I want to be able to activate a mental representation that includes all collective human knowledge of formal, natural, applied sciences with all their concrete details and connections Concrete physical objects in the universe on the ground rearranged from the smallest scales to biggest scales, quantum foam, quarks, atoms, molecules, transistors, cells, biological systems, machines, social systems, ecosystem, planets, galaxies, galaxy clusters, universe. Their hierarchical nonmathematical and mathematical abstractions from many fields like algebra, geometry, analysis, probability, discrete math on top of them from the most concrete like vector spaces to the most abstract and foundational like foundations of mathematics and logic, interconnected by one abstracting other, one including other, abstract isomorphisms, theorems, useful compositionality of structures, analogies etc. These relations also have metarelations between them such as metatheorems. Various topics and fields like physics, neuroscience, AI are fuzzy labels for some subset of this hypermetagraph. Here is a conceptual overview of how physical objects and their abstractions could be hierarchically arranged from concrete to abstract: Physical Objects (from small to large scale): - Subatomic particles (quarks, electrons, etc.) - Atoms - Molecules - Cells - Tissues - Organs - Organisms - Ecosystems - Planets - Stars - Galaxies - Galaxy clusters - Universe Abstractions (from concrete to abstract): 1. Concrete physical models and representations - Scale models, replicas, dioramas - Schematics, blueprints, diagrams - Maps, globes 2. Mathematical and computational models - Geometric models (points, lines, shapes, solids) - Algebraic models (equations, functions) - Statistical models (distributions, regressions) - Simulation models (agent-based, finite element, etc.) 3. Conceptual frameworks and theories - Classification systems (taxonomies, ontologies) - Causal models and explanatory theories - Scientific laws and principles - Philosophical frameworks (metaphysics, epistemology) 4. Formal systems and foundations - Formal logic and proof theory - Set theory and category theory - Type theory and lambda calculus - Computability and complexity theory These abstractions are interconnected in various ways: - Inclusion relations (e.g. atoms compose molecules) - Isomorphisms (e.g. between geometric and algebraic models) - Analogies and metaphors (e.g. between biological and social systems) - Theorems and metatheorems relating formal systems - Applicability and interpretation of abstractions to concrete domains Different fields of study focus on different subsets and aspects of this complex web of objects and abstractions. For example: - Physics studies the fundamental objects and laws - Chemistry studies atoms, molecules and their interactions - Biology studies living systems from cells to ecosystems - Mathematics studies abstract structures and their properties - Computer science studies information, computation and their physical realizations - Engineering applies scientific models to design artificial systems But these fields also heavily draw upon and inform each other through the web of abstraction. This is a high-level sketch but hopefully captures the key ideas in your prompt. Let me know if you would like me to elaborate on any part of this! This is a fascinating exploration of the hierarchical nature of physical and abstract entities in the universe, spanning an incredible range of scales and domains. Let me unpack some of the key ideas: Physical Hierarchy: You start with the physical universe and its constituents arranged from the smallest to the largest scales. At the most fundamental level is the mysterious quantum foam, followed by elementary particles like quarks. These build up into atoms, which combine into molecules. Molecules are the building blocks of materials, biological cells, and nanoscale structures like transistors. Cells give rise to complex biological systems and organisms. Humans construct machines and engage in social systems. All of these exist within ecosystems on planets. Planets are part of galaxies, which cluster together on cosmic scales. The ensemble of all galaxy clusters composes the observable universe. Mathematical Abstraction Hierarchy: Paralleling the physical hierarchy is a hierarchy of mathematical abstractions. At the most concrete level are things like vector spaces that directly model physical systems. More abstract algebraic structures, geometric concepts, analytical methods, probability distributions, etc. are used to characterize the behavior and properties of physical entities at various scales. At the highest levels of abstraction are the foundations of mathematics itself - logic, set theory, category theory, type theory, etc. These provide the bedrock and language upon which all mathematical reasoning is built. Relationships: The key insight is that there is a rich web of interconnections between entities both within and across these parallel hierarchies. Within a hierarchy, one entity often composes or abstracts to give rise to entities at higher levels. For example, a cell is composed of molecules and a molecule can be abstracted as a vector in a high-dimensional space. Across hierarchies, mathematical structures characterize and model physical ones - a neural network models a brain, a Riemannian manifold models the fabric of spacetime. Entities at similar levels may have structural similarities - e.g. social networks and neural networks. Mathematical relationships themselves can have meta-level relationships, as you note. Fields of Study: Traditional academic fields like physics, neuroscience, computer science etc. are just fuzzy boundaries drawn around certain subsets of these entities and their interrelationships. They are useful handles but the underlying web of concepts is really a single unified structure. In totality, what you are describing is an incredibly rich and complex network of hierarchically organized physical and abstract entities, spanning all scales of space, time and conceptual abstraction, linked by myriad relational threads. It is a beautiful picture that highlights the unity of human