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Member (Idle past 4865 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
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Author | Topic: Jerry's Calculation of Entropy in Genome | |||||||||||||||||||||||||||
JustinC Member (Idle past 4865 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
I've been away from the computer for a while, and sadly the topic where Jerry and I were discussing his calculation was closed. The conversation was getting a bit messy anyway, so I would just like to comment on your calculation one more time and get a response. The original conversation started with this message:
http://EvC Forum: Intelligent Design in Universities -->EvC Forum: Intelligent Design in Universities The calculation was
quote:Jerry is putting nucleotides into two categories for this calculation, ancestral and deleteriously mutated. After this, he uses the equation (N1+N2)!/(N1!N2!) to calculate the supposed gain in entropy of the genome after one generation of deleterious mutations using the Eyre-Walker results of 1.6 per generation. So here's my counter, using a Reductio Ad Adsurdum type argument. It's very simple. Jerry supposes the entropy will go up from some ideal ancestral state, and this will be correlated with an information loss. He uses the calculation above. N1 will represent ancestral nucleotides, N2 will represent deleteriously mutated nucleotides. The original entropy, before the mutations, is: (N1+0)!/(N1!0!)=1 After one round of mutations: (N1+N2)!(N1!N2)!> 1 Eventually, we'll reach a point where we have more deleterious mutations than we have ancestral nucleotides. After this, entropy will begin to decrease. So, the more deleterious mutations that accumlate after that point, the more the entropy will decrease until it reaches 1 again. This goes against the original statement that "an increase in entropy is correlated with a loss of information", since now a decrease in entropy will be correlated with a loss of information. It also goes against the notion that entropy is measure of disorder, since as disorder goes up (in the sense that information is being lost) entropy decreases. This seems absurd. I would like to remind Jerry that entropy is a state function, and doesn't depend on the path taken to get that particular state. So replying that an organism will be extinct by the time the mutations reach that level is not a counterargument. It's also way off target since we are not talking about an organism but the entropy associated with the genome. The fate of the organism after the change in the genome isn't relevant. So to summarize, if I have understood the calculation, it seems that a decrease in information can result in a decrease in entropy (not an increase). Anyone is welcome to comment, especially if they see an error in my reasoning. This message has been edited by JustinC, 05-12-2005 06:53 PM
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AdminNosy Administrator Posts: 4754 From: Vancouver, BC, Canada Joined: |
It would be useful to have a link to the old thread and, if needed, a summary of that discussion.
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JustinC Member (Idle past 4865 days) Posts: 624 From: Pittsburgh, PA, USA Joined: |
Link Added
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AdminNosy Administrator Posts: 4754 From: Vancouver, BC, Canada Joined: |
Thread moved here from the Proposed New Topics forum.
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PaulK Member Posts: 17825 Joined: Member Rating: 2.2 |
Some comments
1) Jerry is wrong about the biology. 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. 2) Jerry is wrong about the maths. He certainly DIDN'T calculate(41469.4 + 1.6)! / (41469.4)!(1.6)! How do I know ? Because the factorial operation (denoted by '!') is only defined for integers. The calculation is nonsense, since the denominator for the ratio is undefined. 3) 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. There are other serious problems, but I think that those will do for now.
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Dead Parrot Member (Idle past 3367 days) Posts: 151 From: Wellington, NZ Joined: |
LOL. I'm glad someone was paying attention...
Nice catch. Mat 27:5 And he went and hanged himself Luk 10:37 Go, and do thou likewise.
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Jerry Don Bauer Inactive Member |
Um...Don't celebrate just yet. Nitwit Ned has not got me silenced just yet. But he's working on it. I fully intend to get to this thread.
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Dead Parrot Member (Idle past 3367 days) Posts: 151 From: Wellington, NZ Joined: |
Um...Don't celebrate just yet. Nitwit Ned has not got me silenced just yet. But he's working on it. I fully intend to get to this thread. At which you will prove that 1.6! isn't gibberish? We await with baited breath... Mat 27:5 And he went and hanged himself Luk 10:37 Go, and do thou likewise.
