Remarks on Nondeterministic Computation, Choices, and Formal Language

Abstract

Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schrödinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic computation -a time-reversal process of the irreversible computations presented since the big bang. The goal of this paper is to extend the proposed subjective universe model, i.e., the universe as a quantum measurement: Motivated by the relationship between quantum theory and classical probability theory with continuity, it is argued that the frame of reference of the observer may be identified with classical probability theory where its choice, along with big bang singularity, should correspond to the quantum observable. That is, the physical version of singularity resolution corresponds to the case, where big bang singularity is equivalent to the continuity of the negative sea, or aether, filling the universe as a frame of reference of the observer. Moreover, based on the holographic principle, we identify the choice of the observer with the degrees of freedom proportional to the Planck area on the horizon. We also discuss that the continuity or infinity present in every formal language of choice acceptable in nondeterministic computation may be associated with the universal grammar proposed by Chomsky in linguistics.

Semantics of Information

“…This suggests that the continuity or infinite aspect may not be something that is transferred or learned, i.e., the semantic aspect of language ought to be innate and shared. Indeed, as indicated earlier [25], this continuous or infinite side of consciousness may be associated with universal grammar, which argues that all languages have a universal structure that is not learned but is innate in human nature [3][4][5]. A similar argument of the shared Dirac-type negative sea of consciousness was discussed [27] in terms of entanglement and nonlocality.…”

“…The argument in [7] was that classical probability theory may be considered equivalent to quantum theory, except for the aspect of continuity. Moreover, [25] argued that one can exploit this idea such that classical probability theory can be considered to involve a classical choice made by the observer, whereas continuity is associated with the quantum part. Thus, while the experience of physical reality is discrete or finite, conscious awareness, which corresponds to quantum evolution, is continuous.…”

Relational Decision-Making Processes

“…That is, the inside of the horizon fills up the outside as the negative sea of the observer's conscious reference frame (Song, 2014a). Moreover, the argument was extended to the cosmological model, and it was discussed that the observer's choice of reference frame corresponds to a time-reversal process of irreversible computations since the big bang such that it fills up the vacuum as the Dirac-type negative sea (Song, 2016) (Figure 2). Figure 2.…”

“…In this paper, we have outlined that in the subjective model, entanglement implies correlation between the observer's choices of reference frame rather than the state vectors (or the observed). In particular, in the proposed model where vacuum is considered to be filled with the Dirac-type negative sea of consciousness (Song, 2016) (or the aether (Song, 2017a)), entanglement implies the interaction between Alice's and Bob's reference frames in the conscious negative sea (Figure 3). This is rather different from the previous understanding that individuals share and interact in the same physical world while possessing their own consciousness.…”

“…In (Song, 2016), the potentially important role of free will in building the definitive model of the universe using nondeterministic computation was explored. Nondeterministic computation chooses the acceptable path of the computational process (i.e., the observer's choice), which is different from probabilistic computation (Song, Figure 3.…”