# Really Big Math Question

Calling all great mathematicians!

The not so infrequently discussed “Monkeys on a Typewriter” thread got me to thinking. There was a lot of mathematical heavy lifting in that discussion, so I feel confident in asking this.

I believe there were a few here on the board that had calculations that approximated the length of time it would take a million random letter-generating computers to produce “Hamlet”. Instead of “Hamlet”, I propose deoxyribonucleic acid; DNA in its present form. Slightly more complex than Hamlet, I know, but hey, ya gotta love a challenge!

Is there a way to determine the amount of time it would take for a single-celled organism to eventually “evolve” its way to the present state of life on the Earth?

It is important to keep in mind that we’re just going to start with a single celled organism, rather than try and comprehend the amount of time it took for said organism to arrive in a lifeless world…that’s a whole other calculation, and I haven’t the foggiest idea where to begin.

After we get to that, perhaps we could extrapolate it to include all the different forms of DNA that currently exist, as well as have ever existed…simultaneously.

I’m real good at thinking up ways to figure stuff out (and I’m sure there will be plenty who respond otherwise), I’m just short on the technical knowledge…like understanding the DNA strand of humans well enough or the processes involved in mutation, etc. There’s got to be a way to mathematically prove that it could have happened within the life-span of the Earth right? That should be great ammunition for all the Evolutionists out there, and would send all us Creationists scurrying back to our “faith-holes”.

I’m thinking we’ll need a few extra spiral-notebooks to handle the scrap paper needs.

Any takers?

Anybody?
Bueller?

Are you implying that each successive DNA strand is organized completely randomly, with absolutely no relation to its “parent”? Because that would be the best analogy to the “monkeys on keyboards” question.

DNA is, however, not completely random. That’s the major phenomenon that lets organisms pass on traits to their children. Thus the “monkeys on keyboards” “arguments” against evolution are flawed.

I am not trying to say that DNA is random. But, there is “chance” involved in which genes mutate in which ways, and how often they mutate, and how often said mutations are beneficial. Then you’ve got the problem of how damn many mutations it would take to get from amoeba to human. This takes time. I’m just looking for a “coulda happened” versus a “not likely from a mathematical standpoint”. I understand Evolution well enough to know that I’ve got a damn good point here somewhere, I’m just not sure if I know how to communicate it to others.

Know what I mean?

Right, because if evolutionists only had the random mutation model, we would be screwed. That would take many times the life of the universe for all of those base pairs to assemble together just so and make a higher life-form. Non-random selection is the thing that makes it all come together and that has nothing to do with the Monkeys at a typewriter problem.

All I’m saying is that it got me to thinking. I’m not trying to imply any sort of continuity between the arguments.

If I’m stupid enough to have made it seem that way, my bad.

Then why bring up the monkeys on keyboards argument at all?

The human genome only contains around 20-25,000 genes. If you assume each of them were there from the beginning of time, it would take far less than 6 billion years to evolve the right combinations of the human genome. Just look at how we selectively breed captive mammals over the course of only a couple centuries and realize life has been on this planet for over 10 million times that.

I’m not well-versed enough in evolutionary biology to tell you how long it takes to evolve each gene, or even if that process is well-understood.

OK…if you can’t follow this, I suppose it’s hopeless.

The thread about the monkeys got me to thinking. It was an intellectual stimulant. I understand that it is not directly related. However, the people involved in that debate showed significant mathematical ability. Hence, I wondered if there were a way to determine mathematically how organisms evolved. There is obviously a certain number of genes involved, a certain number of them changed over a certain period of time. Do you follow?

I intend no offense, forgive my offensive straightforwardness. But hey, it’s frustrating being misunderstood…look at all the teen angst!

[QUOTE=Ludovic]
The human genome only contains around 20-25,000 genes. If you assume each of them were there from the beginning of time,
QUOTE]

Ok, assumptions like that are dangerous. That defeats the purpose of the conversation entirely…also defeats the purpose of scientific method.

The only assumption I’m making is that we start with an amoeba, and only because it’s an entirely different and uniquely complex discussion that pertains to the spontaneous rise of life from lifeless muck.

AND, as far as I remember from high school biology, every organism on Earth does not contain the exact same DNA assembled differently…in other words, there aren’t a bunch of African Grey Parrot genomes floating around in our DNA strand just going unused and therefore keeping us human as opposed to birdy. Therefore, we have to say that a certain {something} occurred to get from one set of genomes to another, and that the {something} took X years to occur, and had to happen X times, and that of those times, X percent would be a beneficial change that led down the eventual path to human.

