The holy grail is to create the most predictive and explanatory (mathematical) model/s of everything in this physical universe across all levels of reality, including many information processing systems, including foundational physics. Scientists have finite time in their lives, but longevity and immortality could give them more time. Scientists have finite limited brains, but transhumanist upgrades to brains could enhance their intelligence towards this goal. And computers, AIs, machines broadly, and posthumans can also contribute in out-of-distribution ways, and at scales beyond our current comprehension. I want a gigantic mind palace of all possible mathematical patterns (objects, structures, equations, theorems,...) across all possible abstraction levels, that as a subset include all possible physically possible objects, that as a subset include all physical objects that currently exist, ever existed, and will exist, that as a subset include all physical objects that currently exist, with all correspondences between them highlighted " I wish we had a mathematical theory that predicts all the potential capabilities and exact limitations of artificial neural networks much more generally than what we have so far in current theory, that is made from what we know so far empirically. And I wish we had a more general predictive mathematical theory of machine learning more generally, of artificial intelligence more generally, and of intelligence, and of information processing in general. But we don't have that. Yet. It is one of the holy grails of science to reach. One of the holy grails that many of the smartest minds on this planet try to work on, and slowly make progress on. In AI, we're in a stage similar to when steam engines were developed and worked, but the mathematical theory of thermodynamics, that grounded much more why they work, and what are their limitations, came like 100-150 years later, and opened countless others previously unthinkable possibilities thanks to discovering many general principles of phenomena in thermodynamics, like entropy. Which, among many other big scientific theories, enhances our technology to this day. We have just bits of this holy grail so far. So far we have: - a bunch of empirical results like finding what the models can do already now in practice, like surprisingly relatively coherent generation of code or mathematics in its extremely high dimensional space of possibilities - a bunch of empirical analyses like finding some of the emergent circuits that are present in the models as they solve various tasks, like the geometric rotating of manifolds when doing linebreaking, that have various kinds of structure, that is sometimes less optimal, and sometimes more optimal, or directions that gradient descent tends to favor flatter minima - a bunch of partly unifying theory that is predictive in different ways, like various ways to generalize and predict the found emergent circuits, or applying statistical physics on training dynamics, or proving some properties in the network's infinite width limit in neural tangent kernel theory - a bunch of somehow, somewhat, in some ways working, systems to study, like all the models out there, built using a bunch of duck taped empirical recipes like scaling laws, common tricks around training algorithms or common architectures choices, like AdamW with transformers - and other things We don't really fully know why and how does gradient descent find so many of the solutions that it's finding in the highdimensional nonconvex landscapes, growing so many emergent representations in the nonlinear neural network architectures like transformer in the process, and what is it's full potential and what is it's absolute limitations, and how to predict it much more. We don't fully know what all can still be improved and what all is at its limits. There are so many unsolved open questions in this whole scientific field. There is so much potential for empirical experiments and theoretical unifying and novel predictions. This is still a largely open scientific problem for many curious minds to solve, that are trying to solve it, and making slow progress together collectively, more and more with the help of AIs themselves. " Towards "unification between physics and computer science to understand the relationship between energy and information" https://x.com/hadivafaii/status/2033653562774007812 The universe is undergoing a grand and majestic self-organizing process, and at this moment in time, in this corner of the universe, we are the stars of the show " Walking around in nature and looking at everything and seeing how it's made of quarks that compose with more fundamental forces into atoms that compose into chemical elements into molecules and more complex proteins and into biological bodies and other more complex structures together it's absolutely fascinating all of that makes you feel like you're seeing through the simulation's code and it's absolutely glorious feeling and it feels like everything is just decomposing into these atomic parts and that's extremely euphoric. Walking through nature, you start to see everything in layers. Every object, every living thing, is made of quarks — bound together by fundamental forces into atoms, which combine into chemical elements, then into molecules, then into complex proteins, and finally into biological bodies and still larger structures. Once you perceive this, it's as if you're reading the simulation's source code. The world around you quietly decomposes into its atomic parts right before your eyes. The trees, the soil, your own hands — all of it resolves into the same elemental building