Some Conceptual and Measurement Aspects of Complexity, Chaos, and Randomness from Mathematical Point of View
One of the main purposes of the mankind is to understand and explain the dynamics of real-world phenomena, i.e., modeling them, and also to build predictive models for their behaviors. The most powerful tool in modeling a deterministic dynamic is mathematics, and the most powerful tool in modeling a stochastic dynamic is statistics. Some characteristics of deterministic chaotic systems are well known, as well as of stochastic systems. Distinguishing deterministic dynamical systems from stochastic ones, based on observed data, is a difficult and yet unsolved statistical problem. Natural phenomena and human behaviors dynamics are very complex. If the existing complexity and chaos in natural dynamical systems, also inherited in their mathematical models, is not well understood, then management and control processes in such systems may result in catastrophes. This study aims to reveal and emphasize the role of mathematics in formulating the conceptual and measurement stages of complexity, chaos, and randomness.
KeywordsChaos Complexity Randomness Mathematics
- Atakan, C., Dağalp, R., Potas, N., & Öztürk, F. (2017). Randomness and chaos. In Ş. Ş. Erçetin & N. Potas (Eds.), Chaos, complexity and leadership (pp. 621–646). Cham: Springer.Google Scholar
- Balibrea, F. (2006). Chaos, periodicity and complexity on dynamical systems. In A. Sengupta (Ed.), Chaos, nonlinearity, complexity, the dynamical paradigm of nature. Berlin: Springer.Google Scholar
- Bensoudane, H., Gentil, C., & Neveu, M. (2008). The local fractional derivative of fractal curves. IEEE International Conference on Signal Image Technology and Internet Based Systems, pp. 522–529.Google Scholar
- Cernenoks, J., Iraids, J., Opmanis, M., Opmanis, R., & Podnieks K. (2014). Integer complexity: Experimental and analytical results II. arXiv:1409.0446v1 [math.NT] 1 Sep 2014.Google Scholar
- Cordwell, K., Epstein, A., Hemmady, A., Miller, S. J., Palsson, E., Sharma, A., Steinerberger, S., & Vu, Y. N. T. (2018). On algorithms to calculate integer complexity. arXiv:1706.08424v3 [math.NT] 5 Aug 2018.Google Scholar
- Rao, C. R. (1989). Statistics and truth Puting chance to work. Dordrecht: International Co-operative Publishing House.Google Scholar
- Rovelli, C. (2017). Fizik Üzerine Yedi Kısa Ders. Can Sanat Yayınları. (Translation to Turkish from: Rovelli, C. (2014) Seven Brief Lessons on Physics.)Google Scholar
- Rovelli, C. (2018). Gerçeklik Göründüğü Gibi Değildir. Can Sanat Yayınları. (Translation to Turkish from: Rovelli, C. (2014) Reality Is Not What It Seems: The Journey to Quantum Gravity.)Google Scholar
- Tomé, L., & Açıkalın, Ş. N. (2017). Complexity theory as a new Lens in IR: System and change. In Ş. Ş. Erçetin & N. Potas (Eds.), Chaos, complexity and leadership (pp. 621–646). Cham: Springer.Google Scholar
- Wikipedia, free encyclopedia, https://en.wikipedia.org/.