accuracy

On the one hand, the word exactness (from Latin: exactus "exactly") is seen as a synonym for many terms such as accuracy , meticulousness , precision . These stand for a (mostly desired) completeness and freedom from errors. But they allow a certain amount of blurring. For example, a result “with high accuracy” or “sufficiently accurate” can be indicated. These formulations contain a characteristic that cannot be achieved or in individual cases not achieved. - On the other hand, especially in the mathematical and scientific context , exactness is strictly understood in the sense of uniqueness - without any deviation. With this understanding, accuracy is based on definitions , modeling and theoretical calculations; See also measurement uncertainty # Exact values .

There are two systematically differentiated concepts of exactness. Some sciences can be exact in the sense of a total agreement, because they work with abstract things that remain completely identical (ideal exactness). In sciences without idealization, exactness can be meant in a completely different sense (real-based exactness). Strictly speaking, in this respect one cannot speak of exactness at all, but only of greater or lesser exactness.

Existing theoretical descriptions are differentiated, for example, into “exact”, “approximate” and “empirical”. "Exactly" is explained as follows: "There is a theory for the structure and properties of the system with solutions that describe the interaction of the elements analytically and quantitatively with known functions of mathematics."

Furthermore, a distinction is made between exact laws and inexact modeling and inexact metrological verification: In contrast to mathematically formulated natural laws that represent exact relationships between different physical quantities, all measured values ​​are subject to a measurement uncertainty . ... Repeated measurements never give exactly the same results in a mathematical sense. ... Theories of physics always describe an idealization of natural occurrences.

EXAMPLE 1 With the circle ratio , the relationship between circumference and diameter of a circle given exactly . The best possible approximation to having a five-digit decimal is 3.1416. It delivers a statement with inadequate or appropriate or excessive accuracy for the respective application; but it does not provide any mathematical precision. ${\displaystyle \pi }$ ${\displaystyle U}$ ${\displaystyle d}$ ${\displaystyle U=\pi \;d}$ ${\displaystyle \pi }$

Example 2: The statement is exact; it is not based on calculation and rounding ; it cannot be checked by measurement. ${\displaystyle \mathrm {0\;^{\circ }C=273{,}15\;K} }$

Example 3: For a countable size , the number of elements to indicate precisely when the number of elements is small and constant over time.

Example 4: The number read on a digital multimeter is exact without any estimation uncertainty ; However, the measured value obtained from this is subject to an uncertainty within the limit deviations of the measuring device and the quantization deviation .

One facet of the meaning of the term exactness can also be found in the way in which exact science is explained: “The knowledge of exact science does not have to consist merely of numbers, but it has to be freed from the“ inexactness ”of natural language to such an extent that they can be formulated with a standardized vocabulary. "

Web links

Wiktionary: Exactness  - explanations of meanings, word origins, synonyms, translations

Individual evidence

1. ^ Uni Leipzig: Wortschatz-Portal [1] , accessed on Jan 13, 2020.
2. ^ Digital dictionary of the German language [2] , accessed on Jan. 13, 2020.
3. ↑ Udo Scherz Quantum Mechanics: An introduction with applications to atoms, molecules and solids. Verlag Teubner, 1999, p. 190
4. ↑ Jürgen Tiemeyer: On the question of method of legal sociology: About the theoretical theoretical possibility to operate the legal sociology like a natural science. Duncker & Humblot Verlag, 1969, p. 74
5. ↑ Günter Dedie: The power of natural laws: Emergence and collective skills from elementary particles to human society. Verlag tredition, 2014, chapter 1
6. ^ Klaus Lüders, Gebhard von Oppen: Classical Physics - Mechanics and Heat. Verlag de Gruyter, 2012, p. 2
7. ^ Paul Lorenzen: The emergence of the exact sciences , Springer-Verlag, 1960, p. 10