evilution is good for you

Sunday, November 25, 2007

Five facts about 'Darwinism'

When reading creationist articles, I often get surprised by the extent to, which they get things wrong. Therefore I have here gatherede five central facts about, what Charles Darwin actually wrote, so I have somewhere to refer to, when debating creationists ;-)

Fact #1:

Charles Darwin was building on an already established idea of transformation or evolution.

In Origin of Species, Preface, Darwin writes:

I will here give a brief sketch of the progress of opinion on the Origin of Species. Until recently the great majority of naturalists believed that species were immutable productions, and had been separately created. This view has been ably maintained by many authors. Some few naturalists, on the other hand, have believed that species undergo modification, and that the existing forms of life are the descendants by true generation of pre-existing forms. Passing over allusions to the subject in the classical writers, the first author who in modern times has treated it in a scientific spirit was Buffon. But as his opinions fluctuated greatly at different periods, and as he does not enter on the causes or means of the transformation of species, I need not here enter on details.

Lamarck was the first man whose conclusions on the subject excited much attention. This justly-celebrated naturalist first published his views in 1801; he much enlarged them in 1809 in his "Philosophie Zoologique,' and subsequently, in 1815, in the Introduction to his "Hist. Nat. des Animaux sans Vertébres.' In these works he upholds the doctrine that species, including man, are descended from other species. He first did the eminent service of arousing attention to the probability of all change in the organic, as well as in the inorganic world, being the result of law, and not of miraculous interposition. Lamarck seems to have been chiefly led to his conclusion on the gradual change of species, by the difficulty of distinguishing species and varieties, by the almost perfect gradation of forms in certain groups, and by the analogy of domestic productions. With respect to the means of modification, he attributed something to the direct action of the physical conditions of life, something to the crossing of already existing forms, and much to use and disuse, that is, to the effects of habit. To this latter agency he seemed to attribute all the beautiful adaptations in nature; -- such as the long neck of the giraffe for browsing on the branches of trees. But he likewise believed in a law of progressive development; and as all the forms of life thus tend to progress, in order to account for the existence at the present day of simple productions, he maintains that such forms are now spontaneously generated.

So, the key to it all was, whether new species were possible or not.

[Remaining four facts will follow]

Sunday, November 11, 2007

One Flew Over The Cuckoo's Nest

Antony Flew was until 2004 a rather unknown philosopher, whose earlier claim to fame was a disproof in the 1950s of the possibility of the Christian god. However, in 2004 it was announced thathe had become a deist -- seeing that the complexity of living organisms made abiogenesis unfeasable. The IDists were not slow to celebrate the event, while atheist Richard Carrier tried to downplay the conversion. Carrier's version of the conversion can be found here. Recently, a book, There Is a God: How the World’s Most Notorious Atheist Changed His Mind, listing Antony Flew as author together with the Christian apologist Roy Abraham Varghese. Mark Oppenheimer has written a New York Times article (here), which critically examines the book, the friendship between Flew and various Christians and the correspondence between Carrier and Flew. Several bloggers have addressed the issue, and I will here list the blog entries:
  • PZ Myers (Pharyngula): Roy Varghese and the exploitation of Antony Flew
  • Myers mainly quotes Oppenheimer for the mental decline of Antony Flew.
  • Richard Carrier (RCs Blogs): Antony Flew's Bogus Book
    Carrier claims that the book isn't written by Flew -- it is written as comtemporary Christian apologetics.
  • Mark Perakh (Talk Reason): Flew, Schroeder, Varghese: What a company!
    Perakh tones down the conversion; deists are really just a variety of atheists.
  • William Dembski (Uncommon Descent): I Liked the Old Atheists Better

    Dembski prefers the intellectual honesty and civility of an old-school atheist like Antony Flew for the crass and unruly behavior of the newer varietysuch as Richard Dawkins. Add to that the Flew is no longer an atheist.

    The article is followed by a message from Flew stating that he stands by the book. It was written by Varghese, because Flew is too old to write, but he has read the book and claims that it is his words.

Tuesday, January 02, 2007

Review of Lee M. Spetner: Not by chance!

Quotes and page references are from Dr. Lee M. Spetner: Not by chance! - Shattering the Modern Theory of Evolution, The Judaica Press, Inc., 1998.

All ends well that begins well, and the very first words in the Preface of the book are (cf. p. vii):

Conventional wisdom holds that life arose spontaneously. In the remote past a simple living organism is supposed to have formed by chance out of inert matter. That organism is then supposed to have reproduced and developed into the life of today through random variation shaped by natural selection.

Oh well, yet another strawman on its way to the stakes, it would seem.

According to Spetner, a few bologists have pointed out that discoveries in biology together with elementary principles of information theory have made this view untenable. His key point is that "[t]he information required for large-scale evolution cannot come from random variations." (ibid.) And for Spetner it is not only evolutionary theory that will fall down, it's the whole modern show. On p. viii, he writes:

Why is randomness important? It is important because it has had a profound influence on the shaping of the Weltanschauung of Western Society. It has led to atheism and to the belief that we human beings are no more than a cosmic accident. This belief serves as a basis for the social values and morals held by Western intellectuals, and for their attitudes toward religion. If the belief is unfounded, then the resulting world view and its implications must be reexamined.

So, everything bad can be attributed to that belief in randomnesss, and Spetner is going to show us that randomness just doesn't cut it, and we'll all realize our delusions and go back to church, right?

Not that Spetner is against evolution as such, but he claims that evolution proceeds through a combination of cues from the environment with information already in the genes; that is, nothing new ever comes around, it is only a question of, which information is used when (cf. p. xi). And if random variation cannot be the mechanism of evolution, we must search for some nonrandom mechanism. A mechanism that could not itself have evolved, so how did it ever arise? A question, Spetner claims, science may never be able to answer – however, he asks, is Creation an option? (ibid.).

The Preface ends with the words (p. xii):

I hope you will read the book with an open and inquisitive mind, that you will follow my arguments and finally agree with my conclusion. I hope you enjoy reading it.

Well, as should be clear, I may be somewhat prejudiced against this book, and I may even have decided beforehand not to enjoy it; but I will try as well as I can to follow Spetner's arguments and check how well they work. I think that's as much as I can promise.

Chapter 1, "Historical Background", is actually well-written and gives, as its name suggests, the historical background from the 18th century through Darwin's Origin of Species to the Modern Synthetic Theory of Evolution (cf. pp. 20-21), which combined Darwinian evolution with Mendelian inheritance. While Darwin had rejected randomness as the source of variation, attributing it instead to the influence of the environment and use and disuse of organs, the neo-Darwinians rejected environmental influence on variation, which they attributed to random, genetic variations, mutations. As Spetner mentions, after the rediscovery of Mendel's results around 1900, genetic mutations had been observed, but being generally harmful to organisms, they had been rejected as the source of evolutionary variation, and Darwin's theory of evolution was actually in deep trouble in the early 20th century.

On pp. 21-22, Spetner sums this development up:

The neo-darwinians then built their theory on random variation culled and directed by natural selection. They identified the heritable variations needed by the theory with the mutations discovered and named by De Vries some forty years earlier. A decade later, Watson and Crick identified the heritable variation with the random errors in DNA replication.

