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Detachability

Any chance of a quick rundown on detachability? IMO, that's where a lot of controversy about CSI lies. For example, if the item being looked at is the string "Methinks it is like a weasel" (to pick a completely random example), which of the following specifications is detached?

• 'The phrase "Methinks it is like a weasel"'
• 'A phrase in English'
• 'A phrase in a human language'
• 'A string that I recognise as having meaning'
• 'A string that I recognise as being in some way interesting'

Critics of CSI would generally claim that only the last one is truly detached because, if the next string you were shown was "QWERTYUIOP", you'd probably think that that also had high CSI (so the underlying specification that you're testing the strings against must include both of these).

Anyway, debate over the validity of CSI is probably an issue for another day, I just wanted to highlight the importance of detachedness. Will shut up now. [Corkscrew]

OK, I'll add an extra point which I've just noticed. When I've seen specifications defined on UncommonDescent.com, the level of specification chosen has apparently correlated strongly with the perceived "coolness" of the object at that level (see, for example, this discussion). That would mean that the CSI argument basically boiled down to "it's very cool, hence it couldn't have evolved", which would then be pretty much identical to the classic Creationist argument from incredulity. To conclude: we really need that definition of detachability! -- Corkscrew 05:11, 29 March 2006 (CST)

Actually Dembski seems to have decided to dispense entirely with the idea of detachability in his latest discussion. I'm still trying to sort out what the crucial differences between this and previous treatments such as No Free Lunch are (also only a third year maths student, so it takes a bit of muddling through) --Arctura 07:36, 29 March 2006 (CST)

Really? That's kind of a shame - I actually thought it was a pretty neat idea, despite not agreeing with his conclusions. -- Corkscrew 11:36, 29 March 2006 (CST)

Well, never mind; he doesn't. He just makes it implicit rather than explicit. Now that we have LaTeX (three cheers for Joseph!) where do we want a treatment of "The Equation", ? I was going to stick it somewhere in this page and then I couldn't quite find the room for it. --Arctura 20:52, 8 August 2006 (CDT)

I'll put the equation under the "Definitions" section, with a link to the new article about the equation. Obviously, the equation article should have much more detailed information than this article. --Joseph "Joey" C. Campana 07:37, 9 August 2006 (CDT)

The question is whether this article will be based on Dembski's latest paper or on his previous work. In the paper referred to by Arctura:

• Detachability is dispensed with, as Arctura noted.
• Conditional independence is subsumed by pattern simplicity.
• Specificity is a function of improbability as well as simplicity, so it doesn't make sense to present specificity and complexity as separate components. The only difference between specificity and specified complexity is a constant of 400 bits.

It should also be noted that Dembski has explicitly stated that SC is subjective, contrary to the first sentence in this article.

secondclass

We should base this article on his latest work. Secondclass, could you put some clean-up proposals on this talk page, and if those watching this page have no quams, post your proposals? -- JosephCCampana 08:28, 27 June 2006 (CDT)

Thanks for the invite, Joseph, but I'm probably not the right person. I consider specified complexity to be an ill-defined subset of algorithmic information theory with no practical utility. --Secondclass 15:28, 27 June 2006 (CDT)

Secondclass, thank you for your honesty. It may be too late for thinking it has no practical utility. -- JosephCCampana 15:45, 27 June 2006 (CDT)

Joseph, I'm familiar with Horst's papers. His metric is loosely based on Dembski's SC, but is his metric useful, or even useable?

I know of nobody, not even Dembski, who has ever calculated the specified complexity of anything according to Dembski's formula. Likewise, I'm not aware of anyone, including Horst, who has ever calculated the Native Intelligence Metric of any system. Note that Horst's NIM consists of two numbers, both of which he says are essential, but in the paper you referenced he completely skips the calculation of the first number. All he calculates is the probability of the system behaving correctly by random chance, rendering his example nothing more than a trivial probability analysis.

--Secondclass 17:29, 27 June 2006 (CDT)

I don't know if Dembski and Horst would agree, but you are entitled to your own analysis. Once we get around to making an article about Horst's NIM, I invite you to submit a criticism. Regards, JosephCCampana.

In Specification ... Dembski writes p. 33:

The underlying pattern here [the Champernowne sequence], in virtue of its descriptive simplicity, is therefore tractable with respect to information that is conditionally independent of any actual coin tossing event. In The Design Inference, I referred to this relation between tractability and conditional independence as detachability and used detachability to define specification. But given that descriptive simplicity instantly yields conditional independence, detachability itself becomes a dispensable concept once descriptive simplicity supplants tractability in the definition of specification.

Apparently the meaning is that descriptive simplicity replaces both tractability and detachability. As I have understood matters (and I might have misunderstood them!), tractability refers to the ability of an observer to generate a pattern at random. For instance, if the observer has a vocabulary of 100,000 words and has to generate a certain specification N words long, the computational complexity would be of order N^100,000; that is, exponential and therefore intractable. To generate the specification the observer would need to derive it from the event, and the specification is therefore not detachable (independent of the event).

IOW, Dembski has cleaned up the terminology, which is good (in particular for those of us that haven't read his earlier works :-)).

I would suggest that the article uses the current definition, but also gives a short definition of the older terminology, because these terms still float around on the Internet.

--FreezBee 10:58, 28 June 2006 (CDT)

Re. Definition

There is still some confusion over specified complexity, out on the Internet, so maybe a more detailed definition would be appropriate? Based on Dembski's Specification paper I have considered something along the lines of the following:

The definition of contextdependent specified complexity of a pattern T given a (chance) hypothesis H is given in section 7, "Specified Complexity", p. 21 as:

χ = –log₂[M·N·φ_S (T)·P(T| H)].