blocks, assembled by the same deep logic. The feeling is euphoric. Not unsettling, but glorious — like being granted a glimpse behind the curtain of reality itself. " https://www.youtube.com/watch?v=ukpCHo5v-Gc Terrence Tao Brian Keating Biology is to first approximation a subset of dissipative self-replicating physical systems that are far from thermodynamic equilibrium by continuously eating free energy and spitting out entropy Complexity explosion is happening since the first technology, since the first human, since the fist mammal, since the first animal, since the first cell, since big bang. " scifi story or game idea: final boss is acually not final, and there's meta final boss, and meta meta final boss, and meta meta meta fin... that gets more and more insane until the game simulation breaks under its load and you wake out of the matrix, but that matrix itself lives in a meta matrix, and that one in meta meta meta matrix, and that one in meta meta... and then void eats everything, and even that void gets eaten by meta void, and meta meta void, and... until there are just random patterns with infinite complexity until the heat death of the universe, but you manage to survive the heat death of the universe and get big crunched into another universes endlessly heat death after heat death until you escape into other multiverses, and meta multiverses, and meta meta multiverses but then you wake up out of physical multiverses into platonic mathematical universes that cannot be implemented then you become all possible concepts and eventually all possible qualia and neither nothing nor everything and all of it at the same time 🌀 " " I love flying in mathematical abstractions i ncategory theory But now my path is more towards deeper understanding of mathematical and physics theories of deep learning (or AI and intelligence more generally) And towards deeper understanding the mathematics of the standard model of particle physics, general relativity, and maybe attempts at their unifications There's so much more math describing everything in the physical and platonic world that I want to understand I will need more than one lifetime and more than this limited biological lifeform for understanding it all " according to wolfram and other fans of computational physics, every single physical system is computational when superhuman levels of reverse engineering the structure of the intelligence and of the universe for the sake of curiosity Creativity I want her equation I will get her equation one day Someone: "its just adding noise to function describing gradient of the goal" Myslím že je v tom víc, i když tohle je taky součást hodně typů kreativity Přidání šumu může zvětšit robustness nebo vytvořit míň pravděpodobný výsledky Ale furt mi příjde že u dost typů kreativity je i nějaká deterministická část V tvý formalizaci by možná kreativita byly random forces v langevin rovnici https://en.wikipedia.org/wiki/Langevin_equation Na Langevin dynamice jsou založený i diffusion modely https://en.wikipedia.org/wiki/Diffusion_model Mám pocit že pro stronger out of distribution kreativitu co zároveň produkuje prediktivní modely existuje nějaký deterministický faktor co jsme ještě nenašli diffusion modely jsou pod většinou image/video modelama a teď to začíná být i pod text modelama víc a víc, nebo se hodně používají ve vědě specializovaně the fact that diffusion models learn to make structure out of noise is the most mindblowing thing ever to me it uses nonequilibrium thermodynamics the second law of thermodynamics reversed and biological life also resists the second law of thermodynamics globálně druhý thermodnamický zákon život akceleruje konvertováním pockets negentropie do entropie How does quantum mechanics prove free will? If quantum randomness was influenced by free will, then by definition, it wouldn't be random, but determined. And afaik there's not much important enough quantum stuff really happening in the brain according to current empirical investigation. Quantum mechanics "picks" an option at random in it's math Classical chaos theory is deterministic There's also quantum chaos theory where it's random again. >we dont have enough info of quantum phenomena to see the deterministic pattern This branch of thought is called hidden variable theories, and the most currently discussed model seems to be superdeterminism that I linked above, and people critique that one a lot https://en.wikipedia.org/wiki/Hidden-variable_theory In what way could quantum gravity allow free will? I fail to see any possibility. One issue why I struggle to see the connection is that quantum gravity is iirc relevant at very microscopic scales, at very high energies, so idk how that relates to the brain choosing actions https://en.wikipedia.org/wiki/Quantum_gravity I think there's a way to model the feeling of free will computationally in the brain as an agent that is weighting and picking different actions with policies, like in reinforcement learning, but I think all of that is an emergent pattern on top of fundamental physics, just like gliders in Conway's game of life cellular automata https://en.wikipedia.org/wiki/Reinforcement_learning https://en.wikipedia.org/wiki/Conway's_Game_of_Life I think reinforcement learning can help this, here's it discussed in the brain here https://www.princeton.edu/~yael/Publications/Niv2009.pdf I like this model of emergent complexity: Software in the natural world: A computational approach to hierarchical emergence https://arxiv.org/abs/2402.09090 I think we might also be a form of software https://youtu.be/34VOI_oo-qM?si=8P_ruvMaFl7OimCR Maybe we are emergent selforganized causal pattern that colonizes