There were several requests on the next-to-last thread for definitions of specified complexity, so to redeem a promise and– I hope–eliminate the need for repeating the same definition ad infinitum, I’ll attempt to summarize the major points of Dembski’s paper on the subject here.
The context dependent measure of specified complexity is given by the following formula:
(pg 21)
This is the definition we are using in this course.M and N represent the replicational resources. In a general case, we may replace them by 10120 (upper bound of bit operations our universe could have accomplished throughout her history) to get
(pg 24)
Specificity is calculated by means of the following formula
(pg 18)
Aside from the ommision of replicational resources (M and N), this formula is identical to the above formula for specified complexity. It is dependent on two components, φs(T) and P(T|H).
φs(T) is defined as a measure of the specificational resources, and is given by the cardinality of {U ∈ patterns(Ω) | φ’s(U) ≤ φ’s(T)} where patterns(Ω) is the collection of all patterns that identify events in Ω. φ’s(T) is the descriptive complexity of T (a measure of the simplest way for s to describe T).
(pg 21)
“S” represents the subject who determines & describes, with the languages available to him, the pattern.
To make this simple, consider the special case where the only language is the language used in programming register machines, and the patterns being described are bit strings. When analyzing a string of a given length, you determine first how long the program describing it must be, and then determine how many other bit strings of that length there are with descriptions at least as short. This second number is equal to φs(T).
In the general case we have many more languages and patterns far more complex than bit strings, but the same concept holds.
P(T|H) is the probablity of pattern T given the relevant chance hypothesis H. P(T|H) ≠ 1 in cases where H, the chance hypothesis, is known, unless H is completely deterministic.
P(T|H) where T=heads and H is a fair coin toss is 1/2.
P(T|H) where T=(heads)(tails)(heads)(tails) and H is a series of independent fair coin tosses is 1/16.
Finally, T is considered a specification if the measure of specified complexity is strictly greater than 1.
Corrections from anyone comfortable with the paper are very welcome. In the meantime…
Michal wrote
Where is the complex specified information defined in a clear fixed unambiguous way, along with all the key sub-terms, Hannah?
Is there anything ambiguous about those definitions?
Thanks for that, Hannah.
I’m sure that others will be thrashing these terms out. But maybe class members and others might want to think about this in a somewhat different way.
The formula for specified complexity that is posted here is not unlike that that physical chemists might use to describe or calculate thermodynamic entropy. (I’m not the first or only one to notice this.) Recall (for the first time - LOL) that, in thermodynamics, entropy is a state variable. In other words, the absolute value of the entropy of a system is something that is independent of the pathway by which the system was attained.
My question for the class is this - is specified complexity a “state variable”? I think that this question makes one think about the issue, especially as it relates to the computation of things like specificational resources, in ways that we usually don’t see in discussions of CSI.
What do others think?
Comment by Art G — July 24, 2006 @ 4:58 pm
I’ve done pchem, but hadn’t thought of the resemblance.
No, because our calculations are dependent on the hypthetical path (through P(T|H)). Perhaps if one needed one could formulate a more general version, but I wonder if it might be too general to be actually useful.
Comment by Hannah — July 24, 2006 @ 5:06 pm
Thanks Hannah.
Okay, now using the definitions you provided, show me (1) each step in the calculation of the probability that ftsK protein in E. coli was designed and (2) please state your assumptions for each step and the reliability/standard error at each step.
Comment by Michal Hubl — July 24, 2006 @ 5:44 pm
I would have thought, after this, you’d be the one to owe me a favor? You seem to think it’s the other way round. ;)
It probably hasn’t occured to you, but we actually don’t all have infinite amounts of time, and some of us have in fact our own studies and research. That would suggest there might be a limit as to how much you can reasonably ask of another person.
Comment by Hannah — July 24, 2006 @ 5:56 pm
It probably hasn’t occured to you, but we actually don’t all have infinite amounts of time, and some of us have in fact our own studies and research. That would suggest there might be a limit as to how much you can reasonably ask of another person.
If you feel like you can’t meet my request in its entirety, then how about just showing us how you start out? Using your definitions, of course.
Maybe someone else who finds this stuff as straightforward as you make it sound can jump in and finish the job.
I mean all that’s at stake is the credibility of evolutionary biology and a shot at fame for you. I find it odd that you aren’t interested in following through. On the other hand, it seems like everyone is too busy to do these calculations, including ID promoters. That’s sort of an interesting data point.
Comment by Michal Hubl — July 24, 2006 @ 6:07 pm
Hannah
It probably hasn’t occured to you, but we actually don’t all have infinite amounts of time, and some of us have in fact our own studies and research.
Thanks for the insult, by the way. As a matter of fact, Hannah, I believe the fact that scientists don’t have infinite time is one of the many reasons that most scientists ignore creationists and ID promoters.
And you already know this because it’s been explained to you here on this blog.
Comment by Michal Hubl — July 24, 2006 @ 6:10 pm
I admit, I can’t follow what the mathematical representations of specificity and complexity imply, but what of the common complaint that Dembski describes specification as function, and that he only defines complexity as something which cannot (yet) be explained by regularity and/or chance, such that he’s mathematically arguing that something functional whose origin we do not (yet) understand is designed.
That may or may not be an accurate description, but at the very least, CSI is a vague mathematical representation, with no tangible feature in biology as an example, correct?
IOW - has Dembski or anyone else actually found and empirically identified any features with these equations, or is it just an abstract assertion?
Comment by Dan — July 24, 2006 @ 6:22 pm
I’d like to point out at what appears to be a glaring incosistency in the definition of
Phi_S(T). T refers to an element of Omega - the event space - as indicated by applying the probability measure P(.|H) to T. However, in the definition of Phi_S(T), the function Phi’(.) is applied both to T, which is a member of Omega, and to U, which is a member of Patterns(Omega). Even if patterns Omega is a well-defined set - which is far from certain - Phi’(.), the descriptive complexity of a pattern or event, is not a well-defined function, since it is being applied to two distinct domains.
Dembski tries to get around the problem by proclaiming that “Alternatively, T can be conceived abstractly as a pattern that
precisely identifies the event (target) T.” (p. 16). This definition, aside from being circular, is non-sense. The set patterns(Omega) is a subset of the power set of BasicCommunicationSymbols(S), where S is the semiotic agent in question. (It should really be Patterns(Omega, S), to underscore the dependence on S). Omega is the physical event space. The same entity T cannot belong to both spaces at once.
I’m not saying that this definition isn’t of CSI is necessarily irredeemable, but right now it is completely broken. Hannah, care to try and fix it?
Comment by Leonid Meyerguz — July 24, 2006 @ 6:38 pm
I admit, I can’t follow what the mathematical representations of specificity and complexity imply
With respect to their application to natural (not engineered by humans) biological systems, nobody can … except for maybe Hannah and Sal and Bill Dembksi. That’s why we’re waiting to see them apply this fantastic concept to a biological protein and prove that evolutionary biologists are wrong. Or something.
(checks watch)
Still waiting.
Comment by Michal Hubl — July 24, 2006 @ 6:38 pm
Silly SPAM filter can’t identify mathematical symbols. Hannah, I hope you get the chance to take a look at my last post once you fish it out of the SPAM filter. I think there are good reasons to attack Dembski’s definition of CSI on mathematical grounds alone, though it is the near-impossibility of applying the concept that constitutes CSI’s greatest weakness, IMO.
I’m on campus, so if Allen doesn’t mind, I might drop by the class when you guys are discussing Dembki’s work. Arguing on this forum may prove too time-consuming in the near future.
Comment by Leonid Meyerguz — July 24, 2006 @ 6:48 pm
Slight clarification: The various formulas entered are for bit-measures of specified complexity, not the CSI itself.
There is a difference between the measure and the actual information itself.
For example, I may say that the information in a file is 5000 bits, but that is shorthand for saying the MEASURE of information in the file is 5000 bits. The actual contents of the file are the information.
The formulas above are technically the measures of information. Dembski uses a common industry shorthand. But one should be aware of this nuance in discussion.
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 6:52 pm
Well, crackey! I had a not so long post ready to go, but didn’t type the anti-spam number and lost it down the memory hole!
So, here’s my question and comment:
First, thanks to Sal and other participants for hashing this out (sometimes a bit exhaustively, however necessary). As a layman in biology, genetics and math (you math geeks are sumpin’!), I’m learning a great deal and humbled by some of the intellects participating here.
I think Dan asks a good question: What is the practical application of Dembski’s CSI formula to biological systems?
Take e coli for example - in light of Sal’s recent comments, what factors would one use in the forumlae posted by Hannah to menaure the CSI for this system? Would one only look at a subsystem, such as the flagellum, or the whole cell or both? Is the quantity of genetic base pairs relevant? How about the number of proteins needed to construct the flagellum? Or would we need the amino acid count?
Or, do we need a baseline to measure from (as in, an ancestral bacterium)?
Forgive me my great ignorance if these questions aren’t framed properly.
Comment by todd — July 24, 2006 @ 7:21 pm
There are several hypotheses H that can be proposed, actually an infinite number. CSI is offered with respect to each H, but if Dembski’s displacement theorem is correct (which is still debated), a simple distribution is no worse on average than blind watchmakers trying to find the optimal distribution by random chance either. Thus average CSI from all possible distributions will not be any less CSI than simple distributions like the uniform one. Thus one does not have to explore an infinte number of H’s to make a reasonable design inference….
