Thanks for the detailed response. I still have some significant issues with “specification”, but I’ll hold those for now and focus on what I believe are two key problems with your formulation of CSI.

CJYman:
“then we can calculate for specificity, and then calculate the probability of the event given a uniform probability distribution.”

Of course evolutionary algorithms aren’t random.

That demonstrates that a uniform probability distribution is not biologically relevant. If you are using this calculation to demonstrate that biological evolution by known natural processes cannot account for the diversity of life that we observe then you must take into account those known natural processes.

Once CSI is determined to be “present,” then we know that we aren’t dealing with a uniform probability distribution.

I’m sorry, I don’t follow that. I thought we were calculating CSI here. To do so, we need to take into account everything we know about the biological artifact under consideration.

However, merely having a non-uniform probability is still no help. According to the NFLT, we need a matching between the non-uniform distribution and the correct search algorithm which can make use of that distribution. That’s how we get an evolutionary algorithm.

The No Free Lunch theorems merely state that any particular search strategy is only as good as random search over the space of all possible fitness landscapes. We’re not dealing with a space of fitness landscapes, we’re dealing with the physical reality we all know. That’s one fitness landscape and the NFL theorems say nothing about the ability of evolutionary mechanisms to perform better than random search.

Mustala:
“The uniform probability distribution assumption is equivalent to the assumption that the DNA arose in its present form de novo. That does not correspond to either modern evolutionary theory nor to observed evolutionary mechanisms.”

Exactly, since CSI really only tells us that chance is not a viable option. Therefore the only two options left on the table are intervention by an intelligence or an evolutionary algorithm. Now, the reason CSI is used to signify previous intelligence is because ID proponents claim that the fortuitous matching between search algorithm and non-uniform distribution is just as difficult to arrive at by chance as is the original pattern in which CSI was measured. So if chance can’t get us to the original pattern, it won’t get us to the evolutionary algorithm. In fact, I see evolutionary programming as a hallmark of intelligence.

There are a lot of assumptions in this one paragraph. First, we haven’t seen an actual calculation of CSI, so claiming that CSI shows anything is premature. Second, there are more choices than an intelligent agent or an evolutionary algorithm. Known physical and chemical processes can’t be ruled out. Third, there is no reason to consider the search algorithm to be “matched” to anything. We live in a universe with a particular set of physical laws (for lack of a better term). Those are a given. There is no “search for a search” taking place.

Mustela Nivalis:
“the mechanisms identified by modern evolutionary theory do not create things like genomes de novo — they do so incrementally and therefore cannot be modeled so naively.”

Physicists are also interested in fine tuning of laws to produce life and the ratios of variables of those laws which would allow life to exist and evolve vs. which variables would not even allow life enough time or material or non-uniformity to form. BTW, I am in no way an “interventionist.”

I’m afraid that doesn’t address the problem with your calculation. There is no “search for a search”. The NFL theorems don’t apply. Known evolutionary mechanisms work far better than random search in this universe.

Mustela:
“You might be able to construct an argument for cosmological ID based on “search for a search”, but if you want to apply CSI to real biological systems, you have to take known evolutionary mechanisms into account.”

If what I have explained above is true, then any measure of CSI will show that chance is not capable of producing said pattern/event, evolutionary algorithm or not.

Because you fail to take into consideration the physics of this universe and the known mechanisms of modern evolutionary theory, your calculation has no biological relevance.

Can you modify your calculation to address these issues? I’m still very interested in implementing a CSI calculator in software.

Mustala:
“I’ve read that, but it seems very difficult to apply. What does it mean for a pattern to be independent? What is an example of a dependent pattern? Can’t anything be described by a pattern separate from itself?”

I’ve explained “specified patterns” in more detail in
this thread on my blog and in the thread “Polanyi and Ontogonetic Emergence” comment #8 here on UD. Sorry ’bout the lack of link. I couldn’t get it to work for some reason.

Now, I’ll let you answer your own question of “can’t anything [be specified].”

Here are two events:

1. You look on your computer and you see a string of symbols “Hello Mustela, how are you today?” The meaningful event that has appeared on your screen is specified since it conforms to a pre-set pattern of rules for the english language and the english dictionary (including slang). So f(english language+dictionary)= meaningful sentences — when operated by a semiotic agent whether that be a computer program or human. That is why a semiotic agent is important — the agent is the one that specifies the pattern to the event.

2. You wake up early in the morning and you go to the mailbox to get your mail. You notice that the weather is getting colder and leaves are beginning to fall. You see an event of leaves scattered on your front lawn. Is this event specified?

