Time and Mnemonic Morphism

Abstract

This chapter provides a temporal topos theoretic formulation for the relationship of the conscious (cognitive) states of an entity for the past, present, and future in terms of nonfunctorially induced mnemonic morphisms. The past is recalled by memories, and the future consists of possible states with a probability space of possibilities. When our present consciousness and behavior change, through our memory our interpretation of the past changes, and simultaneously the range of probability distribution of future states will be affected. We describe the internal relationship among the conscious states in terms of the temporal topos (t-topos) theory. A conscious entity can be expressed as a pair (p, δ^p), where p is an object of the t-topos S^ over t-site S, and δ^p is a uniquely determined morphism from an initial object α of t-topos to p. For three objects U, V, and W in the t-site S (which correspond to the past, present, and future), we introduce noncanonical (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 $\delta_{{{U}}}^{{{p}}}$, $\delta_{{{V}}}^{{{p}}}$ and $\delta_{{{W}}}^{{{p}}}$ of p corresponding to the past, present, and future.