I cannot possibly go into all the details. I can only give a crude and very crude approximation.
We can explore the design of a protein under a lock-and-key metaphor. That is, there is no a-priori reason why a certain protein must be picked out over another. However, if we have pairs or sets of proteins, we can characterize the likelihood they will be well-matched.
Given protein-A in a system, protein-B will be the only one that can fit the role. This is a simplification of course, but we must start somewhere.
Let us start with the purely stochastic uniform distribution case first then move one to more sophisticated ones where H involves selection, not just chance.
For example, a 100-mer protein may has 20^100 possible configuratons. It may require 25 monomers to characterize it, with the other 75 permitted to be variable. P(T|H) for hitting that protein is CRUDELY approximated by 20^25/ 20^100 = 1/ 20^75. That’s a crude approximation because I did not include the issue of synonymous codons, but that’s kind of how the basic calculation is done.
If one argues natural selection improves the odds over random chance, it must justify that in view of Dembski’s displacement theorem which says evolutionary algorithims, without specific direction perform no better than random chance on average. That is, the selective forces themselves have to be an engineered search strategy. One cannot merely assume statistically that there existed a selective force to improve the search….
Crude CSI measure in this case for a single trial is:
-log2( 1 / 20^75) = 324 bits
For multiple trials one can put an MN that they think appropriate. Since this is not presumed an algorithmically compressible case, one can drop the Phi_s(T) term.
That’s a sketch. It is not complete, but that’s a start. We do not assert intelligence, we merely assert the confidence we can have the H is the correct hypothesis. The more bits the higher the confidence we can reject the hypothesis H.
One does not need UPB if that’s not the level of confidence one is trying to assert. If one will reject a theory because it is likely to be 99.99% wrong, then there is an appropriate number of bits to reach that conclusion. UPB is for context-independence.
For chance hypothesis H, we are trying to show it lead to a contradiction of the form: “E implies not-E” with X% amount of confidence.
Given that, I rather prefer this example since it explores ALL possible probabiliity measures P on any arbitrary H, both known and unknown:
Perfect Architectures Which Scream Design.
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 7:38 pm
Given protein-A in a system, protein-B will be the only one that can fit the role.
What role?
Why do you insist on abstraction, Sal? I can imagine why you might insist on abstraction — and particular abstractions as that — but maybe you can tell us why you refuse to show us how Dembski’s “theory” which you are so enamored with can be applied to a real world example.
Try it with ftsK. I picked it off the top of my head, by the way. I can give you another if ftsK frightens you for some reason.
Comment by Michal Hubl — July 24, 2006 @ 7:49 pm
Allen, Hannah,
I object to students being interrogated like this. The questions should not be directed at Hannah.
This weblog is for students to learn, IMHO, not for outsiders to demand they be taught by Cornell students or for Cornell students to be subjected to demands to “fix” Dembski’s work.
I think this is highly rude, IMHO.
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 7:51 pm
Actually, I agree with Sal.
Allen should put Mike’s question on the final examination for the course …
Comment by Don Baccus — July 24, 2006 @ 7:55 pm
Geez, I’m out of depth! Please let me know if I understand Sal’s post correctly: Simply put, one begins with what we know about the arrangement of a given system’s components, then determine the probability those components would assemble into a functional whole without purposeful arrangement?
Comment by todd — July 24, 2006 @ 7:59 pm
How about a simple example then instead of biology, and then we work our way up. :-)
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 8:06 pm
OK, for the sake of argument, let’s just say everyone agreed that overwhelming evidence indicated that the bacterial flagellum evolved via natural processes. Here’s my question: in this case, would the bacterial flagellum exhibit specified complexity?
Answer “yes” or “no”, and support your answer…
Comment by nmatzke — July 24, 2006 @ 8:09 pm
I’m afraid that’s incorrect becuase T is subset of of Omega, thus it is not an element of Omega since T contains elements of Omega.
I illustrated that the calculation can be done here
If it is countably finite, patterns Omega is the Power Set of Omega, thus it is well defined for the issues under consideration.
That is not correct, he is merely saying certain T can be a singleton set within Omega. That has nothing to do with trying to get around the problem of defining Phi.
I already hinted how to calculate Phi_S(T). It is merely the cardinality of the set T. Sometimes the set T is hard to characterize. Fine, chose another T where Phi_S(T) is tractable. If the T under consideration is too hard to characterize with a Phi, then don’t use it. Better to make a false negative than a false positive.
I don’t think that’s correct. Dembski did not say that, he said
Thus he did not say T belonged to both. Even though Phi(T) which is a positive integer calculateble by through semiotic agents.
I think you need to fix your critique first. Finally, I don’t think it’s approriate to make students studying a theory defenders of it as well.
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 8:34 pm
Sal,
I was going on Dembski’s prison term coin toss scenario in the paper.
1. We need the playing field.
2. We need the equipment
3. We need the game permutations
Right?
Comment by todd — July 24, 2006 @ 8:36 pm
Sal (and Hannah):
I actually agree with Sal here, and I’m sorry if my comment #7 comes across as too pushy. Hannah, please don’t take my comment above as a “demand” that you fix Dembski’s definition; rather, I am primarily curious what you, as a math major, think about my observations above. I am generally quite impressed with the quality of your posts, and your genuine efforts to convey a clear and persuasive arguments: hence my interest in your PoV. However, please don’t feel like I’m trying to give you a homework assignment; if anything, most undergrads here at Cornell have plenty of those as it is.
Comment by Leonid Meyerguz — July 24, 2006 @ 8:36 pm
Let me suggest this thread would not be a good place to peer-review of Dembski’s math. We can proceed with the discussion without delving into the higher recesses of it. Especially the math that is already well accepted in the disciplines of statistics.
However, before I completely dismiss the topic let me illustrate how semeiotic agent can calculate Phi_S for certain T’s. I apologize for the extreme brevity. Again let’s work with 500 fair coins.
1. “take first coin and repeat” There are two members that conform, thus Phi_S(T_take_first coins_and_repeat) = 2 = Phi_S(T_all_heads) = Phi_S(T_all_tails)
H H H H H
T T T T T
2. “take first two coins and repeat” There are two members that conform,
Phi_S(T_take_first_coins_and_repeat) = 4 = Phi_S(T_all_heads) = Phi_S(T_all_tails)= Phi_S(T_HT_repeat) = Phi_S(T_TH_repeat)
H T H T H T
T H T H T H
H H H H H
T T T T T
etc.
Notice Phi_S(T_all_heads) can be either a member of T with cardinatily 2 or 4. Under Dembski’s definition, one will choose the lower cardinality.
Also, it did not matter that I used english to help me judge whether the members of set T belong together as they are describable by the same sentence.
Ok, any further disucssion, perhaps, we take it elsewhere or just wait till the end of the weblog. Otherwise we’ll lose the readers.
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 8:58 pm
Dan–
A mathematical formulation, yes, but nothing vague about it.
Michal–
Oh, it wasn’t meant to be an insult– or at least, not an insulting one. Just a reminder that there is such a thing as an unreasonable request, even if the request is only made to an annoying student who spends too much time arguing :).The calculation of CSI in e. coli sounds like a fun research project. Unfortunately, I haven’t any time to take away from my other research project. So this one will have to wait.
Leonid–
No problem, you weren’t too pushy. And I was grateful you didn’t demand a doublespaced manuscript by midnight tonight (absolute deadline), because I want a bit of time to think about the set issue.
We went through Dembski’s work last week, and this week are on Johnson and all the random loose ends we haven’t yet covered. And after that is Ernst Mayr and the EB perspective on teleology. Ofcourse, maybe we could call a special meeting to hash out CSI….
Comment by Hannah — July 24, 2006 @ 9:13 pm
Close enough. :-)
It is highly suited to the origin of life question (i.e. what’s the chances it happened naturally). As far as the bacterial flagellum we can analyize the plausibility of various evolutionary scenarios. The higher the numbers that are generated by the above formulas, the less likely we are to accept a particular evolutionary pathway was the one.
But where IDers believe Dembski’s methods will eventually prevail is in the detection of linguistic constructs within biology, not so much asking “could this evolve via Darwinian evolution”? Most IDers are well past believing that. The more interesting question is detecting undiscovered designs in biology. Dembski’s methods are highly optimized to detect such linguistic constructs.
The question of evolution is only a fraction of what ID attempts to investigate.
Also in many instances the I is irrelevant to applying the majority of ID theory, but the D is very important. The above formula deals with D.
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 9:18 pm
Salvador writes:
Right you are. I should have written “subset of the power set of Omega”, or “element of the power set of Omega”.
You’re doing no such thing. You are showing us how to compute P(T|H) for a series of coin tosses. This is trivial. You are not giving us a clue as to how to compute Phi_S(T).
Aside from a slight quibble - namely, every finite set is countable - this actually makes sense. Specifically, if we define Patterns(Omega) as the power set of Omega - call it PS(Omega) - then Phi’(T) is a well-defined function. It still doesn’t give us any means to compute except by vague analogy to compressability, but it’s a start.
