Abstract
This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics.
Highlights
Chaitin has announced the decline and fall of reductionism in mathematics, considering the randomness in arithmetic elucidated by some results of the computation theory.The concluding remark concerns experimental mathematics in order to stress the impact of computers that have an enormous contribution to the mathematical experience, which impels people to proceed in a more pragmatic fashion
Chaitin remarked that the question of how one should do mathematics requires at least another generation of work [1]
It has been demonstrated by operators corresponding to evolution of wavelets, which are not induced by any pointwise dynamics
Summary
Chaitin has announced the decline and fall of reductionism in mathematics, considering the randomness in arithmetic elucidated by some results of the computation theory.The concluding remark concerns experimental mathematics in order to stress the impact of computers that have an enormous contribution to the mathematical experience, which impels people to proceed in a more pragmatic fashion. Chaitin has announced the decline and fall of reductionism in mathematics, considering the randomness in arithmetic elucidated by some results of the computation theory. Mathematicians are coerced to go ahead proof, postulating hypotheses based upon results of computer experiments. He points out a relation to the contemporary physics wherein randomness is a crucial agent, which is regarded to be the core of an emergent science paradigm. Randomness that emerges in a formal theory set upon deterministic assumptions concerns the complex system physics, which considers systems wherein the best method of description is not clear a priori [2] Being the amalgam of both, complex patterns have an inherent tendency towards hierarchical organization [2] (p. 200)
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