So far, so good, and would even be recommended reading for creationists.

It may be worth noting that in Darwin's time, the ideal in natural science was deterministic laws; but increasingly during the last half of the 19th century, statistics increased in importance, even within natural sciences. The early 19th century even introduced quantum mechanics and truly random events, so the neo-Darwinists were in many ways dependent on the acceptance of randomness within the scientific community.

DNA and mutations as random errors in DNA replication is the cue for Chapter 2, "Information and Life", which presents an introduction to DNA.

On pp. 28-29, Spetner introduces the four DNA bases adenine, i>guanine, thymine, and cytosine, and on p. 29 he writes:

There is no chemical restriction on the order of the bases along a strand of DNA; the order can be anything at all. The order of the bases is then free to carry information.

And, according to Spetner, this information is written with the four DNA bases as an alphabet. While what Spetner writes is quite fine, there are a few details of importance left out. The bases are actually read in triplets called codons, which Spetner mentions later (p. 44), and since there are 64 different possible codons, the actual alphabet has 64 letters. The bases in a codon are not like Scrabble blocks with letters painted on them, but otherwise identical. Chemically the bases can be divided into two groups with two bases each: pyrimidines = cytosine and thymine, and purines = adenine and guanine. A codon encodes either an amino acid or functions as a stop code, and since there are only 20 amino acids, some codons have the same translation, and the translation is mostly dependent on the sequence of pyrimidines and purines in the codon, not actually going down to the level of the bases.

For Spetner, the sequence of bases makes up a message, and bottom p. 29 he writes:

How did that message get written in the first place? The standard answer of the biologist is that the message got written by itself, through evolution, and that evolution works the way the neo-Darwinian theory says it does. But I shall show that evolution cannot work that way.

The meaning here being that as DNA is copied, some copy errors may occur and lead to mutations. Spetner's claim is that information theory shows that no new information can be gained this way.

On pp. 31-34, Spetner mentions proteins, including enzymes, that are made up of the amino acids encoded in the DNA, ending with the paragraph:

The information in the genome [= the DNA in the cell] tells the cell what kind of proteins to make. Because proteins play a dominant role in cell function, they play a dominant role in the whole organism. The information in the genome, by controlling the making of protein, fixes the form and function of the entire organism.

So, the organism is basically defined by its DNA.

In Chapter 3, "The Neo-Darwinian Theory of Evolution", Spetner presents the NDT, and on pp. 68-69 also the theory of punctuated equilibria.

On p. 71, Spetner writes:

According to the NDT, information can be added only through selection. Selection tests if the mutation is positive or negative, preserving it if positive and destroying it if negative. Even the most complicated mutation serves only as grist for the mill of selection.

And a paragraph later:

According to the NDT, the receiver of the information is the genome — not the genome of any one individual, but the average genome of the population. That's where the message is ultimately supposed to be received, and that's where the information is supposed to build up.

What Spetner refers to by "the average genome of the population" would be the gene pool of the population, not actually the avarage genome.

Continuing, Spetner writes:

When a mutation occurs, selection can choose only between the mutant and the rest of the population. It can choose the better from the good, the more adaptive from the less adaptive. In one step, selection can add no more than one bit of information. That's because it makes only a binary choice between yes and no, no matter how complex the two options.

Well, not exactly. Selection does not work in this binary way. The organism with the mutation might reproduce better than any other; but the other organisms don't stop reproducing completely based only on that.

On p. 73, Spetner writes:

If a copying error were to damage a gene so it no longer functioned, the genome will have become less complex, and some of its information will have been lost. You might think the mutation has wiped out all the information in that gene. You might think that after the mutation, the genetic information is as if the gene weren't there. But the damaged gene is still there and nearly intact. The only defect is the one mutated nucleotide.

The meaning here being that either a gene functions or it does not function. In actual practice it is rarely like that; but that is of less importance here. Spetner's point is that just as one tiny mutation can switch off an entire gene, a tiny mutation can switch on an entire gene; but the gene had to be there already. That is, according to Spetner, mutations do not make genes; they only turn them on or off. This indeed is 1 bit of information for a specific genome; but when we talk about evolution, we deal in populations, not in individual organisms.

As in the last quote from p. 73, Spetner is rather equivocative about 'information'. This tendency gets worse in Chapter 4, "Is the Deck Stacked?". 

On p. 96, Spetner defines two criteria for cumulative selection. The definitions are reformulated on p. 106:

  1. [The evolutionary steps] must be able to be part of a long series in which the mutation in each step is adaptive.

  2. The mutattions must, on the average, add a little information to the genome.

But what is "a little information"?

Continuing, Spetner writes:

The information a mutation adds in a typical step of cumulative selection must fall within strict limits. On the average. each step must add some information. Yet it cannot be much more than one bit. Each step must add some information on the average so that information can build up over the full chain of steps that make up macroevolution. But if a mutation seems to have much more than one bit it can't be a  part of cumulative selection. We would have to interpret that mutation as the switching on of information already in the genome, as I noted in Chapter 3.

This doesn't make it any clearer, does it? We really need to know, how Spetner measures information in a genome.

On pp. 108-109, Spetner compares cumulative evolution to finding a path through a huge tree-like maze starting at the root. Spetner assumes that it takes 500 evolutionary steps to turn one species into another, so there are 500 levels of nodes in the tree, and with a genome of one million nucleotides, there are one million branches from each node.

First, at any time, there will be more than one mutation in the population gene pool at a time, and second, one million choices corresponds to 20 bits of information, if we interpret information as the bits to indicate the choices not taken, so each step would add 20 bits of information, not a maximum of 1 bit.

The title of Chapter 5 is "Can Random Variation Build Information?", and that at least sounds promising. Hopefully, Spetner is going  in this chapter to tell us more about, how he measures information.

And we are in luck here. On p. 134, Spetner writes:

Before we enter the subject of mutations and information, let's first see how information is related to specificity. The more specific a gene, the more information it contains. In general, the more specific any message, the more information it contains. The information in a gene is the same as the information in the protein it encodes.

Or, the more possibilities ruled out, the more information.

Spetner's subsequent discussion has a few oddities to it. For example he discusses on pp. 139-142 bacterial resistance to antibiotics such as streptomycin, a drug that attaches to a matching site on a ribosome and interferes with the bacterium's production of proteins. A mutation can change the site so that streptomycin can no longer attach to the site. Bottom p. 141, Spetner sums up:

Although such a mutation can have selective value, it decreases rather than increases the genetic information. It therefore cannot be typical of mutations that are supposed to help form small steps that make up macroevolution. Those steps must, on the average, add information. Even though resistance is gained, it's gained not by adding something, but by losing it. Rather than say that the bacterium gained resistance to the antibiotic, we would be more correct to say that it lost its sensitivity to it. It lost information.

Maybe so, if it wasn't because Spetner is contradicting himself here. On p. 137, he introduces a word-enzyme, that matches to all words that contain a certain string. As an example, Spetner mentions the string "ghtsha", and claims that there is only one english word with that as a substring, the word nightshade. That is, such a word-enzyme would have a high specificity. Spetner then erites (cf. p. 137):

If we reduce the information in the match string by dropping the "a" at the end, and match only to "ghtsh," the match becomes less specific since there are now two more words that match, namely, nightshirt and lightship. These matches, however, would be "weaker" than the previous one because they match to only five letters, whereas the previous match was to six.