Mustela:
“Are you using this mathematical notation formally or informally? If formally, could you explain the nature of the function f?”

I am using this mathematical notation because in f(x)=y, x is independent of y. Therefore, f(pattern)=event, I believe is a formal way to show the specified event/pattern relationship. The given event is literally a function of a pattern. Therefore, the event is specified.

CJYman:
“So, if we have an event such as a folding and biologically useful protein,”

Mustella:
“A protein is an event? I apologize if this is a simple question, but I have read a fair bit of ID material and I find this terminology confusing. Can you rephrase it in more standard biological terms?”

I don’t think there is a need to get overly technical with the word “event” other than to use it as “something that happens” — basic dictionary definition. Yes, a pattern of amino acids and ultimately a pattern of DNA can produce a folding and biologically useful event — a protein.

CJYman:
“and an independent pattern such as a stretch of DNA,”

Mustela:
“Again, I apologize if I appear pedantic, but why would we consider the DNA that encodes for a protein to be an “independent pattern”? What is the precise definition you’re using?”

No problem, I appreciate when people ask for clarification unless the clarification descends into continual nitpicking. Independent here is used as independent is used in ‘”x” is independent of “y” in f(x)=y.’ Again, that is why I believe that if you follow a function where f(patter)=event, you can’t go wrong.

CJYman:
“then we can calculate for specificity, and then calculate the probability of the event given a uniform probability distribution.”

Mustela:
“Why a uniform probability distribution?”

Because chance (randomness) is characterized statistically as a uniform probability distribution and all that CSI is doing is removing the chance hypothesis.

Mustela:
“We know from observation that many mechanisms identified by modern evolutionary theory are not random in their behavior (mutation is assumed to be, but selection, for example, is not).”

Of course evolutionary algorithms aren’t random. Once CSI is determined to be “present,” then we know that we aren’t dealing with a uniform probability distribution. However, merely having a non-uniform probability is still no help. According to the NFLT, we need a matching between the non-uniform distribution and the correct search algorithm which can make use of that distribution. That’s how we get an evolutionary algorithm.

Mustala:
“The uniform probability distribution assumption is equivalent to the assumption that the DNA arose in its present form de novo. That does not correspond to either modern evolutionary theory nor to observed evolutionary mechanisms.”

Exactly, since CSI really only tells us that chance is not a viable option. Therefore the only two options left on the table are intervention by an intelligence or an evolutionary algorithm. Now, the reason CSI is used to signify previous intelligence is because ID proponents claim that the fortuitous matching between search algorithm and non-uniform distribution is just as difficult to arrive at by chance as is the original pattern in which CSI was measured. So if chance can’t get us to the original pattern, it won’t get us to the evolutionary algorithm. In fact, I see evolutionary programming as a hallmark of intelligence.

Mustela Nivalis:
“the mechanisms identified by modern evolutionary theory do not create things like genomes de novo — they do so incrementally and therefore cannot be modeled so naively.”

CJYman:
“The point is that according to Marks and Dembski’s recent work on active information, it is just as improbable to find something such as CSI as it is to generate a set of laws that would create an evolutionary algorithm to produce an incremental pathway to that CSI in question.”

Mustela:
“But we don’t need to find a set of laws. Physics, and therefore chemistry, is a given. Modern evolutionary theory attempts to explain what we observe, with the physical laws that exists.”

Physicists are also interested in fine tuning of laws to produce life and the ratios of variables of those laws which would allow life to exist and evolve vs. which variables would not even allow life enough time or material or non-uniformity to form. BTW, I am in no way an “interventionist.”

Mustela:
“You might be able to construct an argument for cosmological ID based on “search for a search”, but if you want to apply CSI to real biological systems, you have to take known evolutionary mechanisms into account.”

If what I have explained above is true, then any measure of CSI will show that chance is not capable of producing said pattern/event, evolutionary algorithm or not.

Oh, and referencing any questions about semiotic agents, a semiotic agent is merely an agent that utilizes sign systems, therefore does not have to be either human or conscious. The cell itself is a semiotic agent and thus we use the language of the cell (the language of life) to specify and measure for the CSI of a biological object. In fact, we don’t even have to specify anything, the cell has already done that by objectively converting patterns into events.