No, no, no! I am amazed that you, the man who has all of Dembski’s books, would make such a claim. The cardinality of T - call it card(T) - is what lets us compute P(T|H) under the uniform null hypothesis H. Namely, Card(T)=P(T|H)*Card(Omega). Phi_S(T) is a different beast entirely. It is, to use your definition of Patters(Omega) above, the number of subsets of Omega whose “descriptive complexity” (the Phi’(.) value) is at least as complex as that of T. If I were a churlish knave, I would suggest you start misrepresenting Dembski and go read his latest paper. ;)
However, you did address my one concern - the incosistency in the definition of Phi’(.) Of course, the fact that Dembski never explicitly defines Patterns(Omega) doesn’t do wonders for the clarity of the paper.
Comment by Leonid Meyerguz — July 24, 2006 @ 9:35 pm
Once again, about state variables and the like. Trying to link “the math” with some biology. (Just trying, mind you.)
I’d agree with you, Hannah, that specified complexity is not a state variable. Accepting this, perhaps you can reflect on the usual ID theorist’s approach (an example of which Sal give in this thread) for estimating the specified complexity in a protein:
“For example, a 100-mer protein may has 20^100 possible configuratons. It may require 25 monomers to characterize it, with the other 75 permitted to be variable. P(T|H) for hitting that protein is CRUDELY approximated by 20^25/ 20^100 = 1/ 20^75. That’s a crude approximation because I did not include the issue of synonymous codons, but that’s kind of how the basic calculation is done.”
Dembski uses the same approach, as does Meyer and most (if not all) other IDists. I think that this method is not consistent with the (correct) notion that specified complexity is not a state variable.
(Sal makes different, basic but oft-repeated error in his calculation. But that’s for another discussion.)
Comment by Art G — July 24, 2006 @ 9:37 pm
Sal,
I meant to thank you in the last post for giving a cogent definition of Patterns(Omega). Somehow, that didn’t make it into the final version of my post. Anyhow, thanks.
Also, since that didn’t make it into my final post, I’d like to point out that the biggest problem in the definition of Phi_S(T) are now the Phi’(.) functions. Depending on how you define it Phi’(.), these quantities are either not computable, highly subjective, or can chosen so as to be very low for any T under consideration. (Meaning that every improbable event would exhibit SCI by definition.) While it may be possible to bound these quantities in the case of neatly constructed toy examples, it is probably impossible to compute them in the real world.
Comment by Leonid Meyerguz — July 24, 2006 @ 9:46 pm
You’re welcome.
I still don’t think that is quite right. T is a subset of Omega. T is a member of the powerset of Omega.
I was not very clear in my earlier link. My apologies. You may want to look at the example above then where I make explicit Phi_S(T) calculations.
There is no reason one needs a generalized method to cover every algorithmically compressible situation under the sun. If Phi_S(T) is intractable, then one would simply decide to characterized T as a pre-specification versus a specification, or simply drop T altogether.
My point was showing to the reader that Phi_S(T) does not have to be some super mysterious entity. If one is not comfortable with the conception, then one shouldn’t characterize T as a specification…
My language was inexact and thus led to confusion.
Phi_S(T) is the cardinality of the superset of T call it T_superset which all members have the same or less algorithmic complexity as T. For the readers benefit I gave a slight illustration of how that cardinality is calculated.
As I said, it’s only of interest if one is trying to identify every last designed algorithmically compressible string. One need not do that.
The issue is one does not have to compute it to make the formulas work. Domains where Phi_S(T) cannot be tractably computed imply we just don’t use T as a specification.
If it cannot be computed, then the domain of inquiry is beyond reach at that time, it does not negate the formulas for other domains of inquiry.
As I pointed out above, there is no absolute Phi_S, it is on a case by case basis, assuming T is even algorithmically compressible in the first place. If Phi_S is intractable, then treat T as a pre-specification, or simply admit for a pariticular inquiry, CSI cannot be asserted even though it might possibly be there.
For more examples, let’s say we discover we have a pattern of 500 coins where the first 250 coins mirroring the last 250 coins.
Call it T_single_target. If T_single_target is a member of a superset of symmetric T’s where each member of a 500 coin string has the first 250 coins mirroring the last 250 coins.
Phi_S(T_symmetric) = | T_symmetric | = 2^250
Phi_S(T_symmetric) P(T_single_target|H) = P(T_symmetric|H)
There are two ways to approch this. We can express context-dependent CSI crudely
A. -log2 ( Phi_S(T_symmetric) P(T_single_target|H) ) = 250 bits
or
B. -log2 ( P(T_symmetric|H) ) = 250 bits
A is the more proper approach, B would get the job done, get the same answer, but it takes a slightly unwholesome shortcut
Note: T_all_heads is a member of T_symmetric. For every element of T_symmetric one could use 2^250 as Phi_S(T) however in some cases that would be overkill as Phi_S(T_all_heads) = 2, but the formula would still work with Phi_S(T) = 2^250.
I’m sorry for delving into this more, but I wanted to reassure the readers Dembski’s conception do not rise or fall on the ability to calculate Phi_S(T) for every T under the sun!
Comment by Salvador T. Cordova, IDEA GMU — July 24, 2006 @ 10:33 pm
The one problem I have with the CSI calculation is that there is no concrete method (that I’m aware of, anyway) for determining equality between a specification and an actual manifestation.
As a quick example, for Mount Rushmore, where we know that there was Complex Specified information involved in its building, what sort of equality is required between the manifestation and the specification in order to register it as a match? This can have a very large impact of specificational complexity.
I think there is an intuitive comparison that is generally done (and is generally correct), but I think it should be a goal of ID to determine both how and why an object should be considered an implementation of its specification.
Comment by Jonathan Bartlett — July 24, 2006 @ 11:38 pm
In comment #10 Leonid Meyerguz wrote:
As Hannah pointed out above, we have finished with our discussion of Dembski (as far as this course is concerned), and are now moving on to a consideration of Phillip Johnson’s The Wedge of Truth. However, I think it would be very interesting to continue this discussion elsewhere, and suggest that the best venue might be at one of the weekly meetings of the Cornell IDEA Club. Hannah, what do you think? My impression from last week is that we have not exhausted this topic by any means….
Comment by Allen MacNeill — July 25, 2006 @ 12:16 am
Leonid:
That said, if you would still like to attend the seminar, feel free. The more, the merrier!
Comment by Allen MacNeill — July 25, 2006 @ 12:23 am
My claim that P(T|H)=1 where H is the hypothesis which actually matches the how T arose, was met with some justified opposition. Only when H is fully regular we are justified in arguing that P(T|H)=1. So we have established that for regularities, by definition, CSI cannot be generated. Sal and others raised the concept of chance but pure chance is also not really a likely explanation provided by science. In fact, a chance hypothesis of the order of 10^120 makes chance highly implausible or at least highly unsatisfying as an explanation. And since science when it comes to evolution does not rely on chance ‘explanations’ we cannot reject chance hypotheses as well. Note that in Dembski’s original formulation chance was excluded because it lacked specification.
So now we have left evolutionary hypothesis, what challenge does such a hypothesis face? Well, according to Dembski the hypothesis has to be causally specific and then science has to show that
The probability of each step has to be ‘reasonably large’. But a reasonably large probability would also have an unreasonably low Complexity.
We can understand this intuitively: A pathway which is so unlikely does not make for a very good scientific hypothesis and thus has to be rejected. In other words, any hypothesis which is sufficiently detailed and probable will by definition have little complexity and any hypothesis sufficiently improbable will have complexity but it will now be rejected because of its low probabilities.
Hence my claim that regularities are exempted by definition from generating complexity because P(T|H)=1 and that for regularity and chance hypotheses, P(T|H) has to be sufficiently large for the hypothesis to be sufficiently probable which also eliminates any hope for P(T|H) to generate any complexity. In fact, complexity as used by Dembksi is merely a transformed probability. When probability is too small, it is complex but then any regularity and chance hypothesis will fail as it is too unlikely and when the probability is sufficiently large, it will fail because of too low complexity. In other words, the deck is fully stacked against ID.
Worse, for a given T, ID cannot even show it contains CSI given the hypothesis H is T is designed since ID provides to specifics allowing one to calculate P(T|H) where H is the hypothesis that T is designed.
Which is why Dembski, when it comes to known hypotheses does not calculate P(T|H) where H is the design hypothesis but rather P(T|H) where H is the uniformly distributed probability function and thus P is easily turned into an unreasonably unlikely chance process which is now used as evidence that P must have been designed BUT no calculation of P(T|H) where H is the design hypothesis is provided.
If high P(T|H) where H is a regularity/chance hypothesis is needed to explain T then why is design decided based upon low P(T|H) where H most of the time is the uniformly distributed random distribution?
Of course, this conflation of terms leads to interesting problems since Dembski had to accept the concept of actual versus apparent CSI. In other words, there were cases which appeared to be designed (CSI) but in fact the CSI was generated/displaced by a natural process. So how does one distinguish between displaced and generated CSI? The Explanatory Filter does not tell us how.
So in short
1. CSI can only be generated by improbable hypotheses and thus are rejected as too improbable
2. It has yet to be shown that ID can generate CSI, so far only chance has been shown to be able to generate complexity.
3. Apparent and actual CSI or generated versus displaced CSI are introduced but no way is presented to differentiate between the two.
