×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aczel P, Non-Well-Founded Sets (1988)
[2] DOI: 10.1142/S0129626409000109 · Zbl 05793347
[3] Adamatzky A., Physarum Machines: Computers from Slime Mould (World Scientific Series on Nonlinear Science. Series A) (2010)
[4] DOI: 10.1109/ISMVL.1993.289558
[5] DOI: 10.1103/PhysRevD.21.1698
[6] DOI: 10.1016/0375-9601(88)90114-4
[7] DOI: 10.1063/1.529353 · Zbl 0746.46067
[8] DOI: 10.1007/978-94-009-1483-4
[9] Khrennikov A., Bulletin of the Section of Logic 35 (1) pp 49– (2006)
[10] DOI: 10.1134/S2070046609040037 · Zbl 1258.81047
[11] DOI: 10.1007/978-1-4612-1112-9
[12] DOI: 10.1007/BF01333127
[13] DOI: 10.1038/35035159
[14] DOI: 10.1016/S0301-4622(01)00179-X
[15] DOI: 10.1103/PhysRevLett.99.068104
[16] DOI: 10.1016/j.biosystems.2010.02.002
[17] DOI: 10.1007/BF01394786
[18] DOI: 10.1016/j.nancom.2011.05.002
[19] DOI: 10.3166/jancl.18.29-48 · Zbl 1187.03024
[20] DOI: 10.1007/978-3-540-85027-4_8
[21] DOI: 10.1142/S1793005711002037 · Zbl 1235.68111
[22] Schumann A., Annals of Computer Science and Information Systems. Proceedings of the 2013 Federated Conference on Computer Science and Information Systems pp 225– (2013)
[23] Schumann A., Proceedings of the Workshop on Concurrency, Specification and Programming (CS &P’2013) pp 389– (2013)
[24] DOI: 10.1103/PhysRev.179.752
[25] DOI: 10.1109/NEMS.2009.5068710
[26] DOI: 10.1016/j.biosystems.2003.08.001
[27] DOI: 10.4018/jnmc.2011040104
[28] DOI: 10.1007/BF01218590 · Zbl 0688.22004
[29] Volovich I. V, CERN preprint CERN-TH.4791/87 (1987)
[30] DOI: 10.1016/S0019-9958(65)90241-X · Zbl 0139.24606
[31] DOI: 10.1103/RevModPhys.60.1067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.