It would be very nice if there was a magic scanner that automatically gave you a readout of the total amount of complex specified information (CSI) in a system when you pointed it at that system, wouldn’t it? Of course, you’d want one that could calculate the CSI of any complex system – be it a bacterial flagellum, an ATP synthase enzyme, a Bach fugue, or the faces on Mt. Rushmore – by following some general algorithm. It would make CSI so much more scientifically rigorous, wouldn’t it? Or would it?
This essay is intended as a follow-up to the recent thread, On the calculation of CSI by Mathgrrl. It is meant to address some concerns about whether CSI is sufficiently objective to qualify as a bona fide scientific concept.
But first, some definitions. In The Design of Life: Discovering Signs of Intelligence in Biological Systems (The Foundation for Thought and Ethics, Dallas, 2008), Intelligent Design advocates William Dembski and Jonathan Wells define complex specified information (or CSI) as follows (p. 311):
Information that is both complex and specified. Synonymous with SPECIFIED COMPLEXITY.
Dembski and Wells then define specified complexity on page 320 as follows:
An event or object exhibits specified complexity provided that (1) the pattern to which it conforms is a highly improbable event (i.e. has high PROBABILISTIC COMPLEXITY) and (2) the pattern itself is easily described (i.e. has low DESCRIPTIVE COMPLEXITY).
In this post, I’m going to examine seven demands which Intelligent Design critics have made with regard to complex specified information (CSI):
(i) that it should be calculable not only in theory but also in practice, for real-life systems;
(ii) that for an arbitrary complex system, we should be able to calculate its CSI as being (very likely) greater than or equal to some specific number, X, without knowing anything about the history of the system;
(iii) that it should be calculable by independent agents, in a consistent manner;
(iv) that it should be knowable with absolute certainty;
(v) that it should be precisely calculable (within reason) by independent agents;
(vi) that it should be readily computable, given a physical description of the system;
(vii) that it should be computable by some general algorithm that can be applied to an arbitrary system.
I shall argue that the first three demands are reasonable and have been met in at least some real-life biological cases, while the last four are not.
Now let’s look at each of the seven demands in turn.
(i) CSI should be calculable not only in theory but also in practice, for real-life systems
This is surely a reasonable request. After all, Professor William Dembski describes CSI as a number in his writings, and even provides a mathematical formula for calculating it.
On page 34 of his essay, Specification: The Pattern That Signifies Intelligence, Professor Dembski writes:
In my present treatment, specified complexity … is now … an actual number calculated by a precise formula (i.e., Chi=-log2[10^120.Phi_s(T).P(T|H)]). This number can be negative, zero, or positive. When the number is greater than 1, it indicates that we are dealing with a specification. (Emphases mine – VJT.)
The reader will recall that according to the definition given in The Design of Life (The Foundation for Thought and Ethics, Dallas, 2008), on page 311, specified complexity is synonymous with complex specified information (CSI).
On page 24 of his essay, Professor Dembski defines the specified complexity Chi of a pattern T given chance hypothesis H, minus the tilde and context sensitivity, as:
Chi=-log2[10^120.Phi_s(T).P(T|H)]
On page 17, Dembski defines Phi_s(T) as the number of patterns for which S’s semiotic description of them is at least as simple as S’s semiotic description of T.
P(T|H) is defined throughout the essay as a probability: the probability of a pattern T with respect to the chance hypothesis H.
During the past couple of days, I’ve been struggling to formulate a good definition of “chance hypothesis”, because for some people, “chance” means “totally random”, while for others it means “not directed by an intelligent agent possessing foresight of long-term results” and hence “blind” (even if law-governed), as far as long-term results are concerned. In his essay, Professor Dembski is quite clear in his essay that he means to include Darwinian processes (which are not totally random, because natural selection implies non-random death) under the umbrella of “chance hypotheses”. So here’s how I envisage it. A chance hypothesis describes a process which does not require the input of information, either at the beginning of the process or during the process itself, in order to generate its result (in this case, a complex system). On this definition, Darwinian processes would qualify as a chance hypotheses, because they claim to be able to grow information, without the need for input from outside – whether by a front-loading or a tinkering Designer of life.
