Pedro deals with the “one in a million” fallacy

3 December 2007

Pedro over at Way Of The Mind has recently posted about the fallacy often used by creationists to argue that “life could never happen by chance”. Go and read it, then come back, and I’ll give you my take on it.

Back? Ok.

One of the things that Pedro didn’t address is his post was the notion of the passage of time. He’s quite correct in saying that rolling a dice however many time to get 66666666666666666666 is extremely unlikely in any realistic lifetime, but that’s if we think that all life came about because of a lucky of a one-time hit. Thankfully, that’s not what evolution (in the timescales offered by the evidence of geophysics, palaeontology, cosmology and the other long-time sciences) predicts.

So, carrying on with Pedro’s dice analogy, and written using simplified terms from the language of biology, I decided to knock-up this little Ruby program (because it’s relatively easy to read, even for a non-programmer) to demonstrate this:



AVAILABLE_GENES = (1..6).to_a
WINNING_GENES = [6]
SUCCESSFUL_GENERATIONS = 15
@genome = ""
@generations = 0
 
while @genome.length < SUCCESSFUL_GENERATIONS
  @generations = @generations + 1
  @point_mutation = AVAILABLE_GENES[rand(AVAILABLE_GENES.size)]
  puts "Generation #{@generations}: " + @genome + @point_mutation.to_s
  @genome << @point_mutation.to_s if WINNING_GENES.include?(@point_mutation)
end
 
puts "Successful genome #{@genome} took #{@generations} generations."

I’ll explain a little about the program works here:

AVAILABLE_GENES is the range of possible “genes”, including both “good” (aiding to survival and reproduction) and “bad” (no surviving offspring) mutation possibilities (in this case, the range of values from 1 to 5)
WINNING_GENES is the list of “genes” that allows a generation of offspring to survive and reproduce (in this case, just 6)
SUCCESSFUL_GENERATIONS is the number of generations of surviving offspring that we want
@genome is the “genome” of the current generation
@generations is a counter to see how many generations that we’ve tried so far

When we run this program, it adds “mutations” (in the form of dice rolls) to a “genome”. If the new mutation is advantageous (i.e. a ‘6′) and aids in survival and reproduction then the gene is added to the genome. If the gene is bad (not a ‘6′) then that generation dies without reproducing, and the current genome remains the same.

Each generation, it tries to “reproduce” with a new gene mutation, the successful survive and the unsuccessful remains the same

Of course, this program is (deliberately) incredibly simplistic (it doesn’t take into account populations, retrograde mutations, what constitutes a successful gene, predators, environment, etc.) but it should serve to illustrate the basic point that a successful genome can be arrived at quite easily over time given enough opportunity to reproduce.

Running the program, what do we see? I’ll save the full listings, but I’ll run it a few times to see what we get (further runs are truncated for space):

Desktop:$ ruby dice_simulation.rb 
Generation 1: 2
Generation 2: 4
Generation 3: 6
Generation 4: 66
Generation 5: 661
Generation 6: 663
Generation 7: 664
Generation 8: 661
Generation 9: 661
Generation 10: 661
Generation 11: 662
Generation 12: 663
Generation 13: 662
Generation 14: 661
Generation 15: 665
Generation 16: 662
Generation 17: 665
Generation 18: 666
Generation 19: 6661
Generation 20: 6663
Generation 21: 6666
Generation 22: 66662
Generation 23: 66666
Generation 24: 666666
Generation 25: 6666664
Generation 26: 6666664
Generation 27: 6666665
Generation 28: 6666666
Generation 29: 66666661
Generation 30: 66666661
Generation 31: 66666661
Generation 32: 66666666
Generation 33: 666666661
Generation 34: 666666663
Generation 35: 666666666
Generation 36: 6666666665
Generation 37: 6666666664
Generation 38: 6666666661
Generation 39: 6666666663
Generation 40: 6666666664
Generation 41: 6666666666
Generation 42: 66666666661
Generation 43: 66666666663
Generation 44: 66666666663
Generation 45: 66666666664
Generation 46: 66666666664
Generation 47: 66666666664
Generation 48: 66666666661
Generation 49: 66666666665
Generation 50: 66666666664
Generation 51: 66666666663
Generation 52: 66666666666
Generation 53: 666666666665
Generation 54: 666666666664
Generation 55: 666666666665
Generation 56: 666666666666
Generation 57: 6666666666663
Generation 58: 6666666666661
Generation 59: 6666666666664
Generation 60: 6666666666662
Generation 61: 6666666666666
Generation 62: 66666666666661
Generation 63: 66666666666665
Generation 64: 66666666666661
Generation 65: 66666666666662
Generation 66: 66666666666665
Generation 67: 66666666666666
Generation 68: 666666666666661
Generation 69: 666666666666662
Generation 70: 666666666666665
Generation 71: 666666666666666
Successful genome 666666666666666 took 71 generations.

