Quantification of randomness

Randomness is an extremely ambiguous word not only in everyday language but also or even especially in science. Almost each branch of science has its own interpretation and hence own ways of handling the characteristic randomness. This confused situation is typical whenever there is no generally acknowledged unit defined for a characteristic.

The fact that there is no standard unit for randomness has strange consequences. For example, the probability that an interaction of a given kind will take place between a nucleus and an incident neutron is called cross-section or "effective cross-sectional area" and the unit for the probability is given as square centimeter.[1]

Quantification

Any characteristic in the physical world can adopt one out of a set of values. Quantification of a characteristic may have several meanings; however, according to the Free Dictionary it is used for "the act or process of assigning numbers to phenomena according to a rule".[2] Accordingly, quantification of a characteristic means that the set of values of the characteristic is mapped on a suitable set of numbers. In other words, a characteristic is represented by a variable. The rules take care that all the relations like order, distance or a natural zero among the values of the characteristic are preserved within the obtained set of real numbers. An appropriate quantification necessitates therefore that the relations and hence the nature of the characteristic are sufficiently well understood. In physics metric characteristics[3] are of interest and quantification of a metric characteristic is obtained by selecting, for example, the values which are mapped on the real numbers 0 and 1, where the letter is called unit with a particular name like meter, mass or second.

An appropriate quantification of a characteristic is a difficult task as illustrated by the development of the International System of Units (SI). For example, the evolution of quantification of the characteristic "length" started in 1872 with deciding to produce a prototype of the metre. In 1892−93 the Michelson interferometer was used to determine the length of the metre in terms of the wavelength of the red line of cadmium. In 1960 the CGPM adopted a definition of the metre in terms of the wavelength in vacuum of the radiation corresponding to a transition between specified energy levels of the krypton 86 atom and finally in 1997 the CIPM modified the 1992 instructions for the practical realization of the definition by further reducing the uncertainties and increasing the number of recommended radiations from eight to twelve. However, work continues at the BIPM and elsewhere to identify those factors that at present limit the reproducibility of lasers as wavelength and frequency standards.[4]

The characteristic "randomness"

Randomness is a characteristic property of future events and makes them either occur or not occur. This can be seen when a process is repeated several times. The results are different events which occur with different frequencies. Randomness as a property of a future event describes therefore its propensity to occur. The value of randomness depends on the actual initial conditions analogously to any other physical characteristic.

More than 300 years ago, the Swiss theologian and mathematician Jacob Bernoulli succeeded in quantifying randomness of a future event. He selected the two extreme values of propensity, namely impossibility of occurrence and certainty of occurrence, as 0 and 1 for the characteristic "randomness" of a future event, and named this measure by the Latin word "probabilitas" with the English translation "probability". Accordingly, he defined probability as the degree of certainty that the event will occur.[5]

The probability of a future event thus quantifies its propensity to occur. It may adopt a value between 0 and 1, which are the two extreme values. Similarly, as the mass of an object consisting of two parts is the sum of the masses of the two parts, the probability (= propensity) of the union of two disjoint events equals the sum of the probabilities of the two events.

See also

References

  1. ↑ In nuclear physics often the non-SI unit barn is used where 1 barn = 10−24.
  2. ↑ Free Dictionary .
  3. ↑ A characteristic is called "metric", if there is a notion of distance (called a metric) defined among the elements of its set of values.
  4. ↑ The BIPM and the evolution of the definition of the metre, "Archived copy". Archived from the original on June 7, 2011. Retrieved August 15, 2010..
  5. ↑ "Probability, indeed, is degree of certainty, and differs from the latter as a part differs from the whole." in: Jacob Bernoulli, The Art of Conjecturing, translated by Edith Dudley Sykka, 2006, Johns Hopkins University Press, Baltimore, p. 315.

External links

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