Hope this clarifies and extends my comments that P(T|H)=1 when H is the hypothesis which matches in sufficient causal specificity the actual pathway. Rather than being 1, P(T|H) has to be sufficiently large to be accepted as a valid hypothesis but such would also eliminate any CSI…
Comment by PvM — July 25, 2006 @ 12:38 am
In fact, my original comment was in response to a statement by Dembski (or another ID proponent) who argued that if science proposes a hypothesis which explains T sufficiently, P(T|H) has to be probable, destroying thus any CSI. But I cannot find the original quote.
Patience…
Comment by PvM — July 25, 2006 @ 12:39 am
Remember Dembski calculating the probability for the flagellar protein?
In fact Dembski shows that P(T|H) is so small that it has to be rejected as a valid hypothesis, although the probabilities involved show large amounts of CSI (read extremely low probabilities).
Miller et al observe
Dembski then offers his readers a calculation showing that the flagellum could not have possibly have evolved. Significantly, he begins that calculation by linking his arguments to those of Behe, writing: “I want therefore in this section to show how irreducible complexity is a special case of specified complexity, and in particular I want to sketch how one calculates the relevant probabilities needed to eliminate chance and infer design for such systems” (Dembski 2002a, 289). Dembski then tells us that an irreducibly complex system, like the flagellum, is a “discrete combinatorial object.” What this means, as he explains, is that the probability of assembling such an object can be calculated by determining the probabilities that each of its components might have originated by chance, that they might have been localized to the same region of the cell, and that they would be assembled in precisely the right order. Dembski refers to these three probabilities as Porig, Plocal, and Pconfig, and he regards each of them as separate and independent (Dembski 2002a, 291).
This approach overlooks the fact that the last two probabilities are actually contained within the first. Localization and self-assembly of complex protein structures in prokaryotic cells are properties generally determined by signals built into the primary structures of the proteins themselves. The same is likely true for the amino acid sequences of the 30 or so protein components of the flagellum and the approximately 20 proteins involved in the flagellum’s assembly (McNab 1999; Yonekura et al 2000). Therefore, if one gets the sequences of all the proteins right, localization and assembly will take care of themselves.
To the ID enthusiast, however, this is a point of little concern. According to Dembski, evolution could still not construct the 30 proteins needed for the flagellum. His reason is that the probability of their assembly falls below what he terms the “universal probability bound.” According to Dembski, the probability bound is a sensible allowance for the fact that highly improbable events do occur from time to time in nature. To allow for such events, he agrees that given enough time, any event with a probability larger than 10-150 might well take place. Therefore, if a sequence of events, such as a presumed evolutionary pathway, has a calculated probability less than 10-150 , we may conclude that the pathway is impossible. If the calculated probability is greater than 10-150, it’s possible (even if unlikely).
When Dembski turns his attention to the chances of evolving the 30 proteins of the bacterial flagellum, he makes what he regards as a generous assumption. Guessing that each of the proteins of the flagellum have about 300 amino acids, one might calculate that the chances of getting just one such protein to assemble from “random” evolutionary processes would be 20-300 , since there are 20 amino acids specified by the genetic code. Dembski, however, concedes that proteins need not get the exact amino acid sequence right in order to be functional, so he cuts the odds to just 20-30, which he tells his readers is “on the order of 10-39″ (Dembski 2002a, 301). Since the flagellum requires 30 such proteins, he explains that 30 such probabilities “will all need to be multiplied to form the origination probability”(Dembski 2002a, 301). That would give us an origination probability for the flagellum of 10^-1170, far below the universal probability bound. The flagellum couldn’t have evolved, and now we have the numbers to prove it. Right?
Or were the calculations without any relevance?
Comment by PvM — July 25, 2006 @ 1:05 am
Note: this the corrected (i.e., unmangled) version of this post — Hannah
Salvador writes:
I am not sure I agree. Little of Dembski’s math has actually been
peer-reviewed, as he never publiishes his work in relevant
mathematical journals. Many of his ideas are similar to those in
well-established computational theory, but are still new enough that
they should be scrutinized on their own. Therefore, I think this
forum is as good a place as any to discuss his work, especially where
interested mathematically inclined students might be concerned. The
worst thing that can happen is that we might all learn something.
Again, this is just plain wrong, and I strongly encourage you to
re-read what Dembski actually says. First, we need to compute
Phi’({HHHHH….H}), the “descriptive complexity” of the event T
described by the words “All Heads”. For instance, let’s take Phi’(T)
to be the number of English words needed to describe T (this is very
similar to what Dembski is doing on p. 18 of the paper when computing
the specificity inherent in the flagellum). Thus, Phi’(T) = 2. Now,
recall that Phi_S(T) = card({U in Patterns(Omega): Phi’(U) <=
Phi’(T)}, where Patterns(Omega)=PS(Omega), the power set of Omega.
Note Phi_S(T) counts events in the event space Omega: that is
subsets U of PS(Omega) s.t. Phi’(U)<=Phi’(T)=2, in our example.
So, how many events U in the space Omega have Phi’(U)=2?. Well,
except “All heads”, there is “All tails”, {TTTTTT…..}. Then there
is “All Alternating”, {THTHTHTH…., HTHTHTHT…}. Then there is
“Head First”, a very large set consisting of {HTTTT…T, HTTTT…H,
… HHHHH….T, HHHHH…H}; the set contains 2^(n-1) elements, where n
is the number of coins. In short, there is exactly one event
corresponding to any description, though the event could be a very
large compound one. Now, assume we have w words in our language.
Then, only w^2 two-word descriptions are possible. Since there is at
most one event per any description, there are at most w^2 events U in
PS(Omega) s.t. that Phi’(U)<=2. Hence, Phi_S(T) <=w^2 .
Thus, the specificity of T given the null hypothesis H for our
semiotic agent S, Spec_S(T|H, C) is given by:
Spec_S(T|H) = -log_2(Phi_S(T) * P(H|T)) >= -log_2(w^2 * 2^-n)
(Notice the sign flip above due to negation of the logarithm.)
Thus, if N=500 and w=1e5, Spec_S(T|H) >= 466.78 bits. Or
equivalently, an event of “descriptive complexity” no higher than T
has a probability of less than or equal to 1e10 ** 2^-500 = 3.055e-141
of happenning, from S’s limited perspective.
I hope the above clarifies an important point in Dembski’s work. I
think understanding Phi_S(.)is crucial before we can discuss the
mathematical and practical shortcomings of CSI. But hey, what do I
know - I don’t even own “The Design Inference”! ;)
Comment by Leonid Meyerguz — July 25, 2006 @ 2:34 am
Hannah or Allen:
My post #35 above is all mangled: I had some “less than” signs in my mathematical formulas, and the software mistook them for HTML tags, cutting out large portions of the text. I followed up with a post that removed the offending tags, but it was intercepted by the nefarious SPAM filter. Would you mind, when you get a minute replacing #35 with the post in the SPAM filter? Thanks in advance.
Comment by Leonid Meyerguz — July 25, 2006 @ 2:45 am
Sal: If one argues natural selection improves the odds over random chance, it must justify that in view of Dembski’s displacement theorem which says evolutionary algorithims, without specific direction perform no better than random chance on average.
Which of course assumes that 1) Dembski’s displacement theorem makes sense (I argue it doesn’t) and that 2) random search (not to be confused with random chance) is hard. As I have shown, under the No Free Lunch theorem, random search is actually trivially effective.
So in other words, the displacement theorem does little to help out resolve the issues here.
Other than that…
Sal: For chance hypothesis H, we are trying to show it lead to a contradiction of the form: “E implies not-E” with X% amount of confidence.
This could benefit from some clarification. In fact, I’d say it is mostly content free as presented here.
Comment by PvM — July 25, 2006 @ 2:47 am
Sal: If one argues natural selection improves the odds over random chance, it must justify that in view of Dembski’s displacement theorem which says evolutionary algorithims, without specific direction perform no better than random chance on average.
Which of course assumes that 1) Dembski’s displacement theorem makes sense (I argue it doesn’t) and that 2) random search (not to be confused with random chance) is hard. As I have shown, under the No Free Lunch theorem, random search is actually trivially effective.
So in other words, the displacement theorem does little to help out resolve the issues here.
Other than that…
Sal: For chance hypothesis H, we are trying to show it lead to a contradiction of the form: “E implies not-E” with X% amount of confidence.
This could benefit from some clarification. In fact, I’d say it is mostly content free as presented here.
Leonid, interesting posting.
Comment by PvM — July 25, 2006 @ 2:47 am
PvM:
Thank you, but as of right now, the posting is completely broken, with crucial terms undefined. The (hopefully) correct version is still languishing in Limbo that is the SPAM filter; hopefully, one of our heroic moderators will rescue it before long.
As for your own comment, #38, I am with you on everything you say, except, possibly, the part about random search. I read your Panda’s Thumb article, and totally agree with it from a technical standpoint. However, it doesn’t address the scenario, promoted by ID proponents, that the combinatorially large majority of, say, DNA sequences have no utility whatsoever, and only an exponentially small (in sequence length) minority of sequences can give rise to some function. If the ID assumption is correct - and while there is no convincing to support it yet, I think it is plausible - and if this set of possibly functional sequences remained frozen in evolutionary time, then random search would indeed be woefully ineffective in locating such “targets”. So, I think the statement “random search is trivially effective” should be cautiously qualified.