CSI has already been calculated for some quite large real-life biological systems. In a post on the recent thread, On the calculation of CSI, I calculated the CSI in a bacterial flagellum, using a naive provisional estimate of the probability P(T|H). The numeric value of the CSI was calculated as being somewhere between 2126 and 3422. Since this is far in excess of 1, the cutoff point for a specification, I argued that the bacterial flagellum was very likely designed. Of course, a critic could fault the naive provisional estimate I used for the probability P(T|H). But my point was that the calculated CSI was so much greater than the minimum value needed to warrant a design inference that it was incumbent on the critic to provide an argument as to why the calculated CSI should be less than or equal to 1.
In a later post on the same thread, I provided Mathgrrl with the numbers she needed to calculate the CSI of another irreducibly complex biological system: ATP synthase. As far as I am aware, Mathgrrl has not taken up my (trivially easy) challenge to complete the calculation, so I shall now do it for the benefit of my readers. The CSI of ATP synthase can be calculated as follows. The shortest semiotic description of the specific function of this molecule is: “stator joining two electric motors” which is five words. If we imagine (following Dembski) that we have a dictionary of basic concepts, and assume (generously) that there are no more than 10^5 (=100,000) entries in this dictionary, then the number of patterns for which S’s semiotic description of them is at least as simple as S’s semiotic description of T is (10^5)^5 or 10^25. This is Phi_s(T). I then quoted a scientifically respectable source (see page 236) which estimated the probability of ATP synthase forming by chance, under the most favorable circumstances (i.e with a genetic code available), at 1 in 1.28×10^266. This is P(H|T). Thus Chi=-log2[10^120.Phi_s(T).P(T|H)]=-log2[(10^145)/(1.28×10^266)]
=-log2[1/(1.28×10^121)]=log2[1.28×10^121]
=log2[1.28x(2^(3.321928))^121]=log2[1.28×2^402],
or about 402, to the nearest whole number.
Thus for ATP synthase, the CSI Chi is 402. 402 is far greater than 1, the cutoff point for a specification, so we can safely conclude that ATP synthase was designed by an intelligent agent.
[Note: Someone might be inclined to argue that conceivably, other biological structures might perform the same function as ATP synthase, and we’d have to calculate their probabilities of arising by chance too, in order to get a proper figure for P(T|H) if T is the pattern “stator joining two electric motors.” In reply: any other structures with the same function would have a lot more components – and hence be much more improbable on a chance hypothesis – than ATP synthase, which is a marvel of engineering efficiency. See here and here. As ATP synthase is the smallest biological molecule – and hence most probable, chemically speaking – that can do the job that it does, we can safely ignore the probability of any other more complex biological structures arising with the same functionality, as negligible in comparison.]
Finally, in another post on the same thread, I attempted to calculate the CSI in a 128×128 Smiley face found on a piece of rock on a strange planet. I made certain simplifying assumptions about the eyes on the Smiley face, and the shape of the smile. I also assumed that every piece of rock on the planet was composed of mineral grains in only two colors (black and white). The point was that these CSI calculations, although tedious, could be performed on a variety of real-life examples, both organic and inorganic.
Does this mean that we should be able to calculate the CSI of any complex system? In theory, yes; however in practice, it may be very hard to calculate P(T|H) for some systems. Nevertheless, it should be possible to calculate a provisional upper bound for P(T|H), based on what scientists currently know about chemical and biological processes.
(ii) For an arbitrary complex system, we should be able to calculate its CSI as being (very likely) greater than or equal to some specific number, X, without knowing anything about the history of the system.
This is an essential requirement for any meaningful discussion of CSI. What it means in practice is that if a team of aliens were to visit our planet after a calamity had wiped out human beings, they should be able to conclude, upon seeing Mt. Rushmore, that intelligent beings had once lived here. Likewise, if human astronauts were to discover a monolith on the moon (as in the movie 2001), they should still be able to calculate a minimum value for its CSI, without knowing its history. I’m going to show in some detail how this could be done in these two cases, in order to convince the CSI skeptics.
