DOI: 10.14704/nq.2018.16.5.1343

Remarks on Computability and Stability

Daegene Song


Previously, it has been suggested that the Gödel-type non-algorithmic process may be associated with consciousness. This paper discusses the halting problem and the non-computability of self-referential consciousness. Specifically, this discussion outlines the distinguishability between the halting and looping of computation, or the semantic understanding between true and false, that may be associated with the non-computability of consciousness. The nonlocality intrinsically possessed in quantum theory is one of the striking features of nature that has received a lot of attention. In particular, Bell-type inequalities have been not only extremely powerful but practical tools in quantum information technology. A numerical approach is used to describe different cases of Bell-CHSH inequalities, particularly with different numbers of the choices of measurement bases. It is shown that there are variations of inequalities that are relatively stable against measurement errors.


Algorithms, Consciousness, Nonlocality, Numerical Methods

Full Text:



Aspect A, Dalibard J, Roger G. Experimental test of Bell's inequalities using time-varying analyzers. Physical Review Letters 1982; 49(25):1804-07.

Bell JS. On the Einstein Podolsky Rosen paradox. Physics 1964; 1: 195-200.

Clauser JF, Horne MA, Shimony A, Holt RA. Proposed experiment to test local hidden-variable theories. Physical Review Letters 1969; 23(15):880-84.

Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete?. Physical Review 1935; 47(10): 777-80.

Ekert AK. Quantum cryptography based on Bell's theorem. Physical Review Letters 1991; 67(6): 661-63.

Ghirardi GC, Rimini A, Weber T. A general argument against superluminal transmission through the quantum mechanical measurement process. Lettere Al Nuovo Cimento (1971-1985). 1980; 27(10):293-98.

Gisin N. Stochastic quantum dynamics and relativity. Helvetica Physica Acta 1989; 62 (4): 363-71.

Hardy L. Quantum theory from five reasonable axioms. arXiv:quant-ph/0101012. 2001

Hofstadter DR. I am a strange loop. Basic Books, 2007.

Kauffman LH. Self-reference and recursive forms. Journal of Social and Biological Structures 1987; 10(1):53-72.

Nielsen MA and Chuang I. Quantum computation and quantum information, Cambridge: Cambridge University press, 2000.

Peres A. Quantum Theory: Concepts and Methods. Dordrecht: Kluwer Academic Publishers, 1997.

Reynolds M. Axiomatisation and decidability of F and P in cyclical time. Journal of Philosophical Logic 1994; 23(2):197-224.

Song D. Non-computability of consciousness. NeuroQuantology 2007; 5: 382-91.

Song D. Decision-making process and information. NeuroQuantology 2017a; 15(4): 31-36.

Song D. Semantics of information. NeuroQuantology 2017b; 15(4): 88-92.

Tittel W, Brendel J, Zbinden H, Gisin N. Violation of Bell inequalities by photons more than 10 km apart. Physical Review Letters 1998; 81(17):3563-66.

Turing AM. On computable numbers, with an application to the Entscheidungs problem. Proceedings of the London Mathematical Society 1936; (2) 442: 230-65.

Yin J, Ren JG, Lu H, Cao Y, Yong HL, Wu YP, Liu C, Liao SK, Zhou F, Jiang Y, Cai XD. Quantum teleportation and entanglement distribution over 100-kilometre free-space channels. Nature 2012; 488(7410):185-88.

Yin J, Cao Y, Li YH, Liao SK, Zhang L, Ren JG, Cai WQ, Liu WY, Li B, Dai H, Li GB. Satellite-based entanglement distribution over 1200 kilometers. Science 2017; 356(6343):1140-44.

Supporting Agencies

| NeuroScience + QuantumPhysics> NeuroQuantology :: Copyright 2001-2019