Let's reverse this. Assume our word-enzyme starts out with looking for the string "ghtsh" and then changes to "ghtsha", then there would have been an increase in information due to the extra letter and an increase in specificity, because fewer strings match. However, with the logic from the example with resistance to streptomycin, we might as well say that the word-enzyme had lost its sensitivity to nightshirt and lightship and therefore lost information.

As Spetner has it, a loss and a gain in information is only a question of how we look at it. His concluding remarks on p. 143 are therefore somewhat on the comical side:

The NDT is supposed to explain how the information of life has been built up by evolution. The essential biological difference between a human and a bacterium is in the information they contain. All other biological differences follow from that. The human genome has much more information than does the bacterial genome. Information cannot be built up by mutations that lose it.

But since the example of a mutation mentioned by Spetner could be interpreted as an increase in information rather than as a decrease in information, there's really no reason to panic.

Ian Musgrave in the TalkOrigins article Information Theory and Creationism: Spetner and Biological Information goes into much more detail about this.

Chapter 6, "The Watchmaker's Blindness", is a critique of Richard Dawkins' evolution simulations in the book The Blind Watchmaker. There is little to comment on here – Dawkins' point was to illustrate the difference between no selection and selection, and his examples did that quite well. The mutation rates in the examples are unrealistic high, but in return the population sizes are unrealistic small, so Spetner's critique doesn't quite hit.

In Chapter 7, "The Deck is Stacked!", Spetner claims that mutations can be induced by the environment and thus are not 'random' as required by the NDT.

Ian Musgarve also comments on this subject in the above linked TalkOrigins article in the section Spetner and "directed" mutation.

Spetner mentions pp. 187-191 experiments by Barry Hall and John Cairns, where mutations occur that enable bacteria to feed on nutrients they usually cannot feed on. And these experiments indicate that it is the presence of the nutrient that induces the mutations as if the bacteria could choose which genes to enable depending on available nutrients.

On p. 190, Spetner writes:

If the results of these experiments indicate that adaptive mutations are stimulated by the environment, they contradict the basic dogma of neo-Darwinism. According to that dogma, mutations are random, and the kind of mutations that occur are independent of the environment. If mutations are really nonrandom in the sense that the environment can stimulate adaptive mutations, then the paradigm of Darwinian evolution, which has dominated the biological sciences for close to 150 years, must be replaced.

How can something that might disprove a statement about mutations force a replacement of the paradigm of Darwinian evolution, when Darwin knew nothing about mutations? It would be the same as disproving the existence of, say, magnetism by disproving a particular theory about magnetism.

Spetner provides us with an answer in a passage in the last paragraph on p. 191:

Resistance to the nonrandom-variation interpretation stems from a refusal to abandon the Darwinian agenda that evolution must confirm that life arose and developed spontaneously. With that agenda, nonrandom adaptive variation, arising from an environmental signal turning on an already present set of genes, is hard to account for.

The reasoning here is that organisms can only turn genes on or off, if those genes already exist, and if all that mutations can do is to turn genes on or off, mutations cannot explain evolution of the genes in the first round.

In general, this chapter presents a neo-Lamarckian concept of evolution, where new traits are acquired dependent on the environment, inclusive the kind of food eaten, and these new traits are inherited. It is unclear to me, if Spetner's examples are not just, what is called forms of a species, environmentally dependent variations that are not actually new traits.

In Chapter 8, the Epilogue, Spetner sums up his critique of the NDT and proposes a theory called the nonrandom evolutionary hypothesis, NREH, and he concludes with the words (cf. p. 208):

The NREH is a hypothesis that explains many observed phenomena that the NDT does not explain. According to the NREH, adaptive modifications in organisms occur when the environment induces a change in either the phenotype or the genotype. It can account for the environmentally induced adaptive mutations reported in bacteria. It can account for the pervasive convergences found throughout the plant and animal kingdoms. The NREH does not suffer from the contradictions of the NDT, and promises therefore to provide a more consistent picture of life.

And it's even consistent with the Torah.

For the layman, this may all appear very persuasive, and it is beyond my qualiications to give much of an in depth critique. However, even I can see some obvious problems with the NREH as presented by Spetner, such as his inconsistent information metric and what he considers to be different species may simply be different forms of the same species.

Carl Wieland of AnswersInGenesis has written a review of Not By Chance! (first published in Creation 20(1): pp. 50–51, December 1997), which begins with the words:

‘See, speak, or hear no evidence against evolution’ seems to be the golden rule in the academic world—so it will be interesting to see the response to this devastating assault, by a highly qualified author, on the very core of evolutionary theory.

As should be clear from the above, Spetner's 'assault on the very core of evolutionary theory' can hardly be considered devastating, simply because chance is not the very core of evolutionary theory.

Later, Wieland writes:

In a memorable turn of phrase, he says that anyone who thinks that an accumulation of mutations (information-losing processes) can lead to macroevolution (a massive net gain of information) ‘is like the merchant who lost a little money on every sale but thought he could make it up on volume.’

After such a ‘king hit’, Dawkins’ computer simulations of ‘insects’ and literary weasels seem somewhat puerile, and are easily dealt with by the author, who, from reliable information received, is rather keen to debate Dawkins on this whole issue. Why not, when one appears to be equipped with such decisive scientific weapons?

Except that Spetner is somewhat equivocative about that information thing, so let us try to go more into details about Spetner's method of measuring information.

On TalkOrigins, Edward E. Max has posted an article The Evolution of Improved Fitness by Random Mutation Plus Selection, and subsequently a longer exchange between Max and Spetner followed. This exchange is summed up by Spetner in the TrueOrigins article A Scientific Defense of a Creationist Position on Evolution.

In this article, Spetner writes:

The information content of the genome is difficult to evaluate with any precision.  Fortunately, for my purposes, I need only consider the change in the information in an enzyme caused by a mutation.  The information content of an enzyme is the sum of many parts, among which are:

  • Level of catalytic activity
  • Specificity with respect to the substrate
  • Strength of binding to cell structure
  • Specificity of binding to cell structure
  • Specificity of the amino-acid sequence devoted to specifying the enzyme for degradation

These are all difficult to evaluate, but the easiest to get a handle on is the information in the substrate specificity.

This is a more elaborated version of, what Spetner wrote in Chapter 5 of Not By Chance! Information rules out possibilities, so the more specificity we have, the more information we have.

Spetner continues:

To estimate the information in an enzyme I shall assume that the information content of the enzyme itself is at least the maximum information gained in transforming the substrate distribution into the product distribution.  (I think this assumption is reasonable, but to be rigorous it should really be proved.)

Who is gaining information here? Are we supposed to think that an enzyme gains information by "transforming the substrate distribution into the product distribution"? What Spetner is refering to is that we can make an experiment involving various substrates and observe the result, if any, of enzymatic activity. So, the one gaining information is the experimenter, not the enzyme. That is, the information content is not something within the enzyme, but something that is generated by the experiment.

