Bob's bad math?

Status
Not open for further replies.

Stone Mason

New member
In looking at today's BEL topic it pointed me to the http://kgov.com/did_life_evolve_0 Did life Evolve link. On the page it allows you to download a program that attempts to get the letters of the alphabet in sequence and it shows that it should take about 1.95 x10^24 years to accomplish the task with 100,000 attempts every second. (That is 26^26/365/24/60/60/100,000, but that isn't correct, it should be 26!/365/24/60/60/100,000 which is 1.28x10^14 years. That is still a really long time though. But for now lets assume that the bigger number is correct.) But there is a flaw in the reasoning which is applying a singular process to something that is fundamentally a parallel process.

For instance if you ran 1000 computers on the same task you would reduce the time to 1.95 x 10^24/1000 = 1.95 x10^21 years. Its still a big big number but as you can see the more computers you throw at the problem the faster it comes up with the right answer.

Doing some fast looking around the net, you can see that there is about 326,000,000,000,000,000,000 gallons (326 million trillion gallons) of water on the planet and that under optimal conditions that there can be about 1,000,000,000 single cell animals in a gallon of sea water. For simplicity lets chop that down to 1,000,000 on average, and that they reproduce once an hour. So how many years would it take for those cells to do a mutation that would create the 26 letter sequence.

1 Million x 326 million trillion x24 reproductions a day x 365 days = 2.83 x10^30. This means that it would take approximately 0.0217 seconds to hit the 26 letters in sequence.

Additionally the above example was just using cells. That is not really good because to get life started you would need to have self reproducing molecules first. So really you would need to change that from 1 million single celled animals in a gallon of seawater to 1.266 x 1026 molecules in a gallon of sea water. Now the bulk of that would be water, so lets just say that only 1 part per trillion is an organic-ish molecule that reduces the number down to 1.266x 10^14 per gallon. However the chemical reactions will be much more frequent on average then once an hour. But for the sake of being really conservative lets just say they have 10 reactions per hour. Cranking through the math it comes out to 1.266x10^9 times faster then in the above example.

Now the smallest self replicating molecule known is 32 peptides long. But there are only 4 letters in the sequence so that would also be faster since 32^4 is 1.84x 10^19 which makes this 3.3^17 times faster to reach than having to do the whole alphabet which could as we saw above be done in under 1/200th of a second.

So what does all of this mean? The experiment that Bob is proposing is based on a bad premise, i.e. that all of this stuff has to happen serially, not in parallel.

While researching some of the basics for this post I stumbled upon the following web site that goes into this kind of math in much more detail.
http://www.talkorigins.org/faqs/abioprob/abioprob.html
 

Stripe

Teenage Adaptive Ninja Turtle
LIFETIME MEMBER
Hall of Fame
that isn't correct, it should be 26!/365/24/60/60/100,000 which is 1.28x10^14 years.
It is correct. The chances of getting all the letters in the alphabet correct is 1 in 2626, not 1 in 26!.
 

Frayed Knot

New member
It depends on whether the program can choose any of the 26 letters for each position (so for example "ZZZZZZZZZZZZZZZZZZZZZZZZZ" would be a possibility), or if it takes the set of 26 letters and just re-orders them randomly. I didn't see any source code so don't know for sure which it does, but if they say it's 1 in 2626, then I assume they know which way they did it.

The real question is why anyone would think this has anything to do with evolution or abiogenesis.
 

CabinetMaker

Member of the 10 year club on TOL!!
Hall of Fame
I am not sure that the algorithm used us a valid model of evolution. I think that program attempts to get all 26 letters in order at the same time. That is not what evolution says. It seems that a more reasonable model how long does it take to get A in the first position. Now that we have A in the first position, how long to get B in the second position. Noe, given that A and B are correct, how long to get C. It is a propagation based on previous success. If Bob's program does not do that it is not a valid model and the results are meaningless and worse, they are misleading.
 

Stripe

Teenage Adaptive Ninja Turtle
LIFETIME MEMBER
Hall of Fame
The real question is why anyone would think this has anything to do with evolution or abiogenesis.
It has nothing to do with evolution. It has everything to do with abiogenesis.

I am not sure that the algorithm used us a valid model of evolution. I think that program attempts to get all 26 letters in order at the same time. That is not what evolution says.
You're right!

It seems that a more reasonable model how long does it take to get A in the first position. Now that we have A in the first position, how long to get B in the second position. Noe, given that A and B are correct, how long to get C. It is a propagation based on previous success.
On average that would take 26x26=676 iterations.

If Bob's program does not do that it is not a valid model and the results are meaningless and worse, they are misleading.
You need to go have a nice long lie down, I think. :chuckle:
 

Stone Mason

New member
It is correct. The chances of getting all the letters in the alphabet correct is 1 in 2626, not 1 in 26!.

Stripe,
You might have thought that it was a typo but the exclamation point after the 26 means that the number is 26 factorial. That is 26x25x24x23x22... all the way down to 1.
 

fool

Well-known member
Hall of Fame
So Stone Mason;
Twenty posts in under five years.
Tell us about that.
 

Stripe

Teenage Adaptive Ninja Turtle
LIFETIME MEMBER
Hall of Fame
Stripe, You might have thought that it was a typo but the exclamation point after the 26 means that the number is 26 factorial. That is 26x25x24x23x22... all the way down to 1.

Uh, yeah I know.

Your correction is unnecessary.

Just like most all the other posts in this thread. :)
 
Status
Not open for further replies.
Top