Posted on 12/28/2005 3:01:53 PM PST by johnnyb_61820
The creation of DNA seems to violate the 2nd LoT, as it relates to information entropy.
Whatever system created DNA is required to have more information (lower entropy) than the DNA itself. Diffusion of information must occur. The resulting system must be "less informed", so to speak. The DNA would have to be a dispersion or diffusion of the proto-DNA.
No such proto-DNA has yet been discovered.
Nor has an encoding, or evolutionary-type, process been discovered that would allow the creation of properly coded DNA to be formed in an open system in which energy/field forces were available to "drive" the amino acids into proper configuration, or to allow the selection of the "correct" string after being randomly assembled in the soup.
In the case of a living being the evolutionary criteria needed to perform the natural selection process are self-contained within the organism, within the DNA. There are (theoretically) no external systems making the determination of which mutation should live or die. The criteria for life to exist are encoded in the DNA.
But DNA cannot carry the criteria for the existence of DNA before it is created! So who has that criteria?
Why should long-chain polymers floating in a puddle decide they need to reproduce?
Why would these moelcules have a "need" to convert sunlight or other energy sources into stored energy to be used later to reproduce new even more complex molecules? over and over and over...
Why should these happy little molecules have any desire to live at all? (life can be so depressing, I'm sure, but still...)
Why should any molecules care to live at all? Whats the point?
;^)
Here are 3. It took me just a few seconds to find them.
Walter L. Bradley received his Ph.D. in Materials Science from the University of Texas. He has participated as principal or co-principal investigator on over three million dollars of contract research and has consulted for many major corporations. He has published over 90 refereed papers in technical journals and conference proceedings. He has been a Texas Engineering Experiment Station Research Fellow since 1982 and was elected as an American Society for Materials Fellow in 1991. He is currently Professor and Head of the Department of Mechanical Engineering at Texas A & M University.
Roger L. Olsen received his Bachelor in Science degree in Chemistry in 1972 and his Ph.D. degree in Geochemistry in 1979. Both degrees were from the Colorado School of Mines. Dr. Olsen has worked at the Colorado School of Mines as an Instructor in Chemistry/Geochemistry, at Rockwell International as a Research Chemist, and at D'Appolonia Consulting Engineers/International Technology Corporation as a Project Geochemist. Dr. Olsen has made over 40 presentations at conferences and seminars and has published over 30 papers. He is a member of the American Chemical Society, Sigma Xi and the Hazardous Materials Research Institute. Dr. Olsen is a recognized expert in the fields of geochemistry and environmental chemistry and has been an expert witness in 12 cases.
Charles B. Thaxton received his Ph.D. in Chemistry from Iowa State University. He was a Postdoctoral Fellow at Harvard University for two years where he studied the history of science. He had a Postdoctoral appointment in the biological laboratories at Brandeis University for three years. He co-authored with Nancy Randolph Pearcey, Light Through a Prism: A World View Approach to History of Science (Crossway, 1993). He was the Academic Editor for a high school biology supplement, Of Pandas and People (Haughton, 1989). Dr. Thaxton is President of Konos Connection, a non-profit corporation in Julian, California, and has lectured within the U.S. and Europe. In January, 1992 he moved with his family to Prague, Czechoslovakia. During 1992 he held appointments at both the Slovak Technical University in Bratislava, Czechoslovakia and the Biomathematical Institute in Craiova, Romania. He holds memberships in the American Chemical Society, the American Association for the Advancement of Science, and is a Fellow of both the American Institute of Chemists and the American Scientific Affiliation.
Actually, now that I read the paper he doesn't really tell us much of anything at all. He just obliquely refers to other reports. I am disappointed.
The second law of thermodynamics does not apply to informational entropy. It's a law of thermodynamics, not information science.
Not one of these guys is a physicist.
DNA is pretty much a crystal. Both DNA and RNA have crystaline forms that preserve all of the so-called information. What law of thermodynamics is violated by the formation of a crystal?
It seems to, because you don't know what entropy is and neither do you understand information theory. Information theory is not thermodynamics.
"Whatever system created DNA is required to have more information (lower entropy) than the DNA itself."
Information is not entropy. The information theory entropy before the reaction is Hbefore. After the reaction it's Hafter. The information after the reaction is R,
R=Hbefore - Hafter.
Notice before the reaction the informaitonal entropy was large, not small and was reduced after the reaciton. R, the information, is less after the reation.