But Spetner sees it differently:

We can think of the substrate specificity of the enzyme as a kind of filter.  The entropy of the ensemble of substances separated after filtration is less than the entropy of the original ensemble of the mixture. We can therefore say that the filtration process results in an information gain equal to the decrease in entropy.  Let’s imagine a uniform distribution of substrates presented to many copies of an enzyme.  I choose a uniform distribution of substrates because that will permit the enzyme to express its maximum information gain. …

The products of a substrate on which the enzyme has a higher activity will be more numerous than those of a substrate on which the enzyme has a lower activity. Because of the filtering, the distribution of concentrations of products will have a lower entropy than that of substrates.

That is, for Spetner it is the enzyme that gains information. Are we to think that the enzyme takes a nip of each substrate to figure out which ones are tasty and which ones are not? And even if so, where is the memory of the enzyme, in which it stores the gained information?

The entropy, Spetner refers to, is Shannon entropy (almost defined by Spetner a few paragraphs later), which indeed assumes its maximum for a uniform distribution. However, Shannon's model was a communication system, where the sender can choose among a number of messages to send, where all the messages are possible, but not necessarily equally likely. The entropy measures the receiver's uncertainty about which message was sent, an uncertainty that assumes its maximum, if all messages are equally probable. In Spetner's case the entropy would be the experimenter's uncertainty about, which substrates the enzyme will catalyze. However, that is not related to the substrate distribution, but to the experimenter's prior assumption about, which substrates the enzyme will catalyze. Using equal amounts of the substrates does make calculations easier, but it has nothing to do with entropy.

The word 'ensemble' used by Spetner refers to, what is called a statistical ensemble, the set of possible states of some system, often subject to some conditions. A simple example would be the entire set of sequences of 100 tossings of a coin. Each specific sequence is a member of the ensemble. Tossing a coin 100 times would return a sample from this ensemble; tossing the coin 100 times again would return another sample. If we tossed the coin 1,000 times, there would be be 901 positions, where a sub-sequence of 100 tosses begins, and each such sub-sequence would be a sample from the ensemble of possible sequences of 100 coin tosses. That is, an ensemble only exists conceptually, whereas a sample has real existence. Therefore Spetner's use of the expressions "[t]he entropy of the ensemble of substances separated after filtration" and "the entropy of the original ensemble" is meaningless. What might be meaningfull is to consider the ensemble of samples from these collections, say samples of X ml each.

However, we'll leave this subject and return to Spetner, who defines entropy like this:

The entropy of an ensemble of n elements with fractional concentrations f1,…,fn is given by

 H = ∑1≤in fi log fi,(1)

and if the base of the logarithm is 2, the units of entropy are bits.

Well, not quite, unless Spetner actually wants to define entropy in that way. What is missing is a minus-sign in front of the ∑-symbol. 

However, we'll leave that subject as well and return to Spetner, who first illustrates the formula by assuming that the enzyme is active on only one of the substrates, which he describes as perfect filtering; that is f1,…,fn = 1/n. The input entropy in this case is given by Spetner as HI = log n, which is quite correct, though not according to his formula (1); which would give HI = n•(1/n log 1/n) = log 1/n = − log n. The output entropy is given by Spetner as HO = 0. The decrease in entropy is therefore H = HIHO = log n, which equals the gain in information.

Spetner next considers the opposite extreme: an enzyme which does not discriminate between the substrates, it leaves products from all substrates. Here the input entropy and the output entropy are the same, HI = HO = log n, and the difference, the decrease in entropy is H = 0.

The problem with all this, even if using the correct formula for Shannon entropy, is that it doesn't make any sense. The number n is chosen by the experimenter, so how can it be encoded in the enzyme? Assume the enzyme does not catalyze any of the substrates, then the output entropy is HO = n•(0 log 0) = 0, just as in the case where the enzyme catalyzes exactly one substrate. How meaningfull is it to say that an enzyme that can catalyze no substrate has the same information encoded as one that can catalyze exactly one substrate? And not only that; while it would be possible to have a collection of substrates, none of which a given enzym can catalyze, the sum of the fi's must be 1. That is, the experimenter must make sure that the enzyme is able to catalyze at least one of the substrates. How can that have been encoded in the enzyme?

Assume that we are to guess a number between 1 and n, and that we have no reason not to assume each number to be equally probable. We can guess at random, or more systematically start with 1 and increase our guess by 1 until we hit. The minimum number of guesses needed is 1, if we hit in the first guess, and the maximum number is n-1 (if all those guesses were wrong, we know the answer without having to guess the nth time), and the average number of guesses needed will be n/2. Even better would be to bisect the remaining candidates in each round. That is, first ask if the number is smaller than or equal to n/2. If that returns a 'yes', then ask, if the number is smaller than or equal to n/4, and if it returns a 'no', then ask , if the number is smaller than or equal to 3n/4. And so on. The minimum number of guesses needed will be log n rounded down, and the maximum number will be log n rounded up, and the average number of guesses needed will be log n.

In a situation such as my example with guessing a number, it would be appropriate to talk about entropy, because there is an initial uncertainty concerning which number is chosen, and the information provided by the answer to each guess reduces the uncertainty. But in Spetner's example, this is not the case. If there is some uncertainty, it would be the experimenter's uncertainty concerning the number of substrates among the chosen substrates the enzyme can catalyze. Without any other prior information, this could be from 0 to n, and assuming equal probability, that would give an entropy of  log (n+1), not log n.

In his article, Spetner moves on to giving more details about an example from Chapter 5 of Not By Chance!:

Ribitol is a naturally occurring sugar that some soil bacteria can normally metabolize, and ribitol dehydrogenase is the enzyme that catalyzes the first step in its metabolism.  Xylitol is a sugar very similar in structure to ribitol, but does not occur in nature.  Bacteria cannot normally live on xylitol, but when a large population of them were cultured on only xylitol, mutants appeared that were able to metabolize it.  The wild-type enzyme was found to have a small activity on xylitol, but not large enough for the bacteria to live on xylitol alone.  The mutant enzyme had an activity large enough to permit the bacterium to live on xylitol alone.

As Spetner explains, the mutant bacterium had gained an increased activity on xylitol at the expense of a decreased activity on ribitol. But Spetner warns against seeing this as evidence for the neo-Darwinist position:

An evolutionist would be tempted to see here the beginning of a trend. He might be inclined to jump to the conclusion that with a series of many mutations of this kind, one after another, evolution could produce an enzyme that would have a high activity on xylitol and a low, or zero, activity on ribitol.  Now wouldn’t that be a useful thing for a bacterium that had only xylitol available and no ribitol?  Such a series would produce the kind of evolutionary change NDT calls for.  It would be an example of the kind of series that would support NDT.  The series would have to consist of mutations that would, step by step, lower the activity of the enzyme on the first substrate while increasing it on the second.

Where is the problem? According to Spetner, the problem is that not enough data is considered. As he explains, experiments indicated that the mutant also had increased catalyzation of L-arabitol relative to the wild bacterium, and:

With the additional data on L-arabitol, a different picture emerges. No longer do we see the mutation just swinging the activity away from ribitol and toward xylitol. We see instead a general lowering of the selectivity of the enzyme over the set of substrates.

