TY - JOUR

T1 - Psychological origin of quantum logic

T2 - An orthomodular lattice derived from natural-born intelligence without Hilbert space

AU - Gunji, Yukio Pegio

AU - Nakamura, Kyoko

N1 - Funding Information:
This work was supported by JSPS JPJS00120351748 .
Publisher Copyright:
© 2022

PY - 2022/6

Y1 - 2022/6

N2 - While the role of quantum theory becomes increasingly important through molecular computing and quantum cognition, it is still unclear how quantum mechanics can be involved in macroscopic phenomena. We previously argued the origin of quantum logic in terms of lattice theory; however, we do not refer to Hilbert space very much. Here, we show the psychological origin of quantum logic (i.e., orthomodular lattice) by not using Hilbert space. After showing how Hilbert space plays a role in constructing an orthomodular lattice, we show the idea of natural-born intelligence, in which a binary opposition pair can constitute not only positive but negative antinomy. In taking an object outside and an image inside a brain as that binary opposition pair, the structure entailing positive and negative antinomy is expressed as a specific binary relation consisting of multiple diagonal relations, which is called traumatic relation. Finally, we show that the traumatic relation leads to an orthomodular lattice without Hilbert space.

AB - While the role of quantum theory becomes increasingly important through molecular computing and quantum cognition, it is still unclear how quantum mechanics can be involved in macroscopic phenomena. We previously argued the origin of quantum logic in terms of lattice theory; however, we do not refer to Hilbert space very much. Here, we show the psychological origin of quantum logic (i.e., orthomodular lattice) by not using Hilbert space. After showing how Hilbert space plays a role in constructing an orthomodular lattice, we show the idea of natural-born intelligence, in which a binary opposition pair can constitute not only positive but negative antinomy. In taking an object outside and an image inside a brain as that binary opposition pair, the structure entailing positive and negative antinomy is expressed as a specific binary relation consisting of multiple diagonal relations, which is called traumatic relation. Finally, we show that the traumatic relation leads to an orthomodular lattice without Hilbert space.

KW - Cognition

KW - Hilbert space

KW - Lattice theory

KW - Natural-born intelligence

KW - Quantum theory

UR - http://www.scopus.com/inward/record.url?scp=85126562344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85126562344&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2022.104649

DO - 10.1016/j.biosystems.2022.104649

M3 - Article

C2 - 35227803

AN - SCOPUS:85126562344

SN - 0303-2647

VL - 215-216

JO - BioSystems

JF - BioSystems

M1 - 104649

ER -