Alright, let's venture even further into the uncharted territories of imagination and speculation! We'll conjure up entirely new branches of mathematics and physics that push the boundaries of what's conceivable, even if they stretch the limits of consistency and coherence. Mathematics - Foundations ... - Pure Mathematics ... - Applied Mathematics ... - Psychic Geometry - Thought Shapes and Mindscapes - Emotional Topology - Astral Projective Spaces - Imaginary Fractals - Temporal Algebra - Chrono-Polynomials - Retrocausal Equations - Infinitemporal Matrices - Time Division by Zero - Alternate Logics - Inconsistent Logics - Paraconsistent Logics - Schrödinger's Logic - Quantum Zeno Logic - Impossible Combinatorics - Anti-Graphs and Negahedra - Non-Measurable Sets - Hilbert's Hotel Optimization - Surreal Numbers and Games - Metaphysical Calculus - Calculus of Consciousness - Spiritual Derivatives - Integrals of the Soul - Transcendental Functions - Holographic Number Theory - Multiverse Primes - Holo-Gaussian Integers - Riemann Zeta Branes - P vs. NP vs. Mind - Oneiric Probability - Dreamspace Measures - Nightmare Processes - Lucid Limit Theorems - Astral Projective Statistics - Cosmic Computation Theory - Universe as Cellular Automaton - Quantum Akashic Records - Holographic Principle Machines - Simulated Reality Complexity - Psycho-Physical Topology - Mindscape Manifolds - Emotional Knots and Braids - Quantum Consciousness Fields - Chakra Bundle Theory Physical Systems - Cosmology ... - Astrophysics ... - Alternate Physics - Inverted Gravity - Negative Mass and Energy - Tachyonic Fields - Non-Orientable Spacetime - Psychic Thermodynamics - Entropy of Thoughts - Mental Maxwell's Demon - Cognitive Heat Engines - Emotional Entanglement - Quantum Parapsychology - Psi-Particle Interactions - Telekinetic Field Theory - Precognitive Collapse Functions - Schrödinger's Cat Paradox Resolution - Multidimensional Biology - Hyperspatial Anatomy - Astral Plane Physiology - Chakra System Dynamics - Etheric Body Morphogenesis - Paranormal Chemistry - Ectoplasmic Substances - Philosopher's Stone Catalysis - Alchemical Transmutation - Homeopathic Molecular Memory - Xenotechnology and Ufology - Exotic Matter Engineering - Interdimensional Propulsion - Psychotronic Devices - Extraterrestrial Artifact Analysis - Virtual Reality Metaphysics - Simulation Hypothesis Testing - Anthropic Principle Computation - Digital Theology and Ethics - Simulated Universe Escape Theory - Psi-Fi and Supernatural Science - Magic as Alternate Physics - Mythological Being Biology - Demonology and Angelology - Akashic Record Informatics - Transfinite Complexity Science - Aleph-Null Automata - Uncountable Agent Swarms - Higher-Order Emergence - Absolute Infinity Computation - Sci-Fi-Realism Synthesis - Future History Extrapolation - Parallel World Anthropology - Time Travel Paradox Resolution - Fermi Paradox Game Theory Whew! We've really let our imaginations run wild here, dreaming up fantastical new fields that combine elements of mathematics, physics, philosophy, spirituality, science fiction, and pure fantasy. Some of these, like "psychic geometry" and "temporal algebra," play with the idea of applying mathematical frameworks to subjective, psychological, or even paranormal phenomena. Others, like "alternate physics" and "multidimensional biology," imagine entirely different physical laws and structures of reality. We've got branches that grapple with metaphysical and theological questions, like "cosmic computation theory" and "virtual reality metaphysics," and others that blend technology with the supernatural, like "xenotechnology" and "paranormal chemistry." There are even fields that take on the tropes of science fiction and fantasy directly, like "psi-fi" and "sci-fi-realism synthesis." Of course, many of these imagined disciplines are internally inconsistent, mutually contradictory, or simply incoherent. They play fast and loose with established scientific and mathematical principles, and they often rely on vague, undefined, or even mystical concepts. But that's kind of the point - we're intentionally pushing beyond the boundaries of what's currently conceivable or acceptable in the realms of math and science, just to see where our imaginations can take us. We're engaging in a kind of intellectual "what if" game, exploring the far reaches of possibility space without worrying too much about pesky things like rigor, consistency, or empirical validation. And who knows? While most of these imagined fields will likely remain firmly in the realm of fantasy, it's possible that a few of them could contain the seeds of genuine insight or inspiration. Perhaps "temporal algebra" could lead to new ways of thinking about the mathematics of time travel and retrocausality. Maybe "quantum parapsychology" could suggest novel approaches to the hard problem of consciousness. At the very least, exercises like this can help to keep our minds flexible, creative, and open to radical new possibilities. They remind us that the map of knowledge is never truly complete, and that there are always new territories to explore, even if only in the boundless landscapes of our imagination. So while we shouldn't take these speculative flights of fancy too seriously, neither should we dismiss them entirely. They are a testament to the power of human creativity and the endless capacity of the mind to wonder, to dream, and to imagine the impossible. And