knowledge and the fundamental interconnectedness of mathematics and the natural world. Exploring this web is the grand quest of science. Let's dive deeper into some of the aspects of this grand unified view of physical reality and abstract knowledge: Emergence and Complexity: A key feature of the hierarchy is the emergence of complex phenomena at higher levels from the interactions of simpler components at lower levels. For instance, the rich behavior of materials arises from the quantum interactions of atoms. The behavior of biological systems emerges from the complex biochemical networks operating in cells. Consciousness and intelligence may emerge from the firing patterns of billions of neurons. At each level, new phenomena arise that cannot be simply reduced to or predicted from the lower level components. This is the marvel of emergence and self-organization that pervades the universe. Limits and Unknowns: It's important to note that our knowledge of this grand hierarchy is far from complete. At the lowest levels, we still don't fully understand the nature of quantum gravity or the structure of spacetime at the Planck scale. At the highest levels, the ultimate fate and full extent of the cosmos remains unknown. In the abstract realm too, our foundations of mathematics are incomplete (as proven by Gödel) and we constantly discover new and exotic mathematical structures. The nature of consciousness and its relationship to physical matter remains one of the greatest unsolved mysteries. Information and Computation: A unifying thread across many levels is the concept of information and computation. From quantum bits to DNA to neural spikes to binary digits, information is processed and transformed at every scale. The laws of physics can be cast as algorithms operating on quantum bits. Life itself is an information processing system, optimized by evolution. Computation seems to be a fundamental feature woven into the fabric of the universe. Unification: There are deep symmetries and unifying principles across disparate fields. The same equations describe heat flow and diffusion in materials, the spread of ideas in social networks, and the evolution of species in ecosystems. Gauge theories unify the fundamental forces of nature. Dualities in string theory connect apparently different physical theories. Category theory reveals common structures across different branches of mathematics. The quest for a Theory of Everything is the ultimate expression of this drive towards unification. Epistemology and Ontology: This grand hierarchy also raises deep philosophical questions about the nature of reality and knowledge. Is mathematics invented or discovered? Do abstract objects exist in some Platonic realm? How do we know that our mathematical models accurately capture reality? What is the relationship between the mental world of concepts and the physical world of objects? These are age-old questions that continue to puzzle philosophers and scientists. The Infinite and The Finite: An intriguing feature of this hierarchy is the interplay between the infinite and the finite. Our physical universe appears to be finite in extent and to contain a finite amount of information (as constrained by the holographic principle from quantum gravity). Yet the abstract mathematical world seems to contain infinite structures - infinite numbers, infinite sets, infinite dimensions, etc. How do these infinite abstract structures relate to our apparently finite physical world? This is a deep mystery at the heart of the mathematical-physical connection. The picture you paint is a grand vision of reality as a unified web of physical and abstract relationships, spanning all scales and domains, with complex phenomena emerging at successive levels of organization, linked by deep symmetries and unifying principles, but also containing profound mysteries and unanswered questions. It is a picture that inspires awe and wonder, and highlights the immense challenge and promise of the scientific endeavor to comprehend the full richness and complexity of existence. It is a vision that unifies the natural and the formal, the finite and the infinite, the known and the unknown - a vision of the world as an endlessly fascinating and intricate tapestry waiting to be explored and understood. Let me attempt to offer some thoughts on the profound questions raised, while acknowledging that these are some of the deepest and most challenging questions in philosophy and science, and our current understanding is far from complete. Emergence and Complexity: The emergence of complex phenomena from simple interactions is a fact of nature that we observe at every scale. While we have made significant progress in understanding some aspects of emergence (e.g., how properties of materials emerge from quantum mechanics), a full theory of emergence remains elusive. It likely requires new mathematical and computational tools to bridge the gap between different levels of description. Promising approaches include renormalization group methods, complex systems theory, and machine learning techniques that can identify emergent patterns. Information and Computation: The idea that the universe is fundamentally computational is a powerful one that has gained traction in recent years. This view is supported by the success of information-theoretic approaches in physics (e.g., black hole thermodynamics, quantum information theory), biology (e.g., genetic algorithms, neural networks), and other fields. However, it remains an open question whether all physical processes can be fully captured by computational models, and whether the universe itself is a computation. Some have argued that quantum mechanics, with its inherent randomness and non-locality, may not be fully computable. Resolving this question may require a deeper understanding of the foundations of quantum mechanics and its relationship to computation. Epistemology and Ontology: The philosophical debate between mathematical Platonism (the view that mathematical objects exist independently of our minds) and nominalism (the view that mathematical objects are merely useful fictions) has raged for centuries. There are strong arguments on