Great Circle of Mysteries [electronic resource] : Mathematics, the World, the Mind /
Gromov, Misha.author.
This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. 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. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.
Beautiful Elsewhere -- Science -- Numbers -- Laws -- Truth -- Life -- Evolution -- Brain -- Mind -- Mysteries Remain -- Ergo Project. 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 is Limits -- Numbers, Symmetries and Categories -- Logic and Illusion of Rigor -- Infinte inside, Finite outside -- Small, Large, Inaccessible -- Probability: Particles, Symmetries, Languages -- Signal Flows from the World to the Brain -- Characteristic Features of Linguistic Signals -- Understanding Structures and the Structure of Understanding -- Sixteen Rules of 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 Classifcations, Trees and Coordinatizations -- Clustering, Biclustering and Coclustering -- Bibliography. .
This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. 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. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.
Mathematical logic.
Mathematical Logic and Foundations.