Digital Mind Math Chapter Summaries
Digital Mind Math is a complete mathematical model of the mind and cognition—a model for the sciences of artificial intelligence, neuroscience, and cognitive psychology, and also of interest to anyone who thinks and anyone who enjoys having a mind.
The two critical components of the Digital Mind Math model are p-adic mathematics and reconfigured spacetime, both of which are central to the theory`of physics Topological Geometrodynamics (TGD) that Digital Mind Math is based on.
In Digital Mind Math, details are grouped to form concepts, as the mind identifies the boundaries of thoughts, which are intricately linked in real spacetime. The contents, sequences, and interconnections among thoughts are efficiently labeled using p-adic mathematics.
P-adic mathematics—the mathematics of enclosure and sequencing—is our first mathematics, how we organize our world from infancy onward, the natural mathematics of cognition. Throughout Digital Mind Math, it is shown how p-adic mathematics describes the exact processes identified by cognitive development theorists such as Jean Piaget and Lev Vygotsky, even though they did not label their work p-adically.
Digital Mind Math's core cognitive process is identical to the core quantum process—quantum decoherence, or the quantum transition, or the collapse of quantum wave function, or the transition from the sum over histories to a single classical event—which is entirely standard in contemporary physics at the level of elementary particles, but which in Topological Geometrodynamics applies at all levels, macroscopically and macrotemporally, in biophysics and the mind.
P-adic mathematics exists in a vast informational space, in which each p-adic number represents an enormous quantity of information about the contents, sequences, and interconnections of our thoughts. Digital Mind Math's core quantum cognitive process proceeds by taking advantage of p-adic mathematics' great efficiency to model all possible next thoughts in the quantum configuration space, then select the next thought to experience by tending to maximize information content. Information content is the p-adic norm, the way that p-adic size is measured. The selected p-adically labeled thought is then experienced as mapped out by its mathematically real analog.
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The elementary concepts of Digital Mind Math are presented in Part One. Each concept is fairly ordinary, in that it may have crossed the mind in idle speculation about life and the universe. Taken together, though, these basics provide a revised worldview and a model of how we think—the mathematics of the mind.
Digital Mind Math is based on the theory of physics Topological Geometrodynamics (TGD). So the whole book, Digital Mind Math, is about TGD. The scope of TGD is much larger than the scope of Digital Mind Math, however, since TGD is a theory of modern physics, and Digital Mind Math is a detailed development of the aspect of TGD having to do with thinking and the mind.
Chapter 1. Enclosings. Digital Mind Math emphasizes the enclosings of the physical world. Objects at every level enclose and are enclosed by other objects that each are virtual universes—bounded universes, finitely extended, ending at their outer boundaries. In Topological Geometrodynamics, and therefore in Digital Mind Math, an object is represented by a bounded spacetime sheet, enclosed within and enclosing multiple levels of other spacetime sheets. This is many-sheeted spacetime, a hierarchy of bounded universes.
Chapter 2. Connecting Enclosures. Spacetime sheets are connected through tiny wormholes. These tiny wormholes implement the organization of many-sheeted spacetime's enclosings. Wormholes are the connections from one macroscopic and macrotemporal four-dimensional spacetime sheet to another. Mathematicians are able to model these four-dimensional spacetime sheets and their four-dimensional wormholes very simply, in eight dimensions. TGD's and Digital Mind Math's eight-dimensional spacetime consists of four dimensions of macro-extended spacetime—four dimensions of spacetime extended macroscopically and macrotemporally—and four tiny dimensions of space in which the connecting wormholes reside.
Chapter 3. Thinking Enclosures and P-Adic Math. Thinking proceeds by processes of enclosing and becoming enclosed. Digital Mind Math uses a special mathematical system, called p-adic mathematics, to model both the process of thinking and the organization of real spacetime sheets within many-sheeted spacetime. The basics of p-adic mathematics are introduced.
Chapter 4. Our Blinking Moments of Time. Spacetime sheets extend not just in three spatial dimensions, but also in the fourth dimension-time. As a result, an object in TGD—a four-dimensional spacetime sheet—is a time history of the object's extension in three spatial dimensions. Wormholes, connecting TGD's spacetime sheets, reside in four tiny dimensions of space. Our mind advances from moment to moment according to the processes of physics' quantum transition. The mind applies p-adic mathematics to label the spacetime sheets within TGD's eight-dimensional spacetime, which consists of four-dimensional spacetime sheets hierarchically linked by four-dimensional wormholes.