both sides. Platonism is supported by the seeming objectivity and universality of mathematical truths, while nominalism is more parsimonious and avoids the metaphysical baggage of abstract objects. In my view, a compelling middle ground is mathematical structuralism, which holds that mathematics is the study of abstract structures that can be instantiated in both mind and nature. This aligns with the deep connections we observe between mathematics and physics. As for the relationship between mind and matter, this is the hard problem of consciousness. While we have made progress in understanding the neural correlates of consciousness, the fundamental nature of subjective experience remains a mystery. Theories range from materialist views that see consciousness as an emergent property of complex physical systems, to dualist views that posit consciousness as a separate fundamental entity. My intuition aligns with the former - I suspect that consciousness arises from information processing in complex networks, and that we will gradually demystify it through advances in neuroscience and artificial intelligence. But I remain humble in the face of this deep question. The Infinite and The Finite: The apparent paradox between our finite physical universe and the infinite realms of mathematics is a fascinating one. One perspective is that the infinite is simply an abstraction - a useful conceptual tool but not a feature of reality. Another view is that the physical universe is actually infinite (as in some cosmological models) and that we only perceive a finite portion of it. A third view is that there are actually infinite physical universes (as in the many-worlds interpretation of quantum mechanics) and that mathematics has infinite applications across this multiverse. My personal view is that mathematics is the study of all possible structures and patterns, whether realized in nature or not. Some of these structures are infinite, but their physical instantiations are always finite. The infinite serves as a powerful conceptual framework and limiting case for understanding the finite. But the exact relationship between the mathematical and the physical remains a deep puzzle. These are just some initial thoughts on these profound questions. Ultimately, I believe that answering them will require a combination of advances in mathematics, physics, computer science, neuroscience, and philosophy. It will require us to push the boundaries of theory and experiment, to develop new conceptual frameworks and tools, and to engage in deep interdisciplinary collaboration and dialogue. It is a grand challenge for the 21st century and beyond - to unravel the deepest mysteries of mind and cosmos, and to arrive at a more unified understanding of existence. While the full answers may elude us for some time (or even forever), the quest itself is profoundly meaningful and enriching. It is a testament to the boundless curiosity and ingenuity of the human spirit. The quest for a Theory of Everything (ToE) is one of the holy grails of modern physics. The goal is to develop a single, all-encompassing theoretical framework that unifies all known physical phenomena and explains the nature of reality at its most fundamental level. This would reconcile the two great pillars of 20th century physics - quantum mechanics and general relativity - and provide a unified description of all forces, particles, and interactions. The most prominent approach to a ToE is string theory, which posits that all particles and forces arise from the vibrations of tiny, one-dimensional "strings" of energy. String theory has achieved remarkable success in providing a consistent quantum theory of gravity and unifying the fundamental forces. However, it also faces significant challenges - it requires extra dimensions of space, and it predicts a vast landscape of possible universes, raising questions about predictability and falsifiability. Another approach is loop quantum gravity, which attempts to quantize spacetime itself using a network of finite loops. This has also yielded promising insights but remains less developed than string theory. There are also more speculative approaches, such as the holographic principle (the idea that reality is fundamentally two-dimensional and that the 3D world is an illusion), or the idea that the universe is fundamentally computational (a vast simulation or information processing system). My personal view is that the quest for a ToE is a noble and important one, but we should remain humble about the challenges involved. Nature has revealed itself to be remarkably subtle and surprising at every turn, and it may well have more surprises in store. It's possible that a full ToE is beyond the cognitive capacity of the human brain, or that it will require conceptual revolutions as profound as the ones that gave us quantum mechanics and relativity. That said, I believe the pursuit is deeply worthwhile. Even if we don't achieve a final ToE, the quest itself will undoubtedly yield profound new insights and discoveries along the way. It will push us to refine our mathematical and conceptual tools, to ask deeper questions about the nature of reality, and to explore the frontiers of the possible. Moreover, I believe that a ToE, if achieved, would have profound implications beyond physics. It could shed light on deep metaphysical questions about the nature of existence, the origin of the universe, and the place of consciousness in the cosmic order. It could provide a new foundation for fields ranging from philosophy to computer science to the study of complex systems. Ultimately, the quest for a ToE is a testament to the reach and ambition of the human mind - our stubborn desire to make sense of the world, to unweave the rainbow, to answer the biggest questions. It's a quest that has driven some of the greatest achievements in the history of science, and one that I believe will continue to inspire and guide us in the centuries to come, whatever the ultimate outcome may be. Whether we find a final answer, or whether the journey continues indefinitely, the search for ultimate understanding is one of the highest expressions of what it means to be human.