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

Nutters.org ^ | 13-Dec-1995 | Brett Watson

[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:

[general_re]

'm not so smart, so it may be that you're using "proof" in some esoteric sense which I don't comprehend, but if I invited you over to my house to observe my driveway, which you found littered with 50,000 pennies, all of which were facing heads up , would you not test my statement that "I flipped 'em that way at random" by multiplying probabilities to gether to arrive at a vast sum?

For me, it would depend on what you told me as I rolled up to your house. If you said "I flipped 'em all at once, and they all landed heads-up at once, just by random," I might be suspicious. I'd figure the odds of such a random event and probably conclude that you were one lucky guy fellow who I should get to know better ;)

If, however, you said to me "I flipped them a series of times in a way designed to mimic the iterative nature of natural selection in an evolutionary process," why, then I'd say to you "Good show. Nice work - I bet you're surprised by how fast you got them all to land heads-up." And I'd conclude that you were a remarkably thoughtful fellow who I should get to know better. ;)

Evolution is an additive, iterative process. It's not really analogous to flipping a bunch of pennies and crossing your fingers, no matter how much some people would like you to think that.

[gore3000]

You've hit on the right answer, but nobody's paying attention. There's no fitness check. If we posit an environment with selective pressures, where a sentence that is more like the final sentence is favored over a sentence that is less like the final product, then we will very, very quickly arrive at the final sentence - within 40 or 50 generations.

That's the Stephen Dawkings explanation for the possibility of evolution. Unfortunately, like most of what he says it is absolute nonsense, not science. A gene is essentially a code for performing a function. It can either perform it or not. There is no middle ground. There is no feedback because until the whole gene is created (there's that word again!) there is no function, where there is no function, there is nothing to test, nothing to give feedback about.

[general_re]

Except that there is a middle ground. Dysfunctional traits are selected against. Adaptive traits are selected for. And traits that confer neither benefit nor penalty are neither selected for nor against.

You're essentially falling into the logical fallacy of the excluded middle, where, according to you, genes are an all-or-nothing deal. All it takes is some slight improvement in some trait for it to be advantageous - you don't have to go from totally blind all the way to full-on 3-d color vision to gain an advantage. Just being able to tell the difference between light and dark gives you an advantage over the blind.

[gore3000]

>You'll never model everything that was going on in the pre-biotic earth. It was a long time ago, and no experiment or supercomputer will ever be big enough. A hundred billion non-random, literate monkeys wouldn't be enough.

In your attempt to discredit an opponent, you show the impossibility of evolution! Are you switching sides? You are clearly showing the impossibility of abiogenesis. Are you going to start attending Church to give thanks to your Creator?

[Tolerance Sucks Rocks]

Sounds like the Million Monkey March is coming to town!

[gore3000]

Nobody requires DNA formation to be a random process.

Really? Care to explain to us what a single piece of DNA does? Care to explain to us how a single piece of DNA can perform the miracle of say providing a species with hearing, eyesight, legs, etc.? This needs to have happened for man and other living things to have descended from a single celled bacteria.

[gore3000]

Funny how Creationists accept, what do they call it, micro-evolution. Especially since micro-evolution is the same thing as Evolution.

Christians accept that God made species able to survive in the world. They do not accept the atheist belief that species, the world, the universe was created by random chance.

They have a point though, a very good point. Has anyone seen a bunch of trees build a house? Purposeful complexity does not arise at random.

Micro-evolution is not the same as evolution. Finches with large beaks and finches with small beaks are still finches, they are not monkeys, they are not even parrots, they are finches. People of white skin are still humans, people of black and yellow skin are still humans. Evolutionists would like us to believe that new more advanced, more complex species arise through micro-evolution, but this is not the case. All that micro-evolution does is change some small characteristic of the species, it does not create new more complex functions which is what is needed for new more complex species to have arisen which is what the theory of evolution asserts.

[Doctor Stochastic]

The posted article had no computations or discussion about DNA. It only had comments which didn't have anything to do with the rest of the article.

[Doctor Stochastic]

"Random" simply means unaided by any intelligent bias.

This means that naturally occurring bias doesn't rule out "random", of course. (Is this your definition of "random"?)

[Quix]

You really seem to think your response illustrates rational thought and applicability to his math? . . . . to reality?

