Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Applications of Non-Standard Analysis in Topoi to Mathematical Neuroscience and Artificial Intelligence: Infons, Energons, Receptons (I)

Version 1 : Received: 9 January 2020 / Approved: 11 January 2020 / Online: 11 January 2020 (10:36:37 CET)
Version 2 : Received: 3 August 2020 / Approved: 3 August 2020 / Online: 3 August 2020 (08:24:27 CEST)

How to cite: Badea, I.R.; Mocanu, C.; Pasarescu, O. Applications of Non-Standard Analysis in Topoi to Mathematical Neuroscience and Artificial Intelligence: Infons, Energons, Receptons (I). Preprints 2020, 2020010102 (doi: 10.20944/preprints202001.0102.v2). Badea, I.R.; Mocanu, C.; Pasarescu, O. Applications of Non-Standard Analysis in Topoi to Mathematical Neuroscience and Artificial Intelligence: Infons, Energons, Receptons (I). Preprints 2020, 2020010102 (doi: 10.20944/preprints202001.0102.v2).

Abstract

This work promotes new methods in Mathematical Modeling, consisting in the use of the methods of Non-standard Analysis in Topoi, having as its main purpose, the mathematical definitions of the pseudoparticles from the title, with arguments from Biology/Physiology (Mathematical Neuroscience), Physics (String Theory and Emergent Quantum Mechanics), and Cybernetics (Global Brain, including Natural and Artificial Intelligence). The connections between brain and mind will be scketched via the genetic/epigenetic interplay. The topoi model the intuitionistic logic (multi-valued) and have been used in Quantum Physics while Non-Standard Analysis in SET (= the Category of sets) has been applied in Mathematical Economics; topics from Theory of Categories were also used in the study of Consciousness; however, the combination topoi - non-standard analysis was never used until now in Applied Mathematics. Another important objective is to produce progress in this aria of Pure Mathematics also - the build of non-standard analysis in classes of topoi, already used in Physics. We propose the logic of non-standard extensions in topoi as a model of the human thinking (based on infons/receptons), these theories representing new top and very difficult results in Abstract Mathematics either.

Subject Areas

non-standard analysis; topos theory; artificial intelligence; brain studies; intuitionistic logic

Comments (1)

Comment 1
Received: 3 August 2020
Commenter: Ovidiu Pasarescu
Commenter's Conflict of Interests: Author
Comment: This version does not contain anymore the section 9 of the previous version, entirely written by dr. Florin Nichita, who included it in Section 3 from https://arxiv.org/pdf/2002.05345.pdf, in a different context. Moreover the Section 4 of the second version is new. This makes the manuscript more focussed on the relation Information/Reception and we prefered the new tite; moreover, the previous author dr. Florin Nichita has been replaced with the new author drd. Ileana Ruxandra Badea.
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