "promoters" - "START" markers for transcription. That's three different codes that mean exactly the same thing. The first two are four letters long - find me two four-byte sequences in your compiled code that only share the second byte in common (order matters here) AND mean functionally the same thing. And then find me a six-byte sequence that also means the same thing without sharing any bytes at all with the first two ;)

Stop to think about the consequences of arguing from introns: you have now abandoned evolutionary theory, because by definition natural selection cannot be the engine that shoves incremental intron changes along a path of somatic change.

Oh, I don't think so. Mutations can accumulate in introns with no selection pressure at all, true. But it's when (and if) those introns become active that the selection pressures come into play. And because of that, intron changes don't necessarily have to be "incremental". Changes to functional genes are incremental (or deadly), but because introns can drift arbitrarily with no penalty until they are turned on, the change can be very much wholesale when they are turned on.

"Mutations can accumulate in introns"??? The odds of "accumulating" a useful variation are too long without some mechanism (like natural selection) to cut down the odds. If twenty letters are needed for one feature or sub feature, the odds are roughly n raised to the 20th, where n is the random probability of one correct letter. It's worse than that--any one of the correct letters can be erased by a subsequent random bit flip. Arguing from introns gets you nowhere at all, whether introns are 3% of the genome or 97%. The math just doesn't work. And as you acknowledged (you now tell me in a moment of weakness), arguing from extrons doesn't work, because incremental changes are very likely to be harmful, and because it is very difficult to see (even conceptually) how there could be a path of helpful or at least benign incremental changes leading to a somatic change of any significance. One of the greatest discoveries in the 20th c has been the discovery of DNA, and the full implications of that discovery are still being absorbed. I would predict that future historians of science will say that the existence of DNA showed that Darwin was largely wrong (though in an interesting and helpful way). Mountains and oceans are analog, and one can view them as photomorphing over millions of years. Life is digital, and applying the photomorph concept to life just doesn't work (except in a low-level sense, like feather colors or other simple variations). A few posts back, you gave a little rehash of the ancestry of the human species, but you didn't address the central point, which is why roughly 200,000 years ago homo sapiens sapiens came onto the scene with a brain much more powerful than hunter gatherers needed. Think about this--99% plus of that primitive crowd had brains capable of reading, but alphabets had not yet been invented.

Nope, the math doesn't work that way. That's only true if you're predicting the odds of a particular variation. Since there are many possible enhancements, there are many possible successful variations, and hence the odds of producing something useful are higher than you indicate here. Which, BTW, is also one of the critical flaws of the article we are ostensibly discussing here.

The math just doesn't work. And as you acknowledged (you now tell me in a moment of weakness), arguing from extrons doesn't work, because incremental changes are very likely to be harmful, and because it is very difficult to see (even conceptually) how there could be a path of helpful or at least benign incremental changes leading to a somatic change of any significance.

Yes, very likely to be harmful. But every once in a while, it can be beneficial. It doesn't have to be often, and it really isn't - once in a million transcriptions, there's an error in transcription, and once in every million errors, it proves beneficial. Given time, that's enough. Given enough time, what seems impossible really becomes inevitable.

One of the greatest discoveries in the 20th c has been the discovery of DNA, and the full implications of that discovery are still being absorbed. I would predict that future historians of science will say that the existence of DNA showed that Darwin was largely wrong (though in an interesting and helpful way).

If anything, I think it's quite easy to demonstrate that molecular biology has confirmed the basic outlines and structure of Darwinism by showing the fundamental interrelatedness of all life on earth. You have to go back a long, long way to find the common ancestor that you share with the oak tree in your yard, but the evidence for such a common ancestor is right there in your DNA. And the tree's ;)

A few posts back, you gave a little rehash of the ancestry of the human species, but you didn't address the central point, which is why roughly 200,000 years ago homo sapiens sapiens came onto the scene with a brain much more powerful than hunter gatherers needed. Think about this--99% plus of that primitive crowd had brains capable of reading, but alphabets had not yet been invented.