Of course, evolution is not “random search” by any measure, and the “displacement theorem” is pure fluff when it comes to eliminating non-intelligent causes of bias in a search procedure (and, I think, when it comes to even defining what a search procedure is). So we don’t really need random searches to refute Dembski and company. :)
Comment by Leonid Meyerguz — July 25, 2006 @ 3:26 am
PvM says: “ID provides no specifics allowing one to calculate P(T|H) where H is the hypothesis that T is designed.”
This concerns me also. The usual method of hypothesis testing using likelihoods goes something like:
1) Observe some data D
2) Compute P(D|H0) for some sensible choice of null hypothesis H0
3) Compute P(D|Hi) for some range of competing hypotheses Hi
4) Compare the values obtained in 2) and 3) - bigger is better.
So the obvious question is how to find P(D|H) when H is the design hypothesis. Without that, we seem to be having a barbeque but missing the beef, as it were.
At present CSI seems simply like a way to handwave around the hard work required in step 3, and jump straight from a small value under one hypothesis to a conclusion. Perhaps there’s something to it I’m missing, however. I’d be interested to hear more from the ID proponents.
Comment by MartinM — July 25, 2006 @ 6:59 am
Perhaps I should point out that I ignored the issue of priors in my post above. If all we’re interested in is whether or not a given piece of data favours one hypothesis over another, that’s an unneccesary diversion. The sketch I gave above shouldn’t be taken as complete, by any means.
Comment by MartinM — July 25, 2006 @ 7:28 am
Leonid–
I don’t see any post from you in the spam filter. Has it been released? Else maybe you could resubmit it, or email it to me (netid=hom4) and I’ll replace the old one.
We’d love to have you (and anyone else in the vicinity) join us for an IDEA discussion meeting on this topic. It’s not that anymore long till the semester begins…
Comment by Hannah — July 25, 2006 @ 8:51 am
“random search (not to be confused with random chance) is hard. As I have shown, under the No Free Lunch theorem, random search is actually trivially effective.”
I must have missed this. Which post was that? Remember, it must be “trivially effective” in a large search space. The search space for a given 3 base-pairs to change in a 2 megabase genome is roughly 10^19. If I had to change 3 amino acids, it could be much more than that.
Comment by Jonathan Bartlett — July 25, 2006 @ 8:54 am
Hannah(23),
What biological parameters, that we can actually test and observe, it is characterizing then? If
nothing, as I think is the case, then it certainly seems to be an abstraction to me…
Sal(24),
It is highly suited to the origin of life question
And anything else we don’t know much about. Is there any example of CSI not relying on
ignorance, was my earlier question in comment 7.
Jonathan Bartlett hits the nail on the head in comment 29, with the very reason why CSI is useless:
But anyway, PvM has been doing a great job reviewing Dembski’s math - and if I’m not mistaken, he has a great post on this very topic on The Panda’s Thumb somewhere that might be worth reading.
Comment by Dan — July 25, 2006 @ 11:12 am
Just an interesting tangential topic related to the probability of peptide (short chains of amino acids that make up proteins) formation. Here an inventive scientist somehow bypassed the slow, gradual, and improbable process. Is this kind of work factored into the equations Dembski uses when calculating chance?
http://www.firstscience.com/site/articles/genesis.asp
“Genesis by comets is a controversial idea, but it has received an important boost with the knowledge that a NASA supported experiment has revealed that complex molecules hitchhiking aboard a comet could have survived an impact with Earth.
“Our results suggest that the notion of organic compounds coming from outer space can’t be ruled out because of the severity of the impact event,” says Jennifer Blank, a geochemist at the University of California, Berkeley. Blank and colleagues simulated a comet collision by shooting a soda-can sized bullet into a metal target containing a teardrop of water mixed with amino acids - the building blocks of proteins.
Not only did a good fraction of the amino acids survive, but many polymerized into chains of two, three and four amino acids, so-called peptides. Peptides with longer chains are called polypeptides, while even longer ones are called proteins.
“The neat thing is that we got every possible combination of dipeptide, many tripeptides and some tetrapeptides,” said Blank. “We saw variations in the ratios of peptides produced depending on the conditions of temperature, pressure and duration of the impact. This is the beginning of a new field of science.”
Comment by Mike Hannigan — July 25, 2006 @ 11:28 am
In evaluating CSI, even the simplest ball park estimates could provide significant insight. e.g., see:
Ouzounis CA, Kunin V, Darzentas N, Goldovsky L. A minimal estimate for the gene content of the last universal common ancestor–exobiology from a terrestrial perspective. Res Microbiol. 2006 Jan-Feb;157(1):57-68. Epub 2005 Dec 19
Even an extremely optimistic estimate of 50% probability per gene family suggests probabilities less than 1/2^1000, which I think is a tad bit beyond Dembski’s Universal Probability Bound of 10^120!
Good luck in trying to showing abiogenesis to a minimum self reproducing cell within the UPB - AFTER which you get a chance to invoke the wonderous powers of natural selection.
Comment by David L. Hagen — July 25, 2006 @ 11:59 am
David,
Thank you for the opportunity to revisit the topic of creationist abiogenesis - that’s topic I’ve been looking for an excuse to segway into for a few days now.
Please see my post on revisiting creationist abiogenesis for my response to your comments.
Comment by Dan — July 25, 2006 @ 12:33 pm
Hannah,
I just resubmitted post #35. It’s still not showing up. Please let me know if it’s stuck in the SPAM filter. Thanks again for your help.
Comment by Leonid Meyerguz — July 25, 2006 @ 12:36 pm
How did you compute this, and how did you decide it’s “optimistic”?
Comment by Don Baccus — July 25, 2006 @ 12:36 pm
Leonid–
It isn’t. I’m not sure what’s wrong here– what browser/operating system do you use?
Comment by Hannah — July 25, 2006 @ 12:47 pm
Regarding PvM’s notes on Dembski, Wolpert, NFL and co-evolution:
Dembski stated: Fitness among Competitive Agents: A Brief Note
Dembski, William A. (2002) No Free Lunch: Why Specified Complexity Cannot be Purchased Without Intelligence (Lanham, Md.: Rowman and Littlefield).
Dembski, William A. (2005) “Searching Large Spaces: Displacement and the No Free Lunch Regress”
In his “jello” article on Dembski, David Wolpert, author of the NFL theorems then stated:
Wolpert, D.H. Macready, W.G. Coevolutionary free lunches IEEE Trans. Evolutionary Computation, Dec. 2005 V 9, #6 pp 721- 735
“In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. However, in the typical coevolutionary scenarios encountered in biology, where there is no champion, the NFL theorems still hold.”
Dembski responded in Fitness among Competitive Agents: A Brief Note
I suspect PvM overestimates his claims on No Free Lunch (NFL)
Comment by David L. Hagen — July 25, 2006 @ 12:57 pm
All right, I’m not averse to going though it, but bear in mind I am doing my best to put the ideas in non-technical terms for the readers. You and I, given our backgrounds are capable of going into such a level of formalism that it become mostly undreadable except to the uninitiated. I’m trying to put in terms at least some people will understand. Thus if you see some of my descriptions to be simplistic, it is because I’m not trying to kill the readers with formalisms.
Leonid,
I’m afraid you are presuming I didn’t understand what Dembski said given that I tried to give a simplified account of how to calculate Phi_S(T), but I don’t think that is the case.
But if we have to go formal, so that we don’t talk past each other, we go formal. I will hope the readers will forgive the rigor, otherwise we’re not going to resolve the impasse….
Dembski gives the definition of Phi_S(T) :
First of all Phi_S(T) is an integer number, it is the cardinality of a subset of Omega, call it |T_Superset| , T is subset of an appropriate T_superset
to clarifiy our notations
| T_Superset | = CARD (T_superset)
The cardinality of a set is merely the number of elements in tha set.
Again, I’m going back to our example of 500 fair coins. Consider the set T_all_heads it has one member. I’ll represent it as such with spacing for clairty only:
T_all_heads =
{
HH HH HH HH ……
};
likewise
T_all_tails =
T_all_tails =
{
TT TT TT TT……
};
T_all_tails_OR_all_heads =
{
HH HH HH HH ……,
TT TT TT TT……
};
CARD(T_all_heads) = 1
CARD(T_all_tails) = 1
CARD(T_all_tails_OR_all_heads) = 2
moving on
T_all_tails_OR_all_heads_OR_THrepeat_OR_HTrepeat =
{
HH HH HH HH ……,
TT TT TT TT……,
TH TH TH TH ……,
HT HT HT HT …..
}
CARD(T_all_tails_OR_all_heads_OR_THrepeat_OR_HTrepeat) = 4
however note
T_repeat_first_two_coins = T_all_tails_OR_all_heads_OR_THrepeat_OR_HTrepeat
Thus, the same decompression algorithm (independent of whatever language), will generate all members of T_all_tails_OR_all_heads_OR_THrepeat_OR_HTrepeat when only a fraction (2 coins) is provided as input.
