@Article{AAMM-14-799,
author = {Liao , Shijun and Qin , Shijie},
title = {Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {4},
pages = {799--815},
abstract = {<p style="text-align: justify;">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 Gödel&#39;s incompleteness theorem, such kind of &quot;incompleteness of reproducibility&quot; 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0364},
url = {http://global-sci.org/intro/article_detail/aamm/20285.html}
}