Alphabets are one of the many side-effects of evolution. The evolution of the hominid brain conferred advantages to the holders of those brains, of which alphabets are only one. Part of basic problem-solving is the ability to engage in abstract reasoning, to think about and consider contingencies other than what is present in the immediate moment. That is, the ability to comprehend past events and draw patterns and conclusions from them, and to consider future events in light of past ones. I don't know about you, but to me that sounds an awful lot like what writing and alphabets are all about. ;)

Given that, why is it so hard to think that alphabets were an inevitable result of brain development?

Sorry to disagree, but your math is wrong. Imagine a twenty-page document into which random alphabetic strings are typed. Imagine the memory in which the document resides is bombarded with X-rays, causing bit flips. The odds are astronomical that any particular limerick would turn up somewhere in the document. But, you say, there are many good limericks, and even more bad ones. The odds are still astronomical that a limerick will turn up in our "evolving" document. The fact is that the proportion of useful bits of code in the probability space of a living being's genome is very small. Moreover, "useful" has to be defined in terms of what might be useful to the current state of the life form's DNA, so the oddsa re even smaller. Finally, even if some recognizably useful bit of DNA turns up by accident in the introns, there must be a chance event that somehow turns an intron into functional code, and puts that code in the right place in the DNA sequence. You're whistling in the dark. As for what the existence of DNA has proved--I would say DNA only shows the common descent, not why life forms changed. Natural selection explains small incremental changes, but not macro-changes. Some OTHER force explains macro-changes.

But again you're artificially restricting the possible outcomes. If we consider the chances of producing anything cogent - a limerick, a haiku, a sonnet, a knock-knock joke, a single grammatical sentence - then the odds are better than just producing a limerick. And who's to say which of those is more useful?

Moreover, "useful" has to be defined in terms of what might be useful to the current state of the life form's DNA, so the oddsa re even smaller.

No, I think you're still shortchanging the situation. I can, with a little bit of thought, come up with dozens and dozens of ways to improve the human body, for example - it's not a perfect machine. And there are surely hundreds or thousands more that I just can't imagine. The fact that there are so many possible improvements ups the odds significantly. For example, here's a really short list, right off the top of my head:

Imagine that your optic nerve was placed slightly differently, so that you didn't have the blind spot that you do now. Imagine that the tendons and ligaments of your knees were slightly rearranged, such that a sharp blow to the outside of your knee was much less likely to cripple you. Imagine a slight modification to your cellular membranes that rendered you immune to a particular virus. Imagine a small change in the density of the cilia of your inner ear, such that you were able to hear sounds across a greater range, and of a higher pitch than you are now able to. Imagine one small new protein that confers a greater resistance to certain types of cancers. Imagine a slightly more efficient digestive process, such that you could survive with a caloric intake 10% lower than you can now. Imagine a slight change in the chemistry of the junctions of nerve cells such that the nerve conduction velocity was increased, and hence your reflexes were faster than before.

And on, and on, and on....give me some time, and I'll come up with lots and lots more. And there will be potential improvements that simply exceed my ability to imagine them, either because they are improvements that exist in other organisms, but that I am not familiar with, or because they'd be completely new and unique. There's really more than just limericks possible, I think. ;)

As for what the existence of DNA has proved--I would say DNA only shows the common descent, not why life forms changed. Natural selection explains small incremental changes, but not macro-changes. Some OTHER force explains macro-changes.

Actually, I agree with your first sentence there. DNA shows common lineages, and gives us a picture of a family tree. But as for why life forms change over time, for that you have to look at the environments in which they lived and died.

As for the second part, what is a large change but the accumulation of many small changes? Remember the steps in the development of the human brain? If you take only the "beginning" and "end" brains - Australopithecus and us - then the change looks like a huge quantum leap. But when you see all the intermediate steps, it becomes a rather orderly progression, and the end product no longer looks like something that just sprang forth, sui generis. It wasn't an accident that I picked that example ;)

