Friston's free-energy principle is based on the premise that living systems are ergodic. Kauffman begins his new book with the premise that life is non-ergodic. Who is right? My money is on Kauffman on this one, but what do I know? A World Beyond Physics https://global.oup.com/academic/product/a-world-beyond-physics-9780190871338#.XNGVGw1PdIQ.twitter …
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1/ Source of my information regarding ergodic theory as a basis of fractal geometry:https://www.researchgate.net/publication/268066325_Ergodic_theory_and_fractal_geometry …
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2/"The properties of fractals come to light under repeated magnification, which we refer to informally as “zooming in”. This zooming-in process has its parallels in dynamics, and the varying “scenery” corresponds to the evolution of dynamical variables."
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3/"The present monograph focuses on applications of one branch of dynamics – ergodic theory – to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages."
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4/ It could be possible that living systems could be a mix of ergodic and non ergodic processes to possess fractal features.
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Maybe a set of states emerge non-ergodically, but together these states form a complex landscape. These states approximately act as a set of ergodic states. This happens at a "working fractal scale" related to the embodied structural coupling, of the living system.
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