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Author
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Topic: Thermodynamics for Intelligent Design
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gedanken
Member
Member # 594
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posted 30. April 2003 01:53
quote:
I've consistantly asked you to tell me what is unclear to you and you seem do not want to do this.
How can this be?
What is unclear is that you claim that the value of the entropy S is positive, then claimed that fact as evidence that the delta or change in that necessarily positive value S over time cannot be towards a lower (positive) value for the system.
(And then you repeated that claim in exactly that form so as to emphasize it as your fundamental argument.)
For example Rex's case, the initial value of S was 29, then the later value was 19. Both values are positive. Yet the entropy decreased, the delta in S was negative! deltaS= -10.
And please don't bring up Boltzmann's constant or the like again. Since K is positive, a value like K*19 - K*29 will simply give a deltaS = K*(-10), still a negative number.
A little tutorial on logarithms to end my week:
Assume we have W states, microstates, information states, whatever. W is an integer number of states, and cannot be less than 1 state.
Now call the 'informational' entropy S', where ' mark indicates the informational calculated with log2. So:
S' = log2( W )
Now another calculation of microstates and entropy might look like this:
S = K ln( W ), where K is Boltzmann's constant.
Note no ' mark for this formula. So how do the two entripies relate, if they are based on the same number of microstates or information states W?
First we need to know the relationship of log2(W) and ln(W).
log2(W) = ln(W)/ln(2)
So S' = ln(W)/ln(2)
S = K ln(W)
So S = K ln(2) * S'
S and S' are related by a positive constant.
Now here is another aspect of logarithms and entropies:
ln(W2/W1) = ln(W2) - ln(W1)
This is fundamental relationship of logarithms, which is why division and multiplication used to be done by looking up logs and then subtracting or adding them.
Note this is true in any base, for example:
log2(W2/W1) = log2(W2) - log2(W1)
So when we find the increase (or decrease) of the entropy from initial number of microstates or information states W1 to final states W2, we have
deltaS’ = log2(W2) - log2(W1) = log2(W2/W1).
Equivalently for S:
deltaS = K*ln(W2) - K*ln(W1) = K*ln(W2/W1).
Now the implication is that when Rex gave the case of counting the number of microstates or informational states in the combustion of hydrogen and oxygen in a small container (and after the exhaustion of any heat to the environment) then the initial and final number of microstates or information states could be labeled W1 and W2, just as above.
So whether or not we include Boltzmann’s constant, and whichever logarithm we take, we have:
deltaS’ = log2(W2) - log2(W1) = log2(W2/W1).
deltaS = K*ln(W2) - K*ln(W1) = K*ln(W2/W1).
deltaS = K*ln(2)*deltaS'
If the number of microstates or informational statest decreased, then W2 is less than W1. But if it increased, then W2 is greater than W1. No matter how we calculate the entropy, if W2>W1, then deltaS is positive, and if W2<W1 then deltaS is negative.
And it does not mater whether we use ln or log or log2, and it does not matter whether we multiply in Boltzmann’s constant.
Since no argument has been given to convince us that W2 > W1, there is no reason for deltaS to necessarily be positive. Rex’s case was precisely a case in which deltaS was negative. This shows that real-world systems can have negative deltaS changes, even though S is positive in all cases because W (W1 or W2) is greater than 1. That S is positive all the time is irrelevant to the question of whether deltaS is positive or negative. To answer that, we need to know whether W2 > W1 or W2 < W1. Chronos has given no argument to demonstrate that W2 > W1, only that S>0. And since usually W >1, then S>0 all the time, without regard to whether deltaS is positive or negative.
Thus many of us find unclear why Chronos argues that entropy must be increasing, since there are clearly cases where deltaS is negative or decreasing for very common systems. And this does not matter whether we use ln, log, or log2, and whether we multiply in Boltzmann’s constant K. Chronos claims that S > 0 is his argument, and I have shown with simple logarithm calculations that is the case all the time, whether entropy is increasing or decreasing. So the confusion on our part is specifically that Chronos is not making a logical argument since his claims don’t imply his conclusion.
