Justin:
Shouldn't take long to put this whole thread to bed. The math I used simply estimated the entropy increase in the FIRST GENERATION.
I calculated S. This math will not calculate continually changing entropies from generation to generation because that it is not S, but deltaS. You are assuming:
W = (41469.4 + 1.6)! / (41469.4)!(1.6)! --- 3.66 x 10^173494 / 2.14 x 10^173487
W = 1.71 x 10^7
Boltzmann's math:
S = K log W, S = (1.38 x 10^-23) log(1.71 x 10^7)
deltaS = 9.98 x 10^-23,
This is not correct!
To get deltaS you then have to take that first generation down the lineage:
deltaS = S(final) - S(initial)
As you can see, since the study showed a steady accumulation of 1.6 mutations per generation, entropy will NEVER begin to decrease, so this should communicate to you that you're probably not doing something right.
Paul:
quote:
The figure of 1.6 is NOT directly related to the figure of 41,471. The first is the estimated number of deleterious mutations per generation. The second is the number of nucleotides examined in the study. Jerry's use of the figures has no basis in the study.
Ok, I just went with nucleotides rather than the triplex. Had you rather I divide the nucleotides into codons and calculate it that way? Doesn't matter to me as you STILL are going to see rising entropy.
quote:
Because the factorial operation (denoted by '!') is only defined for integers.
I would teach it this way too if I were instructing high schoolers but it ISN'T true and especially so when we get into higher math. I was simply showing whether entropy was positive or negative. When absolute accuracy is necessary, this is not a problem either as there are many excellent programs out there which will accurately calculate fractions of integers using the natural log of a continuous probability distribution. In fact, if I'm not mistaken (couldn't tell with a brief Google) this is what the Windows calculator does.
quote:
If you chose to look at beneficial rather than detrimental mutations you would find that each beneficial mutation increased the entropy.
You can't show me a half dozen beneficial mutations. Much less enough accumulating to offset the kind of dramatic accumulations of deleterious ones we see in the human genome. Not a factor to consider at all.
RAZD:
quote:
as would be the case where you had an identified number of microstates (you don't get half a state)
Normally true but we often come across fractional states when we average something as was done in that study.
That's all that needs addressed on this thread. I think the rest of you are just slinging some mud because you do not like what that study showed. I didn't do it, I just quoted it. Don't kill the messenger.
Design Dynamics