|Theories: theories are statement systems for the explanation of observations, e.g. of behavior or physical, chemical or biological processes. When setting up theories, a subject domain, a vocabulary of the terms to be used and admissible methods of observation are defined. In addition to explanations, the goal of the theory formation is the predictability and comparability of observations. See also systems, models, experiments, observation, observation language, theoretical terms, theoretical entities, predictions, analogies, comparisons, evidence, verification, reduction, definitions, definability._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
Theory/Success/Genz: measures whether the amount of data it is supposed to analyze is compressed by the theory.
GenzVs: however, this only applies at a very high level of abstraction. Everything would be ruined by the slightest development.
Solution/Genz: the requirement is a necessary but not sufficient condition.
Random/Random sequences/Genz: are not compressible!
N.B.: the random numbers generated by computers, however, can be compressed, simply because they are generated by a program. This is shorter than they themselves.
Understanding: true coincidence is not to be understood.
Understanding/Genz: this requires the data sequences to be compressible.
Compressibility/Decidability/Genz: there can be no computer program that decides if any amount of data is compressible.
Stronger: there is no way to prove that it is not compressible.
Compressibility: can be proven but not disproved.
Number π: can be generated by a finite program.
There are numbers that cannot be calculated in principle:
Omega/Chaitin/Genz: this is what Chaitin calls a certain number of which not a single digit can be calculated. It is not accessible to any rule, it is outside mathematics._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Gedankenexperimente Weinheim 1999
Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002