First--"quantum leap" literally means very short hops, and shouldn't be used in the way you used it. Second, you are stuck with the photomorph concept, and that's why you don't get it. Let me try a third metaphor. Say you and your son are asked to compete in a soapbox derby, but are given only 48 hours to come up with an entry. Fortunately, your garage is well stocked with all the necessary tools and hardware. Moreover, you and your son are mechanical geniuses. It is certainly plausible, based on these assumptions, that the result of the 48 hours of work will be a derby winner. Now add another constraint. Every hour, or half hour, or minute, your vehicle in its state at that time will be taken out on the track. If it doesn't make a circuit, you are disqualified. You protest against the new rule: most of my engineering ideas will take a while to implement, and it's not fair to test the vehicle while I'm in the middle of one of my ideas--the idea may be great, but the vehicle may be temporarily inoperable. I think that's how it is with all these nifty improvements you suggest to the human body. If you could actually code these changes (without harming some other useful process), more than a few bit flips would be needed. So the path to the improvement probably will pass through (and necessarily pass through) intermediates that don't run, or are hopelessly defective in some significant way. According to evolutionary theory, genetic change is entirely the product of chance bit flips, so changes to the DNA happen piecemeal, and every slightly modified life form is required to survive in its environment, just as the referees hauled out the unfinished soapbox racer every hour, half hour, or minute against your protests, onto the track.

First--"quantum leap" literally means very short hops, and shouldn't be used in the way you used it.

Actually, it means "an abrupt change, sudden increase, or dramatic advance", so I think I pretty well said what I wanted to say.

In any case, now we're off to the soapbox derby. Just speaking generally, you're still falling into the teleological trap of think of evolution in terms of goals and end-products - either you have a working racer, or you have a pile of junk. Either you have a working clock, or you have a bunch of gears and springs. Either you have a fully-formed human, or you have nothing. Either you have a fully-formed bird, or you have nothing.

And it just doesn't work that way. There is no "goal" such that you can declare the intermediate steps unfit and therefore unable to have existed. Over time, a group of smallish dinosaurs accumulate changes and improvements such that they gradually become birds. Over time, a group of smallish primates accumulate changes and become early humans. Nowhere in there is there the sense that we either have fully formed book-reading humans, or we have nothing - which is exactly what I am expected to draw from the soapbox racer analogy. It's an evolutionary process, not a quantum leap from a pile of junk to the finished product. Every creature is transitional. Every creature is a "final" product. Organisms exist of themselves, according to what they are right now, not according to some standard of what they might be someday.

It's just not a very good analogy. You want to judge an organism's fitness against what it could become in the future. But it's precisely because there is no "goal" that you can't do that. All of the organisms on the planet today are still subject to selection pressures - evolution is continuing, even as we speak. All of the plants and animals around you are transitional forms that in millions of years, whose descendants very likely to bear little or no resemblance to what they are today. Now, if your analogy held true, you ought to be able to tell me what they will become, and we could then thereby judge which of the organisms that we see around us can't possibly exist ;)

But it is a teleological example - it is entirely goal-driven. If I sit down with a pile of parts and an instruction booklet, I know the final product is going to be a soapbox derby racer long before I so much as pick up a hammer. And Dawkins's Hamlet metaphor, while a good analogy about how information is transmitted in evolutionary systems, is not a perfect analogy for evolution for exactly the same reason - we know that the final product must be Hamlet. But we don't know that, and can't know that, about living things.

But what we can do for living organisms is to sit down and look to see what we can find out about those intermediate forms. Evolution is not goal-driven - "what good is an intermediate, less-than-fully-functional step"-type questions betray something of a misunderstanding of the process. The ultimate goal of hominid brain development was not big-brained creatures like us, just as the ultimate goal of small-dinosaur evolution was not birds, for one simple reason - there is no ultimate goal. None. What we are today is as much accident as anything else. Same for the birds. Same for everything else that lives, breathes, walks, swims, or crawls.

Even if Archaeopteryx couldn't fly as well as modern birds, or Australopithecus couldn't think as well as we can today, or whatever, they were still an improvement over what came before. And as a slight improvement, with a slight advantage, they survived when others did not. They didn't plan it that way - no one planned it that way. It only looks like that.

I can't stress that enough - there is no goal, no finished product where we can say "done." It just looks that way - where we are now, and what we are now, is pure happenstance. Had the dinosaurs not gone extinct, you and I might very well have been large-brained reptiles, having this same discussion, and trying to avoid falling into the trap of thinking normatively and teleologically, that how we were was somehow the natural order of things and the way things must be, that the world was designed for our sole pleasure. Re-run life's grand experiment again, and we might not even be vertebrates - we could have just as easily been large-brained worms, given the right set of conditions.

Any goal-driven analogy is necessarily imperfect - Dawkins's just as much so as anyone else's.