Aliens visiting Earth after a calamity had wiped out human beings would not need to have a detailed knowledge of Earth history to arrive at the conclusion that Mt. Rushmore was designed by intelligent agents. A ballpark estimate of the Earth’s age and a basic general knowledge of Earth’s geological processes would suffice. Given this general knowledge, the aliens should be able to roughly calculate the probability of natural processes (such as wind and water erosion) being able to carve features such as a flat forehead, two eyebrows, two eyes with lids as well as an iris and a pupil, a nose with two nostrils, two cheeks, a mouth with two lips, and a lower jaw, at a single location on Earth, over 4.54 billion years of Earth history. In order to formulate a probability estimate for a human face arising by natural processes, the alien scientists would have to resort to decomposition. Assuming for argument’s sake that something looking vaguely like a flat forehead would almost certainly arise naturally at any given location on Earth at some point during its history, the alien scientists would then have to calculate the probability that over a period of 4.54 billion years, each of the remaining facial features was carved naturally at the same location on Earth, in the correct order and position for a human face. That is, assuming the existence of a forehead-shaped natural feature, scientists would have to calculate the probability (over a 4.54 billion year period) that two eyebrows would be carved by natural processes, just below the forehead, as well as two eyes below the eyebrows, a nose below the eyes, two cheeks on either side of the nose, a mouth with two lips below the nose, and a jawline at the bottom, making what we would recognize as a face. The proportions would also have to be correct, of course. Since this probability is order-specific (as the facial features all have to appear in the right place), we can calculate it as a simple product – no combinatorics here. To illustrate the point, I’ll plug in some estimates that sound intuitively right to me, given my limited background knowledge of geological processes occurring over the past 4.54 billion years: 1*(10^-1)*(10^-1)*(10^-10)*(10*-10)*(10^-6)*(10^-1)*(10^-1)*(10*-4)*(10^-2), for the forehead, two eyebrows, two eyes, nose, cheeks, mouth and jawline respectively, giving a product of 10^(-36) – a very low number indeed. Raising that probability to the fourth power – giving a figure of 10^(-144) – would enable the alien scientists to calculate the probability of four faces being carved at a single location by chance, or P(T|H). The alien scientists would then have to multiply this number (10^(-144)) by their estimate for Phi_s(T), or the number of patterns for which a speaker S’s semiotic description of them is at least as simple as S’s semiotic description of T. But how would the alien scientists describe the patterns they had found? If the aliens happened to find some dead people or dig up some human skeletons, they would be able to identify the creatures shown in the carvings on Mt. Rushmore as humans. However, unless they happened to find a book about American Presidents, they would not know who the faces were. Hence the aliens would probably formulate a modest semiotic description of the pattern they observed on Mt. Rushmore: four human faces. A very generous estimate for Phi_s(T) is 10^15, as the description “four human faces” has three words (I’m assuming here that the aliens’ lexicon has no more than 10^5 basic words), and (10^5)^3=10^15. Thus the product Phi_s(T).P(T|H) is (10^15)*(10^(-144)) or 10^(-129). Finally, after multiplying the product Phi_s(T).P(T|H) by 10^120 (the maximum number of bit operations that could have taken place within the entire observable universe during its history, as calculated by Seth Lloyd), taking the log to base 2 of this figure and multiplying by -1, the alien scientists would then be able to derive a very conservative minimum value for the specified complexity Chi of the four human faces on Mt. Rushmore, without knowing anything specific about the Earth’s history. (I say “conservative” because the multiplier 10^120 is absurdly large, given that we are only talking about events occurring on Earth, rather than the entire universe.) In our worked example, the conservative minimum value for the specified complexity Chi would be -log2(10^(-9)), or approximately -log2(2^(-30))=30. Since the calculated specified complexity value of 30 is much greater than the cutoff level of 1 for a specification, the aliens could be certain beyond reasonable doubt that Mt. Rushmore was designed by an intelligent agent. They might surmise that this intelligent agent was a human agent, as the faces depicted are all human, but they could not be sure of this fact, without knowing the history of Mt. Rushmore.
