Lexicon of Arguments

 

II 205
Theory/success/Genz: the success 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: random sequences 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.
>Algorithms.
Understanding: true coincidence is not to be understood.
>Random, >Coincidence.
Understanding/Genz: this requires the data sequences to be compressible.
II 206
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: compressibility can be proven but not disproved.
II 207
Number pi: 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.
>Gregory Chaitin, >Calculability.