This reaction is not driven by information though. It's driven by energy and thermodynamics applies. The energy comes from the heat of reaction. Here's a link that notes the difference and contains a link to relevant applied info theory(Schneider). In my post I note Schneider's failure to grasp thermodynamics with his example of a copper penny flip. That's very important to note, because information theory generally must and does ignore background to focus on particular relevant aspects. It also must invoke informational entropy when the real entropy doesn't change during a reaction, or is hidden in the background as I noted with the penny flip. His Emin calc is good.
"Why should long-chain polymers floating in a puddle decide they need to reproduce? "
They don't decide anything. It happens, because it can. IOWs the laws of physics and the system components allow it.
"Why should any molecules care to live at all? Whats the point?
Molecules don't have will. They follow the physics. Systems of molecules that comprise sentient, intellegent machines have will. They aquire/create and decide their own reasons.
Here's another misconception. there is no such thing as proto DNA. All chemical reactions follow thermodynamics, not information theory. All DNA and the reactions it's involved in are equivalent, regardless of sequence. The idea that any particular sequence is thermodynamically different, allowing one to tag it as special is ridiculous.
LOL. I'm an idiot? ok
There are published works on this very subject. You may wish to look them up.
The folowing is an excerpt from a book by Dr.'s Thaxton. Olsen and Bradley.
Information and Entropy
There is a general relationship between information and entropy. This is fortunate because it allows an analysis to be developed in the formalism of classical thermodynamics, giving us a powerful tool for calculating the work to be done by energy flow through the system to synthesize protein and DNA (if indeed energy flow is capable of producing information). The information content in a given sequence of units, be they digits in a number, letters in a sentence, or amino acids in a polypeptide or protein, depends on the minimum number of instructions needed to specify or describe the structure. Many instructions are needed to specify a complex, information-bearing structure such as DNA. Only a few instructions are needed to specify an ordered structure such as a crystal. In this case we have a description of the initial sequence or unit arrangement which is then repeated ad infinitum according to the packing instructions.
Orgel9 illustrates the concept in the following way. To describe a crystal, one would need only to specify the substance to be used and the way in which the molecules were to be packed together. A couple of sentences would suffice, followed by the instructions "and keep on doing the same," since the packing sequence in a crystal is regular. The description would be about as brief as specifying a DNA-like polynucleotide with a random sequence. Here one would need only to specify the proportions of the four nucleotides in the final product, along with instructions to assemble them randomly. The chemist could then make the polymer with the proper composition but with a random sequence.
It would be quite impossible to produce a correspondingly simple set of instructions that would enable a chemist to synthesize the DNA of an E. coli bacterium. In this case the sequence matters. Only by specifying the sequence letter-by-letter (about 4,000,000 instructions) could we tell a chemist what to make. Our instructions would occupy not a few short sentences, but a large book instead!
Brillouin,10 Schrodinger,11 and others12 have developed both qualitative and quantitative relationships between information and entropy. Brillouin,13 states that the entropy of a system is given by
S = k ln (8-1)
where S is the entropy of the system, k is Boltzmann's constant, and corresponds to the number of ways the energy and mass in a system may be arranged.
We will use Sth and Sc to refer to the thermal and configurational entropies, respectively. Thermal entropy, Sth, is associated with the distribution of energy in the system. Configurational entropy Sc is concerned only with the arrangement of mass in the system, and, for our purposes, we shall be especially interested in the sequencing of amino acids in polypeptides (or proteins) or of nucleotides in polynucleotides (e.g., DNA). The symbols th and c refer to the number of ways energy and mass, respectively, may be arranged in a system.
Thus we may be more precise by writing
S = k lnth c = k lnth + k lnc = Sth + Sc (8-2A)
where
Sth = k lnth (8-2b)
and
Sc = k lnc (8-2c)
Determining Information: From a Random Polymer to an Informed Polymer
If we want to convert a random polymer into an informational molecule, we can determine the increase in information (as defined by Brillouin) by finding the difference between the negatives of the entropy states for the initial random polymer and the informational molecule:
I = - (Scm - Scr) (8-3A),
I = Scr - Scm (8-3b),
= k lncr - k lncm (8-3c)
In this equation, I is a measure of the information content of an aperiodic (complex) polymer with a specified sequence, Scm represents the configurational "coding" entropy of this polymer informed with a given message, and Scr represents the configurational entropy of the same polymer for an unspecified or random sequence.
