Ultra-chaos: an insurmountable objective obstacle of reproducibility and replicability

TL;DR

The paper introduces the concept of ultra-chaos, a higher-level disorder that fundamentally challenges the reproducibility and replicability of scientific results due to its inherent sensitivity to tiny disturbances.

Contribution

It proposes the novel concept of ultra-chaos, highlighting its widespread existence and implications for scientific reproducibility and the limitations of traditional scientific paradigms.

Findings

Ultra-chaos is widely present in scientific phenomena.

Statistical properties of ultra-chaos are highly sensitive to disturbances.

Reproducibility of results involving ultra-chaos is fundamentally impossible.

Abstract

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-chaos is widely existed and thus has general scientific meanings. It is found that statistical non-reproducibility is an inherent property of an ultra-chaos so that an ultra-chaos is at a higher-level of disorder than a normal-chaos. Thus, it is impossible in practice to 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 G\"{o}del'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 a new door and possibility to study chaos theory, turbulence theory, computational fluid dynamics (CFD), the statistical significance, reproducibility crisis, and so on.