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The double-slit experiment with Physarum polycephalum and $$p$$-adic valued probabilities and fuzziness. (English) Zbl 1338.68076
Summary: Physarum polycephalum is a single-cell slime mould visible by unaided eye. When foraging for sources of nutrients the slime mould optimizes its body shape, or a network of protoplasmic tubes. This optimization can be interpreted as computation. Many experimental laboratory prototypes of Physarum-based non-silicon computing devices have been implemented recently yet the scope of the slime mould as a fuzzy processor was never explored. We are filling this gap and show, by implementing the double-slit experiment, that self-inconsistencies in the slime mould’s behaviour cannot approximate atomic individual acts of Physarum. This finding is analogous to our inability to approximate single photons. We further interpret the Physarum’s behaviour in terms of individual-collective duality using $$p$$-adic valued probabilities and fuzziness. We also construct a system of $$p$$-adic many-valued logic to describe experimental responses of Physarum and we show how this logic can be used in $$p$$-adic fuzzy logic controllers on the medium of Physarum.

##### MSC:
 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 03B52 Fuzzy logic; logic of vagueness 03E72 Theory of fuzzy sets, etc. 60A86 Fuzzy probability 92C80 Plant biology 93C42 Fuzzy control/observation systems
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