Likewise, if human astronauts were to discover a monolith on the moon (as in the movie 2001), they should still be able to calculate a minimum value for its CSI, without knowing its history. Even if they were unable to figure out the purpose of the monolith, the astronauts would still realize that the likelihood of natural processes on the moon being able to generate a black cuboid figure with perfectly flat faces, whose lengths were in the ratio of 1:4:9, is very low indeed. To begin with, the astronauts might suppose that at some stage in the past, volcanic processes on the moon, similar to the volcanic processes that formed the Giants’ Causeway in Ireland, were able to produce a cuboid with fairly flat faces – let’s say to an accuracy of one millimeter, or 10^(-3) meters. However, the probability that the sides’ lengths would be in the exact ratio of 1:4:9 (to the level of precision of human scientists’ instruments) would be astronomically low, and the probability that the faces of the monolith would be perfectly flat would be infinitesimally low. For instance, let’s suppose for simplicity’s sake that the length of each side of a naturally formed cuboid has a uniform probability distribution over a finite range of 0 to 10 meters, and that the level of precision of scientific measuring instruments is to the nearest nanometer (1 nanometer=10^(-9) meters). Then the length of one side of a cuboid can assume any of 10×10^9=10^10 possible values, all of which are equally probable. Let’s also suppose that the length of the shortest side just happens to be 1 meter, for simplicity’s sake. Then the probability that the other two sides would have lengths of 4 and 9 meters would be 6*(10^(-10))*(10^(-10)) (as there are six ways in which the sides of a cube can have lengths in the ratio of 1:4:9), or 6*10^(-100). Now let’s go back to the faces, which are not fairly flat but perfectly flat, to within an accuracy of one nanometer, as opposed to one millimeter (the level of accuracy achieved by natural processes). At any particular point on the monolith’s surface, the probability that it will be accurate to that degree is (10^(-9))/(10^(-3)) or 10^(-6). The number of distinct points on the surface of the monolith which scientists can measure at nanometer accuracy is (10^9)*(10^9)*(surface area in square meters), or 98*(10^81) or about 10^83. Thus the probability that each and every point on the monolith’s surface will perfectly flat, to within an accuracy of one nanometer, is (10^(-6))^(10^83), or about 10^(-10^84), which dwarfs 10^-100, so we’ll let 10^(-10^84) be our P(T|H), as a ballpark approximation. This probability would then need to be multiplied by Phi_s(T). The simplest semiotic description of the pattern observed by the astronauts would be: flat-faced cuboid, sides’ lengths 1, 4, 9. Treating “flat-faced” as one word, this description has seven terms, so Phi_s(T) is (10^5)^7=10^35. Next, the astronauts would multiply the product Phi_s(T).P(T|H) by 10^120, but because the index 10^84 is so much greater in magnitude than the other indices (120 and 35), the overall result will still be about 10^(-10^84). Thus the specified complexity Chi=-log2[10^120.Phi_s(T).P(T|H)]=3.321928*10^84, or about 3*(10^84). This is an astronomically large number, much greater than the cutoff point of 1, so the astronauts could be certain that the monolith was made by an intelligent agent, even if they knew nothing about its history and had only a basic knowledge of lunar geological processes.
Having said that, it has to be admitted that sometimes, a lack of knowledge about the history of a complex system can skew CSI calculations. For example, if a team of aliens visiting Earth after a nuclear holocaust found the body of a human being buried in the Siberian permafrost, and managed to sequence the human genome using cells taken from that individual’s body, they might come across a duplicated gene. If they did not know anything about gene duplication – which might not occur amongst organisms on their planet – they might at first regard the discovery of two neighboring genes having virtually the same DNA sequence as proof positive that the human genome was designed – like lightning striking in the same place twice – causing them to arrive at an inflated estimate for the CSI in the genome. Does this mean that gene duplication can increase CSI? No. All it means is that someone (e.g. a visiting alien scientist) who doesn’t know anything about gene duplication, will overestimate the CSI of a genome in which a gene is duplicated. But since modern scientists know that gene duplication does occur as a natural process, and since they also know the rare circumstances that make it occur, they also know that the probability of duplication for the gene in question, given these circumstances, is exactly 1. Hence, the duplication of a gene adds nothing to the probability of the original gene occurring by chance. P(T|H) is therefore the same, and since the verbal descriptions of the two genomes are almost exactly the same – the only difference, in the case of a gene duplication, being “x2” plus brackets that go around the duplicated gene – the CSI will be virtually the same. Gene duplication, then does not increase CSI.