Thus “repeat_first_two_coins” ojbectively describes that T_all_heads is can be adequately characterized by Phi_S(T) = 4 even though 4 is overkill since Phi_S(T) = 2 is sufficient for T_all_heads. One can see by way of extension for T_all_heads, letting Phi_S(T) = 10^30 is adequete, but absolute overkill — i.e, one seeing 500 heads coins will still infer design whether Phi_S(T) =2 or Phi_S(T) = 10^30….
Two issues characterizing Phi_S(T)
1. number of elements of an appropriate T_superset
2. amount of info from the description of each elements of T_superset needed for Semiotic agent to generate all elements of T_superset
#2 wasn’t explicitly addressed in Dembski’s paper, but as rule, if half of the bits in a string define the other half unequivocally, then chance is probably not at work, thus any algorithmic compression/decompression that can operate with no more than half of the bits string, such a semiotic description will probably identify good T_supersets
I think, Leonid, you’re making this a million times harder than it needs to be. Further CSI does not live or die on ones inability to calculate Phi_S(T), being able to calculate Phi_S(T) is merely icing on the cake.
PS
I was a bit disconcerted to see fractional numbers in your calculation above, CARD(T) should always be an integer. Did I read your calculation correctly? I may have misunderstood.
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 1:12 pm
David Hagen: I suspect PvM overestimates his claims on No Free Lunch (NFL)
I suspect that morely likely Dembski overestimated the relevance of NFL theorems to his claims.
Bartlett: I must have missed this. Which post was that? Remember, it must be “trivially effective” in a large search space. The search space for a given 3 base-pairs to change in a 2 megabase genome is roughly 10^19. If I had to change 3 amino acids, it could be much more than that.
In fact, random search’s efficiency under NFL does not depend on the size of the search space either.
In No Free Lunch Theorems and random search, I showed how Tom English showed that
Let’s first look at Dembski’s claim
This may suggest to the uninformed reader that thus evolutionary algorithms cannot really work…
Imagine their surprise when they find out that
Source: English T. (1999) “Some Information Theoretic Results On Evolutionary Optimization”, Proceedings of the 1999 Congress on Evolutionary Computation: CEC99, pp. 788-795
Comment by PvM — July 25, 2006 @ 1:20 pm
49 Don: If the “ball park” probability of 50% for obtaining a “gene family” by abiogenesis in a closed system of natural forces is not “extremely optimistic”, may I suggest trying 50% each per ball park of 300 codons or nucleotides in typical gene or protein to nominally give 2^300 per gene family. Then estimate the cumulative probability for 1000 gene families! I expect this new “wildly optimistic” ball park estimate is still a tad shy of the UPB of 10^-120. It appears to takes amazing “faith” in evolution to ground one’s career on such “high” probabilities.
See Sal and Hannah’s discussions for formal math and CSI etc. If you want to delve into serious probabilities, may I suggest you read (Sir) Fred Hoyle, The Mathematics of Evolution, 1999 ISBN 0-9669934-0-3. As I recall, he suggests 10^-4000 for the probability of evolution.
After that, you could look at the probabilities of population genetics popularly reviewed by geneticist John C. Sanford in Genomic Entropy and the Mystery of the Genome, 2005 (with serious abstracts in the appendix and full references.) He concludes that “The Emperor has no clothes.”
If that still does not satisfy, may I recommend taking up betting in Vegas. I expect the Casinos would be absolutely delighted to take you up on your estimate of the odds of abiogenesis and evolution. They would probably even give graduate courses and diplomas in the College of Hard Knocks.
Comment by David L. Hagen — July 25, 2006 @ 1:24 pm
Leonid I read your Panda’s Thumb article, and totally agree with it from a technical standpoint. However, it doesn’t address the scenario, promoted by ID proponents, that the combinatorially large majority of, say, DNA sequences have no utility whatsoever, and only an exponentially small (in sequence length) minority of sequences can give rise to some function. If the ID assumption is correct - and while there is no convincing to support it yet, I think it is plausible - and if this set of possibly functional sequences remained frozen in evolutionary time, then random search would indeed be woefully ineffective in locating such “targets”. So, I think the statement “random search is trivially effective” should be cautiously qualified.
Which is why it is qualified “under the NFL assumption”. The posting on PT shows that contrary to Dembski’s suggestion, under the NFL theorem, random search is trivial. And I think Dembski must have realized this since in Searching Large Spaces, he changes from the NFL assumptions of averaged over all fitness functions, to a ‘needle in the haystack’ kind of search.
Leonid Of course, evolution is not “random search” by any measure, and the “displacement theorem” is pure fluff when it comes to eliminating non-intelligent causes of bias in a search procedure (and, I think, when it comes to even defining what a search procedure is). So we don’t really need random searches to refute Dembski and company. :)
Of course we agree, but showing how under Dembski’s own assumptions, random search is actually quite efficient is just the icing on the cake.
ID’s hopes that sequence space is constrained to a small part may also be undermined by the following findings:
1. Gavrilets has shown that fitness landscapes become ‘Holey Landscapes’ when the dimensions increase. Such seems to be the case for DNA sequence space for instance.
2. In case of RNA it has already been shown that sequence space is ’scale free’ and that structures extend throughout sequence space and are connected via neutral networks that extend throughout sequence space.
It’s just an added ‘bonus’ that such scale free networks also explain robustness as well as evolvability, modularity and various other relevant aspects to evolution.
Combine this with coevolving fitness functions and the fact that evolvability (read neutrality) itself is selectable and one may start to understand how evolution has been so succesful. Oh yes, scale free systems can be explained ‘trivially’ via the processes of gene duplication and preferential attachment. Imagine the surprise that these processes can in fact be observed in the genome…
Comment by PvM — July 25, 2006 @ 1:34 pm
David Hagen: As I recall, he suggests 10^-4000 for the probability of evolution.
As is so often the case with probability theory, it is trivial to make something improbable, it’s much harder to find the relevant hypothesis that makes evolution possible and plausible. Just note Dembski’s calculations about the probability of flagellar proteins forming the flagella.
But it seems that ID may be slowly retreating to the probability arguments of its creationism roots while abandoning the unnecessary transformation of probability into ‘complexity’ or ‘information’, leading to much confusion with how these terms are used commonly in science.
Comment by PvM — July 25, 2006 @ 1:39 pm
PvM
Exactly. Dembski’s SC formula is a general hypothesis test. He tells us to use it to falsify hypotheses of “Darwinian and other material mechanisms”, but there’s no reason that it can’t be used to falsify any hypothesis, including one of design. Let’s do it.
Let E be the evolution of bacterial flagella, and T be “motor-driven propeller,” and H is the design hypothesis. The only designers we know of are human, and the probability of a human existing hundreds of millions of years ago, much less one with nanobiotechnology skills, is close to zero. So specified complexity obtains and the design hypothesis is falsified.
But shouldn’t we consider the possibility of an unknown non-human designer? No, says Dembski: Appealing to the unknown to undercut what we do know is never sound epistemological practice.
(If IDers object that my analysis is hardly rigorous, I reply that such is the nature of Dembski’s method.)
Comment by secondclass — July 25, 2006 @ 1:46 pm
Even the Needle in the haystack search may not be that hard as long as neutrality is present.
Tina Yu, Julian Miller Finding Needles in Haystacks is Not Hard with Neutrality (2002) European Conference on Genetic Programming
Abstract. We propose building neutral networks in needle-in-haystack fitness landscapes to assist an evolutionary algorithm to perform search. The experimental results on four different problems show that this approach improves the search success rates in most cases. In situations where neutral networks do not give performance improvement, no impairment occurs either.
We also tested a hypothesis proposed in our previous work. The results support the hypothesis: when the ratio of adaptive/neutral mutations during neutral walk is close to the ratio of adaptive/neutral mutations at the fitness improvement step, the evolutionary search has a high success rate. Moreover, the ratio magnitudes indicate that more neutral mutations (than adaptive mutations) are required for the algorithms to find a solution in this type of search space.
and
Vesselin K. Vassilev, Julian F. Miller The Advantages of Landscape Neutrality in Digital Circuit Evolution (2000)
I hope this shows that without specifics, one cannot make the general claim made by Dembski based on the NFL theorems that evolutionary search is hard/impossible.
And we agree that the ‘displacement argument’ is flawed as well.
Comment by PvM — July 25, 2006 @ 1:47 pm
Hannah,
This is very interesting. I’m using Firefox with Win XP Pro, and up until now, I’ve had no trouble posting. The only reason I can think my post keeps getting lost is because I’ve started using HTML escape sequences in (for the “less than” and “greater than” signs). Do you mind if I just email you the text, and you try to submit it yourself?
Comment by Leonid Meyerguz — July 25, 2006 @ 1:50 pm
A quick example to illustrate a problem with English language specifications:
Let’s apply the SC formula to the specification “Himalayas”. This word identifies a set of hundreds of mountains, each with distinct characteristics. Given our understanding of geological processes, the odds that these exact mountains would appear are miniscule. Thus P(T|H) is small, and so is phi_s(T) since T contains only one word. So, according to Dembski, the Himalayas are designed.
Comment by secondclass — July 25, 2006 @ 1:50 pm
Please do.
