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SUMMARY:Ultra-chaos: statistics instability and crisis of reproducibility 
 - Shijun LIAO
DTSTART:20230913T083000Z
DTEND:20230913T093000Z
UID:TALK205126@talks.cam.ac.uk
CONTACT:Xianyang Jiang
DESCRIPTION:Chaos theory is widely regarded as the third greatest scientif
 ic revolution in physics in 20th century\, comparable to Einstein’s theo
 ry of relativity and the quantum mechanics.  It is widely believed that\, 
 although trajectories of a chaotic system are unstable due to “butterfly
 -effect”\, its statistics should be stable and thus its results should b
 e reproducible in the meaning of statistics.  Note that reproducibility is
  the cornerstone of modern science.  Unfortunately\, more and more experim
 ents have been reported to be not reproducible\, which leads to the so-cal
 led “crisis of reproducibility”.  By means of a new strategy of numeri
 cal technique\, namely the “clean numerical simulation” (CNS)\, we fou
 nd that there exist the so-called “ultra-chaos” whose statistics are u
 nstable to small disturbances\, corresponding to statistics instability.  
 Since random tiny disturbances are unavoidable\, in practice any experimen
 tal and/or numerical results of an ultra-chaotic system cannot be repeated
  even in the meaning of statistics.  Therefore\, even if all artificial di
 sturbances are excluded\, the crisis of reproducibility still cannot be av
 oided in practice.  Ultra-chaos as a new concept reveals the incompletenes
 s of the modern paradigm of scientific researches\, which is based on the 
 reproducibility of experiments.  In this talk\, we briefly introduce the b
 asic ideas of the “clean numerical simulation” (CNS)\, describe the de
 finition of ultra-chaos\, give a few examples of ultra-chaos\, and suggest
  some conjectures and open questions\, including the so-called “modified
  fourth Clay millennium problem”.  
LOCATION:MR14\, DAMTP
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