Even in this case, where the aliens, not knowing anything about gene duplication, are liable to be misled when estimating the CSI of a genome, they could still adopt a safe, conservative strategy of ignoring duplications (as they generate nothing new per se) and focusing on genes that have a known, discrete function, which is capable of being described concisely, thereby allowing them to calculate Phi_s(T) for any functional gene. And if they also knew the exact sequence of bases along the gene in question, the number of alternative base sequences capable of performing the same function, and finally the total number of base sequences which are physically possiblefor a gene of that length, the aliens could then attempt to calculate P(T|H), and hence calculate the approximate CSI of the gene, without a knowledge of the gene’s history. (I am of course assuming here that at least some genes found in the human genome are “basic” in their function, as it were.)
(iii) CSI should be calculable by independent agents, in a consistent manner.
This, too, is an essential requirement for any meaningful discussion of CSI. Beauty may be entirely in the eye of the beholder, but CSI is definitely not. The following illustration will serve to show my point.
Supose that three teams of scientists – one from the U.S.A, one from Russia and one from China – visited the moon and discovered four objects there that looked like alien artifacts: a round mirror with a picture of what looks like Pinocchio playing with a soccer ball on the back; a calculator; a battery; and a large black cube made of rock whose sides are equal in length, but whose faces are not perfectly smooth. What I am claiming here is that the various teams of scientists should all be able to rank the CSI of the four objects in a consistent fashion – e.g. “Based on our current scientific knowledge, object 2 has the highest level of CSI, followed by object 3, followed by object 1, followed by object 4” – and that they should be able to decide which objects are very likely to have been designed and which are not – e.g. “Objects 1, 2 and 3 are very likely to have been designed; we’re not so sure about object 4.” If this level of agreement is not achievable, then CSI is no longer a scientific concept, and its assessment becomes more akin to art than science.
We can appreciate this point better if we consider the fact that three art teachers from the same cultural, ethnic and socioeconomic backgrounds (e.g. three American Hispanic middle class art teachers living in Miami and teaching at the same school) might reasonably disagree over the relative merits of four paintings by different students at their school. One teacher might discern a high degree of artistic maturity in a certain painting, while the other teachers might see it as a mediocre work. Because it is hard to judge the artistic merit of a single painting by an artist, in isolation from that artist’s body of work, some degree of subjectivity when assessing the merits of an isolated work of art is unavoidable. CSI is not like this.
First, Phi_s(T) depends on the basic concepts in your language, which are public and not private, as you share them with other speakers of your language. These concepts will closely approximate the basic concepts of other languages; again, the concepts of other languages are shareable with speakers of your language, or translation would be impossible. Intelligent aliens, if they exist, would certainly have basic concepts corresponding to geometrical and other mathematical concepts and to biological functions; these are the concepts that are needed to formulate a semiotic description of a pattern T, and there is no reason in principle why aliens could not share their concepts with us, and vice versa. (For the benefit of philosophers who might be inclined to raise Quine’s “gavagai” parable: Quine’s mistake, in my view, was that he began his translation project with nouns rather than verbs, and that he failed to establish words for “whole” and “part” at the outset. This is what one should do when talking to aliens.)
Second, your estimate for P(T|H) will depend on your scientific choice of chance hypothesis and the mathematics you use to calculate the probability of T given H. A scientific hypothesis is capable of being critiqued in a public forum, and/or tested in a laboratory; while mathematical calculations can be checked by anyone who is competent to do the math. Thus P(T|H) is not a private assessment; it is publicly testable or checkable.
Let us now return to our illustration regarding the three teams of scientists examining four lunar artifacts. It is not necessary that the teams of scientists are in total agreement about the CSI of the artifacts, in order for it to be a meaningful scientific concept. For instance, it is possible that the three teams of scientists might arrive at somewhat different estimates of P(T|H), the probability of a pattern T with respect to the chance hypothesis H, for the patterns found on the four artifacts. This may be because the chance hypotheses considered by the various teams of scientists may be subtly different in their details. However, after consulting with each other, I would expect that the teams of scientists should be able to resolve their differences and (eventually) arrive at an agreement concerning the most plausible chance hypothesis for the formation of the artifacts in question, as well as a ballpark estimate of its magnitude. (In difficult cases, “eventually” might mean: over a period of some years.)