I hope you understand that I'm not doing this just to be difficult - while I can play devil's advocate as well as anyone, I hope to give as full of an explanation as I can of why I am skeptical of all of these analogies.

All of that may be true...and nonetheless it would be utterly irrelevant. The analogies assume an actor and intentionality, but actors and intentionality are not critical to what the analogies are getting at. EVEN IF someone was deliberately trying to edit the ur-Hamlet into the final Hamlet by small changes, there is no plausible path through intermediates that are of the class "plays." EVEN IF someone was deliberately trying to modify DOS a line at a time or by bit flips, there is no plausible path through intermediates that are of the class "software programs." EVEN IF someone was deliberately trying to build a soapbox racer, there is no plausible path through intermediates that are of the class "self-propelled vehicles." Each of these tasks would be much harder if there was no actor but rather random changes. So, if the analogies show that piecemeal changes are utterly implausible assuming actors with intent, a fortiori the analogies show how ridiculous the claim would be assuming random changes. Your objections are a strawman.

Your objections are a strawman.

No. What is becoming increasingly clear, however, is that I am failing to adequately impress upon you the nature and relevance of my objections. For that, allow me to apologize and take another whack at it.

The analogies assume an actor and intentionality, but actors and intentionality are not critical to what the analogies are getting at. EVEN IF someone was deliberately trying to edit the ur-Hamlet into the final Hamlet by small changes, there is no plausible path through intermediates that are of the class "plays." EVEN IF someone was deliberately trying to modify DOS a line at a time or by bit flips, there is no plausible path through intermediates that are of the class "software programs." EVEN IF someone was deliberately trying to build a soapbox racer, there is no plausible path through intermediates that are of the class "self-propelled vehicles."

I fear that I have been less than clear if that is the impression I have given about my skepticism. My objections are not based on the fact that there is an actor in these analogies, although that is a clear difference between them and evolution via natural selection. My objections are based on the fact that, as I have been saying all along, they are all goal-driven (with the possible exception of the software analogy, which I think could be made viable with some tweaking), with known outcomes.

Now, by goal-driven, I don't mean that there is someone working to make something - I don't particularly care about that for the moment. What I mean is that the universe of possible outcomes in all these cases is restricted to a single "end" product. The pile of parts can only become a soapbox racer - it can never be an airplane, or a bicycle, or a tractor, or a car, or a unicycle, or a skateboard. Just a soapbox racer - nothing else. And even if we allow for all forms of vehicles as possible outcomes, that is still too restrictive - it can never become a computer, or a wingback chair, or a fire hydrant, or a piano, or anything other than a soapbox racer.

But evolution via natural selection isn't like that. It doesn't work that way. Essentially, what you are doing is taking a particular path and saying "look how difficult it is to go from 'A' to 'Z' and all points in between." But evolution via natural selection doesn't work that way - it's not trying to go from "A" to "Z", it's just trying to go from "A" to somewhere. Anywhere will do.

Take a primitive single-celled organism - there is no force trying to make it into a tree or a worm or a lizard over a billion years' time. It just happens that way - everything you see around you is an accident, that could have just as easily been something else. There was no set path from blue-green algae to oak trees - it just looks that way.

That's what I'm trying to get across - unlike building a soapbox racer, there is no set path for evolution, where you start with a pile of parts and end up with a specific something. Any living thing at all is a valid outcome, whether it's like the things we recognize or not. No matter whether it's a tree or a slug or a mushroom or a cheetah or a human or something no person has ever set eyes upon - any living thing at all is a valid possible outcome.

Evolution via natural selection is not limited in the valid possible outcomes - that is my objection to all these analogies. Any analogy that starts off by assuming a particular final product is flawed by definition, because natural selection has no such fixed outcome. There is no requirement that it end up at a particular "Z".

That's the gist of my objections, and hopefully it is somewhat clearer now. I will have to think for a while to see if there is some other way that I can express it, as I have obviously not done a good job up to this point.

