Topological Geometrodynamics (TGD)—the theory of particle physics cosmology, biophysics, and cognition of Finnish physicist Matti Pitkänen, which Paster selects as his Number One Radical Theory of New Physics and the Mind—is not simply a reductionist translation of quantum phenomena to the mind or the brain. Rather, TGD offers a unified holistic understanding of the processes of cognition replicating physical processes at all levels—microscopic, macroscopic, cosmological, biophysical, cognitive.
Paster’s 2016 book Digital Mind Math illustrates with anecdotes from everyday life the TGD organization of the mind and the TGD cognitive process. A branch of mathematics called padic mathematics plays a central role, in what Paster refers to as PAdic Quantum Cognition.
Padic mathematics is the numbering system for the paths of a hierarchy tree. Each path is labeled by one padic number. The size of padic numbers increases with longer paths or with more choices p at each node of the hierarchy tree.
Padic numbers have a special role because mathematicians have proven that there are only two ways to measure size—which mathematicians call the norm—in order to create a complete numbering system: the normal way by which we measure our familiar real numbers by their absolute value, and this second norm, the padic norm, which is defined by path length and node choices.
In PAdic Quantum Cognition, our thinking proceeds padically, guided by a biological urge to increase information, which TGD calls the Negentropy Maximization Principle. Upon selection of a highinformation path, we experience the real analog of the selected thought. This use of padic numbers for organization and analysis, and use of corresponding real numbers for experience, is adelic mathematics—the dual mathematics of padic and real numbers, the only two complete mathematical numbering systems.
Digital Mind Math offers a stepbystep description of how PAdic Quantum Cognition works. Paster’s current research involves taking this all to a next level of scientific and mathematical detail, exploring the brain as a natural evolutionarily defined information maximizer, and going deep into advanced padic mathematics to detail its capabilities as the mathematics of the mind’s operating system:
BRAIN, MIND, COGNITION
 Negentropy Maximization Principle
 Biophysical processes and mechanisms
 Piaget and Vygotsky
 Natural selection
 Philosophy of mind
 Structure and labeling of thoughts, memories, and their interconnections
 Cognitive analysis and experience
 Emotions
PADIC MIND MAPPING AND THE PADIC COGNITIVE COMPUTATIONAL MODEL
 The vast informational space of padic numbers
 Information measurement and maximization
 Hierarchy trees, sequences, categorization, interconnections and links, enclosure, content, algorithms
 Witt vectors; Frobenius, Verschiebung, restriction maps
 Hensel’s Lemma and its converse
 Crystalline cohomology; deRhamWitt complex
EXACTLY HOW THIS WORKS
 The central role of the converse of Hensel’s Lemma: How an obscure mathematical concept explains how the brain evolved and explains the ideal way to think, teach, learn, interact, and evolve as a society
 Cognitive science, cognitive psychology, cognitive biophysics
 Artificial intelligence and computer science: machine learning, cognitive computing, quantum computation, internet of things
 Teaching and learning
 Neuroscience
 Social evolution: bees, emerging social consciousness, the K3 civilization
PAdic Quantum Cognition resonates strongly with core theories of cognitive development, such as those of Jean Piaget and Lev Vygotsky. Paster shows how Piaget’s basic twin processes of assimilation and accommodation have precise padic mappings. Piaget’s life drive toward higher levels of equilibration is TGD’s Negentropy Maximization Principle. And the region described by the converse of Hensel’s Lemma is Vygotsky’s Zone of Proximal Development.
PAdic Quantum Cognition offers a rich basis for 21stcentury developments in cognitive psychology, education, neuroscience, artificial intelligence, machine learning, evolutionary biology, and universal social advancement.
