Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, a new concept, i.e., ultra-chaos, is proposed for the first time.Unlike a normal-chaos, statistical properties such as the probability density functions(PDF) of an ultra-chaos are sensitive to tiny disturbances. We illustrate that ultra-chaosis widely existed and thus has general scientific meanings. It is found that statisticalnon-reproducibility is an inherent property of an ultra-chaos so that an ultra-chaos isat a higher-level of disorder than a normal-chaos. Thus, it is impossible in practiceto replicate experimental/numerical results of an ultra-chaos even in statistical meanings, since random environmental noises always exist and are out of control. Thus,the ultra-chaos should be an insurmountable obstacle of reproducibility and replicability. Similar to Gödel's incompleteness theorem, such kind of "incompleteness of reproducibility" reveals a limitation of our traditional scientific paradigm based on reproducible experiments, which can be traced back to Galileo. The ultra-chaos opens anew door and possibility to study chaos theory, turbulence theory, computational fluiddynamics (CFD), the statistical significance, reproducibility crisis, and so on.