That is, the mutant bacterium has a lowered activity on ribitol and an increased activity on both of the other sugars. Concluding, Spetner writes:

In Fig. 1 [comparison of activity on ribitol and xylitol] alone, there appears to be a trend evolving an enzyme with a high activity on xylitol and a low activity on ribitol. But Fig. 2 [activity on L-aribitol added] shows that such an extrapolation is unwarranted. It shows instead a much different trend.  An extrapolation of the trend that appears in Fig. 2 would indicate that a series of such mutations could result in an enzyme that had no selectivity at all, but exhibited the same low activity on a wide set of substrates.

And then the punch line:

The point to be made from this example is that conclusion jumping from the observation of an apparent trend is a risky business.  From a little data, the mutation appears to add information to the enzyme.  From a little more data, the mutation appears to be degrading the enzyme’s specificity and losing information.

Well, not exactly, it is only a consequence of Spetner's way of seeing things. The mutation has increased the ability of the enzyme in the mutant bacterium to catalyze other sugars than ribitol, which certainly is quite usefull, if there is no ribitol around, and one of the other sugars is available. Whether it adds information to the enzyme or not depends on, how we measure information and is not really of relevance for evolution. Evolution is not about adding information.

However, Spetner sees it that way and showa that the the mutant has lost information:

Just as we calculated information in the two special cases above, we can calculate the information in the enzyme acting on a uniform mixture of the three substrates for both the wild type and the mutant enzyme. Using the measured activity values reported by Burleigh et al. we find the information in the specificities of the two enzymes to be 0.74 and 0.38 bits respectively. The information in the wild-type enzyme then turns out to be about twice that of the mutant.

Yes, with Spetner's information metric; but as noted above, that metric is Spetner's own artificial product of the way in which these experiments are carried out and has nothing to do with any intrinsic information in the enzyme.

Spetner quotes from the exchange with Max:

Max: I want to make it clear that I don’t buy your interpretation of certain specific mutations as reflecting a ‘loss of information.’ You state that the ‘information content of an enzyme is the sum of many parts, among which are:  level of catalytic activity, specificity with respect to the substrate, strength [and specificity] of binding to cell structure, [and] specificity of the amino-acid sequence devoted to specifying the enzyme for degradation.’ This formulation is vague, non-quantitative, not supported by clear logic, not accepted in the scientific literature (to the best of my knowledge; please educate me if I am wrong), and in my view not useful.

To which Spetner comments:

Ed, the level of your argument here is quite low.  You have seen this entire section (above), and you took from the introduction my list of what characteristics can contribute to the information content of an enzyme and criticized it for being non-quantitative (followed by other pejorative epithets). Is that supposed to be some sort of debating tactic?  In any case, the tactic is out of place in this discussion.  From the context of what I wrote, it should have been clear to you that this partial list of characteristics that can contribute to the information in an enzyme was an introduction to my quantitative estimate of one of the characteristics of specificity of an enzyme.  After I showed how one might calculate the information related to a type of specificity, I showed how a mutation that appeared to enhance activity on a new substrate actually reduced the information by about 50%.

The problem here is that Spetner's "quantitative estimate of one of the characteristics of specificity of an enzyme" doesn't work. It is quantitative indeed, but the quanta will vary depending on the number of substrates (the value of n in Spetner's examples) and therefore it can hardly be considered to prove anything.

Back to Spetner:

It is elementary that specificity translates into information and vice versa. Have you ever played 20 questions? With the YES/NO answers to 20 judicious questions, one can discover a previously-chosen number between 1 and a million. If the questions are well chosen, those YES/NO answers can be worth one bit of information each, and 20 bits can specify one object out of a million. Twenty bits of information translates to specificity of one part in a million. Ten bits—to one part in a thousand.

Well, yes and no. Does specificity translate into information and vice versa? As Spetner writes here, it takes more bits (on the average) to specify an object out of a larger collection than out of a smaller collection, but that's exactly the problem: it's relative to collection size. If we were to guess a number between 1 and a million, we would need 20 guesses, even if that number is less than or equal to one thousand. That is, the information required is not related to the number chosen, but to the size of the collection, from which the number is drawn.

Later, Spetner quotes Max for a critique of Spetner's example with streptomycin. Here Spetner comments:

The wild-type S12 proteins that bind to the streptomycin molecule also form a subset of the universe of all possible S12 proteins.  The set of S12 proteins that allow bacterial growth in streptomycin (i.e. that do not bind to the antibiotic) form a disparate subset of the universe of S12 proteins. My intuition tells me that the set that binds (the susceptible set) is smaller, and therefore has a smaller entropy, than the set that does not bind (the resistant set).  Mutations that appear in the presence of the antibiotic convert one subset to the other.  A mutation that transfers the enzyme from a low-entropy set to a higher-entropy set loses information; it does not gain it.

Ok, if we were one day to guess a number between 1 and 1,000, we would have an entropy of 10 bits, and if we were the next day to guess a number between 1,001 and 1,001,000, we would have an entropy of 20 bits, therefore we have lost information from the first day to the second.

(Note: I am aware that 210 = 1,024, not 1,000, and I am aware that 220 = 1,048,576, not 1,000,000. And I am sure that Spetner is aware of this as well.)

An obvious problem with Spetner's argumentation here is that a potential S12 protein need not be a possible S12 protein. If we toss a coin, we generate samples as we toss along. But that's not how S12 proteins are sampled. Of course, if we were to produce them synthetically, the situation might ne more like coin tossing; but synthetically produced S12 proteins would not be of relevance here. However, since I have no idea about how many S12 proteins of any kind there are, I will not pursue that subject any further.

Another problem is that Spetner's use of 'entropy' is rather confusing here. He considers a smaller set to have a smaller entropy, which would be in analogy to the example with guessing numbers.

In Not By Chance!, Spetner uses an example with specification of a room in an apartment in a building to illustrate specificity of addressing; but in the article he uses another example:

The Zip codes in the US also demonstrate that specificity and information are two sides of the same coin and go hand in hand.  An address in the United States can be completely specified by the nine-digit zip code. One digit of information will narrow down the address from being anywhere in the United States to being in just a few states. Thus if the first digit is a 6, the address is located somewhere in Illinois, Missouri, Kansas, or Nebraska.

A second digit of information will add specificity by narrowing down the address further.  A 3, 4, or 5 in the second digit puts the address in Missouri. A 3 in the second digit puts it in the eastern portion of the state. Two digits of information are more specific than one.

A third digit of information is still more specific, narrowing down the address even more, making it still more specific.  If the third digit is a 1, the address is specific to St. Louis and its suburbs.  The next two digits of information pin down the address to within a few blocks.  The last 4 digits of information can locate a specific building.  Thus, it is clear that the information contained in the digits of the zip code translate into specificity.

There is no question about it:  SPECIFICITY = INFORMATION.

That is, for Spetner, more digits = more specificity = more information. What goes for digits, goes for bits (= binary digits) as well. Assuming there to be 1,000 binding S12 proteins, each of these could be specified with 10 bits, and assuming there to be 1,000,000 non-binding S12 proteins, each of these could be specified with 20 bits. That is, more bits would be required to specify any non-binding protein than to specify any binding protein, and therefore, assuming Spetner's intuition about there being more possible non-binding than binding S12 proteins, then transfering a protein from the binding group to the non-binding group increases information.