Does anybody follow me? Is there anyone out there with enough education to explain how this is entirely impossible to determine in the way that I am attempting?

I’ve got a very large and very complex computing apparatus working on this right now. So far, the outside estimate appears to be about 3.9 billion years.

You would be correct in your remembrance, but also remiss in not noticing that I said the exact same thing.

[QUOTE=echo6160]

Have you read Richard Dawkins’ “The Blind Watchmaker”? It’s been a while since I did, but I’m pretty sure some of what you’re thinking about is addressed. I believe he even wrote a computer program to simulate the process.

I think that may be AN answer to the original question, I just checked out the Amazon reviews.

Still, I think what I’ve got to do is go and get me an edjamacashum in biology, with an emphasis on genetics, then rephrase my question.

So everybody just hang on a minute, I’ll BRB.

Well the simple answer is that it took as long as it did.

Reality always trumps theory and math.

The problem is knowing how many variations are infeasible. For instance, it’s easy to know how many possible values there are for a set of n-base digits. Given 26 letters and the space character, I can tell you that there are 10[sup]27[/sup] possible combinations with a sequence of ten characters. But the grand majority of those combinations are meaningless.

Take for instance the fact that a 120-bit value can probably uniquely identify any document ever written by man, even though each individual one might be on an average of 2000000-bits in length. The amount of meaningful combinations for sequence is an amazingly small percentage.

But anyways, I believe though that something like 2% mutation per a generation (I have no idea where I got that from, but just to run with it.) By randomly sorting in 2% of a set for each shuffle, you’ll get an average loss of original DNA of:

100%
98%
96.04%
94.41%
etc.

To change out half of your DNA you would need:

50 = 100 * .98[sup]x[/sup]
0.5 = .98[sup]x[/sup]
log[sub].98/sub = x
x = ~35

So after 35 generations you “can” change out 50% of all the DNA at a rate of 2% mutation per a year. In reality, of course, there will be lots of back-and forthing for any one mutation-created trait due to the population cancelling each-other out, and probably a steady 2% would be prone to leading to unfit mutations, so those die.

Oddly similar to what I just wrote, but looking up The Blind Watchman and following the links, I found a page on an evolution-simulation by Mr. Dawkins:

This doesn’t do exactly what I think you’re looking for (it’s hard for me to see how anything could) but it is software simulation of evolution and it includes mutations, selection, and something resembling sexual reproduction. It has apparently produced some very interesting results which some might mistake for deliberate design. http://www.nis.atr.jp/~ray/tierra/

The answer is: there are lots of answers and none of them are right or wrong.

The present state was arrived at based on the beginning state and all of the states in between (e.g. environment, random mutations, etc.). There could be possible “earth histories” that would have increased the rate of variation in DNA substantially, or slowed it down. Even if we assume the same beginning state and all of the same intermediate state, we don’t know what those were. What was the exact chemical makeup of the atmosphere 750million years ago? How about the chemical makeup of fresh water on each continent 200million years ago? Of the oceans 50million years ago? Everything plays a part and our current state is just a by product of exactly what came before it.

Rather the writing Shakespeare, I prefer the example of mixing together a bunch of letters so they stick together randomly, with those who form valid English words being “viable” (and thus able to have offspring of their own, with “make” begetting “made”, “making”, “model”, “mode”, “machine” etc.) and those who don’t form valid English words being broken up and tossed back. After a few million shakes of the letter bag, I expect you’d have pretty much a near-complete English vernacular, which could be used to write Shakespeare.

As for the specific question of the OP, well, aside from our real-world example of ~3 billion years, the calculations of how long it might take are… pretty damn hard, actually.

Is the OP asking for the odds on producing the exact set of genomes we have today, or just for something of equivalent complexity? If you’re asking for the exact same set, then it’s pretty damn unlikely. But then, any other exact set is equally unlikely. It’s like me looking at a five-card-stud poker hand and saying “Wow, the odds of this hand are only 1 in 2,598,960!” It’s a true statement, and yes, those are some pretty long odds, but I don’t think it’s very impressive.

If, on the other hand, you’re asking for the odds for this set or any equivalent set, then you have to define what constitutes “equivalent”. In poker, this is pretty easy: Only three other hands are equivalent to 10H JH QH KH AH, but thousands of hands are equivalent to 9H 9D 2H AS 5C, so even though those two hands are equally likely, the former one is considered much more significant. In evolution, though, it’d be a lot more difficult to say what’s “equivalent to” our own world and history, and until we answer that, we can’t say how likely it is.