Universal probability bound

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A universal probability bound is a probabilistic threshold whose existence is asserted by William A. Dembski and is used by him in his works promoting intelligent design. It is defined as "A degree of improbability below which a specified event of that probability cannot reasonably be attributed to chance regardless of whatever probabilitistic resources from the known universe are factored in."[1]

Dembski asserts that one can effectively estimate a positive value which is a universal probability bound. The existence of such a bound would imply that the occurrence of certain kinds of events whose probability lies below this value can be rejected, given the resources available in the entire history of the universe. Contrapositively, Dembski uses the threshold to argue that the occurrence of certain events cannot be attributed to chance alone. However, this argument is not new in the creationist literature and has been called the basic argument from improbability.[2]

The idea that events with fantastically small, but positive probabilities, are effectively negligible[3]was discussed by the French mathematician Émile Borel primarily in the context of cosmology and statistical mechanics.[4] However, there is no widely accepted scientific basis for claiming that certain positive values are universal cutoff points for effective negligibility of events. Borel, in particular, was careful to point out that negligibility was relative to a model of probability for a specific physical system.[5]

Dembski appeals to cryptographic practice in support of the concept of the universal probability bound, noting that cryptographers have sometimes compared the security of encryption algorithms against brute force attacks by the likelihood of success of an adversary utilizing computational resources bounded by very large physical constraints. An example of such a constraint might be obtained for example, by assuming that every atom in the known universe is a computer of a certain type and these computers are running through and testing every possible key. However, universal measures of security are used much less frequently than asymptotic ones.[6] The fact that a keyspace is very large is useless if the cryptographic algorithm used has vulnerabilities which make it susceptible to other kinds of attacks.[7]

The concept of intelligent design, and by extension the arguments used to further it such as the universal probability bound, are rejected by the scientific community[8] as pseudoscience[9] or junk science.[10] Mathematician Jeffrey Shallit has analyzed Dembski's ideas and declared that Dembski's "approach to complexity through probability is very seriously flawed." According to Shallit, Dembski's ideas are so flawed as to be irreparable. [11]

[edit] Dembski's estimate

Dembski's original value for the universal probability bound is 1 in 10150, derived as the inverse of the product of the following approximate quantities:[12]

  • 1080, the number of elementary particles in the observable universe.
  • 1045, the maximum rate per second at which transitions in physical states can occur (i.e., the inverse of the Planck time).
  • 1025, a billion times longer than the typical estimated age of the universe in seconds.

Thus, 10150 = 1080 × 1045 × 1025. Hence, this value corresponds to an upper limit on the number of physical events that could possibly have occurred since the big bang.

Dembski has recently (as of 2005) refined his definition to be the inverse of the product of two different quantities:[13]

  • An upper bound on the computational resources of the universe in its entire history. This is estimated by Seth Lloyd as 10120 elementary logic operations on a register of 1090 bits[14][15]
  • The (variable) rank complexity of the event under consideration.[16]

If the latter quantity equals 10150, then the overall universal probability bound corresponds to the original value.

[edit] References

  1. ^ ISCID Encyclopedia of Science and Philosophy
  2. ^ Jason Rosenhouse, (2001). How Anti-Evolutionists Abuse Mathematics The Mathematical Intelligencer, Vol. 23, No. 4, Fall 2001, pp. 3-8.
  3. ^ Negligible means having probability zero. Effectively negligible means, roughly, that in some operational sense or in some computational sense, the event is indistinguishable from a negligible one.
  4. ^ Émile Borel, Elements of the Theory of Probability (translated by John Freund), Prentice Hall, 1965, Chapter6. See also Citations from Borel's articles.
  5. ^ Though Dembski credits Borel for the idea, there is clear evidence that Borel, following accepted scientific practice in the foundations of statistics, was not referring to a universal bound, independent of the statistical model used.
  6. ^ For a precise definition of effective negligibility in cryptography, see Michael Luby, Pseudorandomness and Cryptographic Applications, Princeton Computer Science Series, 1996.
  7. ^ Though Dembski repeatedly appeals to cryptography in support of the concept of the universal probability bound, in practice cryptographers hardly use measures which are in any way related to it. A more useful concept is that of work factor. See p. 44, A. J. Menezes, P. C. van Oorschot, S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
  8. ^ See: 1) List of scientific societies rejecting intelligent design 2) Kitzmiller v. Dover page 83. The Discovery Institute's Dissent From Darwin Petition has been signed by about 500 scientists. The AAAS, the largest association of scientists in the U.S., has 120,000 members, and firmly rejects ID. More than 70,000 Australian scientists and educators condemn teaching of intelligent design in school science classes. List of statements from scientific professional organizations on the status intelligent design and other forms of creationism.National Academy of Sciences, 1999 Science and Creationism: A View from the National Academy of Sciences, Second Edition
  9. ^ National Science Teachers Association, a professional association of 55,000 science teachers and administrators in a 2005 press release: "We stand with the nation's leading scientific organizations and scientists, including Dr. John Marburger, the president's top science advisor, in stating that intelligent design is not science
  10. ^ H. Allen Orr. Annals of Science. New Yorker May 2005.Devolution—Why intelligent design isn't., Robert T. Pennock Tower of Babel: The Evidence Against the New Creationism.
  11. ^ Shallit
  12. ^ William A. Dembski (2004). The Design Revolution: Answering the Toughest Questions About Intelligent Design
  13. ^ William A. Dembski (2005). ""Specification: The Pattern That Signifies Intelligence (382k PDF)".
  14. ^ Seth Lloyd, Computational Capacity of the Universe, arXiv:quant-ph/0110141 v1
  15. ^ The number 1090 seems to play no role in Dembski's analysis, On page 23 of Specification: The Pattern That Signifies Intelligence, Dembski says
    "Lloyd has shown that 10120constitutes the maximal number of bit operations that the known, observable universe could have performed throughout its entire multi-billion year history."
  16. ^ The rank complexity is Dembski's φ function which ranks patterns in order of their descriptive complexity. See specified complexity.

[edit] See also

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