I would guess that what goes wrong is that Spetner thinks about it this way: with the Zip code, each additional digit narrows down the area addressed by the Zip code. That is, more information = more digits = smaller area. However, that only works for subsets. St. Louis and its suburbs is not only a smaller area than the eastern part of Missouri, it is a sub-area. But the binding proteins are not a subset of the non-binding proteins, so the analogy doesn't work.

Returning to Wieland's review, Wieland introduces Spetner with these words:

Jewish scientist Dr Lee Spetner’s book aims a death-blow at the heart of this whole Neo-Darwinian story. The crucial battleground has always been the origin of information, and in this field, Spetner is uniquely qualified to comment. With a Ph.D. in physics from MIT, Spetner taught information and communication theory for years at Johns Hopkins University. In 1962 he accepted a fellowship in biophysics at that institution, where he worked on solving problems in signal/noise relationships in DNA electron micrographs. He subsequently became fascinated with evolutionary theory, and published papers concerning theoretical and mathematical biology in prestigious journals such as the Journal of Theoretical Biology, Nature, and the Proceedings of the 2nd International Congress of Biophysics.

These are fine credentials, and I am certainly not claiming that Lee Spetner doesn't have excellent qualifications. However, for some reason, his use of information theory doesn't quite work. Spetner commits too many simple errors in that use, and considering his qualifications, I would suggest it is because he has let his wish of disproving neo-Darwinism get the better of him. I am quite sure Spetner could have done better than he has.

Wieland ends his review with the words:

To say that Spetner’s book is an absolute ‘must’ for anyone defending Scripture in this increasingly educated age is an understatement. To put it succinctly, it seems that unless evolutionists can pull a brand new rabbit out of the hat, Spetner has just blown the whole evolutionary mechanism out of the water once and for all. The evolutionary/humanist establishment cannot allow this to happen, of course, so it will be interesting to see their reaction and attempts at damage control. I trust that readers of this review will make it as hard as possible for them to ignore this groundbreaking work, by spreading it as far and fast as they can.

Hyperbolic language comes cheap, doesn't it?

To finish off, I must admit that I enjoyed reading Not By Chance!, even if I disagree with Spetner's conclusion. And I must say that the book would have deserved a more thoeough review from the creationist camp than Wieland's review that is little more than standard creationist troop mustering that doesn't even mention the parts of the book that are really good.

Tuesday, December 05, 2006

Gilder, O'Leary, and lactose

In Part Four, The hierarchy of information vs. "nothing but", of Denyse O'Leary five part series on George Gilder, there is an interesting little detail.

O'Leary writes:

Regarding the "causes of economic growth," its [sic] worth remembering that - at every stage - "economic growth" is first and foremost an idea in the minds of men. It always begins with an idea of a better life - clean water or public schools, for example. The material advance follows the idea. Without the idea the advance never happens. Ignoring this principle has led to much waste in foreign aid efforts by wealthy countries. Why? Because things have been forced on people as "improvements" before they wanted or cared about them, and they responded by ignoring, subverting, or destroying them.

So, instead of just forcing our things on other people, we also have to force our ideas on them.

O'Leary continues:

Example: My own country (Canada) once exported tins of powdered milk to a poor country where the malnourished people did not normally drink milk after they were weaned. But the recipients threw away the powdered milk and used only the aluminum tins! The people were not stupid. They easily understood the value of the tins in their daily life. But they did not understand the value of the milk. They did not know about the importance of proteins in the diet. So an effort to improve health in that region did not depend on supplying a physical substance such as powdered milk. It depended on getting the people to accept the idea that a higher protein diet would alleviate illness and the idea that the donated powdered milk could help them do so. In that case, only a change at the highest level of the system (the ideas in the minds of men) could change centuries of misery. Indeed, once they accepted the idea, they might seek local sources of milk, and might not end up needing much help from Canada.

See, things are not that simple. To metabolize lactose, an ingredient in milk and other dairy products, you need the enzyme lactase, an enzyme produced, for obvious reasons, by young mammals, but usually not by adult mammals. For humans, the production generally cease between the ages two and five. This is called lactose intolerance (Wikipedia article).

Northern Europeans (and people elsewhere of Northern European origin) with their long tradition of living on dairy products have very few lactose intolerant people, whereas among African Bantus 89% are lactose intolerant, and among Native Americans 100% are lactose intolerant. So, it's not just a question of giving people the idea that milk is healthy, because maybe it isn't.

It is not possible from O'Leary's short story above to see, if the milk was cow milk or plant milk, and if it was cow milk, whether it had been treated with lactose catalysing bacteria or another process with the same purpose. But all in all, it is possible that the milk powder was thrown away, becayúse it really wasn't healthy.

It's not just a question of ideas, lactose intolerance is real, not hysteria, and lactose tolerance is due to a mutation that is most widespread among Northern Europeans. So whether O'Leary likes it or not, she has unknowingly touched upon a subject that favors the evil Darwinists rather than the good IDists.

See also
Gilder, O'Leary, and Dawkins
The ID dilemma

Monday, December 04, 2006

Gilder, O'Leary, and Dawkins

Denyse O'Leary has on her ARN blog, The ID Report, a five part series on Why is tech guru George Gilder not a Darwinist? The second part, Life as architecture of ideas or information, is particularly interesting.

George Gilder is co-founder of the Discovery Institute, a born-again Christian, and he likes glass-fiber cables, so all in all, he is indeed a tech guru.

O'Leary starts out with:

As Gilder explains in his National Review article, the tormented computer genius Alvin Turing stressed that a computer is not wires and metal but "its architecture of ideas."

We'll ignore that it is 'Alan Turing', and only pick up the notion that it is not the material implementation that matters. It's a funny thing with anti-evolutionists: that they believe that all evolutionists are materialists, and that therefore anyone who is not a materialist must be one of their heroes.

My point in this post is to show that by that reasoning, Richard Dawkins must belong right up there with Allan Turing as an ID hero.

O'Leary continues:

Most writers understand this concept quite easily, actually. A book for which the publisher has forwarded $50 000 advance can be lodged on a computer whose market value is $500 - and whose scrap value is 50 cents. The ideas give value to the computer, not the other way around.

Really, it was no different in the days of pen and paper or clay tablets. It was always the ideas that gave value to the material objects, not the other way round.

Yes, we understand this concept quite easily; but, may we ask, is O'Leary aware that 99% of all clay tablets found deal with economic transactions: so and so much grain is paid in tax, so and so much silver is paid in for some goods, and so on. Transactions describing movements of material objects. And without some material embodyment, the architecture of ideas in a computer is of little use.

But ok, we live in the Age of Information, and we have known that for some time, so what is O'Leary's real point?

Of course, that 'Darwinian materialism' must be provable wrong. To this purpose, O'Leray quotes Gilder for the following:

I came to see that the computer offers an insuperable obstacle to Darwinian materialism. In a computer, as information theory shows, the content is manifestly independent of its material substrate. No possible knowledge of the computer's materials can yield any information whatsoever about the actual content of its computations. In the usual hierarchy of causation, they reflect the software or "source code" used to program the device; and, like the design of the computer itself, the software is contrived by human intelligence.