Comment by Hannah — July 25, 2006 @ 1:54 pm
Second Class: You make a good suggestion. Especially since ID claims that intelligent design can generate CSI. For this one has to show that indeed, CSI as calculated by Dembski’s formulate shows that P(T|H) where H is the design hypothesis is both likely and can generate sufficient CSI. It’s insufficient to claim that since ID can explain the unlikely to become likely, ID can generate CSI, one needs to show the actual pathways and show that under such a hypothesis, P(T|H) meets the requirements.
Now we are faced with the following conundrum:
For design to generate CSI, P(T|H) has to be sufficiently small, but for design to generate a plausible hypothesis, P(T|H) has to be sufficiently large or it will lose to other hypotheses. It’s also not sufficient that P(T|H) is larger than other hypotheses without considering the null hypothesis that we have missed a relevant hypothesis. Dembski ends his specification paper with the following
There are several objections to Dembski’s claim
1. Unknown hypotheses indeed may carry no value, thus it is essential that the design hypothesis is specified.
2. Independent information about the designer(s) may not be necessary but this will render the design inference inherently unreliable.
3. Design always is a possibility, it’s just that when it comes to providing relevant hypotheses for design, things a posteriori fall apart.
Comment by PvM — July 25, 2006 @ 1:56 pm
David Hagen states, among other things in his personal attack on me:
Since I live, betting on process that led to my being here would be a bit like betting on the winner of the first superbowl…
As PvM implied above, it’s easy to pick numbers out of thin air that make things seem incredibly improbable.
That’s all you’re doing …
Comment by Don Baccus — July 25, 2006 @ 2:24 pm
Salvador writes:
Salvador, Hannah was kind to fix my post #35 above, so now it (hopefully) makes sense. I am afraid that you still appear to be seriously misunderstanding at least a part of Dembski’s argument: I strongly encourage you to read my post above and Dembski’s paper; especially his definition of Phi_S(T), the specificational resources, on page 17, and his example computing the specificity of the flagellum, on page 18.
Still, let us walk through the example you gave, and I’ll point out the specific errors you are making.
You are right that is an integer - I never suggested otherwise - but it is not the cardinality of a subset of Omega. Rather, it is the cardinality of a subset of PS(Omega) - that is, the numbers of subsets of Omega (events) matching a certain descriptive complexity in the reference frame of S. Again, I urge you to review Dembski’s definition of Phi_S(T), and recall - as you correctly pointed out - that Patterns(Omega) is just PS(Omega).
Just to give you an impression of the “magnitude” of your error, consider that for n fair coins, the size of the even space Omega is 2^n, so no subset of Omega can have cardinality above 2^n. However, the size of PS(Omega) is 2^(2^n) - the number of all possible distinct subsets of Omega. Phi_S(T) potentially ranges between 0 and 2^(2^n), though in Dembski’s examples it is always relatively small even when compared to 2^n.
Your discussion of T_repeat_first_two_coins is absolutely correct, but you have to realize that the description “Repeat First Two Coins” corresponds only to a single event (subset of Omega) T that contains four members: T = {HHHH…, TTTT…, HTHT…, THTH…}. But for the purposes of computing Phi_S(T), we don’t care about the Card(T): rather we care about the number of events with the same descriptive complexity as T. Following the example I gave in post #35, the descriptive complexity of T, Phi’(T)=4 - four words used by our fixed agent S to describe T. Thus, given S has a vocabulary of w=1e5 words, and since each description corresponds to at most one event in Omega, there are less than w^5=1e25 events in Omega whose descriptive complexity is less than or equal to that of T. So, Phi_S(T) is less than 1e25, and the specificity of T can be bounded from below by -log_2(1e25 * 4 * 2^-500) = 414.952.
Not at all - that is the crux of the error you are making. The number of elements in the appropriate T_Superset is only needed to compute the P(T_superset | H), which Dembski argues allows us to rule out any subset of T_superset as a plausible chance event, assuming a sufficiently low value for both P(T_superset | H) and Phi_S(T_superset). The number of elements in T_superset is irrelevant for computing, or rather, bounding Phi_S(T) - that quantity depends only on the number of symbols in S’s communication system and the length of the description of T, Phi’(T). (Again, the function should be labeled Phi’(T,S), to underscore its dependence on S.) Dembski fails to make this explicit, but it is crucial to understanding his work.
I can’t really parse this, but I think what you are trying to describe here is Dembski’s “descriptive complexity” - roughly, length of a description - of T, represented by S’s function Phi’(T). If that is the case, you are correct.
I think, Salvador, I am making this at at least as hard as it needs to be, given that Dembski’s CSI formula does live or die with Phi_S(T) - substitute a very high value if you don’t believe me - and given how vaguely it is defined, and how subjective it is at its core. Certainly you, despite your obvious support and admiration for Dembski’s work, have so far shown that you clearly misunderstand of what he means by “specificational resources”. Surely you won’t claim that the notion of “specificational resources” is non-essential to calculating the value of specificity and the amound of CSI?
You misunderstood, though it is probably not your fault - until Hannah posted the correct version a while ago, my post was very badly mangled. But, no, the fractional values represent probabilities and specificities: Phi_S(T) is, of course, an integer.
Comment by Leonid Meyerguz — July 25, 2006 @ 3:14 pm
Offtopic Since some of our posts are beginning to look rather ugly– how many people would write in LaTeX if I could get LaTeX capabilities here?
Comment by Hannah — July 25, 2006 @ 3:21 pm
Hannah wrote:
Hmmm … You wouldn’t, by chance, be talking about me, would you? ;) But, yes, I think LaTeX is a great idea if other people would agree to it.
Comment by Leonid Meyerguz — July 25, 2006 @ 3:37 pm
[Raises hand]
Comment by secondclass — July 25, 2006 @ 3:44 pm
I’ll third that.
Comment by MartinM — July 25, 2006 @ 4:15 pm
Sal,
From my seat, reading you and Hannah arguing NFL math with Pim and Leonid is akin to Godzilla and Mothra battle Hedorah and Megalon!
You shouldn’t dumb down your formal arguments for readers such as myself. I don’t mind not completely grasping the formal terms, for the time being. Part of my job is making the technical plain for administrators, so I’ll just ask questions to try and get at some non-formal understanding. If you algorythmic geeks will indulge me, that is. I’ve got some questions, but have to run for now.
Comment by Todd — July 25, 2006 @ 4:21 pm
Time out please!
Is U an element of patterns(Omega) or is U a subset of patterns(Omega). Until we resolve this, the discussion is going nowhere.
I read it U is an element of patterns(Omega) or equivalently U is an element of PowerSet(Omega). Which implies U is a subset of Omega.
Notation for member (element) of a set can be found at Set theory.
Notation for subset
Thanks.
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 4:26 pm
I’m still waiting for a valid finding in biology that these mathematical derivations are applicable to…
… I guess I’ll be waiting a long time…
Comment by Dan — July 25, 2006 @ 4:30 pm
Thus {U … | …} is a set within powerset(Omega).
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 4:37 pm
Sal writes:
No problem: set theory can be quite confusing. U is an element of PS(Omega). On the other hand, the set {U in PS(Omega): U has some propery P} is a subset of PS(Omega), which is what I was referring to in the text you bolded above. It is important to keep in mind that PS(Omega) is a set of sets (sometimes called a family of sets to avoid, or in my view, add to, confusion). Thus elements of PS(Omega) are sets, and subsets of PS(Omega) are sets of sets. So, the “cardinality of a subset of PS(Omega) with property P”, means “number of elements (sets) in PS(Omega) with property P”, or alternatively “the number of subsets of Omega that have property P” (since PS(Omega) is a set of all possible subsets of Omega).
Hope this makes my earlier posts easier to parse. Or at least not anymore confusing.
Comment by Leonid Meyerguz — July 25, 2006 @ 5:06 pm
Dan wrote:
A very, very long time. Don’t hold your breath. However, I think discussing Dembki’s mathematical formulations is useful because a) it can show how impractical such formulations are when we try to apply them to real-world phenomena, and b) it’s fun (and for certain definitions of useful, “fun”=”useful”). Besides, where better to discuss specified complexity than in a thread title “Specified Complexity”?
Comment by Leonid Meyerguz — July 25, 2006 @ 5:13 pm
I suppose…… but my mind keeps coming back to if SC is irrelevant (because it’s not connected to anything real), then why bother with it?
Comment by Dan — July 25, 2006 @ 5:30 pm
Thank you. In the post previous to yours I indicated I read “{” as “|”. I should have realized that earlier….
I am accostomed to seeing something like A = {….}, the shorter form threw me off.
In light of that, my earlier calculation of Phi_S(T) needs some revision.
I deliberately chose special cases for Phi_S(T) so that objectivity could be put into the issue where there was some independence from the language choice.
I believe that detecting algorithmic compressibilty given a number of inputs from a description of each element of T would permit characterizations of Phi_S(T) for algorithmically compressible cases.
I’m asserting a conjecture that all elements of A = {U element patterns Omega satisfying Phi_S’(U)
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 6:10 pm
My last post was cut off (the less than or equal to I think threw the weblog software off):
I’m asserting a conjecture that all elements of A = {U element patterns Omega satisfying Phi_S’(U) less than or equal to Phi_S’(T_repeat_first_two_coins) } less than or equal to Powerset (T_repeat_first_two_coins).
I think that is objectively defensible since all members of T_repeat_first_two_coins are essentially describable by the same semiotic description, independent of the language in use. Any objections?
