Understanding through Discussion


Welcome! You are not logged in. [ Login ]
EvC Forum active members: 78 (8896 total)
Current session began: 
Page Loaded: 03-23-2019 3:37 PM
35 online now:
AZPaul3, DrJones*, JonF, PaulK, Phat (AdminPhat), RAZD (6 members, 29 visitors)
Chatting now:  Chat room empty
Newest Member: WookieeB
Post Volume:
Total: 848,593 Year: 3,630/19,786 Month: 625/1,087 Week: 215/212 Day: 30/27 Hour: 0/1


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Prev1
2
Author Topic:   Jerry's Calculation of Entropy in Genome
Limbo
Inactive Member


Message 16 of 23 (208173)
05-14-2005 6:39 PM
Reply to: Message 15 by Jerry Don Bauer
05-14-2005 6:35 PM


Welcome back Jerry! :)
This message is a reply to:
 Message 15 by Jerry Don Bauer, posted 05-14-2005 6:35 PM Jerry Don Bauer has responded

Replies to this message:
 Message 18 by Jerry Don Bauer, posted 05-14-2005 8:30 PM Limbo has not yet responded

  
RAZD
Member
Posts: 19757
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 5.8


Message 17 of 23 (208205)
05-14-2005 7:29 PM
Reply to: Message 14 by derwood
05-14-2005 3:51 PM


Re: is it worth it?
I reached a similar conclusion shortly after he ran away from the first rebuttals of his {arguments\opinions} while launching a salvo of *chuckle* and the odd ad hominum.

still waiting for evidence in the fossil record that shows a {just created} state in the {human\hominid} ancestry and clear evidence of the superior height from which we have since "devolved"

among others


we are limited in our ability to understand
by our ability to understand

RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}


This message is a reply to:
 Message 14 by derwood, posted 05-14-2005 3:51 PM derwood has not yet responded

  
Jerry Don Bauer
Inactive Member


Message 18 of 23 (208228)
05-14-2005 8:30 PM
Reply to: Message 16 by Limbo
05-14-2005 6:39 PM


quote:
Welcome back Jerry!

Thanks, Limbo. Just here to get caught up so I don't leave people hanging. Then I'm out of here. ;)


Design Dynamics
This message is a reply to:
 Message 16 by Limbo, posted 05-14-2005 6:39 PM Limbo has not yet responded

  
JustinC
Member (Idle past 2921 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 19 of 23 (208230)
05-14-2005 8:37 PM
Reply to: Message 15 by Jerry Don Bauer
05-14-2005 6:35 PM


quote:
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)



I honestly have a hard time following this. I'll just calculate W since it is directly proportional to entropy. Also, I know I was only calculating W, not delta W. But, delta W could be found by comparing the different generations. Here is the calculation again. I will assume ancestral nucleotides to begin with.
We start off with a W of:

1. (1000!)/[(1000!)(0!)]=1

After I mutate a quarter of the nucleotides to deleteriously affect some genes:

2.) (1000!)/[(750!)(250!)]>1

After I mutate half of the nuceotides:

3.) (1000!)/[(500!)(500!)] >>1

After I mutate all of the nucleotides, so no information is left in the 1000 nucleotide segment:

4.) (1000!)/[(0!)(1000!)]=1

As you can see, the change in entropy is always positive except for the last change, from (3) to (4), which is:

5.) Delta W= (1-(>>1))= - N

I apologize for the abbreviations since I don't have a calculator handy, but you should get the point.

According to your calculations, if I take a one thousand nucleotide DNA sequence full of genes, and then mutate every nucleotide to deleteriously affect the gene products, then the entropy remains the same. Or, to put it another way, a one thousand nucleotide DNA sequence with half of the nucleotides deleteriously mutated will have a higher entropy than the same sequence with all the nucleotides mutated. The change would be negative if going from the former to the latter using your equation.

quote:
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.


I'm just using the equations you used to show an absurditiy. That should communicate to you that your equations aren't sound. Please show me exactly where my calculation is in error.

