Great circle of mysteries: mathematics, the world, the mind

Description

"The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these "systems" may serve as prototypes for design of universal learning computer programs."--Publisher.  Read more... Abstract: "The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these "systems" may serve as prototypes for design of universal learning computer programs."--Publisher Content: Introduction -- Quotations and ideas -- Beautiful elsewhere -- Science -- Numbers -- Laws -- Truth -- Life -- Evolution -- Brain -- Mind -- Mysteries remain -- Memorandum ergo -- Brain, ergo-brain, and mind -- Ergo Project -- Formality and universality -- Meaning, folding and understanding -- Universality, simplicity, and Ergo-brain -- Freedom, curiosity, interesting signals, and goal free learning -- Information, prediction, and a bug on the leaf -- Stones and goals -- Ego, ergo, emotions, and ergo-moods -- Common sense, ergo-ideas and ergo-logic -- Ergo in the minds -- Language and languages -- Meaning of meaning -- Play, humour and art -- Ergo in science -- Unreasonable men and alternative histories -- Mathematics and its limits -- Numbers, symmetries and categories -- Logic and the illusion of rigor -- Infinite inside, finite outside -- Small, large, inacessible -- Probability: particles, symmetries, languages -- Signal flows from the world to the brain -- Charecteristic features of linguistic signals -- Understanding structures and the structure of understanding -- Sixteen rules of an Ergo-learner -- Learning to understand languages: from libraries to dictionaries -- Libraries, strings, annotations, and colors -- Teaching and grading -- Atoms of structures: units, similarities, co-functionalities, reductions -- Fragmentation, segmentation, and formation of units -- Presyntactic morphisms, syntactic categories, and branched entropy -- Similarities and classfications, trees and coordinatizations -- Clustering, biclustering, and co-clustering.