Desktop:$ ruby dice_simulation.rb 
Generation 1: 3
...
Generation 7: 6
Generation 8: 62
Generation 9: 63
Generation 10: 65
...
Generation 16: 66
Generation 17: 665
...
Generation 27: 666
Generation 28: 6663
...
Generation 42: 6661
Generation 43: 6666
Generation 44: 66664
Generation 45: 66662
Generation 46: 66665
Generation 47: 66666
Generation 48: 666662
...
Generation 55: 666666
Generation 56: 6666662
...
Generation 62: 6666666
Generation 63: 66666664
...
Generation 78: 66666666
Generation 79: 666666665
Generation 80: 666666662
Generation 81: 666666666
Generation 82: 6666666666
Generation 83: 66666666663
...
Generation 90: 66666666666
Generation 91: 666666666663
Generation 92: 666666666665
Generation 93: 666666666666
Generation 94: 6666666666664
...
Generation 97: 6666666666666
Generation 98: 66666666666664
Generation 99: 66666666666662
Generation 100: 66666666666661
...
Generation 107: 66666666666666
Generation 108: 666666666666665
Generation 109: 666666666666662
Generation 110: 666666666666666
Successful genome 666666666666666 took 110 generations.

Desktop:$ ruby dice_simulation.rb 
Generation 1: 6
Generation 2: 61
Generation 3: 66
Generation 4: 665
Generation 5: 665
Generation 6: 666
Generation 7: 6662
Generation 8: 6662
Generation 9: 6666
Generation 10: 66662
Generation 11: 66665
Generation 12: 66666
Generation 13: 666663
...
Generation 23: 666666
Generation 24: 6666662
...
Generation 31: 6666666
Generation 32: 66666663
Generation 33: 66666666
Generation 34: 666666663
...
Generation 42: 666666666
Generation 43: 6666666664
...
Generation 48: 6666666666
Generation 49: 66666666663
Generation 50: 66666666666
Generation 51: 666666666665
Generation 52: 666666666666
Generation 53: 6666666666662
...
Generation 75: 6666666666666
Generation 76: 66666666666664
...
Generation 84: 66666666666666
Generation 85: 666666666666662
...
Generation 88: 666666666666666
Successful genome 666666666666666 took 88 generations.

As we can see, each time we run this, we get different numbers for how many generations it can take to get a successful gene, and sometimes there are 10 or 15 generations without a successful mutation. However we can also see that, eventually, there are successful mutations that add to the genome.

Another thing to note is that if we increase the range of AVAILABLE_GENES to, say 1..9, it will usually take more generations to see the target genome come about. If, however, we add genes to WINNING_GENES (e.g. [1,6,8]) we will reduce the number of generations required.

In fact, in relation to the one-time hit that I mention above, that’s exactly what the creationists propose, and who could blame them for invoking magic in the form of creator-gods with something so unlikely?

My point? One way we can get to a specific genome is by *poofing* it into existence in one step. The other is by adding a little bit per generation over a long period of time.

While evolution doesn’t deal with trying to achieve a specific genome, I know which situation the science supports better.

No other posts are likely to be like this.

Related posts brought to you by Yet Another Related Posts Plugin.

Tags: bad arguments/logical fallacies, blog, code, creationism/intelligent design, evolution, evolution denial, science, simulation, technology

Comments

This website uses IntenseDebate comments, but they are not currently loaded because either your browser doesn't support JavaScript, or they didn't load fast enough.

41112 Responses2007-12-03+21%3A47%3A36nullifidian to “Pedro deals with the “one in a million” fallacy”

No Way on December 4th, 2007 4:20 am

I must say, this is a halfway decent treatment of the issue. Do me a favor, lets run the program with some real order of magnitude numbers and see how your computer handles it.

Also, while the computer is choking on that, lets try to figure out how the genome “knew” it had a beneficial mutation and why it began mutating in the first place.
No Way on December 4th, 2007 4:35 am

One more thing. could you please find me a ample supply of evidence (possibly fossil in nature) to show the existence of all these intermediary creatures?
nullifidian on December 4th, 2007 3:18 pm

@No Way

I was going to respond properly to your comment, until I observed the appeal to Kent Hovind that you posted on WotM. From that, combined with your comments here, I can only conclude that you have no idea what you’re talking about.

One thing you failed to note was that this was a (repeat after me) simple simulation, not a representation of an actual biological process.

As it is, I’ll just let you in on a little secret: where I work, I have access to several of the most powerful supercomputers in the world. If I so chose, and could be bothered and needed to rewrite this program in Fortran, and booked the CPU time needed, I could easily do so.