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Jerry Don Bauer Inactive Member |
I just wonder where that nose has been. ~~~Shudder~~~
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Dead Parrot Member (Idle past 3367 days) Posts: 151 From: Wellington, NZ Joined: |
That's not quite the amazing mathematics I was expecting. Have another go.
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JonF Member (Idle past 189 days) Posts: 6174 Joined: |
How do I know ? Because the factorial operation (denoted by '!') is only defined for integers. The calculation is nonsense, since the denominator for the ratio is undefined. Factorial is defined only for positive integers. There is, of course, the gamma function which equals (N-1)! for all positive integer N and is analytic everywhere in the complex plane except 0 and the negative integers. But I bet the gamma function is far beyond Jerry's abilities. ABE: Of course, the exclamation point is never used to indicate gamma(x), so it's not possible that Jerry really meant gamma(1.6). This message has been edited by JonF, 05-13-2005 08:04 AM This message has been edited by JonF, 05-13-2005 09:20 AM
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arachnophilia Member (Idle past 1365 days) Posts: 9069 From: god's waiting room Joined: |
even if 1.6! weren't uhh, what's the word? irrational? imaginary? impossible? insane?
...i'd seriously doubt they did the calculation anyways. not on a calculator at least. my ti89 (otherwise known as "proof god exists") craps itself trying to do a factorial of a five digit number. it takes maple to crank out this enormous number. anyone else here have maple or a similar program? i considered posting 41471!, but, well, it'd severly piss off everyone trying to READ this thread. instead, i'll just post a screenshot. you'll have to take my word for it that there's 32 and half more screens where that came from. edit: checking the (incorrect) calculation in maple, btw, it does render the same answer. maple uses, probably, the same algorithm that will allow it to (incorrectly) render factorials of decimals. at first, i thought even that bit of calculation was wrong, but i missed a pair of parenthesis. because the op did and i copied that. order of operations, kids.
quote: This message has been edited by Arachnophilia, 05-13-2005 08:13 AM
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RAZD Member (Idle past 1426 days) Posts: 20714 From: the other end of the sidewalk Joined: |
How do I know ? Because the factorial operation (denoted by '!') is only defined for integers. The calculation is nonsense, since the denominator for the ratio is undefined. actually it is a possible lack of math formalism being exhibited ... I enter 1.6 into my windoze {calculator\"scientific setting"} and hit the {n!} button and get 1.4296245588603044182985600527885 I also got a message that "the requested operation may take a long time to complete: do you want to continue?" when I asked it to compute 41469.4! the answer for that is 1.4982978786211478993674730926215e+173487 the actual function for real numbers is called the gamma functionGamma Function -- from Wolfram MathWorld where it "is defined to be an extension of the factorial to complex and real number arguments." and this would be what the calculator is actually using, and someone just using the button would not be aware of this difference. the original use in the formula is for where you have a set on {N} items (an integer) and two (integer) subsets {M} and not{M} where {M}+not{M}={N} as would be the case where you had an identified number of microstates (you don't get half a state) we are limited in our ability to understand by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}
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derwood Member (Idle past 1897 days) Posts: 1457 Joined: |
Jerry Don, the Gospel Music distributor, simply will not (cannot?) admit hi sown limitations. He has started and restarted threads on this topic at ARN, some lasting dozens of pages, most posts showing Jerry Don's his errors (including one comical series of exchanges in which Jerry Don chastized all the 'PhDs' for not being able to handle his math, and later it was discovered that Jerry Don had been pushing the wrong button on his calculator!). Yet no admission, no humility form Jerry Don. I once engaged him in a 'moderated' debate at OCW. The agreed upon topic was "The field of molecular phylogenetics, especially the use of DNA sequence data in reconstructing phylogenies, has provided strong evidence supportive of evolutionary hypotheses of common descent", with me in the affirmative, and in Jerry Don's first response, he was off topic, and never went back on.
He does not understand enough to know when he is wrong. It is like a regular Red Queen exercise trying to get anywhere with him.
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Jerry Don Bauer Inactive Member |
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: 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: 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: 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: 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
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