Nice lecture (PDF) on entropy calculations.
I recommend that Chronos brush up on logarithms, and verify my tutorial above with a good mathematics book.
[ 30. April 2003, 03:42: Message edited by: gedanken ]
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Chronos
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Member # 693
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posted 30. April 2003 03:00
Pim And Ged:
I’m going to give you guys a couple of days to cool off. I’m afraid the mods will move in if I do not, and I wouldn’t blame them. You guys seem like great guys and are obviously very intelligent but you are getting frustrated with the argument.
This is showing, as it seems that now your argument has boiled down to positive whole numbers really mean negative numbers, chemical reactions are just a tendency toward something, even though the chemical reaction in question has already occurred and the results of the reaction are in; and that type of substance.
Take tonight and tomorrow night off and brush up on thermodynamics. There are many great sites around the Net that will teach this to you at any level. Then we can continue in a day or two. And remember:
Concentrate right here: “that "S = log2W, S = log2(100,000,000), S = 26.5754247590989, therefore S is positive showing a tendency of disorder.”"
This is the heart of my argument.
If you cannot get past this fact that the human genome disorders with every generation via an increase in entropy, then you cannot win this debate. The rest is smoke and mirrors.
P1: With every generation in homo sapien, entropy increases in the genome.
P2: Complex macroevolution requires that the genome have a lower entropy over time through the generations.
Therefore, complex macroevolution did not occur.
Now, Aristotelian logic is valid in any form of debate. If you cannot prove at least one of these premises wrong, therefore showing the conclusion to be wrong, then you lose this debate and truth falls on the side of those of us who firmly embrace design in the tenets that macroevolution is not a valid scientific theory and that CSI cannot occur on its own naturally.
Thanks, and good luck! ![[Smile]](smile.gif)
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gedanken
Member
Member # 594
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posted 30. April 2003 03:47
By the way, Chronos has not demonstrated either of his premises P1 nor P2.
He has not demonstrated that the entropy must be increasing, simply because his argument confuses the positive value of entropy with a delta or change of entropy in a positive direction. Even if there were an argument that demonstrated this was a positive delta, Chronos has decided not to give such an argument and relies on the value being positive -- an irrelevant issue.
Then Chronos has not demonstrated that change over time requires an decrease in entropy. (Or any particular change in entropy -- for example changes occur and they are different, but they have the same number of informational or microstates and thus S has not changed.)
[ 30. April 2003, 03:48: Message edited by: gedanken ]
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Pim van Meurs
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Member # 541
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posted 30. April 2003 12:11
May I suggest that Chronos uses his 'time off' to develop a more solid foundation for his claims and realize that a positive value for S does not mean that S has a tendency to disorder or order which is determined by it's derivatives.
Until then I agree with Gedanken that claims like P1 and P2 remain totally unsupported and unsupportable. In fact Chronos has made no efforts at all to support either P1 or P2. In fact the 'heart of his argument' that "S is positive showing a tendency of disorder" has been shown to be fallacious.
In my time I have seen many a flawed SLOT argument that proposes to disprove evolution. All seem to suffer from a similar infliction namely a lack of mathematical foundation allowing the author to make conflicting claims appear as supporting. Only a thorough mathematical foundation can help resolve Chronos' confusion of value and its tendency.
Perhaps in the mean time Chronos may want to check out the works of Shannon, Schneider and Adami who have given information theory a much more solid mathematical foundation and have shown how mutation and selection can decrease entropy in the genome.
And a final thought:
log2(4/100,000,000) is negative
[ 30. April 2003, 12:27: Message edited by: Pim van Meurs ]
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Moderator
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Member # 1
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posted 30. April 2003 12:58
Let me suggest that this discussion is done.
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