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No. This is not my calculation. This is yours and your math is simply incorrect. Please cut and paste where I used a deltaW anywhere.
It doesn't matter if I use W or S, or Delta W or Delta S, W and S are directly proportional. All I would be doing is taking the ln of the of the number and multiplying it by a constant. You can do the extra math if you want, but the results will turn out the same.
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We are calculating entropy, not just the statistical weight. And when you calculate entropy down the lineage you must use deltaS, not just S which will always be the case with this math you are introducing.
Yes, I know I am using W. They are directly proportional. Do the extra math if you would like, the answer will be the same. For instance, look at my last generation, with all the nucleotides deleteriously mutated:
W= (1000!)/(0!)(1000!)=1
S= k ln W= 0
So delta S going from equation (3) to (4) would be:
Delta S= Sf-Si= 0-(k ln (>>1))=-N
That final entropy would be zero, the entropy before that would be a positive number, giving a negative delta S. A decrease in entropy as more deleteriously mutations accumulate.
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You KNOW entropy will not magically begin to decrease when the study clearly shows 1.6 harmful mutations continue to accumulate. So why are you mathematically trying to show something mathematically correct that you know to be mathematically incorrect?
You were the one trying to equate information loss (in the sense of changing the ancestral state of the genome) with entropy increase. You used that equation to show it. I used that equation to show an absurdity, which (if correct) calls into question your whole calculation. Go from (3) to (4) in my calculation, calculate S's for both, and then find delta S. It will be a decrease in entropy as more deleterious mutations occur.
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The combinatorials need only be used once, to calculate the entropic change in an organism with x amount of nucleotides where y mutations are accumulating. Since x and y are always the same, what is there to recalculate using that formula?
I don't see what's so hard to understand. I am increasing y, i.e., mutating more than half of the genes. When I do this, your equation says the entropy will decrease. This calls into question your calculation, since I don't think you want to be saying this.
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Please use deltaS to calculate this changing entropy.
I did above, but I'll do it again for the hell of it. Equation (4) says W=1, so the entropy will be:
Sf= k ln 1= 0
Equation (3) says the entropy is more than 0 (I'll use W=1.3 as an example), so:
Si= k ln (1.3)>0
So Delta S, going from (3) to (4), would be:
Delta S= Sf-Si= 0- (>0)= -N.
It will be negative still.
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Considering change in entropy between 500 and 501 descendants:
Initial entropy in 500th organism = (500) (9.98 x 10^-23) = S(intial)
Final entropy in 501st organism = (501)(9.98 x 10^-23) = S(final)
deltaS = S(final) - S(intial)
deltaS is positive showing the new accumulated mutations we know occurred in that genome. Now THIS is my math.
I have absolutely no idea what that is supposed to show. We are talking about the entropy of a genome if we dichotomize into ancestral and deleteriously mutated nucleotides, using the equation for statistical weight (N1+N2)!/ ((N1!)(N2!)). What does the generation of the organism have to do with that, and how would that factor into the calculation.
The only way I can see it factoring into the equation would be if we write the number of deleterious mutations as a function of the generation. The result will be the same, once we get to a certain point the more delteriously mutations that accumulate the entropy will decrease.
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No you're not. You are trying to extrapolate a formula I used in a way I did not use it. This is your math, not mine.
The formula should be consistent with the point you are trying to prove. You are trying to prove that deleterious mutations in the genome constitute and increase in entropy. You equation says it does this to a point, and then the entropy will decrease.
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Um....I think I did.
I don't. Calculate the entropies. Entropy will decrease after a certain point as more deleterious mutations accumulate.
The reason I am going through the trouble of this is because I think you just pulled that equation of the internet and tried to use it without understanding it.
It works great with the gas in a box, but you can't just extrapolate it to any binary system, as PaulK was saying
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Jerry is wrong about configurational entropy. Jerry's entropy argument works in exactly the same way for ANY binary classification of genes or mutations, not just "detrimental"/"not detrimental". If you chose to look at beneficial rather than detrimental mutations you would find that each beneficial mutation increased the entropy. This form of entropy depends very much how the problem is framed. And it is not valid to assume that the entropy will tend towards the maximum for every possible measure because different measures give different results.
That's the crux.
This message has been edited by JustinC, 05-17-2005 07:45 PM
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