Another source of potential disagreement lies in the fact that the three teams of scientists speak different languages, whose basic concepts are very similar but not 100% identical. Hence their estimates of Phi_s(T), or the number of patterns for which a speaker S’s semiotic description is at least as simple as S’s semiotic description of a pattern T identified in a complex system, may be slightly different. To resolve these differences, I would suggest that as far as possible, the scientists should avoid descriptions which are tied to various cultures or to particular individuals, unless the resemblance is so highly specific as to be unmistakable. Also, the verbs employed should be as clear and definite as possible. Thus a picture on an alien artifact depicting what looks like Pinocchio playing with a soccer ball would be better described as a long-nosed boy kicking a black and white truncated icosahedron.
(iv) CSI should be knowable with absolute certainty.
Science is provisional. Based on what scientists know, it appears overwhelmingly likely that the Earth is 4.54 billion years old, give or take 50 million years. A variety of lines of evidence point to this conclusion. But if scientists discovered some new astronomical phenomena that could only be accounted for by positing a much younger Universe, then they’d have to reconsider the age of the Earth. In principle, any scientific statement is open to revision or modification of some sort. Even a statement like “Gold has an atomic number of 79”, which expresses a definition, could one day fall into disuse if scientists found a better concept than “atomic number” for explaining the fundamental differences between the properties of various elements.
Hence the demand by some CSI skeptics for absolute ironclad certainty that a specified complex system is the product of intelligent agency is an unscientific one.
Likewise, the demand by CSI skeptics for an absolutely certain, failproof way to measure the CSI of a system is also misplaced. Just as each of the various methods used by geologists to date rocks has its own limitations and situations where it is liable to fail, so too the various methods that Intelligent Design scientists come up with for assessing P(T|H) for a given pattern T and chance hypothesis H, will have their own limitations, and there will be circumstances when they yield the wrong results. That does not invalidate them; it simply means that they must be used with caution.
(v) CSI should be precisely calculable (within reason) by independent agents.
In a post (#259) on the recent thread, On the calculation of CSI, Jemima Racktouey throws down the gauntlet to Intelligent Design proponents:
If “CSI” objectively exists then you should be able to explain the methodology to calculate it and then expect independent calculation of the exact same figure (within reason) from multiple sources for the same artifact.
On the surface this seems like a reasonable request. For instance, the same rock dating methods are used by laboratories all around the world, and they yield consistent results when applied to the same rock sample, to a very high degree. How sure can we be that a lab doing Intelligent Design research in, say, Moscow or Beijing, would yield the same result when assessing the CSI of a biological sample as the Biologic Institute in Seattle, Washington?
The difference between the procedures used in the isochron dating of a rock sample and those used when assessing the CSI of a biological sample is that in the former case, the background hypotheses that are employed by the dating method have already been spelt out, and the assumptions that are required for the method to work can be checked in the course of the actual dating process; whereas in the latter case, the background chance hypothesis H regarding the most likely process whereby the biological sample might have formed naturally has not been stipulated in advance, and different labs may therefore yield different results because they are employing different chance hypotheses. This may appear to generate confusion; in practice, however, I would expect that two labs that yielded wildly discordant CSI estimates for the same biological sample would resolve the issue by critiquing each other’s methods in a public forum (e.g. a peer-reviewed journal).
Thus although in the short term, labs may disagree in their estimates of the CSI in a biological sample, I would expect that in the long term, these disagreements can be resolved in a scientific fashion.
(vi) CSI should be readily computable, given a physical description of the system.
