Universal probability limit

A universal probability limit is an assumed value below which the probability of a random event is so low that it can be classified as practically impossible. It is not used in science and is therefore classified as pseudoscience .

Definition and derivation

Émile Borel formulated the idea in the context of considerations on statistical mechanics as follows: Phenomena of very low probability do not occur. (Borel 1943). Borel gave the concrete numerical value . His reasoning is based on considerations about the number of stars in the known universe and the number of observations that can ever be made by terrestrial observers. An event with the probability of , according to Borel, "will therefore never occur, or at least never be observed." ${\ displaystyle 10 ^ {- 50}}$ ${\ displaystyle 10 ^ {- 50}}$

The controversial theologian William A. Dembski uses the concept in his reflections on the creation of specified complexity through undirected natural processes. He criticizes (Dembski 1998) Borel's definition. As a numerical value, it indicates a limit below which specified complex events are so improbable that they can only occur through the cooperation of intelligence . Dembski's value is the estimate of an upper bound for the number of physical events that can have taken place since the Big Bang and is calculated as follows:, the number of elementary particles in the observable universe , the maximum number of physical state transitions per second (i.e. that Inverse of the Planck time ) , the typical estimated age of the universe in seconds, stretched by a safety factor of a billion. . ${\ displaystyle 10 ^ {- 150}}$
${\ displaystyle 10 ^ {80}}$
${\ displaystyle 10 ^ {45}}$
${\ displaystyle 10 ^ {25}}$
${\ displaystyle 10 ^ {80} \ cdot 10 ^ {45} \ cdot 10 ^ {25} = 10 ^ {150}}$

Dembski revised his definition in 2005 on the basis of quantum cosmological work by the physicist Seth Lloyd as follows:

An upper bound on the information processing capacity of the universe: logical operations on a register of bits. ${\ displaystyle 10 ^ {120}}$ ${\ displaystyle 10 ^ {90}}$
The (changeable) descriptive complexity of the observed event.

If one substitutes for the latter quantity , the universal probability limit corresponds to the originally assumed value of . ${\ displaystyle 10 ^ {30}}$ ${\ displaystyle 10 ^ {150}}$

criticism

The supposedly mathematical term of the universal probability limit is actually only used by representatives of the intelligent design movement. The aim of the argument is to “prove” the impossibility of natural evolution . The proponents of the universal probability limit start from the assumption that evolution consists only of chance (which no evolutionary biologist claims) and "calculate" the (in fact astronomically low) improbability of the accidental emergence of species diversity from nothing.

Apart from this premise, however, even the assertion that what is sufficiently improbable is impossible can easily be refuted by a simple reductio ad absurdum :

The probability of a six in the lottery is about 1 in 13,000,000, super numbers and other extras ignored. To make the calculation easier, we assume 10 ⁻⁶ .

The lottery numbers are drawn (at least) 52 times a year, so the result is a sequence of 312 individual numbers, an annual lottery number, so to speak.

The probability that a certain “annual ^{lottery number} ” occurs is 10 ^{−6 · 52} = 10 ⁻³¹² . Based on the considerations outlined above, this event is so unlikely that it is impossible.

If we now take a look at the “annual lottery number” for any given year, it is undeniable that ex ante it was very unlikely that this specific sequence of numbers would occur. Still, this is exactly what happened. It is of course very unlikely that this exact sequence of numbers will occur, but it is not impossible.

Ironically, the conceptual approach of the Universal Probability Bound only works if one assumes that someone or something tries out all possible permutations. With this construct one can at best make credible that there is no such thing as an “unintelligent designer”, because he would probably not have been able to produce this universe in the time that has passed by just trying it out.

literature

Émile Borel: Les probabilités et la vie. Presses Universitaire de France, Paris 1943.
Émile Borel: Probabilité et Certitude. Presses Universitaire de France, Paris 1950.
William A. Dembski: The Design Inference: Eliminating Chance through Small Probabilities. Cambridge University Press, Cambridge 1998, ISBN 0521623871 .
William A. Dembski: No Free Lunch: Why Specified Complexity Cannot Be Purchased without Intelligence. Rowman & Littlefield, Lanham, Md. 2002, ISBN 0742512975 .
William A. Dembski: Specification: The Pattern That Signifies Intelligence. 2005. ( online , PDF file; 382 kB)
Bernd-Olaf Küppers: The origin of biological information. 2nd Edition. Piper, Munich 1990.
Seth Lloyd: Computational Capacity of the Universe. In: Physical Review Letters. June 2002.

Web links

Seth Lloyd: The Computational Universe. 2002