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Author
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Topic: The Microscopic Implications of "Specification."
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William Brookfield
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Member # 565
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posted 23. September 2008 13:55
In order to resolve the Poincare Recurrence problem in thermodynamics, the Second law can be posited, not as a law of thermodynamics but as a law of order (or information) decaying over time to randomness (zero information/order). This allows the finite-system constraint (order) and indeed mathematics itself (an orderly system of non-decaying platonic symbols) to be re-entered as a residual order-adulterating influence upon systems (or system tracking) -- that produces the Poincare recurrence artifact. In a new recurrence-free formulation, "entropy" is indeed synonymous to "randomness" and "low entropy" is indeed synonymous to "order."
The result of this however is that Shannon's "Information entropy" becomes a nonsense phrase. "In-form-ation" is a form of order (of “form”) and "entropy" refers to "randomness" -- the absence of order/form.
It seems to me that Shannon's equation (equation #1.) does not quantify randomness/entropy but instead quantifies independent correlational events of "information" while the Gibbs equation (#2.) quantifies independent fortuitous (random) events. What these two "entropy's" have in common is the notion of "independence" not "randomness/entropy." In Algorithmic Information Theory this "independence," leads to the Kolmogorov complexity of both informational ({i}K-complexity) and random events ({m}K-complexity) -- I.E., algorithmic incompressibility follows logically from "independence."
While the orthodox Second law initially arose from observations of physical systems, the Second Law of Black Hole dynamics arose, not from observations, but as a consequence/prediction of Einstein's theory. "Luckily" Einstein’s theory included an element of continuously variable cosmic decay (curvature) not present in finite* Statistical Mechanics. Both Second Laws can be seen as laws of order/information loss in their respective domains. In order to understand and unify these laws within a “info-dynamic” framework, a solid understanding of “information” is required and the lacuna in Shannon’s information theory needs to be filled.
I see William Dembski’s “specified complexity” as an important step towards the filling of the Shannon-ian lacuna. Dembski’s “specification” however, seems to address only the macroscopic properties of specificity while ignoring the microscopic implications. Thermodynamics originally addressed only the macroscopic properties of “temperature” “pressure” and “volume” until a microscopic formulation (statistical mechanics) was developed. I am suggesting brainstorming the microscopic implication of “specifications” and I am here proposing my notion of “correlational improbability” as the microscopic quantifier of informational “specificity.”
Another way of looking at it is that equations 1 & 2 both quantify “uncertainty” but in the case of the specified “information” (I {A}) all events as “information” are bound to be A>B correlated/ordered due to information’s specified nature. Thus, the pertinent phase space must be doubled to accommodate these orderly correlations. The result of this is that the improbability must be squared for any given informational event (I {A}). The (Event probability) times the (Correlational Probability) provides a new combined Information Event Probability (IEP). (EP)(CP) = P^2
An Example
(1a)rmkjcieroalsjhlj (random letters {naked K-complexity})
(A)rmkjcieroalsjhlj>
(B)rmkjcieroalsjhlj (Compressed “information” is K-complex but is none-the-less A>B correlated {ordered}) = p^2
“Information” (A>) is always “information about something” (B). It is therefore always in a correlated relationship with at least one (B). Random gibberish (1a) is un-correlated.
Random letters or numbers (1a) can indeed be turned into information by choosing to use them in a correlated manner. For example, an initially random number (1a) could be used as an access code to identify a single user within a large system, but once it is thus chosen (specified) correlations are now established and its function is no longer random. Its pattern of use/re-use corresponds to A>B (information) and not randomness (1a).
*By making the phase space infinite, continuous variability can be achieved for Stat.Mech.
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Melvin H. Fox
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Member # 1684
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posted 28. September 2008 08:33
William,
Are the correlations necessarily intelligent or could they be purely mechanical? I ask this because Dembski’s work here was done to devise a filter by which design could be detected. If the correlations can be a product of “just so” mechanical properties, then their presence is neutral with respect to intelligent design. True?
-Mel
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William Brookfield
Member
Member # 565
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posted 29. September 2008 12:25
Hi Mel,
Thanks for dropping back in!
The evidence for ID, as I see it, arises from the observation of certain patterns/structures in nature that have no legitimate causal antecedent in the material (non-telic) world. I am proposing that the "specified correlation" is the smallest logical sub-unit of these larger "patterns."
I am also thinking that both Shannon Information and Kolmogorov Information, are assuming (without explicity stating) the specificity and subsequently correlated (orderly) nature of "information." Digital information is not just "bits" but is instead "specified correlated bits." As I see it, "bits" can be random, meaningless and deviod of information -- or they can be "information" carriers.
quote:
Are the correlations necessarily intelligent or could they be purely mechanical?
In terms of information theory the correlations are necessarily telic. "Randomness/chance" is devoid of correlations. Random events are independent,uncoordinated and uncorrelated events, by definition. "Information" is calibrated in terms of a background uniform probability distribution (randomness).
An inference to intelligent design however requires a statistical argument based upon numerous correlations that together form a complex independent "pattern."
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