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Finite Improbability Calculator
Submitted by Wesley R. Elsberry on Mon, 20061016 03:54.
Specified Complexity  Dembski, William A.
The Finite Improbability Calculator is a collection of routines to permit exploration of very small probabilities. Many antievolutionary arguments are based upon an argument from improbability: some phenomenon is so improbable that it must be due to an intelligent agent. Usage:
Operations
Change of baseFactorialPermutation and CombinationSpecified AntiInformationDembski's p_origin and M/N ratioPage numbers refer to "No Free Lunch". Dembski's p_localPage numbers refer to "No Free Lunch". Dembski's p_perturbPage numbers refer to "No Free Lunch". Error in dembskisHazen Functional ComplexityNotes on calculationsFactorial: The point here is to permit calculation of factorial(n) where n can be a large number, say the number of proteins which an organism codes for. However, even a "double" floatingpoint number overflows at 1.7e308. So factorials are calculated here using a logarithmic representation. The Stirling approximation is used for very large n, and a logarithmic version of the classical iterative method is used for smaller n. Stirling's approximation is taken as n! ~ n^n e^(n) sqrt(2 * pi * n) (1 + 1/(12n)) Change of base: Calculated as new exponent = (old_exponent * ln(oldbase)) / ln(newbase) Permutation and combination: Uses the factorial function discussed above. permutations = n! / (n  k)! combinations = n! / k!(n  k)! Specified AntiInformation Specified AntiInformation is an application of the "universal distribution" of Kirchherr et alia 1997, expounded in Elsberry and Shallit 2003. SAI is a framework intended as an alternative to Dembski's "design inference". The SAI of a bit string is defined as SAI = max(0,y  C(y)) where y is the length of the bit string of interest and C(y) is the Kolmogorov complexity of y. Since C(y) is uncomputable, mostly we should speak of Known Specified AntiInformation, which is just the maximum SAI that can be established by application of known compression techniques. SAI is defined for bit strings, but often we deal with strings based on a symbol set with cardinality > 2. It is straightforward to determine the length of a bit string needed to represent such a string, though, using the "change of base" function presented earlier. The second part of the SAI section permits SAI to be calculated for such strings. Something to note here is the apparent difference in ease of application of SAI with the various measures introduced by Dembski. p_{orig} approximation (as per NFL p.301): p_{orig} ~ symbols^(length (perturbation_tolerance  perturbation_identity))
p_{local} calculation (as per NFL p.293): p_{local }= (units in system * substitutions / total different units) ^{(units in system * copies)} M/N ratio approximation (as per NFL p.297): M/N ratio ~ ((combinations(length, tolerance * length) * (symbols1)^{(tolerance * length)}) / (combinations(length, identity * length) * (symbols1)^{(identity * length)}))
DCO p_{perturb} approximations (as per NFL pp.299 and 300): p_{perturb} (p.299) ~ ((combinations(length, tolerance * length) / (combinations(length, identity * length)) * (symbols1)^{(length * (tolerance  identity))} p_{perturb} (p.300) ~ (symbols)^{(length * (tolerance  identity))} Error in dembskis That error might be measured in a unit called "dembskis" that scaled things in terms of orders of magnitude came up in discussion of errors in an essay by Marks and Dembski. The reference unit of error for the measure is taken from the case mentioned above in the M/N ratio calculation note, where Dembski had an error of about 65 orders of magnitude. "Dave W." formalized the notion with an equation, and W. Kevin Vicklund suggested using a roundedoff value of 150 as the constant in the denominator, based upon Dembski's figure of 10^150 as a universal small probability. Thus, the final form of quantifying error in dembskis (Reed Cartwright proposed the symbol Δ) is Δ =  ln(erroneous measure)  ln(correct measure)  / 150 There is not yet a consensus on what to term the unit, but two proposals being considered are "Dmb" and "duns". Hazen Functional Complexity The calculation is made per the 2007 PNAS paper by Hazen et al.. Given a number of possible configurations, N, and a (smaller) number of functionally equivalent configurations, M(E_{x}), one obtains the functional complexity metric, I(E_{x}) as: I(E_{x}) =  log_{2}(M(E_{x}) / N) ReferencesDembski, William A. 2002. No Free Lunch. Rowman & Littlefield Publishers. Elsberry, Wesley R. and Jeffrey Shallit. 2003. Information Theory, Evolutionary Computation, and Dembski's "Complex Specified Information". http://www.antievolution.org/people/wre/papers/eandsdembski.pdf. Hazen RM, Griffin PL, Carothers JM, Szostak JW (2007) Functional information and the emergence of biocomplexity. Proc Natl Acad Sci U S A 104 Suppl 1:857481. Kirchherr, W., M. Li, and P. Vitanyi. The miraculous universal distribution. Math. Intelligencer 19(4) (1997), 715. http://www.cwi.nl/~paulv/papers/mathint97.ps The Finite Improbability Calculator was first coded in spring of 2002, following publication of William Dembski's book, "No Free Lunch". The original utilized a Perl CGI script. The FIC was ported to a PHP instantiation in January, 2004, with routines added for calculating Specified AntiInformation. The FIC then was altered to work within a Drupal page using the "PHP code" option. The name of this page was inspired by "The Hitchhiker's Guide to the Galaxy" by the late great Douglas Adams.
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RSS SyndicationAntievolutionists Say the Darndest ThingsAntievolutionists often express outrage over alleged incivility from those who oppose their efforts to evade the establishment clause of the First Amendment. But they have no difficulty in dishing out the abuse themselves. Here is a sample from the Invidious Comparisons thread that documents egregious behavior on the part of the religious antievolution advocates. Dembski, as the director of the center, also commented on the report in a oneparagraph email message following its release. "The report marks the triumph of intelligent design as a legitimate form of academic inquiry. This is a great day for academic freedom," Dembski began. He concluded by observing that "Dogmatic opponents of design who demanded the Center be shut down have met their Waterloo. Baylor University is to be commended for remaining strong in the face of intolerant assaults on freedom of thought and expression." ProScience Sites