However, since you lied and didn’t supply a genuine email address, I can only assume that you’re not really interested in the terrabytes of data that would result, and hence I won’t bother. However, if you contact me again and pay for the CPU time and data transfer costs (just to know that you’re serious about asking for the favour) I’d be happy to do so.

I don’t think that showing you the evidence of intermediate forms would be worth my time. Since you think Hovind has good arguments, I’m not naive enough to think that any actual evidence is going to convince you of anything.

However, I will be gentle with your TRINITY rating, seeing as you failed to quote any scripture whatsoever. Kudos to you.
PJ on December 4th, 2007 6:00 pm

“…lets try to figure out how the genome â€œknewâ€ it had a beneficial mutation and why it began mutating in the first place.”

That is an impressive failure to understand anything about evolution by natural selection. Genomes obviously don’t need to ‘know’ that the mutation is beneficial – beneficial in this sense is defined entirely as resulting in increased numbers of offspring compared to other genes (fitness).

The question as to why the genome mutates can be answered mechanically – in that the copying mechanism of DNA/RNA is not 100% accurate and there can be damage to DNA/RNA. It can also be answered teleologically in that while a mechanism that is very innacurate will lead to a loss of fitness by the introduction of lots of errors, a mechanism that is not 100% accurate allows the slow accumulation of beneficial mutations.
TW on December 4th, 2007 10:09 pm

Good post. You were a lot more restrained in your reply to no way than i think i’d have been!

The creationist nonsense about probability infuriates me. How some people who claim degree education (or further) can be so clueless is amazing.
No Way on December 4th, 2007 10:38 pm

Seems I hit a nerve, sorry ;>

Your rant still says (to me at least) you have no true evidence.

PJ’s response was well thought out and written. My question for him is simple, what evidence exists for this and what scientifically based experiments can be performed to test it? Otherwise, this is just as scientific as ether.

I will also note that nobody offered evidence of intermediate species either living or fossilized.
No Way on December 4th, 2007 11:15 pm

Just one more thing.

The nature of the tone of your reply points out the flaw with humans being good because it is the right thing to do. I can’t wait until the genes that control our treatment of one another realizes that a limited number of attitudes are appropriate.

As for the simple simulation. I see it more as simple propoganda. That is why I treated it the way I did. Even if we wrote a fortran (or I could participate in up to seven other programming language choices) program and ran it on the computers either of us have available it still is only propaganda, proof of nothing other than our ability to write code.

To declare my ignorance is simply ignorant. You know nothing about me or my education. As for my trinity rating, let me help you out.

- I asked for some simple evidence and you responded with none. All you had to do was tell me about:

– A book (please not Dawkins, his arguments fall apart too quickly to even be fun),

– A concept to investigate that has some form of validation available for it (I know validation is an out-dated scientific concept but I still like it when I talk science),

– A fossil or statistically relevant link between a multitude of various species.

Now I ask you, which of us is baseless? Without evidence it is simply the one claiming to base their opinion on science.
nullifidian on December 5th, 2007 3:17 pm
@noway

Seems I hit a nerve, sorry ;>

Sorry, no, you didn’t. I try to respond to comments if I can.

Your rant still says (to me at least) you have no true evidence.

Sorry, again, it wasn’t a rant, and I’m not even sure what you’re alluding to: the original post, or my response to you. Either way, neither were rants.

PJâ€™s response was well thought out and written. My question for him is simple, what evidence exists for this and what scientifically based experiments can be performed to test it? Otherwise, this is just as scientific as ether.

I’ll let PJ respond to you directly then, of course if PJ so chooses.

I will also note that nobody offered evidence of intermediate species either living or fossilized.

Wrong. In my previous response to you I offered up links to three separate avenues of evidence, which you’ve obviously failed to either notice or look at, or you chose to ignore them.

As for a living example, may I offer up the coelacanth. Not that I expect this to convince you of anything.

The nature of the tone of your reply points out the flaw with humans being good because it is the right thing to do. I canâ€™t wait until the genes that control our treatment of one another realizes that a limited number of attitudes are appropriate.

Again wrong. Your assertion as to my “tone” is completely groundless. And, for my own curiosity, which gene or genes are these that are responsible for an appropriate response? To help you out, I’ll provide a link to the Human Genome browser so that you don’t even have to look for it yourself.

As for the simple simulation. I see it more as simple propoganda. That is why I treated it the way I did.

How you see it is immaterial: it was a simple simulation, whether you like the outcome or not. The manner in which you treated it (i.e. with bathetic sarcasm) is a red herring.

Even if we wrote a fortran (or I could participate in up to seven other programming language choices) program and ran it on the computers either of us have available it still is only propaganda, proof of nothing other than our ability to write code.

I don’t care how many languages you can program in: it’s irrelevent. I’m not interested in a pissing contest that you think you can win.