Geez, we're talking about how a new somatic feature can (if it can) be the consequence of incremental bit flip type changes, which is natural selection says should be the result. Therefore, we are looking up close and in detail at ONE slight but significant somatic change in an organism, which by definition stays otherwise the same during this time span. The A and the B don't matter--it could be ANY new somatic feature. And in the transition from A to B (through a path A1, A2, A3...) it would MAKE NO SENSE for the organism to grow wings, or gills, or anything else that radical--we're talking about how the living creature comes to state B, which is not that different from state A. And the ONLY constraint I'm putting on the transition is that every intermediate generation SURVIVE and be a functioning creature, not some nonfunctional freak with half the genes for a new kind of heart, or something else. The point is that while the natural selection theory of somatic change is plausible for features dependent on 1 or 2 genetic bit flips (like hair and skin color), more involved features involving many more SIMULTANEOUS coding changes CANNOT BE EXPLAINED using the bit flip (or as I put it the photomorph) explanation--because it is difficult to see what the intermediate steps could be.

Low. How many bits of information in what you're talking about? If low, the segment you are describing could be a basic "word" in the DNA. Then, you would be saying nothing more than somone who shows you the 26 letters of the Roman alphabet, plus punctuation, and claims that all the great literary works are in that set. "Useful" in what context? Let me take a different tack. The software metaphor I've used is more than a metaphor. What I mean by that is that DNA and human-made software are objectively indistinguishable. (That doesn't mean that I necessarily think that someone programmed life on Earth, whether that person would be called God or an alien life form, although those are potential explanations for the facts.) I challenge all readers to find an objective basis for saying that DNA is fundamentally different from man-made software. I say that, objectively speaking, our physical manifestations appear to be as complex carbon-based computing machines "programmed" through DNA. (Whether that is ALL that we are is another discussion.)

How many bits of information in what you're talking about? ... "Useful" in what context?

I should have been more specific. Let's say it's on the order of 100 amino acids giving 20^100 different amino acid strings so which is about 2^432, so 432 bits. By way of comparison, let's say there are 10,000,000 different extant species and that each has 100,000 different proteins. Then an upper bound on the size of the collection genome of all life is 10^12 or about 2^40.

By useful, I mean a new function that is advantageous to an organism. Let's say, for concretenes sake, that it enable the organism to eat something it couldn't before.

With those revisions, doesn't your intuition lead you to conclude that a useful frame shift mutation in the gene for such a protien is so unlikely to be obvserved it is essentially impossible and will never be observed (this a mode of argument used by Dembski et al).

I challenge all readers to find an objective basis for saying that DNA is fundamentally different from man-made software.

I think a criterion could be formulated in terms of complexity. Good man-made designs are simple in a variety of ways whereas evolved stuff only has to work, it doesn't need to be easy to understand.

I say that, objectively speaking, our physical manifestations appear to be as complex carbon-based computing machines "programmed" through DNA.

You'll get no argument from me on that score. The question is whether the program is evolved.

I challenge all readers to find an objective basis for saying that DNA is fundamentally different from man-made software.

Fundamentally speaking, software can be completely analyzed and its behavior predicted. It can, if it handles "events", timing dependencies that make its behavior difficult to predict -- but these dependencies can be seen without running the software, and a good programmer can ensure graceful failure modes.

The behavior of DNA in a living system cannot be predicted. Changes to DNA do not have predictable outcomes, except in trivial cases where working units are transferred form one organism to another. You cannot predict the long term viability of living organisms, and you certainly cannot predict the viability of "engineered" organisms.

The inability to predict is similar to problems encountered in non-living systems. For example, it is impossible to say whether the solar system is stable (even assuming the sun would last forever).

Living systems go off track much faster than planetary systems. The effects of environmental change, coupled with the effects of competition, predation, and luck, make it unlikely htat a stable designed system could be created by any agency that was not omnipotent.

I challenge all readers to find an objective basis for saying that DNA is fundamentally different from man-made software.

I think a criterion could be formulated in terms of complexity.

DNA may look like a computer program, but it runs on a non-deterministic OS.

Among its other pecularities, it benefits from read errors. I know of no software program that can recover from an uncorrected bit error in an instruction. As a result, Mainframe computers and high reliability servers have error-correcting memory. NASA uses multiple computers with voting.

But DNA -- as a system -- ignores errors and if it survives at all, incorporates changes permanently.

All this is a fancy way of saying that DNA has no mission -- not even replication, because it doesn't care if it replicates correctly. We see the results of replication and attribute purpose, but there is no purpose.

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