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 p-adic mathematics plays a central role, in what Paster refers to as P-Adic Quantum Cognition.
P-adic mathematics is the numbering system for the paths of a hierarchy tree. Each path is labeled by one p-adic number. The size of p-adic numbers increases with longer paths or with more choices p at each node of the hierarchy tree.
P-adic 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 p-adic norm, which is defined by path length and node choices.
In P-Adic Quantum Cognition, our thinking proceeds p-adically, guided by a biological urge to increase information, which TGD calls the Negentropy Maximization Principle. Upon selection of a high-information path, we experience the real analog of the selected thought. This use of p-adic numbers for organization and analysis, and use of corresponding real numbers for experience, is adelic mathematics—the dual mathematics of p-adic and real numbers, the only two complete mathematical numbering systems.
Digital Mind Math offers a step-by-step description of how P-Adic 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 p-adic 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
P-ADIC MIND MAPPING AND THE P-ADIC COGNITIVE COMPUTATIONAL MODEL
- The vast informational space of p-adic 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; deRham-Witt 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
- Social evolution: bees, emerging social consciousness, the K3 civilization
P-Adic 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 p-adic 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.
P-Adic Quantum Cognition offers a rich basis for 21st-century developments in cognitive psychology, education, neuroscience, artificial intelligence, machine learning, evolutionary biology, and universal social advancement.