What Darwinian materialism? Unfortunately, materialism can refer to quite a gamut of ideas (ironic, ne'est-ce pas?); but usually implies something about the primacy of matter over ideas, whatever happens to be meant by 'ideas'. For instance, in Marxist historical materialism, the word 'materialism' refers to primacy of material production over the ideology; that is, the organization of material production causes ideologies rather than the other way around. This is obviously a very different kind of materialism than Democritus of Abdera's dictum, "There is nothing but atoms and space, everything else is only an opinion".

O'Leary shortly after writes:

Consider Shannon's concept of entropy. "News" or information cannot be described by purely physical or chemical theories. We can easily see why this is so if we think about it. To you, information is what your mind accepts as information. For example, the discovery via an e-mail that someone you love really prefers someone else [!] is information to you. To the computer, the key information was only more bits 'n bytes. As Gilder says, "Information is defined by its independence from physical determination: If it is determined, it is predictable and thus by definition not information."

Yes, of course, but who doesn't know this? And anyway, Gilder in the quoted passage gets things wrong. There is quite a difference between whether something is determined and whether it is known to be determined, and even if it is known to be determined, whether the entire causal chain is known. If I flip a coin, I have reason to believe that it is fully determined whether it lands heads up or tails up; there is not some fairy that manipulates it underways. Yet I cannot predict the outcome, except statistically.

If I receive an e-mail, the content of that e-mail is fully determined; it doesn't randomly change just because I open and read it. Whether it is information for me or not is a different matter, so O'Leary and Gilder are confusing knowledge and determination.

Quoting Gilder, O'Leary writes:

in all the sciences I studied, information comes first, and regulates the flesh and the world, not the other way around. The pattern seemed to echo some familiar wisdom. Could it be, I asked myself one day in astonishment, that the opening of St. John's Gospel, In the beginning was the Word, is a central dogma of modern science?

If information is something that can only be picked up by a mind, how can information regulate "the flesh and the world"? And, as for the Gospel of John, it was the Word of God, not just any old word.

And a paragraph later:

I can now affirm the principle empirically. Salient in virtually every technical field from quantum theory and molecular biology to computer science and economics is an increasing concern with the word. It passes by many names: logos, logic, bits, bytes, mathematics, software, knowledge, syntax, semantics, code, plan, program, design, algorithm, as well as the ubiquitous "information." In every case, the information is independent of its physical embodiment or carrier

So, it's the word by any other name; but how does that relate to Darwinism?

After having supplied the above quote, O'Leary turns rather mysterious:

But what about DNA?, one might ask. Isn't our DNA a deterministic code that just happened to evolve and create us? Well, the chemistry of DNA is irrelevant to its message. The four DNA code letters - A,C,G,T - do not, in themselves, tell a creature what to be, any more than letters of an alphabet tell you what to write. Additional information does that. For example, the simple nematode worms that survived a recent space shuttle disaster and were returned to their owners have only somewhat fewer genes than humans (20 000 vs. 30 000) - which basically tells you that most of what is really happening is not happening in the genes.

Of course, the letters of an alphabet doesn't tell me, what to write; but the letters in for instance O'Leary's post tell me, what to read, don't they? And how is the 'small' difference between the number of nematode genes and human genes (which is 50% of the number of nematode genes) related to, what is really happening?

Yet another Gilder quote:

Like a sheet of paper or a series of magnetic points on a computer's hard disk or the electrical domains in a random-access memory or indeed all the undulations of the electromagnetic spectrum that bear information through air or wires in telecommunications DNA is a neutral carrier of information, independent of its chemistry and physics. By asserting that the DNA message precedes and regulates the form of the proteins, and that proteins cannot specify a DNA program, Crick's Central Dogma unintentionally recapitulates St. John's assertion of the primacy of the word over the flesh.

It was for some time thought that proteins were the carriers of inheritance, and with the discovery of DNA, it was still discussed, which had which rôle. With Francis Crick's Central Dogma the discussion ended with DNA being the carrier of inheritance, and proteins being encoded in DNA. O'Leary writes that there are four DNA code letters, A,C,G,T. However, these do not encode anything; we need three of them to make, what's called a codon, the actual letter of the DNA code. There are therefore 4*4*4 = 64 different codons, a 64 letter alphabeth. Each codon either encodes an amino acid or is a stop code. There are 20 amino acids, so 64 letter alphabeth of DNA is actually translated to a 21 letter alphabeth, of which the 20 letters, the amino acids, are used in proteins. It is therefore not possible from a protein to reconstruct its gene (the sequence of codons that encoded it), and therefore proteins cannot precede DNA.

So, contrary to O'Leary's statement above, that "what is really happening is not happening in the genes", Gilder follows the general trend by claiming that DNA is the provider of information. 

Perhaps O'Leary has misunderstood Gilders statement that "DNA is a neutral carrier of information, independent of its chemistry and physics"? A statement that by the way is not quite right, but let's just ignore that.

O'Leary does not make a distinction between DNA and genes, while Gilder does not mention genes. However, the way he refers to DNA, he clearly means DNA patterns, not the individuals DNA molecules.

This, interestingly, brings Gilder in exact line with the atheist Darwinist materialist Richard Dawkins, who back in 1986 published The Blind Watchmaker.

On p. 127 of said book, Dawkins writes:

DNA gets the best of both worlds. DNA molecules themselves, as physical entities, are like dewdrops. Under the right conditions they come into existence at a great rate, but no one of them has existed for long, and all will be destroyed within a few months. They are not durable like rocks. But the patterns that they bear in their sequences are as durable as the hardest rocks. They have what it takes to exist for millions of years, and that is why they are still here today. The essential difference from dewdrops is that new dewdrops are not begotten by old dewdrops. Dewdrops doubtless resemble other dewdrops, but they don't specifically resemble their own 'parent' dewdrops. Unlike DNA molecules, they don't form lineages, and therefore can't pass on messages. Dewdrops come into existence by spontaneous generation, DNA messages by replication.

That is, while DNA molecules are material, genes = DNA patterns are not, though each concrete instance needs to exist in a material form. 

For Dawkins as for Gilder, the DNA molecules are carriers of information, an information that is the DNA pattern, which itself is neither physical nor chemical, but apparently, in a Platonistic sense, an idea. An entire genome must therefore, for Dawkins, not be something physical and chemical, but "its architecture of ideas."

Maybe the ID people should study Darwinists a bit more closely, before they run out and claim to have refuted Darwinist materialism?

See also
Gilder, O'Leary, and lactose
The ID dilemma

Wednesday, November 29, 2006

The 6,000 years prophecy

Glenn Morton has on his web-site an article Early Church Fathers on Genesis by John Tobin. The point in this article is that not all the early church fathers didn't believe in a six days creation and a young earth. The article does not deny that some of the ECFs believed in a six times 24 hours creation.

Interestingly, a YEC website, www.creationism.org, has an article named The Early Church Fathers Believed in A Young Earth & Recent Creation, which claims that Origen is the only ECF that maybe interpreted the days of creation as anything but 24 hours days.

And the article begins with a quote from The Epistle of Barnabas:

The Sabbath is mentioned at the beginning of the creation: "And God made in six days the works of His hands, and made an end on the seventh day, and rested on it, and sanctified it." Attend, my children, to the meaning of this expression, "He finished in six days." This implieth that the Lord will finish all things in six thousand years, for a day is with Him a thousand years. And He Himself testifieth, saying, "Behold, to-day will be as a thousand years." Therefore, my children, in six days, that is, in six thousand years, all things will be finished.