Chapter 5. Review of the Basics. The real world is most effectively understood as embedded and embedding objects proceeding along a configuration space of all possible paths—a world of classical worlds—until reduction to a single path when observation or measurement triggers the quantum transition. The organization of the embeddings is most naturally tracked not by real mathematics but by p-adic mathematics, the mathematics of enclosure. P-adic mathematics is the natural mathematics of thinking, memory, imagination, and intention. Our biological systems demonstrate both real and p-adic properties that permit mind-body integration.
Chapter 6. Memories. Memories are recorded within the p-adic structure of the brain. When a memory is triggered, the corresponding real structure directs our experience.
Chapter 7. The P-Adic Surgery of Dreams. Dreams are discussed as everyday phenomena that exhibit the mind's use of p-adic and real mathematics, and that, guided by information maximization, select life paths from a configuration space of possibility.
Chapter 8. Seconds, Minutes, Hours, Days, Weeks, Months, Years. We use several mathematical approaches in thinking about elements of time—purely human-invented numerical relationships, astronomical relationships based on the moon, astronomical relationships based on the sun. This chapter discusses the interactions among these mathematical relationships, as practice for thinking about the relationship between real and p-adic mathematics.
Chapter 9. Cognition, as Modeled by Piaget and Vygotsky. Jean Piaget's and Lev Vygotsky's twentieth-century models of cognitive development remain core to contemporary psychological and educational theory. Piaget's framework—assimilation, accommodation, equilibration—is precisely modeled by TGD's p-adic mathematics. And both theories give us valuable insight into the drive to increase information content.
Chapter 10. Computers vs. the Mind. For many years now, computers have played chess better than the world chess champion. Computers beat the champions of television game shows and the board game Go, and show remarkable agility at tasks such as facial recognition that only a few decades ago seemed humans would always be superior at. But the human brain weighs less than three pounds and uses the energy of a dim light bulb. P-adic mathematics, applied to reconfigured spacetime, accounts for humans' greatly superior efficiency.
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We will now proceed to enhance our intuition for what p-adic mathematics is, how p-adic numbers are written, and what these numbers mean.
We already, from Part One, have a nice head start on this: We have discussed in Part One that the digits of a p-adic number—for example, 623.451—represent an ordered sequence of labeled objects or events. Starting from the last digit to the right, object 1 is p-adically the largest, and encloses or contains the smaller object 5, which encloses or contains the smaller object 4, and so on.
This is an excellent start, but to truly see the power of the p-adic mathematical system, we need to gain an intuition for a few more mathematical concepts.
Of course, gaining an intuition for p-adic mathematics is a bit short of taking a university course in mathematics. The purpose here is not for you to become a mathematical scholar; it is for you to gain a sense for the nature of p-adic mathematics, even though it is typically considered an advanced branch of mathematics.
It is unusual for p-adic mathematics to be introduced into an undergraduate mathematics curriculum; it is generally introduced in a graduate-level course. Even then, the full study of p-adic mathematics is an advanced mathematical specialty, studied as a full Ph.D. specialty and beyond. But here I am writing explicitly for any interested audience, even if their mathematics ended with a bit of high school algebra.
You will learn how p-adic numbers work, so that we'll be able to discuss Part Three's examples in a bit more detail, and also a bit more simply, more concisely.
One of the beauties of mathematics is the elegance with which mathematical shorthand can capture a concept, a thought, a point to be made.
Mathematicians often contrast a proof or an explanation that is accomplished by "brute force" with one that is elegant. This is not just an incidental point; it is one that is often made in criticism of some of today's great achievements of computer science.
Computers today have much faster processing speeds than the human brain, and computers can store much more data than can be stored in the brain. As a result, computers can now accomplish many tasks better and faster than humans can.
But where is the elegance in big data and superfast processors? The brain fits in our skulls—we can walk around with it. It uses a tiny amount of power, and it doesn't require industrial-size cooling systems to keep it functional.
It is the contention of this book that the brain's great efficiency derives from its p-adic structure, the structure of the elegant mathematics of enclosure, order, and organization.
And don't forget that it is a principle of this book that p-adic mathematics is our first mathematics, the mathematics with which, as infants, we begin to organize the world. This is why p-adic mathematics continues, during our whole lifetimes, to be the mathematics of thinking, the mathematics of the mind.
Although the postdoctoral papers exploring p-adic mathematics can be read and understood only by the few mathematicians who have succeeded at years of study of the subject, someone with even an elementary level of exposure—high school algebra, for example—may experience a deeply felt resonance with p-adic concepts by learning the basics of p-adic mathematics.
The hope is that, reading Part Two of this book, you will begin to internalize the mathematical system-p-adic mathematics—that is, the mathematics of the mind.
Chapter 11. What Is P-Adic Mathematics? We introduce and practice the basics of p-adic mathematics, and justify the claim that there are only two complete numbering systems, real and p-adic.