CSI, like any equation (such as those used to calculate the age and size of the universe) relies on estimations of presently available data. And, as already explained, I gave the extreme benefit of the doubt to the skeptic in my assumptions … so yes, the measurement of CSI could easily be updated in either direction in the future. The question is: “what direction will be the overall trend” or will we see the measurement(s) over time and given the error values of each variable stabilizing around an average value? With everything that we know can we even attempt to get a non-CSI value for the protein Titin? If someone can go back to my measurement and find the -log 2 of the end measurement, that would be great so that we can see the size of the value for CSI that we are presently dealing with. And then, how far up the hierarchy of protein multiple protein complexes can we go until there is no reasonable way to even fudge data to get a non-CSI value? Excellent questions for further ID research. In fact, I offer the invitation to the ID critics to help out with this research. I have provided an explanation of how to calculate for CSI above.

Mustela and ROb, I am enjoying reading through your questions and comments and I hope that I have time soon to get back to you guys.

Sorry I’m late to rejoin the discussion. I was following this thread on another computer and then couldn’t remember in which thread I was having this discussion.

I would love to continue, but am getting too busy again. We will definitely have to continue our discussion of CSI in the future. I now have the relevant threads bookmarked.

…later…

Sorry for the delayed response (I just returned from a 5-day extended weekend).

What was my aim in writing my paradox? It was to indicate that the total information can be fractioned only apparently and illusorily. Even I stated it explicitly in the article as follows:

The above proof evidences also another only-seemingly odd thing: the IIS is not properly composed of parts because when we, for hypothesis, divide it into parts we obtain contradictions.

Therefore when you write:

The real root of your absurdum is the following: A set of logical statements cannot be partitioned into subsets each of which are closed under logical derivation. So in your case, the premises that S and ~S are closed under logical derivation result in a contradiction.

you say almost the same thing from the point of view of logic and I agree with your statement for the simple fact that this contradiction was indeed what I wanted to obtain and emphasize. Just before writing step #1 I knew in advance that it was a flawed premise and a mere impossibility. What are for absurdum arguments but arguments where one states an untrue (or alleged untrue) premise to see the consequences?

After all, my premises were a unique premise (although expressed in some steps): A and ~A are disjoint. As a consequence when we obtain the contradiction it is this premise to fall, what else. This premise outputs a contradiction because such sets cannot be disjoint, in that a simple logical AND upon any two elements of them immediately shows us that they cannot be close (this is the job of steps #5-9). Hence, why do you write “your conclusion is a non sequitur” when my conclusion is to refute the premise of impossible closure contained in step #1 exactly as you do? It seems to me there is agreement between us on this ground.

In one of its interpretations, my article wanted to underline that finite information sources cannot be considered really separated from a limitless information source (this is another aspect related to the above conclusion). I could have written it very synthetically as “Total Truth is indivisible” or “Total Possibility has no parts” (both axiomatic in metaphysics) or something like that but I was afraid the thing passed almost unobserved and somehow abstract. So I thought that a 9-step analytic paradox expressed in terms of set theory and showing the unity of logic (which represents sort of “image” or “symbol” of that metaphysical Unity) might generate more interest and debate. Indeed the many technical comments of you and JT show the idea was good.

I admit that my paradox can be misunderstood depending on the interpretations one can assume about. Different interpretations are due to the fact that it is far from being rigorously formalized according to mathematical logic. I never pretended to have provided such exactness of formalization and of course I thank whoever helps to deepen and improve it somehow (as you and JT cleverly did). My goal was only to offer material to the reader for meditating about what, expressed in few words, is the infiniteness and indivisibility of information.

Also if S contained “all statements logically derivable from those it contains” (as you added to refute my argument) my proof would remain valid.

Reductio ad absurdum proves that the premises cannot all be true simultaneously. It doesn’t show that any given premise is false, so your conclusion is a non sequitur, and adding more premises only exacerbates the problem.

The real root of your absurdum is the following: A set of logical statements cannot be partitioned into subsets each of which are closed under logical derivation. So in your case, the premises that S and ~S are closed under logical derivation result in a contradiction. This is proven easily by noting that “a OR not a” follows from any set of axioms, but it cannot reside in multiple disjoint sets.

Unfortunately it seems we never will converge to an agreement. No problem. What is important is that anyone feels comfortable with his own ideas.

Anyway I agree with you that the best thing is to stop here our diatribe to not bother the readers (also if I would like to continue the discussion with you (and R0b too)).

You are a fair and acute debater and I thank you for your contribute to the discussion.

Good weekend.

P.S. I am not from the U.S. and, last but not least, today I am in vacation.

And (once again) if S contains ‘a AND b’ that is not the same as containing ‘b’, as ‘b’ and ‘a AND b’ are not equivalent.

(And it was not my original intention to belabor this obvious point to such an extent.)