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Universal probability bound on Sun Aug 09, 2009 11:20 pm
http://en.wikipedia.org/wiki/Universal_probability_bound
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.
The idea that events with fantastically small, but positive probabilities, are effectively negligible[2] was discussed by the French mathematician Émile Borel primarily in the context of cosmology and statistical mechanics.[3] 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.[4][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]
Another objecton to Dembski's use of the universe probability is based on the existence of observed specific outcomes of an experiment with arbitrary potential outcomes. For example, if a coin is tossed randomly 1000 times, the probability of any particular outcome is roughly one in 10300. For any particular specific outcome of the coin-tossing process, the a priori probability that this pattern occurred is thus one in 10300, which is astronomically smaller than Dembski's universal probability bound of one in 10150. Yet the post hoc probability of its happening is exactly one, since we observed it happening.
[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:[8]
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:[9]
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[10][11]
The (variable) rank complexity of the event under consideration.[12]
If the latter quantity equals 10150, then the overall universal probability bound corresponds to the original value.
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.
The idea that events with fantastically small, but positive probabilities, are effectively negligible[2] was discussed by the French mathematician Émile Borel primarily in the context of cosmology and statistical mechanics.[3] 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.[4][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]
Another objecton to Dembski's use of the universe probability is based on the existence of observed specific outcomes of an experiment with arbitrary potential outcomes. For example, if a coin is tossed randomly 1000 times, the probability of any particular outcome is roughly one in 10300. For any particular specific outcome of the coin-tossing process, the a priori probability that this pattern occurred is thus one in 10300, which is astronomically smaller than Dembski's universal probability bound of one in 10150. Yet the post hoc probability of its happening is exactly one, since we observed it happening.
[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:[8]
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:[9]
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[10][11]
The (variable) rank complexity of the event under consideration.[12]
If the latter quantity equals 10150, then the overall universal probability bound corresponds to the original value.