Astounding!

None are so blind as those who WILL NOT see.

[Doctor Stochastic]

Keep in mind also that if life arose by chance on earth, the chances that it arose anywhere else is the square of the chance that it arose by chance on earth.

Completely incorrect. Proof is left to the reader.

[gore3000]

"You're essentially falling into the logical fallacy of the excluded middle, where, according to you, genes are an all-or-nothing deal. All it takes is some slight improvement in some trait for it to be advantageous - you don't have to go from totally blind all the way to full-on 3-d color vision to gain an advantage. Just being able to tell the difference between light and dark gives you an advantage over the blind.

I do not deny that there can be improvements on a gene. I do not deny that random mutations can cause improvements to some particular functions. What I do deny is that totally new genes with totally new functions can arise at random. That evolution requires that this have happened is beyond doubt. Clearly there are thousands of more functions in a human or even in a cat than in a single celled bacteria. For these thousands of new functions new genes, not just slight modifications to old genes were clearly required.

[mtg]

I believe the saying that an infinite number of monkeys, with an infinite number of typewriters, can in fact recreate any piece of literature...

It's impossible for there to be an infinite number of monkeys.

[Doctor Stochastic]

How would you get a non-uniform, non-random probability distribution without intelligent bias?

I'm not sure what you mean by non-random here, but it's trivial to get non-uniform distributions. Beta decay is exponential in time, not uniform. Ortho and para hydrogen form in various mixtures depending on temperature, 75% to 25% at room temperature, not uniform.

[Doctor Stochastic]

You can't. You die (as an indivitual.) Selection works on pheontypes, mutation and evolution works on genotypes. You might ask how tuberculosis bacteria survived to develop the genes necessary to resist antibiotics. Some didn't, obviously.

[Doctor Stochastic]

...jumping at least grom genus to genus,...

Is this an escalation in the definition of macro-evolution? It used to be denial that new species could form, is it now the denial of new genera? Or kingdoms?

[mlo]

Nobody requires DNA formation to be a random process.

Really? Care to explain to us what a single piece of DNA does? Care to explain to us how a single piece of DNA can perform the miracle of say providing a species with hearing, eyesight, legs, etc.? This needs to have happened for man and other living things to have descended from a single celled bacteria.

How do those questions relate to DNA formation?

[general_re]

What I do deny is that totally new genes with totally new functions can arise at random. That evolution requires that this have happened is beyond doubt. Clearly there are thousands of more functions in a human or even in a cat than in a single celled bacteria. For these thousands of new functions new genes, not just slight modifications to old genes were clearly required.

I love it - they were "clearly" required. As though asserting it will make it so.

Let's talk about traits for a moment. Fully developed traits like your cat has, but an amoeba doesn't, don't just spring forth, sui generis, fully-formed and ready to roll, and nobody but you is asserting otherwise. Rather, they are the cumulative effect of thousands of tiny improvements - tiny improvements which you yourself freely admit occur.

This is, after all, why it's an evolutionary process, and not a miraculous one. ;)

[Doctor Stochastic]

Take the sequence 11011100101... formed by concatenating the integers (base 2). Writing it as: 1,10,11,100,101,... makes it easier to see the construction. Take 5-bit (as in the above article) or 8-bit ASCII or another coding and this sequence will generate the works of Shakespeare. So will almost all (in the mathematical sense of almost all) other sequences.

The rub is that these sequences will also generate the works of Shakespeare with one mistake, and another copy signed by Gorky, and another copy having Doctor Stochastic instead of Hamlet. It will also have the works of Gorky signed by Park. (This is good for evolution but not for literature.)

[medved]

The probabilistic arguments against evolutionism boil down to this. Every single kind of complex creature which has ever walked, flown, swam, crawled, or slithered on the face of this Earth would require beating near-infinite odds to have evolved; the probability is a 10'th - 20'th order infinitessimal. Now, a reasonable person might could at least listen to a theory which demanded one or two probabilistic miracles in the entire history of the Earth, but a theory which demands an essentially infinite series of such violations of probabilistic laws, i.e. one such probabilistic miracle for every kind of creature, living and extinct, is clearly beyond the pale. That stands everything we know about mathematics and probability on its head.