Hold it right there! Hazen is talking about “Functional Information”. You have added a “specified” in there. What is your objective definition of a “specification”. How can we objectively tell a valid specification from an invalid specification?
I added the word “specified” because it’s essential in the proposed defintion. Function itself is a specification – that’s what separates Functional information from Shannon Information.
The information that has to encode a function is specified. It has to communicate certain instructions and not others. That’s what origin of life researchers are testing.
Szostak & Hazen explain …
Functional information, which we illustrate with letter sequences, artificial life, and biopolymers, thus represents the probability that an arbitrary configuration of a system will achieve a specific function to a specified degree.
Notice that they talk about “letter sequences”. So, this is not just a raw quantity of information, but rather “sequences” – and those are specified enough to produce a function.
This is not really the same as what Dembski was proposing – and Dembski’s research is proving to be very much more innovative and correct than his critics gave him credit for.
What Szostak and Hazen have changed is that the specificity of the information is related to the function it has to perform. The problem remains – how can natural processes create functional information? It is possible?
Here’s more from the paper (with my emphasis added):
The Functional Information of Letter Sequences.
Systems of many interacting components can occur in a combinatorially large number of different configurations.
Functional information depends on the fraction of all possible configurations that achieve at least a specified degree of function. Sequences of letters provide a conceptually familiar example.
Consider various **sequences of n letters that convey the message: “A fire has just started in a house at the corner of Main Street and Maple Street.” **Many different sequences of letters are capable of conveying that information. To determine the functional information of any particular sequence we must specify three parameters:
n, the number of letters in the sequence.
Ex , the degree of function x of that sequence. In the case of the fire example cited above, Ex might represent the probability that a local fire department will understand and respond to the message (a value that might, in principle, be measured through statistical studies of the responses of many fire departments). Therefore, Ex is a measure (in this case from 0 to 1) of the effectiveness of the message in invoking a response.
M(Ex ), the total number of different letter sequences that will achieve the desired function, in this case, the threshold degree of response, ≥Ex .
The functional information, I(Ex ), for a system that achieves a degree of function, ≥Ex , for sequences of exactly n letters is therefore
Note that 26 n is the total number of possible arrangements of 26 letters in a sequence of n letters, and in this treatment we assign equal probability to all possible sequences. The important more general case of configurations of unequal probabilities is a straightforward extension of the treatment of Shannon (38, 39), as discussed by Carothers et al. (34). Greater clarity of expression can be added through additional characters such as “space,” “capital,” and “period”; however, in this example we use only 26 letters.
As in all combinatorially large emergent systems, most sequences convey no information (i.e., have no discernable function). Functional information is determined by identifying the fraction of all sequences that achieve a specified outcome.
Notice the specified informaton here:
Consider, for example, sequences of 10 letters that have a high probability (Ex ≅ 1) of evoking a positive response from the fire department. Such sequences might include “FIREONMAIN,” “MAINSTFIRE,” or “MAPLENMAIN.” Additionally, some messages containing phonetic misspellings (FYRE or MANE), mistakes in grammar or usage (FIREOFMAIN), or typing errors (MAZLE or NAPLE) may also yield a significant but lower probability of response (0 ≪ Ex < 1). Given these variants, on the order of 1,000 combinations of 10 letters might initiate a rapid response to the approximate location of the fire.
Only specific combinations of letters will work.