This message has been edited by JustinC, 05-14-2005 08:40 PM


This message is a reply to:
 Message 15 by Jerry Don Bauer, posted 05-14-2005 6:35 PM Jerry Don Bauer has responded

Replies to this message:
 Message 20 by Jerry Don Bauer, posted 05-14-2005 10:21 PM JustinC has responded

    
Jerry Don Bauer
Inactive Member


Message 20 of 23 (208245)
05-14-2005 10:21 PM
Reply to: Message 19 by JustinC
05-14-2005 8:37 PM


quote:
We start off with a W of:

1. (1000!)/[(1000!)(0!)]=1

After I mutate a quarter of the nucleotides to deleteriously affect some genes:

2.) (1000!)/[(750!)(250!)]>1

After I mutate half of the nuceotides:

3.) (1000!)/[(500!)(500!)] >>1

After I mutate all of the nucleotides, so no information is left in the 1000 nucleotide segment:

4.) (1000!)/[(0!)(1000!)]=1

As you can see, the change in entropy is always positive except for the last change, from

(3) to (4), which is:

5.) Delta W= (1-(>>1))= - N

I apologize for the abbreviations since I don't have a calculator handy, but you should get the point.

According to your calculations, if I take a one thousand nucleotide DNA sequence full of genes, and then mutate every nucleotide to deleteriously affect the gene products, then the entropy remains the same. Or, to put it another way, a one thousand nucleotide DNA sequence with half of the nucleotides deleteriously mutated will have a higher entropy than the same sequence with all the nucleotides mutated. The change would be negative if going from the former to the latter using your equation.


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.

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. 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?

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?

Please use deltaS to calculate this changing entropy.

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.

quote:
I'm just using the equations you used to show an absurditiy.

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.

quote:
Please show me exactly where my calculation is in error.

Um....I think I did. ;)

This message has been edited by Jerry Don Bauer, 05-14-2005 10:23 PM


Design Dynamics
This message is a reply to:
 Message 19 by JustinC, posted 05-14-2005 8:37 PM JustinC has responded

Replies to this message:
 Message 22 by JustinC, posted 05-15-2005 6:51 PM Jerry Don Bauer has not yet responded

  
PaulK
Member
Posts: 14751
Joined: 01-10-2003
Member Rating: 1.7


Message 21 of 23 (208307)
05-15-2005 6:47 AM
Reply to: Message 15 by Jerry Don Bauer
05-14-2005 6:35 PM


Shaded quotes are from my previous post.
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.


Your reply is just confused. I made no reference to the genetic code. I simply pointed out that the "1.6" applied to the ENTIRE GENOME not the smaller figure of 41,471 nucleotides referred to in the study.

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.


It IS true that the factorial operation '!' is only defined for positive integers. And if you think about it 0.6 of a point mutation makes no sense whatsoever. You could have just used 1.

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.

Which shows how useless your argument is. My variation of your argument relies only on a simple definitional change - not affecting the validity or changing the premises. And you completely reject it and start talking about evidence instead. So now we know that even you don't consider your argument valid.


This message is a reply to:
 Message 15 by Jerry Don Bauer, posted 05-14-2005 6:35 PM Jerry Don Bauer has not yet responded

    
JustinC
Member (Idle past 2921 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 22 of 23 (208453)
05-15-2005 6:51 PM
Reply to: Message 20 by Jerry Don Bauer
05-14-2005 10:21 PM


quote:
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.

quote:

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.

quote:

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.

quote:

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.

quote:

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.

quote:

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.

quote:
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.

quote:

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

quote:
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


This message is a reply to:
 Message 20 by Jerry Don Bauer, posted 05-14-2005 10:21 PM Jerry Don Bauer has not yet responded

    
derwood
Member
Posts: 1457
Joined: 12-27-2001


Message 23 of 23 (208680)
05-16-2005 2:11 PM


I wonder how Jerry Don's amazin' math takes things like gene duplication, chromosomal segmental duplications, etc. into consideration.

I have a suspicion that it simply does not.


    
Prev1
2
Newer Topic | Older Topic
Jump to:


Copyright 2001-2018 by EvC Forum, All Rights Reserved

™ Version 4.0 Beta
Innovative software from Qwixotic © 2019