In a post (#316) on the recent thread, On the calculation of CSI, a contributor named Tulse asks:
[I]f this were a physics blog and an Aristotelian asked how to calculate the position of an object from its motion, … I’d expect someone to simply post:
y = x + vt + 1/2at**2
If an alchemist asked on a chemistry blog how one might calculate the pressure of a gas, … one would simply post:
p=(NkT)/V
And if a young-earth creationist asked on a biology blog how one can determine the relative frequencies of the alleles of a gene in a population, … one would simply post:
p² + 2pq + q² = 1
These are examples of clear, detailed ways to calculate values, the kind of equations that practicing scientists uses all the time in quotidian research. Providing these equations allows one to make explicit quantitative calculations of the values, to test these values against the real world, and even to examine the variables and assumptions that underlie the equations.
Is there any reason the same sort of clarity cannot be provided for CSI?
The answer is that while the CSI of a complex system is calculable, it is not computable, even given a complete physical knowledge of the system. The reason for this fact lies in the formula for CSI.
On page 24 of his essay, Specification: The Pattern That Signifies Intelligence, Professor Dembski defines the specified complexity Chi of a pattern T given chance hypothesis H, minus the tilde and context sensitivity, as:
Chi=-log2[10^120.Phi_s(T).P(T|H)]
where Phi_s(T) as the number of patterns for which S’s semiotic description of them is at least as simple as S’s semiotic description of T, and P(T|H) is the probability of a pattern T with respect to the chance hypothesis H.
The problem here lies in Phi_s(T). In The Design of Life: Discovering Signs of Intelligence in Biological Systems (The Foundation for Thought and Ethics, Dallas, 2008), Intelligent Design advocates William Dembski and Jonathan Wells define Kolmogorov complexity and descriptive complexity as follows (p. 311):
Kolmogorov complexity is a form of computational complexity that measures the length of the minimum program needed to solve a computational problem. Descriptive complexity is likewise a form of computational complexity, but generalizes Kolmogorov complexity by measuring the size of the minimum description needed to characterize a pattern. (Emphasis mine – VJT.)
In a comment (#43) on the recent thread, On the calculation of CSI, I addressed a problem raised by Mathgrrl:
While I understand your motivation for using Kolmogorov Chaitin complexity rather than the simple string length, the problem with doing so is that KC complexity is uncomputable.
To which I replied:
Quite so. That’s the point. Intelligence is non-computational. That’s one big difference between minds and computers. But although CSI is not computable, it is certainly measurable mathematically.
The reason, then, why CSI is not physically computable is that it is not only a physical property but also a semiotic one: its definition invokes both a semiotic description of a pattern T and the physical probability of a non-foresighted (i.e. unintelligent) process generating that pattern according to chance hypothesis H.
(vii) CSI should be computable by some general algorithm that can be applied to an arbitrary system.
In a post (#263) on the recent thread, On the calculation of CSI, Jemima Racktouey issues the following challenge to Intelligent Design proponents:
If CSI cannot be calculated then the claims that it can are bogus and should not be made. If it can be calculated then it can be calculated in general and there should not be a very long thread where people are giving all sorts of reasons why in this particular case it cannot be calculated. (Emphasis mine – VJT.)
And again in post #323, she writes:
Can you provide such a definition of CSI so that it can be applied to a generic situation?
I would like to note in passing how the original demand of ID critics that CSI should be calculable has grown into a demand that it should be physically computable, which has now been transformed into a demand that it should be computable by a general algorithm. This demand is tantamount to putting CSI in a straitjacket of the materialists’ making. What the CSI critics are really demanding here is a “CSI scanner” which automatically calculates the CSI of any system, when pointed in the direction of that system. There are two reasons why this demand is unreasonable.
First, as I explained earlier in part (vi), CSI is not a purely physical property. It is a mixed property – partly semiotic and partly physical.
Second, not all kinds of problems admit of a single, generic solution that can be applied to all cases. An example of this in mathematics is the Halting problem. I shall quote here from the Wikipedia entry:
In computability theory, the halting problem is a decision problem which can be stated as follows: Given a description of a program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever.
Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. We say that the halting problem is undecidable over Turing machines. (Emphasis mine – VJT.)
So here’s my counter-challenge to the CSI skeptics: if you’re happy to acknowledge that there’s no generic solution to the halting problem, why do you demand a generic solution to the CSI problem – that is, the problem of calculating, after being given a complete physical description of a complex system, how much CSI the system embodies?