I am thus revising my calculations:
not merely
CARD(T_repeat_first_two_coins) as I had earlier stated.
I believe algorithmic compression analysis is the most objective way to characterize Phs_S. Beyond that, characterization of Phi_S(T) will require further exploration. Hopefully it might be apparent how this principle might be generalized to less trivial cases.
Nevertheless, I do not think CSI lives or dies on the ability to characterize Phi_S(T). There is recourse to pre-specifications in case Phi_S(T) cannot be ascertained for generalized specifications.
Salvador
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 6:35 pm
It probably hasn’t occured to you, but we actually don’t all have infinite amounts of time, and some of us have in fact our own studies and research. That would suggest there might be a limit as to how much you can reasonably ask of another person.
Please spread that meme to other ID proponents, such as William Dembski and Michael Behe. They have both made such requests.
Comment by ivy privy — July 25, 2006 @ 7:42 pm
I object to students being interrogated like this. The questions should not be directed at Hannah.
1) It was my understanding that folks from the IDEA club are co-presenting in the course, so that may be an inaccurate characterization of Hannah’s status, even if she is a student in the course (which I don’t know)
2) Hannah started this thread to defend the definition of CSI. That gives her a status obove that of a mere onlooker or learner.
Comment by ivy privy — July 25, 2006 @ 7:48 pm
Salvador:
I probably won’t have time to address your latest post in detail tonight - though I will if I get the chance - but for now, I urge you to re-read Dembski’s work, and to consider the definition of Phi_S(T) specifically. Your latest proposal, while slightly closer to the truth, is still unworkable. In particular, you write:
This is still wrong. The most important point to understand is that “specificational resources”, Phi_S(T), cannot be defined as a function of the size of the set T. For example, using your definition above, I would define Phi_S(”Any Sequence”) = 2^Card(Omega) = 2^(2^n) - the largest possible value for Phi_S - even though I need an extremely simple pattern to describe this sequence. Furhtermore, under your definition, all small sets T will have the same value of Phi_S, regardless of whether or not you could use a simple algorithm to generate their elements.
So, again, you cannot define Phi_S(T) in terms of Card(T). Rather, define it by counting other event descriptions (or, if you will, algorithmic representations) that are as short as the representation of T. If you think you can divorce the notion Phi_S(T) from any form of a coding system, I suggest you review Dembski’s definition: you will be disappointed. Even if you wish to use algorithmic complexity, you will need to pick a coding system: namely, the reference programming language (or, more accurately, Universal Turing Machine). So, pick one - I suggest regular expressions for the fair coin case - define the function Phi’(T), and proceed from there. Count all the representations in your coding systems that are shorter Phi’(T). Voila! That’s how you obtain un upper bound on Phi_S(T).
I also recommend reading Shallit & Elseberry’s paper, particularly the first Appendix. They actually do give a workable definition of specified complexity in terms of Kolmogorov complexity. See my post #295 in the “Analogy, Induction, and Specious Arguments” thread for some clarifications.
Comment by Leonid Meyerguz — July 25, 2006 @ 8:43 pm
Leonid,
Thank you for reading my post and offering your suggestions. I have very early on, prior to Elsberry and Shallit suggested algorithmic compression as one method of specification. Wigner in 1960’s as well….
But recall, I have insisted repeatedly that if Phi_S(T) is not tractable, one has recourse to pre-specification. Pre-specification is far less controversial. I have even proposed one architecture that is pre-specified, namely the Turing machine. We could also use human artifacts or common practice for solving functional problems in engineering as sources of specifications. The code/decode metaphor, the lock-key metaphor, etc. are so prevalent in engineering and computer science, I hardly think we need to worry over the scarcity of pre-specification to project onto biology.
For that matter they are doing linguistic pattern search on all sorts of things in biology. I don’t think chance hypotheses can account for certain linguistic structures. We’re already using pre-specification detection in biology without any of the metaphysical baggage….for example you are probably aware of these recent developments: Hidden codes within codes.
Now, I’m sure you have no reason to describe linguistic structures (like codes) as obeying a chance hypothesis?
I do not think Phi_S(T) as a concept is yet mature enough. It should be discussed and explored, and I don’t not think Dembski represented his internet musing as Gospel.
I can understand the confusion, but I deliberately chose descriptions which would include the most minimally complex patterns (All_heads and All_tails), thus if it did not include these, Phi_S(T) would be invalid according to the way I constructed Phi_S(T). I don’t know of any other way to even begin to construct it objectively.
The reason I chose high symmetry strings, is that even though other patterns are algorithmically compressible, one gets into difficult issues of how much of the compression algorithm was a post-dictive projection onto the data.
If this is giving everyone too much indigestion, there is no reason IDers must adopt Phi_S(T). It has been laid out as a something to consider. But as I said, pre-specification comes with far less issues, and that is what is workable for now, and used unwittingly in practice already…
That is why, I rather focus on finding ANALOGIES to engineering, because ANALOGIES are sources of pre-specifications.
Comment by Salvador T. Cordova, IDEA GMU — July 25, 2006 @ 9:31 pm
Todd wrote in #12
There has been a lot of tooing and froing with coin tosses, why not try a real, simple biological example.
Bacterial TEM betalactamases (for example S. typimurium TEM, NCBI entrez acession number AAS18375, 286 aa long) can hydrolyse cefotaxime with high efficencey after 4 mutations EA42G, E104K,M182T, and G238S
Calculate the CSI involved in going from TEM to cefotaximase.
Comment by Ian Musgrave — July 25, 2006 @ 11:29 pm
David L. Hagen wrote in #46 (after quoting a paper on the LUCA)
The Last Universal Common Ancestor is NOT the first living thing produced by abiogenesis. The LUCA is the last ancestor of archebacteria, eubacteria and eukaryotes. It occurs well after abiogenesis (and the RNA world, origin of self replication and the DNA-RNA transition), the appearance of the first things we would think of as cells and the exhaustion of prebiotic resources of complex organics.
Comment by Ian Musgrave — July 25, 2006 @ 11:37 pm
Thanks for the clarification Ian. However, I expect the complexity to be similar. It has to involve a genome, genomic duplication, cell structure replication, and sustainable conversion of abiotic energy to biotic energy such as ATP via ATPase (Whether from photosynthesis or hydrocarbon conversion.)
Comment by David L. Hagen — July 25, 2006 @ 11:46 pm
63 Don
Apologies for my remarks being taken as a personal attack. None was intended. The casino comment was to give an example of those who make real life calculations of probability and who ensure the odds are for them. Mark Ritchie, God in the Pits, describes other examples of Chicago Board of Trade commodity brokers who make their living by probabilites.
That appears to involve the metaphysical assumption of methodological naturalism and that abiogenesis happened. That is the subject of the debate of ID vs Evo origin theories.
I understand 50% to be “extremely optimistic” compared to a conservative guestimate of the order of 2^-300 for the CSI of the function of a typical gene or protein. I expect the probability of Complex Specified Information in defining the function of each of the 1000 “genome families” to be alot closer to 2^-300 than 50%. Thus my first “ballpark” estimate giving the order of magnitude estimates that are far beyond the Universal Probability Bound are still highly conservative compared to what actual CSI of the functions will be.
If you wish a more precise estimate of the probabilities of genome strings, may I refer you to Hubert P. Yockey, Information Theory, Evolution and the Origin of Life, 2005, Cambridge Press. Yockey cites Pasteur’s
Yockey states:
Like Dembski, Yockey (p 117) observes
. I.e., Yockey is identifying a necessary biotic function that can be used to calculate biotic CSI necessary before probability calculations.In Section 6.4 Yockey
In section 7.1 Yockey calculates the probability of the current DNA code and observes
These two factors alone exceed the Universal Probability Bound. I leave it to you to decide how much beyond the UPB is worth estimating the probability of CSI for the function of the rest of the more than 900 genomic families required for the simplest self replicating cell.
In Section 4.1 p 29, Yockey calculates
i.e., As a rule of thumb, there are about 2.06 bits/amino acid. or triplet codon. So an 300 amino acid seqeuence nominally involves about 2^(2.06*300) or 2^618 (or 618 bits, if my late night math doesn’t have too many errors. (Correction to previous post: I should have said “each per ball park of 300 codons or amino acids”).May I recommend that you dig into Hoyle, Yockey and Sanford (rather than blindly accepting PvM’s superficial dismissals.)
Is 1/2^1000 still not be “extremely optimistic” for the CSI of the functions of the 1000 gene families in a minimal self replicating cell?
Comment by David L. Hagen — July 25, 2006 @ 11:49 pm
Hannah,
My sincere apologies here. Some of the things in Bill Dembski’s paper had somethings I did not have a chance to clarify with him yet as his books have usually been my principle source of information.
Sometimes the discussions between he and I take months as I try to be very sparing of how much I indulge his personal help….
The T1, T2, T3 on top of page 17 was a bit unfortunate….those were unfortunately NOT the same T’s in Omega. This is the first time I ever had serious issues decoding his notation. And as is apparent, some of the conclusions Leonid and I were getting from this were outrageous. I kept thinking to myself, Bill couldn’t possibly have meant this! Cardinalities of large Power Sets!
Turns out, he didn’t mean it the way Leonid and I were