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In this paper, a new concept, i.e. ultra-chaos, is proposed for the firsttime. Unlike a normal-chaos, statistical properties such as the probabilitydensity functions (PDF) of an ultra-chaos are sensitive to tiny disturbances.We illustrate that ultra-chaos is widely existed and thus has generalscientific meanings. It is found that statistical non-reproducibility is aninherent property of an ultra-chaos so that an ultra-chaos is at a higher-levelof disorder than a normal-chaos. Thus, it is impossible in practice toreplicate experimental/numerical results of an ultra-chaos even in statisticalmeanings, since random environmental noises always exist and are out ofcontrol. Thus, the ultra-chaos should be an insurmountable obstacle ofreproducibility and replicability. Similar to G\"{o}del's incompletenesstheorem, such kind of "incompleteness of reproducibility" reveals a limitationof our traditional scientific paradigm based on reproducible experiments, whichcan be traced back to Galileo. The ultra-chaos opens a new door and possibilityto study chaos theory, turbulence theory, computational fluid dynamics (CFD),the statistical significance, reproducibility crisis, and so on.

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