[NOTE: Yockey and Wickens define information slightly differently than Brilloum, whose definition we use in our analysis. The difference is unimportant insofar as our analysis here is concerned].
Note that the information in a sequence-specified polymer is maximized when the mass in the molecule could be arranged in many different ways, only one of which communicates the intended message. (There is a large Scr from eq. 8-2c since cr is large, yet Scm = 0 from eq. 8-2c since cm = 1.) The information carried in a crystal is small because Sc is small (eq. 8-2c) for a crystal. There simply is very little potential for information in a crystal because its matter can be distributed in so few ways. The random polymer provides an even starker contrast. It bears no information because Scr, although large, is equal to Scm (see eq. 8-3b).
In summary, equations 8-2c and 8-3c quantify the notion that only specified, aperiodic macromolecules are capable of carrying the large amounts of information characteristic of living systems. Later we will calculate "c" for both random and specified polymers so that the configurational entropy change required to go from a random to a specified polymer can be determined. In the next section we will consider the various components of the total work required in the formation of macromolecules such as DNA and protein.
DNA and Protein Formation:
Defining the Work
There are three distinct components of work to be done in assembling simple biomonomers into a complex (or aperiodic) linear polymer with a specified sequence as we find in DNA or protein. The change in the Gibbs free energy, G, of the system during polymerization defines the total work that must be accomplished by energy flow through the system. The change in Gibbs free energy has previously been shown to be
G = E + P V - T S (8-4a)
or
G = H - T S (8-4b)
where a decrease in Gibbs free energy for a given chemical reaction near equilibrium guarantees an increase in the entropy of the universe as demanded by the second law of thermodynamics.
Now consider the components of the Gibbs free energy (eq. 8-4b) where the change in enthalpy (H) is principally the result of changes in the total bonding energy (E), with the (P V) term assumed to be negligible. We will refer to this enthalpy component (H) as the chemical work. A further distinction will be helpful. The change in the entropy (S) that accompanies the polymerization reaction may be divided into two distinct components which correspond to the changes in the thermal energy distribution (Sth) and the mass distribution (Sc), eq. 8-2. So we can rewrite eq. 8-4b as
G = H - TSth - T Sc (8-5)
that is,
(Gibbs free energy) = (Chemical work) - (Thermal entropy work) - (Configurational entropy work)
It will be shown that polymerization of macromolecules results in a decrease in the thermal and configurational entropies (Sth 0, Sc 0). These terms effectively increase G, and thus represent additional components of work to be done beyond the chemical work.
Consider the case of the formation of protein or DNA from biomonomers in a chemical soup. For computational purposes it may be thought of as requiring two steps: (1) polymerization to form a chain molecule with an aperiodic but near-random sequence, and (2) rearrangement to an aperiodic, specified information-bearing sequence.
[NOTE: Some intersymbol influence arising from differential atomic bonding properties makes the distribution of matter not quite random. (H.P. Yockey, 1981. J. Theoret. Biol. 91,13)].
The entropy change (S) associated with the first step is essentially all thermal entropy change (Sth), as discussed above. The entropy change of the second step is essentially all configurational entropy reducing change (Sc). In fact, as previously noted, the change in configurational entropy (Sc) = Sc "coding" as one goes from a random arrangement (Scr) to a specified sequence (Scm) in a macromolecule is numerically equal to the negative of the information content of the molecule as defined by Brillouin (see eq. 8-3a).
In summary, the formation of complex biological polymers such as DNA and protein involves changes in the chemical energy, H, the thermal entropy, Sth, and the configurational entropy, Sc, of the system. Determining the magnitudes of these individual changes using experimental data and a few calculations will allow us to quantify the magnitude of the required work potentially to be done by energy flow through the system in synthesizing macromolecules such as DNA and protein.
Quantifying the Various Components of Work
1. Chemical Work
The polymerization of amino acids to polypeptides (protein) or of nucleotides to polynucleotides (DNA) occurs through condensation reactions. One may calculate the enthalpy change in the formation of a dipeptide from amino acids to be 5-8 kcal/mole for a variety of amino acids, using data compiled by Hutchens.14 Thus, chemical work must be done on the system to get polymerization to occur. Morowitz15 has estimated more generally that the chemical work, or average increase in enthalpy, for macromolecule formation in living systems is 16.4 cal/gm. Elsewhere in the same book he says that the average increase in bonding energy in going from simple compounds to an E. coli bacterium is 0.27 ev/atom. One can easily see that chemical work must be done on the biomonomers to bring about the formation of macromolecules like those that are essential to living systems. By contrast, amino acid formation from simple reducing atmosphere gases (methane, ammonia, water) has an associated enthalpy change (H) of -50 kcal/mole to -250 kcal/ mole,16 which means energy is released rather than consumed. This explains why amino acids form with relative ease in prebiotic simulation experiments. On the other hand, forming amino acids from less-reducing conditions (i.e., carbon dioxide, nitrogen, and water) is known to be far more difficult experimentally. This is because the enthalpy change (H) is positive, meaning energy is required to drive the energetically unfavorable chemical reaction forward.
