Universal probability bound
Encyclopedia
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."
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 random 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. Universal probability bound is then used to argue against random evolution
. However evolution is not based on random events only (genetic drift
), but also on natural selection
.
The idea that events with fantastically small, but positive probabilities, are effectively negligible was discussed by the French
mathematician
Émile Borel
primarily in the context of cosmology
and statistical mechanics
. 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.
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 attack
s 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. 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.
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:
If the latter quantity equals 10150, then the overall universal probability bound corresponds to the original value.
William A. Dembski
William Albert "Bill" Dembski is an American proponent of intelligent design, well known for promoting the concept of specified complexity...
and is used by him in his works promoting intelligent design
Intelligent design
Intelligent design is the proposition that "certain features of the universe and of living things are best explained by an intelligent cause, not an undirected process such as natural selection." It is a form of creationism and a contemporary adaptation of the traditional teleological argument for...
. 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."
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 random 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. Universal probability bound is then used to argue against random evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
. However evolution is not based on random events only (genetic drift
Genetic drift
Genetic drift or allelic drift is the change in the frequency of a gene variant in a population due to random sampling.The alleles in the offspring are a sample of those in the parents, and chance has a role in determining whether a given individual survives and reproduces...
), but also on natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....
.
The idea that events with fantastically small, but positive probabilities, are effectively negligible was discussed by the French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Émile Borel
Émile Borel
Félix Édouard Justin Émile Borel was a French mathematician and politician.Borel was born in Saint-Affrique, Aveyron. Along with René-Louis Baire and Henri Lebesgue, he was among the pioneers of measure theory and its application to probability theory. The concept of a Borel set is named in his...
primarily in the context of cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
and statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
. 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.
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 attack
Brute force attack
In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data. Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system that would make the task easier...
s 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. 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.
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:- 1080, the number of elementary particles in the observable universeObservable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...
. - 1045, the maximum rate per second at which transitions in physical states can occur (i.e., the inverse of the Planck timePlanck timeIn physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
). - 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
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
.
Dembski has recently (as of 2005) refined his definition to be the inverse of the product of two different quantities:
- An upper bound on the computational resources of the universe in its entire history. This is estimated by Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
as 10120 elementary logic operations on a register of 1090 bits - The (variable) rank complexity of the event under consideration.
If the latter quantity equals 10150, then the overall universal probability bound corresponds to the original value.