The article supplies a few more quotes of similar content.

So, not only did some of the ECFs believe in a literal six days creation, some of them also believed that everything would be finished in 6,000 years; that is, the end of the world would come 6,000 years after the start of the creation.

This is even clearer in a quote given a few paragraphs later. In Against Heresies, Book 5, Irenaeus writes:

For in as many days as this world was made, in so many thousand years shall it be concluded. And for this reason the Scripture says: "Thus the heaven and the earth were finished, and all their adornment. And God brought to a conclusion upon the sixth day the works that He had made; and God rested upon the seventh day from all His works." This is an account of the things formerly created, as also it is a prophecy of what is to come. For the day of the Lord is as a thousand years; and in six days created things were completed: it is evident, therefore, that they will come to an end at the sixth thousand year.

So, origins may for YECs simply be a part of eschatology, and that might explain why it is so important for them that the earth not be much older than 6,000 years old. As I have mentioned elsewhere, Gerald Aardsma, who formerly worked with ICR, had to leave, because he accepted to push the upper limit to 12,000 years, so it's not just a question of Genesis 1; there is clearly more at stake.

And that more might well be that the real question for the YECs is not, how long the earth has existed, but how long it will continue to exist.

However, is this idea supported by the Bible? The Bible does operate with longer cycles that are based on shorter cycles, such as the sabbathical cycle of seven years, a week of years, based on the seven days week, and the jubilar cycle, fourtynine years made up of seven sabbathical cycles. But these are cycles, something repeating itself, not something with a final ending. So, this particular YEC idea of the earth lasting for as many thousand years as the creation in Genesis 1 spanned days would seem not to be supported by the Bible.

Tuesday, November 28, 2006

Dembski's Law of Conservation of Information

William Dembski provides on p. 8 of the online paper The Conservation of Information- Measuring the Cost of Successful search a definition of his Law of Conservation of Information in the form of a theorem.

However, just to warm us up, we'll do some preliminary definitions first.

Let A and B be two events with probibilty p of A to occur and probability q of B to occur.

The (self-)information or surprisal value of A is defined as

I(A) = − log2 p

The added information of B to A is defined as

I+(A : B) = I(A) − I(B) = − log2 p + log2 q = log2 q/p.

Two immediate consequences of the latter definition is

I+(A : A) = − log2 p + log2 p = 0; and

I+(A : B) = log2 q/p ≤ log2 1/p = − log2 p = I(A).

The last line implies that the added information of B to A cannot exceed the information of A alone.

What should here be understood is that the information of A is exactly a measure of the surprise of the occurence of A, the smaller the probability, the larger the surprise. Assume you live somewhere, where the probability of rain on any one day is 90%, and the always reliable weather forecast says that it will rain the next day. The weather forecast doesn't really give you much information, since you would anyway expect it to rain, so not much surprise in that case. If instead the weather forecast had said that it would be a clear and sunny day the next day, that would have given you more information, since it would be contrary to expectation, therefore a greater surprise.

What the definition of added information says is basically that you know, what you know, and the more you know, the less will there be to learn.

Dembski's motivation for introducing added information (cf. p. 3) is as follows. During a search, the more samples are taken, the higher will be the probability of a success; but a higher probability corresponds with a lower self-information value, and our intuition says that the more samples taken, the more information generated.

A more efficient search will generate more information per sample; but the problem then is, how to figure out which search is more efficient than a random search, which Dembski uses as the base search strategy.

We can now give Dembski's definition of the Law of Conservation of Information:

Theorem (Conservation of Information). Suppose S and T are searches over a given search space, S being a random search with probability p success in a single query and T being a nonrandom search with probability 1 of success in a single query. Suppose further that U and V are searches over the space of searches in which S and T reside so that U on average locates a search of the original space that with probability no more than p successfully searches the original space and that T with probability 1 locates a search of the original space what with probability 1 successfully searches the original space. Then the information that V adds to U is at least as great as the information that T adds to S, i.e.,

I+(U : V) ≥ I+(S : T).

Moreover, by a suitable choice of U, this inequality becomes an equality.

Here U and V are meta-searches; that is, searches for searches. What the theorem therefore says is that is requires at least as much information to figure out how to do a search as to actually do the search itself.

As an illustration, Dembski uses a search for a treasure on an island (cf. p. 6). It may be prohibitive to do a random search for the treasure; but you have a treasure map, so no problem. However, where did you get the treasure map from? You first needed to do a search for that from among all treasure maps. This may have been an even more involved search, which leads to an infinite regress.

In short, information comes at a price, and that price is at least the same amount of information.

Dembski writes p. 9:

According to Douglas Robertson (1999), the defining feature of intelligence is its ability to create information. Yet, if an act of intelligence created the information, where did this intelligence come from? Was information in turn required to create it? Very quickly this line of questioning pushes one to an ultimate intelligence that creates all information and yet is created by none (see Dembski 2004: ch. 19, titled “Information ex Nihilo”).

Here 'Douglas Robertson (1999)' refers to an article "Algorithmic Information Theory, Free Will, and the Turing Test" by Douglas Robertson, and 'Dembski 2004' refers to Dembski's own book The Design Revolution.

The point being that intelligence creates information, which means that intelligence applies some search strategy, and from where does intelligence know about that search strategy? This knowledge is itself information, so there must be an ultimate intelligence.

If not, then, Dembski continues:

On the other hand, if the information is the mechanical outworking of preexisting information, the Conservation of Information Theorem suggests that this preexisting information was at least as great in the past as it is now (this being the information that allows the present search to be successful). But then how do we make sense of the fact (if it is a fact) that the information in the universe was less in the past than it is now? Indeed, our present universe, with everything from star systems to living forms, seems far more information-rich than the universe at the moment of the Big Bang.

The obvious question here is, how do we measure information? If there is more information in the universe today than at the moment of the Big Bang, assuming that to have happened, then we should be able to figure out, what happened all the way back to the Big Bang. The current universe certainly may exhibit more variation than the very early universe; that is, there are more different things to know something about, but is that more information?

All in all, Dembski's main point is that human intelligence might have another source than evolution, which he considers to be a search strategy. Since evolution to produce intelligence must itself have been even more intelligent or guided by something even more intelligent, evolution cannot be a random search. And if evolution is a random search, it cannot have produced intelligence, which must therefore have another source. He does not write this directly; but it's what he is hinting at.

Now, as for Dembski's Law of Conservation of Information, it ignores that we don't always start out with finding an optimal search strategy. Occasional search strategies are made up along the way based on experience. Modern dictionaries are alphabetically ordered, which makes it simple to use relatively efficient searches based on the spelling of a word; in antiquity it was more common to order words by decreasing importance, such that those that corresponded to a more important concept were at the top. However, in antiquity, scrolls were used, so this ordering simply meant that you typically only needed to unscroll a small segment of the scroll. With a book, you can open it anywhere at the same cost. In that way ordering of information and search strategies depend on technology. We simply don't start out with determining the optimal search strategy and then turn everything else around after that.

So, Dembski's theorem may be correct mathematically seen, but he may have wasted his time searching for the wrong solution to the wrong problem.

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A Christian in Satanist clothes