2. Thermal Entropy Work
Wickens17 has noted that polymerization reactions will reduce the number of ways the translational energy may be distributed, while generally increasing the possibilities for vibrational and rotational energy. A net decrease results in the number of ways the thermal energy may be distributed, giving a decrease in the thermal entropy according to eq. 8-2b (i.e., Sth 0). Quantifying the magnitude of this decrease in thermal entropy (Sth ) associated with the formation of a polypeptide or a polynucleotide is best accomplished using experimental results.
Morowitz18 has estimated that the average decrease in thermal entropy that occurs during the formation of macromolecules of living systems in 0.218 cal/deg-gm or 65 cal/gm at 298oK. Recent work by Armstrong et al.,19 for nucleotide oligomerization of up to a pentamer indicates H and -T Sth values of 11.8 kcal/mole and 15.6 kcal/mole respectively, at 294K. Thus the decrease in thermal entropy during the polymerization of the macromolecules of life increases the Gibbs free energy and the work required to make these molecules, i.e., -T Sth > 0.
3. Configurational Entropy Work
Finally, we need to quantify the configurational entropy change (Sc) that accompanies the formation of DNA and protein. Here we will not get much help from standard experiments in which the equilibrium constants are determined for a polymerization reaction at various temperatures. Such experiments do not consider whether a specific sequence is achieved in the resultant polymers, but only the concentrations of randomly sequenced polymers (i.e., polypeptides) formed. Consequently, they do not measure the configurational entropy (Sc) contribution to the total entropy change (S). However, the magnitude of the configurational entropy change associated with sequencing the polymers can be calculated.
Using the definition for configurational "coding" entropy given in eq. 8-2c, it is quite straightforward to calculate the configurational entropy change for a given polymer. The number of ways the mass of the linear system may be arranged (c) can be calculated using statistics. Brillouin20 has shown that the number of distinct sequences one can make using N different symbols and Fermi-Dirac statistics is given by
= N! (8-6)
If some of these symbols are redundant (or identical), then the number of unique or distinguishable sequences that can be made is reduced to
c = N! / n1!n2!n2!...ni! (8-7)
where n1 + n2 + ... + ni = N and i defines the number of distinct symbols. For a protein, it is i =20, since a subset of twenty distinctive types of amino acids is found in living things, while in DNA it is i = 4 for the subset of four distinctive nucleotides. A typical protein would have 100 to 300 amino acids in a specific sequence, or N = 100 to 300. For DNA of the bacterium E. coli, N = 4,000,000. In Appendix 1, alternative approaches to calculating c are considered and eq. 8-7 is shown to be a lower bound to the actual value.
For a random polypeptide of 100 amino acids, the configurational entropy, Scr, may be calculated using eq. 8-2c and eq. 8-7 as follows:
Scr = k lncr
since cr = N! / n1!n2!...n20! = 100! / 5!5!....5! = 100! / (5!)20
= 1.28 x 10115 (8-8)
The calculation of equation 8-8 assumes that an equal number of each type of amino acid, namely 5, are contained in the polypeptide. Since k, or Boltzmann's constant, equals 1.38 x 10-16 erg/deg, and ln [1.28 x 10115] = 265,
Scr = 1.38 x 10-16 x 265 = 3.66 x 10-14 erg/deg-polypeptide
If only one specific sequence of amino acids could give the proper function, then the configurational entropy for the protein or specified, aperiodic polypeptide would be given by
Scm = k lncm
= k ln 1
= 0
(8-9)
Determining scin Going from a Random Polymer to an Informed Polymer
The change in configurational entropy, Sc, as one goes from a random polypeptide of 100 amino acids with an equal number of each amino acid type to a polypeptide with a specific message or sequence is:
Sc = Scm - Scr
= 0 - 3.66 x 10-14 erg/deg-polypeptide
= -3.66 x 10-14 erg/deg-polypeptide (8-10)
The configurational entropy work (-T Sc) at ambient temperatures is given by
-T Sc = - (298oK) x (-3.66 x 10-14) erg/deg-polypeptide
= 1.1 x 10-11 erg/polypeptide
= 1.1 x 10-11 erg/polypeptide x [6.023 x 1023 molecules/mole] / [10,000 gms/mole] x [1 cal] / 4.184 x 107 ergs
= 15.8 cal/gm (8-11)
where the protein mass of 10,000 amu was estimated by assuming an average amino acid weight of 100 amu after the removal of the water molecule. Determination of the configurational entropy work for a protein containing 300 amino acids equally divided among the twenty types gives a similar result of 16.8 cal/gm.