Chapter 12. A Vast Informational Space. The full nature of p-adic mathematics is discussed, providing an overview for why p-adic mathematics permits our minds to efficiently work with enormous quantities of information.
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PART THREE: ANECDOTES AND ANALYSIS Digital Mind Math
Chapter 13. YouTube and Google Video Search. We show how the organization of online video segments available for viewing selection is remarkably similar to the organization of the mind, as modeled in Digital Mind Math. And the process of selecting and viewing videos resembles Digital Mind Math's core cognitive quantum process.
Chapter 14. Pandora. The music streaming service Pandora does a remarkable job of grouping the details of a song to form a holistic concept. And Pandora generates possible next songs, and selects songs for us to experience, based on the principle of offering moderately novel information content for us to experience. Pandora also offers us the opportunity to affirm or contradict its selection, based on how the selection fits into the context of our own personal history of cognitive quantum transitions.
Chapter 15. Magicians. What fascinates us about watching a magician fool us? We look at our drive to figure out the magician's trickery—and at our drive to be tricked—as examples of the natural tendency toward information maximization.
Chapter 16. Boundaries. We examine how easily we create boundaries for concepts, and how adept we are at working with the interconnections among bounded concepts.
Chapter 17.The High-P Personal Style vs. the Urge to Adjust the Informational Framework. We look at personality traits and styles of interpersonal interaction that exhibit characteristics of high-p or high-negative-n p-adic tendencies, as well as traits and styles associated with the tendency to modify one's informational framework.
Chapter 18. Portals. The physical representation of Topological Geometrodynamics' CP2 four-dimensional space is illustrated by a video game and by a military strategy.
Chapter 19. Dogs and Phner: Living the Four-Dimensional Life. The life of a dog and the life of a science fiction character show what it means for each moment to be experienced four-dimensionally, as a Topological Geometrodynamics M4+ moment.
Chapter 20. Deja Vu. We look at phenomena such as the deja vu as Digital Mind Math processes, and explore functional and dysfunctinal aspects.
Chapter 21. Mrs. Wyatt Earp. Reacting to an incidental newspaper reference illustrates the Digital Mind Math core cognitive process and the continual evolution of the organization of the mind.
Chapter 22. The Obsessive-Compulsive Impulse. We look at the urge to complete a thought, and at the advantages that this urge creates.
Chapter 23. The Absent-Minded Professor. This at times comical figure exhibits high-p characteristics: master of details within his area of expertise, but at times inept at making connections, especially in areas outside of his specialty.
Chapter 24. Jokes I: Finding the Boundary. A silly joke illustrates the mind's urge to satisfactorily complete thoughts by grouping details within a bounded concept.
Chapter 25. Jokes II: To a P-Adically Larger Bounded Space. A second joke illustrates how our mind migrates to a component of the most recent thought, a p-adically larger informational space.
Chapter 26. Mysteries I: Finding the Boundary. Some mystery stories reward us for identifying the boundary around the clues, completing the story around the elements of the plot.
Chapter 27. Mysteries II: To a P-Adically Larger Bounded Space. The appeal of other movies is through a plot twist that brings the story to a p-adically larger bounded space by adding in a late detail.
Chapter 28. Where Is I? The core cognitive quantum process culminates in the experience by our conscious self of the selected thought. Each of us—where "I" is—is the accumulation of these conscious moments.
Chapter 29. Informational Structure and Its Weightings. The core cognitive quantum process adopts quantum physics' model of an experienced path selected from all possible paths, which have been probabilistically weighted based on our entire past history.
Chapter 30. Thinking, Considering, Deciding, Planning, Organizing, Wishing, Regretting, Conversing. Everyday cognitive experiences illustrate various aspects of Digital Mind Math's organizational structure and cognitive processes.
Chapter 31. Creativity and Innovation. We look at Digital Mind Math's process of possibility generation, and see how it can at times lead to disruptive novelty and innovation.
Chapter 32. Shared P-Adic Structures: Religions, Philosophies, Memes, Languages. Cultural phenomena are structured like Digital Mind Math's concepts. Individuals incorporate these structures within their own minds in order to participate in shared cultural memes.
Chapter 33. How to Solve Personal and Interpersonal Problems. Maximization of information content is the only value. Therefore, personal and interpersonal problems are solved by increasing information—the information inside individuals' minds, and the information that individuals share.
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In Part Four, we will take great advantage of a detail of p-adic mathematics—"the converse of Hensel's Lemma"—to identify:
The ideal way to think
The ideal way to interact with people
The ideal way to engage in conversation
The ideal way to act
The ideal way to live your life
Yes, this is a completely outrageous claim: There is a mathematical formula that tells us how to think, live, converse, interact, act.
We find this mathematical formula in the universal conditions that tell us when Hensel's Lemma works.
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