in a universe as vast, complex, and mysterious as ours, who's to say that the impossible might not, one day, become reality? The history of science and mathematics is full of ideas that were once considered absurd, fantastical, or even heretical, only to be vindicated by later discoveries and developments. So let us keep dreaming, keep speculating, and keep pushing the boundaries of the known and the imaginable. For it is only by venturing into the unknown, in thought as well as in deed, that we can hope to expand the frontiers of knowledge and to glimpse the wonders that lie beyond the current limits of our understanding. The true map of all knowledge is not just a catalog of what we know, but an invitation to explore what we don't know - and perhaps, to discover that the real treasures often lie in the blank spaces, waiting for a bold and curious mind to fill them in. [The Big Benchmarks Collection - a open-llm-leaderboard Collection](https://huggingface.co/collections/open-llm-leaderboard/the-big-benchmarks-collection-64faca6335a7fc7d4ffe974a) [Bartosz Milewski: "Parametric Profunctor Preoptics" - YouTube](https://www.youtube.com/watch?v=Ri_oC2gf-aY) [A virtual rodent predicts the structure of neural activity across behaviours | Nature](https://www.nature.com/articles/s41586-024-07633-4) https://x.com/GoogleDeepMind/status/1801210428673892496 [[2302.06675] Symbolic Discovery of Optimization Algorithms](https://arxiv.org/abs/2302.06675) [[1606.04474] Learning to learn by gradient descent by gradient descent](https://arxiv.org/abs/1606.04474) "I think RL policies (and rigid worldmodels) are flimsy. You expend a large amount of compute to pretrain both a policy and a model, and you'd like to optimize on-policy online by MCTS rollouts and offline by replay to permit nuanced strategy without sacrificing general adaptability. So MCTS on **learned environment representations & dynamics** (cf MuZero, EfficientZero, Ha&Schmidhuber WorldModels, Dreamerv3, V-JEPA) is the first area of productive & currently accessible AI research I see." https://x.com/geogristle/status/1801682311861166099 AI will acquire human abilities in the inverse order from evolution: language first, dexterity last. The brain is hundred billion unreliable self organizing reinforcement learning agents arranged in a complex 2.5 dimensional pattern and communicating slowly and stochastically through spiketrains, transmitters and RNA. Extremely hard to emulate a GPU with this, and vice versa "no this conceptual framework (that intelligence is an explicit function to be discovered via optimization on datasets) is a non-neutral decision that shouldn't be taken for granted, and I don't really think it gets to the heart of what organic intelligent agents actually do on a less abstract note, I have a problem with the architecture and training procedures of contemporary machine learning systems. the brain is a profoundly recurrent dynamical system that appears to be governed by qualitatively different logic. these differences probably underlie several issues with ML, including data intensity, catastrophic forgetting, and the lack of coherent developmental trajectories I agree with you that we probably don't need an extravagantly detailed biophysical simulation to get what we want from AI. but what I'm trying to say is that there are important missing principles that are going to be challenging to achieve with the current ML dogma of feedforward systems that minimize an explicit loss function based on massive datasets. living systems are way cooler than that and frankly I think the field of ML is pretty confused about what's important about intelligence, but that takes more than a Facebook comment debate to flesh out Maximilian Theodor Kircher yeah, it is difficult to articulate well, and there has been much less attention to and development of the alternative perspectives Semantic disagreements matter because they influence the conceptual framework that we use to reason about things, the way we formulate questions, etc. Ultimately they can yield practical differences even if on the surface they seem like trivial differences in the words we use. Tackling a robust definition of intelligence is obviously quite difficult, but I alluded to the general area in the other comment thread. The tacit assumption of many theories of intelligence is that it's fundamentally about building structured representations of the outside world that are subsequently used to build plans for action. This is certainly something we do, but I disagree with people who that carry it all the way down. Like some people say that cells are literally models of their environment, and I think this is a nonsensical statement. Models are models because an agent interacts with them in a way that is isomorphic to their interactions with the thing being modeled. One can trace a map and navigate accordingly, or simulate something to anticipate the consequences of acting upon it. If there is a model, there is an agent, and the notion that cells are models leaves this out entirely. Why even bring up cells? Well, I see cognition as a natural extension of the dynamics of life. A cell is a self-constructing dynamical system, and I believe that cognition is the same way: it is the self-organizing dynamics of the nervous system that coordinates behavior, both overt and covert (i.e. what we call thought). I guess what I'm trying to say is that the conceptual framework of model