In like manner the configurational entropy work for a DNA molecule such as for E. coli bacterium may be calculated assuming 4 x 106 nucleotides in the chain with 1 x 106 each of the four distinctive nucleotides, each distinguished by the type of base attached, and each nucleotide assumed to have an average mass of 339 amu. At 298oK:
-T Sc = -T (Scm - Scr)
= T ( Scr - Scm)
= kT ln (cr - lncm)
= kT ln [(4 x 106)! / (106)!(106)!(106)!(106)!] - kT ln 1
= 2.26 x 10-7 erg/polynucleotide
= 2.39 cal/gm 8-12
It is interesting to note that, while the work to code the DNA molecule with 4 million nucleotides is much greater than the work required to code a protein of 100 amino acids (2.26 x 10-7 erg/DNA vs. 1.10 x 10-11 erg/protein), the work per gram to code such molecules is actually less in DNA. There are two reasons for this perhaps unexpected result: first, the nucleotide is more massive than the amino acid (339 amu vs. 100 amu); and second, the alphabet is more limited, with only four useful nucleotide "letters" as compared to twenty useful amino acid letters. Nevertheless, it is the total work that is important, which means that synthesizing DNA is much more difficult than synthesizing protein.
It should be emphasized that these estimates of the magnitude of the configurational entropy work required are conservatively small. As a practical matter, our calculations have ignored the configurational entropy work involved in the selection of monomers. Thus, we have assumed that only the proper subset of 20 biologically significant amino acids was available in a prebiotic oceanic soup to form a biofunctional protein. The same is true of DNA. We have assumed that in the soup only the proper subset of 4 nucleotides was present and that these nucleotides do not interact with amino acids or other soup ingredients. As we discussed in Chapter 4, many varieties of amino acids and nucleotides would have been present in a real ocean---varieties which have been ignored in our calculations of configurational entropy work. In addition, the soup would have contained many other kinds of molecules which could have reacted with amino acids and nucleotides. The problem of using only the appropriate optical isomer has also been ignored. A random chemical soup would have contained a 50-50 mixture of D- and L-amino acids, from which a true protein could incorporate only the Lenantiomer. Similarly, DNA uses exclusively the optically active sugar D-deoxyribose. Finally, we have ignored the problem of forming unnatural links, assuming for the calculations that only CL-links occurred between amino acids in making polypeptides, and that only correct linking at the 3', 5'-position of sugar occurred in forming polynucleotides. A quantification of these problems of specificity has recently been made by Yockey.21
The dual problem of selecting the proper composition of matter and then coding or rearranging it into the proper sequence is analogous to writing a story using letters drawn from a pot containing many duplicates of each of the 22 Hebrew consonants and 24 Greek and 26 English letters all mixed together. To write in English the message,
HOW DID I GET HERE?
we must first draw from the pot 2 Hs, 2 Is, 3 Es, 2 Ds, and one each of the letters W, 0, G, T, and R. Drawing or selecting this specific set of letters would be a most unlikely event itself. The work of selecting just these 14 letters would certainly be far greater than arranging them in the correct sequence. Our calculations only considered the easier step of coding while ignoring the greater problem of selecting the correct set of letters to be coded. We thereby greatly underestimate the actual configurational entropy work to be done.
In Chapter 6 we developed a scale showing degrees of investigator interference in prebiotic simulation experiments. In discussing this scale it was noted that very often in reported experiments the experimenter has actually played a crucial but illegitimate role in the success of the experiment. It becomes clear at this point that one illegitimate role of the investigator is that of providing a portion of the configurational entropy work, i.e., the "selecting" work portion of the total -T Sc work.
