arrow
Volume 14, Issue 4
Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication

Shijun Liao & Shijie Qin

Adv. Appl. Math. Mech., 14 (2022), pp. 799-815.

Published online: 2022-02

[An open-access article; the PDF is free to any online user.]

Export citation
  • 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 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 a new door and possibility to study chaos theory, turbulence theory, computational fluid dynamics (CFD), the statistical significance, reproducibility crisis, and so on.

  • Keywords

Chaos, statistical stability, reproducibility and replication.

  • AMS Subject Headings

35N05, 65P20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-14-799, author = {Shijun and Liao and and 22400 and and Shijun Liao and Shijie and Qin and and 22401 and and Shijie Qin}, 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 = {

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'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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0364}, url = {http://global-sci.org/intro/article_detail/aamm/20285.html} }
TY - JOUR T1 - Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication AU - Liao , Shijun AU - Qin , Shijie JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 799 EP - 815 PY - 2022 DA - 2022/02 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2021-0364 UR - https://global-sci.org/intro/article_detail/aamm/20285.html KW - Chaos, statistical stability, reproducibility and replication. AB -

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'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.

Shijun Liao & Shijie Qin. (2022). Ultra-Chaos: An Insurmountable Objective Obstacle of Reproducibility and Replication. Advances in Applied Mathematics and Mechanics. 14 (4). 799-815. doi:10.4208/aamm.OA-2021-0364
Copy to clipboard
The citation has been copied to your clipboard