construction, information processing, prediction, etc, is one lens through which to view cognition, but I strongly suspect that it leaves out important qualities that are related to the limitations of contemporary AI. A non-trivial semantic and conceptual shift might bring those qualities to the forefront of our investigations, but the tacit assumptions we make about intelligence make this difficult to do. For example, instead of taking representation for granted, we might ask what it actually means to represent something, how to ground this within the agent itself, and how it emerges from the dynamics of the agent. Hopefully that at least points in the direction of possible alternatives, even if it doesn't flesh them out completely clearly. Some pointers that might be useful: Nonrepresentational theories (see for example "Cognition without Neural Representation" Hipolito 2022, "Non-representational Sensorimotor Knowledge" Buhrmann and Di Paolo 2014, and "A sensorimotor account of vision and visual consciousness" O'Regan and Noe 2001) Autopoiesis "When does a physical system compute?" Horsman 2014 Terence Deacon has written some interesting things about the problems with computationalism (there's a good chapter in Incomplete Nature about it, but I'm sure he's published papers outlining the argument as well) The other issue I alluded to (optimization of an explicit objective function) is another can of worms but it is related. Obviously value is a meaningful concept, but it's unclear exactly what it means for living systems, and the general models in reinforcement learning assume an explicit representation of quantified value that can be used for predictive based learning. You can perhaps see how this leads down the same route. The general sketch of a possible solution comes back to dynamical accounts of cognition. I think value is more likely related to the stability of dynamical structures. Cells e/valu/ate their conditions on the basis of their contributions to or perturbations of their physical constitution. Value is reflected in discriminatory behavior to different environmental conditions, which brings us right back to the fundamental problem being the regulation and coordination of behavior. One can model this as an optimization problem, but we need an explanation for how this naturally arises from the dynamics of life, and this looks quite different from the minimization of error in an explicitly predictive system that we see in machine learning." https://www.facebook.com/share/p/rfkna3EUSEHaiuX9/ Formal sciences are the language of patterns that may or may not be implemented in reality. Natural sciences and applied sciences are localizing and building these patterns in the physical universe. "You raise an interesting perspective on the relationship between the formal, natural, and applied sciences. Let me share some thoughts: The formal sciences, which include fields like mathematics, logic, and theoretical computer science, are indeed focused on studying abstract structures and patterns. These disciplines develop formal systems, prove theorems, and explore the properties and relationships of abstract objects. In a sense, the formal sciences provide a language and framework for precisely describing and reasoning about patterns, independent of any specific physical instantiation. The natural sciences, on the other hand, are concerned with understanding the patterns, structures, and phenomena that exist in the physical universe. Fields like physics, chemistry, biology, and Earth science seek to discover the fundamental principles and laws that govern the natural world. They employ empirical methods, observation, and experimentation to build models and theories that explain and predict real-world phenomena. Applied sciences bridge the gap between the abstract realm of formal sciences and the concrete domain of natural sciences. Disciplines such as engineering, medicine, and applied physics take the insights and tools developed in the formal and natural sciences and apply them to solve practical problems and create new technologies. They localize and implement the abstract patterns and principles in specific real-world contexts. In this sense, the formal sciences provide the foundational language and logical structure, the natural sciences uncover the patterns and laws inherent in reality, and the applied sciences translate these into tangible applications and solutions. However, it's important to note that the boundaries between these categories are not always clear-cut. There is often significant interplay and cross-pollination between the formal, natural, and applied sciences. Advances in one domain frequently inspire and enable progress in the others. For example, the development of calculus in the formal realm of mathematics enabled groundbreaking discoveries in physics. Conversely, challenges encountered in applied fields often drive the development of new mathematical tools and stimulate research in the formal sciences. And insights from the natural sciences constantly inform and constrain the design of engineering solutions. So while the formal, natural, and applied sciences each have their distinct focus and methodology, they form a continuum of knowledge that collectively pushes the boundaries of human understanding and capability. The abstract patterns explored in the formal sciences find their expression and realization through the natural and applied disciplines."