Of course, I wouldn’t submit this program to be run on an HPC, that would be a massive waste of compute cycles. However, there have been plenty of HPC simulations of biological processes, including evolution: 1, 2, 3.

If you wanted, I’m sure you could do something on your desktop.

To declare my ignorance is simply ignorant. You know nothing about me or my education. As for my trinity rating, let me help you out.

I never claimed to know anything about you or your education. However, since you seemed to be pimping a link to Kent Hovind as some kind of authority on evolution on WotM, I can only assume that you agree with him and his ideas. If you do not, you didn’t make this completely clear. Do you have a doctorate too, like Hovind? What discipline? What was your thesis on? Can I read it?

- I asked for some simple evidence and you responded with none.

Wrong. Again, I refer you back to the three links I provided in my first comment. Obviously the irony of linking to evidence while using the phrase Iâ€™m not naive enough to think that any actual evidence is going to convince you seems to have completely bypassed you. I hope you’re now able to see these links.

All you had to do was tell me about: – A book (please not Dawkins, his arguments fall apart too quickly to even be fun),

1) Why, is only one book required for you to totally and completely accept something? That seems like a rather poor way to inform yourself, but that’s just my opinion. I prefer to read as much literature on a topic as I’m able before coming to a conclusion, and I also like to give myself the option to change my mind if better evidence comes along.

2) I have no idea why you single out Dawkins. I can only presume that you have a preconcieved bias against him. Please, if you have evidence-based counter-arguments to those that you think “fall apart too quickly”, I’d be more than happy to read or hear about them.

As for books, allow me to point you towards:
- Your Body – The Fish That Evolved by Keith Harrison
- The Ancestorâ€™s Tale by Richard Dawkins (yeah, I heard what you said, but you don’t seem to have read this one…)
- The Origin of Humankind by Richard Leakey
- Dinosaur in a Haystack by Stephen Jay Gould
I’m sure you can find others if you cared to search.

Or how about some videos? Are they OK?
Again, I’m sure you can find more if you do a search or two.

Actually, I’ll also point you to the Wikipedia article on evolution. Even if you don’t read it (although it might be useful) there are plenty of signposts to further reading at the references section.

- A concept to investigate that has some form of validation available for it (I know validation is an out-dated scientific concept but I still like it when I talk science),

Aside from the 3 links I posted above? Sure. Why not read the entire of TalkOrigins, and perhaps some of the books and papers that are used as references therein. You might also want to do your own research using the literature available on JEB, OJOSE, JStor, PubMed or any of the other sources of scientific literature (this is a good list). Of course, you may need to have legitimate access to some of these resources. They offer shitloads of experiments you can do. Of course, they will usually require a laboratory and research specimens, and probably some kind of biological education so that you can understand the results.

If you have no experience (as you said, I don’t know you) of scientific literature this introduction might be helpful.

Of course, I would be remiss if I didn’t offer up the alternative sources of “evidence”, so here’s the Institute for Creation Research, Answers in Genesis, the Discovery Institute, the Flying Spaghetti Monster hypothesis, Rael and the reDiscovery Institute.

- A fossil or statistically relevant link between a multitude of various species.

Ah, I see you’ve moved the goal posts. First off you wanted an “ample supply” of evidence (even though you didn’t define what you meant by “ample” and I, as a starting point, gave you three). Now you want the same for a “multitude of various species” (again not defining what you mean by a “multitude”. As I noted before, I don’t think any amount of evidence is going to convince you, but at least I’ve tried.

I also note that you’re still lying about your email address. This does not bode well for me believing anything else you might have to say. But, I’ll let it go this time, although I would in future prefer a bona fide email address (which only I would see). Otherwise, I guess, I should just assume that it’s spam: spammers lie all the time.
PJ on December 7th, 2007 7:20 pm

“My question for him is simple, what evidence exists for this and what scientifically based experiments can be performed to test it?”

Well going through my points in turn, the issue of genes ‘knowing’ their are ‘beneficial’ (i.e. fitness) is definitional and thus tautologous – it is just what ‘fitness’ and ‘evolution by natural selection’ mean. For further information you could read an introductory textbook.

The vulnerability of DNA/RNA to damage, and the infidelity of copying mechanisms is very well attested and, again, I’d suggest a textbook for a description and references to the primary literature.

As for the teleological argument presented, there is ample mathematical/computational modelling on the evolution of mutation rates, and an experimental literature on mutation rates in various organisms under various circumstances. If you want to read about the studies try looking in google scholar.
TW on December 7th, 2007 11:48 pm

Null – you could turn this line of comments into a new post to give it some prominence.
nullifidian on December 9th, 2007 6:25 pm

@TW:

There’s enough craziness in the world, I don’t think I want to subject the world to more.
TW on December 11th, 2007 10:43 pm

Fair one… :-)