In contextindependent specified complexity, the product M·N is replaced by 10¹²⁰.

Let T be some observed event, such as the poker hand Ten, Jack, Queen, King, and Ace of the same suite, also known as a Royal Flush.

The hypothesis H here could be the assumption that the deck of cards was thoroughly shuffled, such that each particular position in the deck could be assigned a probability of 1/52 of holding any particular card, and that each partucular position in the deck with the first card removed could be assigned a probability 1/51 of holding any particular of the remaining 51 cards, and so on.

Subject to H, the probability of being dealt Ten, Jack, Queen, King, and Ace in that order of a specific suite is 1/52·1/51·1/50·/49·1/48, or around 1/3·10^-8. Since there are four suites, we multiply by four, and since the order of the cards makes no difference, we additionally multiply by 5! = 120 to get a probabilty of around 1.6·10^-6, somewhat higher than one in a million.

That is, in the case at hand, P(T| H) = 1.6·10^-6, or at least very close to that value.

If there are M = 20 groups of people playing poker, and each group has played N = 10 games, the probability of at least one Royal Flush having been dealt in the first round of a game is therefore M·N·P(T | H) = 3.2·10^-4. That is, M is the number of independent observers, and N is the numbers of times that each observer checks for an event.

Assume a hand with Deuce and Five of Hearts, Nine of Spades, King of Diamonds, and Six of Spades had been dealt. The probability of this is actually lower than the probability of a Royal Flush; but even if such a hand had been dealt, no-one would have noticed, since it's not really any remarable poker hand, although it has a lower probability. If any cheating is going on, we would not expect any increase in the occurence hands like that, but rather in the high value hands, such as Royal Flush and Four Aces.

This leads us to the term φ_S(T), the specificational resources associated by S with T. The subscript S denotes a semiotic agent, which is simply anyone/anything that can communicate using some symbolic language. An event such as our T must conform to some pattern P for S to be able to communicate its occurence, and such a pattern can be described using a string of symbols such as "Royal Flush", "Ten, Jack, Queen, King, and Ace of the same suite", or "Ten to Ace of the same suite". The descriptive complexity or semiotic cost φ'_S(P) of a pattern P is the number of symbols used in the shortest description of P available to S. Conceptually, we can think of it as that S has a dictionary of descriptions relevant to the subject area beginning with descriptions of length one, continuing with descriptions of length two, and so on, and S goes through this dictionary until a matching description of P is found. Assuming S has found a description for P, yet continues to go through the dictionary to the last entry of the same length, the number of descriptions checked is the number of all descriptions with a length shorter or equal to the length of the shortest description of P.

The formal definition of φ_S(T) can be found in section 6, "Specificity", p. 17:

φ_S(T) = the number of patterns for which S’s semiotic description of them is at least as simple as S’s semiotic description of T.

So, it's not actually the number of descriptions available, but the number of patterns, whose shortest description is shorter than or of the same length as the shortest description of T, or, put differently, whose descriptive complexity is at most the same as the descriptive complexity of T.

That is, the patterns Four Aces and Royal Flush have the same specificational resources, and the pattern Poker Hand has the same specificational resources; but these three patterns have different probabilities subject to the hypothesis H.

What is the point in the specificational resources? Dembski's claim is that a simple pattern, that is a pattern with a short description, is a stronger indicator for design than is a complex pattern. The 'complexity' in 'specified complexity' refers primarily to low probability of an event to occur by chance (what Dembski calls 'statistically complex'). A pattern such as Poker Hand is as simple as Royal Flush, but, of course, any poker hand is a Poker Hand, so simplicity of the pattern is not sufficient to say that we have a case of design. A pattern such as Deuce and Five of Hearts, Nine of Spades, King of Diamonds, and Six of Spades has a very low probability to occur; but it's nor really a pattern we are concerned about, if by 'design' we mean 'cheating', although someone might claim that it's not every day you see exactly this poker hand. It's the combination of a simple pattern and a low probability that should arise our suspecion, according to Dembski.</p>

Why the subscript S? Because dufferent observers may not have the same descriptions at disposition; for instance, a person unfamiliar with poker might not know, what a "Royal Flush" is, and not know that it has special significance within the game. Therefore, specified complexity is a subjective measure.

If we look at the product φ_S(T)·P(T | H), then it is an upper bound on the probability of S to observe an event that is at most as descriptive complex as T and has at most the same probability (cf. p. 18).

In short, the whole product M·N·φ_S(T)·P(T | H) is an upper bound to the probability subject to H that at least one of M independent observers during one of N observations will report to the semiotic agent S at least one event that is at most as descriptive complex as T and has at most the same probability.

Converting to binary logarithm reverses the scale and turns the product into a number of bits. If M·N·φ_S(T)·P(T | H) < 1/2, then χ > 1. That is, if χ > 1, it can be considered more reasonable to conclude design than to conclude chance.

This text is copied from my blog and it will need some sortening, some Wikifying and some reformulations to fit in here, and it's only a suggestion.

--FreezBee 07:38, 10 December 2006 (CST)

Recommend posting this level of technical detail as ISCID.org Brainstorms. DLH 12:39, 11 December 2006 (CST)

Thank you FreezBee for contributing this content. I think DLH has a good idea, although first I will post this to a sub-page. This is information we would want stored natively as well. Based on the suggestions at Brainstorms we could modify our native page: Defining Specified Complexity. --Joseph "Joey" C. Campana 13:47, 11 December 2006 (CST)