Abstract

The purpose of this paper is to promote new methods in mathematical modeling inspired by neuroscience—that is consciousness and subconsciousness—with an eye toward artificial intelligence as parts of the global brain. As a mathematical model, we propose topoi and their non-standard enlargements as models, due to the fact that their logic corresponds well to human thinking. For this reason, we built non-standard analysis in a special class of topoi; before now, this existed only in the topos of sets (A. Robinson). Then, we arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory (IIST); a class of models for it is provided, namely, non-standard enlargements of the previous topoi. We also consider the genetic–epigenetic interplay with a mathematical introduction consisting of a study of the Yang–Baxter equations with new mathematical results.

Highlights

  • This paper contains both known and new results, and it addresses an auditorium of great diversity: neuroscientists, computer scientists, physicians, physicists, biologists, mathematicians, etc

  • We arrive at the pseudo-particles from the title and to a new axiomatics denoted by Intuitionistic Internal Set Theory (IIST); a class of models for it is provided, namely, non-standard enlargements of the previous topoi

  • One is related to pure mathematics and consist in constructing the non-standard analysis in SET-type topoi (Theorem 1); another one is related to foundations of mathematics; arguments from physics, neuroscience, cybernetics are used in order to justify the importance of introduction of the IIST axiomatics and to provide models for it; and, last but not least, the introduction and justification of the infons, energons, receptons: how they should look like and which is their usefulness (Sections 2–4)

Read more

Summary

Introduction

This paper contains both known and new results, and it addresses an auditorium of great diversity: neuroscientists, computer scientists, physicians, physicists, biologists, mathematicians, etc. (2) Presentation of the axiomatics IIST (Intuitionistic Internal Set Theory) (Section 7.1); (3) Theoretical introduction of non-standard analysis in topoi (until now this was known only for the topos SET), at the level of general definition (having higher order language)) (Section 6.2); (4) Topoi of SET-type and the construction of a model class for IIST on them, based on non-standard analysis in SET (IIST is as consistent as ZF(C) is) (Section 5.2 and Theorem 1); (5) Definitions of the notions of infon, energon, recepton, which would use for a simultaneous approach of the natural and artificial neural (quantum) networks, both part of the global brain (Section 7); this approach is based on a novel study of the global brain (Section 4); and this last-one is based on some novel points of view concerning the human brain, mind, genetics, and epigenetics (Section 2). The topics from (7) are review topics, the topics from (1) and (6) are partly original, partly review, while the topics from (2), (3), (4), (5), are original

Information and Reception
Information and Entropy
Information and Reception, Brain and Mind
Information, Energy, and Reception
Max Tegmark’s Multiverses
Infons and Energons in String Theory
What Is the Global Brain?
Cybernetic Principles of Information in the Global Brain
Global Brain Functions Regarding Information
Theories versus
Topos Theory Now let us pass to the main notions used in this paper
Oriented Graphs as Topoi of SET-Type
Intuitionistic Logic in Topoi
Non-Standard Enlargement in SET
Some Properties of
Non-Standard Analysis in SET-Type Topoi
The Intuitionistic Context
Infons, Receptons, Energons
The Yang–Baxter Equations
Findings
Conclusions and Further Considerations

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.