Time and Mnemonic Morphism

Goro C. Kato () and Kazuo Nishimura
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Goro C. Kato: California Polytechnic State University

Chapter Chapter 8 in Creative Complex Systems, 2021, pp 113-120 from Springer

Abstract: Abstract ThisMnemonic morphism chapter provides a temporal toposTopos theoretic formulation for the relationship of the conscious (cognitive) states of an entityEntity for the pastPast, presentPresent, and futureFuture in terms of nonfunctorially induced mnemonic morphisms. The pastPast is recalled by memoriesMemory, and the futureFuture consists of possible states with a probability space of possibilities. When our presentPresent consciousnessConsciousness and behavior change, through our memoryMemory our interpretation of the pastPast changes, and simultaneously the range of probability distributionProbability distribution of futureFuture states will be affected. We describe the internal relationship among the conscious states in terms of the temporal toposTopos (t-topos) theory. A conscious entityEntity can be expressed as a pair (p, δp), where p is an objectObject of the t-toposTopos S^ over t-site S, and δp is a uniquely determined morphism from an initial objectObject α of t-toposTopos to p. For three objectsObject U, V, and W in the t-site S (which correspond to the pastPast, presentPresent, and futureFuture ), we introduce noncanonicalNon-canonical (i.e., nonfunctorial) mnemonic morphisms among the three states of p defined over U, V, and W, respectively. Then we study the interplay among conscious states $$\delta_{{{U}}}^{{{p}}}$$ δ U p , $$\delta_{{{V}}}^{{{p}}}$$ δ V p and $$\delta_{{{W}}}^{{{p}}}$$ δ W p of p corresponding to the pastPast, presentPresent, and futureFuture .

Keywords: Category; Sheaf; Topos; Mnemonic morphism (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:crechp:978-981-16-4457-3_8

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DOI: 10.1007/978-981-16-4457-3_8

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