It is sometimes argued that the type of amino acid that is present in a protein is critical only at certain positions---active sites---along the chain, but not at every position. If this is so, it means the same message (i.e., function) can be produced with more than one sequence of amino acids.
This would reduce the coding work by making the number of permissible arrangements cm in eqs. 8-9 and 8-10 for Scm greater than 1. The effect of overlooking this in our calculations, however, would be negligible compared to the effect of overlooking the "selecting" work and only considering the "coding" work, as previously discussed. So we are led to the conclusion that our estimate for Sc is very conservatively low.
Calculating the Total Work: Polymerization of Biomacromolecules
It is now possible to estimate the total work required to combine biomonomers into the appropriate polymers essential to living systems. This calculation using eq. 8-5 might be thought of as occurring in two steps. First, amino acids polymerize into a polypeptide, with the chemical and thermal entropy work being accomplished (H -T Sth). Next, the random polymer is rearranged into a specific sequence which constitutes doing configurational entropy work (-T Sc). For example, the total work as expressed by the change in Gibbs free energy to make a specified sequence is
G = H - T Sth - T Sc (8-13)
where H - T Sth may be assumed to be 300 kcal/mole to form a random polypeptide of 101 amino acids (100 links). The work to code this random polypeptide into a useful sequence so that it may function as a protein involves the additional component of T Sc "coding" work, which has been estimated previously to be 15.9 cal/gm, or approximately 159 kcal/mole for our protein of 100 links with an estimated mass of 10,000 amu per mole. Thus, the total work (neglecting the "sorting and selecting" work) is approximately
G = (300 + 159) kcal/mole = 459 kcal/mole (8-14)
with the coding work representing 159/459 or 35% of the total work.
In a similar way, the polymerization of 4 x 106 nucleotides into a random polynucleotide would require approximately 27 x 106 kcal/mole. The coding of this random polynucleotide into the specified, aperiodic sequence of a DNA molecule would require an additional 3.2 x 106 kcal/mole of work. Thus, the fraction of the total work that is required to code the polymerized DNA is seen to be 8.5%, again neglecting the "sorting and selecting" work.
The Impossibility of Protein Formation under Equilibrium Conditions
It was noted in Chapter 7 that because macromolecule formation (such as amino acids polymerizing to form protein) goes uphill energetically, work must be done on the system via energy flow through the system. We can readily see the difficulty in getting polymerization reactions to occur under equilibrium conditions, i.e., in the absence of such an energy flow.
Under equilibrium conditions the concentration of protein one would obtain from a solution of 1 M concentration in each amino acid is given by:
K= [protein] x [H2 0] / [glycine] [alanine]... (8-15)
where K is the equilibrium constant and is calculated by
K = exp [ - G / RT ] (8-16)
An equivalent form is
G = -RT ln K (8-17)
We noted earlier that G = 459 kcal/mole for our protein of 101 amino acids. The gas constant R = 1.9872 cal/deg-mole and T is assumed to be 298oK. Substituting these values into eqs. 8-15 and 8-16 gives
protein concentration = 10-338 M (8-18)
This trivial yield emphasizes the futility of protein formation under equilibrium conditions. In the next chapter we will consider various theoretical models attempting to show how energy flow through the system can be useful in doing the work quantified in this chapter for the polymerization of DNA and protein. Finally, we will examine experimental efforts to accomplish biomacromolecule synthesis.
No. This is pure rubbish. See the Cu penny example I gave you above. The entropy of the Cu penny only depends on it's mass-the number of moles. It doesn't depend on whether you can recognize a scratch on one side, or not. Same with DNA. The entropy of DNA doesn't depend on whether you can read it, or not. The authors of your above post are wrong. They understand neither thermodynamics, or information theory.
"Determining scin Going from a Random Polymer to an Informed Polymer"
Ridiculous! Put them both in a bomb calorimeter and you get the same delta H. Which you woudn't if the con Dr.'s Thaxton, Olsen and Bradley are pushing was true. The entropy of the DNA doesn't depend on the order of the base pairs! BTW, the name of the book and publisher wasn't given and the text is a punishing read in addition to being wrong.
Also, I didn't call you an idiot. Try understanding the mat'l I gave you. If you can't understand the Cu penny flip, you can't go beyond that. Here's a link to Schnieder's home page. There you'll find applied information theory, which does NOT equate with thermodynamics, as I noted in the above posts and commented on Schnieder's treatment in practice.
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