# The Time Operator of Reals

### Miloš Milovanović, Srđan Vukmirović

#### Abstract

The purpose of the paper is to establish the continuum in terms of the complex systems physics. It is based upon the intuitionistic mathematics of Brouwer, implying a processual definition of real numbers that concerns the measurement problem. The Brouwerian continuum is proved to be a categorical skeleton of complex systems whose determining feature is the existence of time operator. Acting on continuous signals, the time operator represents multiresolution hierarchy of the measurement process. The wavelet domain hidden Markov model, that recapitulates statistical properties of the hierarchy, is applicable to a wide range of signals having experimental verification. It indicates a novel method that has already been proved tremendously useful in applied mathematics.

Download#### Paper Citation

#### in Harvard Style

Milovanović M. and Vukmirović S. (2019). **The Time Operator of Reals**.In *Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,* ISBN 978-989-758-366-7, pages 75-84. DOI: 10.5220/0007747000750084

#### in Bibtex Style

@conference{complexis19,

author={Miloš Milovanović and Srđan Vukmirović},

title={The Time Operator of Reals},

booktitle={Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,},

year={2019},

pages={75-84},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007747000750084},

isbn={978-989-758-366-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,

TI - The Time Operator of Reals

SN - 978-989-758-366-7

AU - Milovanović M.

AU - Vukmirović S.

PY - 2019

SP - 75

EP - 84

DO - 10.5220/0007747000750084