hardware (cells, biophysics, future silicon neurons,...) Interested in quantum gravity computers doing computation with indefinite causal structure under causaloid formalism? Quantum gravity computers: On the theory of computation with indefinite causal structure https://arxiv.org/abs/quant-ph/0701019 How would an AI working like this look like? Circular levels of generalization: Mathematics of our physical universe -> Mathematics of the space all possible universes -> Space of all possible mathematics -> Space of all possible philosophical constructions -> Space of all possible thoughts -> Space of all possible qualia experienced by the space of all possible minds implemented in the space of all possible universes How does the Hamiltonian of consciousness look like? Minds are quasi-particles https://www.youtube.com/watch?v=-G1SdsRXL7k Free will is in some sense a representation of computational irreducibility. It's a representation that you yourself are making that you cannot predict your own decision before you make it. https://www.youtube.com/watch?v=-G1SdsRXL7k Nebo jsem včera přemýšlel v kontextu teorii kategorií v čistý abstraktní matice: existuje kategorická kvantová mechanika a kategorický deep learning jako dva odděleny odlišný obory, tak by mě zajímalo, či někdy někdo dělal něco na intersekci, tím že existuje dost věcí na intersekci fyziky a deep learningu, a tím že teorie kategorií je taková matematická lingvistika matematiky. Ale nic jsem nenašel na intersekci. Kontext: https://en.wikipedia.org/wiki/Categorical_quantum_mechanics https://arxiv.org/abs/2402.15332 There are so many fun rabbitholes everywhere, so many berries, so much fun stuff in philosophy, mathematics, science, engineering, etc.! But it's impossible to explore all those rabbitholes, to eat all those berries, on your own, since there's not enough time and energy. But because there are so many curious people/creatures out there, it's very likely that someone out there is eating/will be eating that berry, that you don't have time for, so no berry stays uneaten in our collective intelligence! How to create or automate the creation of entities that create outputs that are as out of distribution as possible, while still making sense to human pattern recognition machinery, and either giving us all sorts of interesting emotions like art, or being scientifically useful like scientific discoveries, or mathematically interesting like mathematical results, or philosophically interesting like philosophical theories? " https://schema-harness.github.io/ "Today, we’re introducing [schema]: a harness reaching 99% RHAE with Opus 4.8 + Fable 5 and 95.35% with GPT-5.6 Sol on ARC-AGI-3 Public set. ︀︀ [schema] makes an LLM think like a physicist." Observe, code it up, try to find counterexamples in the real world, update simulation, code a solver for the simulation, try it and loop until it works. The model observes the world, makes a simulation of it, then tries beating it, if the simulation mispredicts it tries correcting it or gathering evidence that could falsify it and tries again. Attempts at replicating parts of scientific methods works! Also I wonder to what degree can you use the trajectories (data) in this harness (that uses llms to generate symbolic programs) for fine-tuning the agents. And how can you turn this into scientific method RL env more properly. Or design more deeply neurosymbolic architectures. I'm thinking of extending it with more possible aspects of the scientific method. In empirical sciences, I believe automated approximations of parts of scientific methods will require loops in this style more: "define domain -> define question in the domain -> gather existing information, data, models related to it -> formulate a hypothesis based on it -> gather more empirical data by experiments to test the hypothesis -> analyze, interpret data, draw conclusions -> refine hypothesis according to that -> test with experiment -> refine with theory -> test -> refine -> replicate ->..." Also since some scientists like Galileo basically broke the scientific method, and still found novel predictive and explanatory models, then I do wonder if some of that can also be put into an algoritm, and get useful results in scientific discovery [https://youtu.be/v7a65AvELdU](https://youtu.be/v7a65AvELdU?is=2xplwF2mnfx__an3) Damn this makes me excited. Automating science is probably the biggest thing for me. I think actual open problems solved in formal and empirical sciences is the real benchmark. The amount of them, and their difficulty. From simplest Erdos problems to stuff like solving Riemann hypothesis to somehow solving quantum gravity or just stuff like incremental better differential equations that model some system. The difficulty of open problems are on a spectrum. But on the top of the mountain, I'm gonna be the most impressed when an AI system builds novel more out of distribution mathematical mountain/s of languages and abstractions to solve a problem in a completely different domain. Analogous to modern algebraic geometry by Grotenderick, or modularity theorem for fermat's last theorem, or coming up with quantum mechanics/relativity. For all of this you need to more properly automate science. But a lot of it is also hard to verify, so RL isn't sufficient. And Goodheart's law is creeping up everywhere. Big part of the puzzle is probably also discovery in domains without clear goals, without clear objectives, without clear metrics, that are good for hillclimbing with reinforcement learning. I like approaches trying to attack this problem space with evolutionary methods, divergent search, novelty search, etc. that Stanley et al propose. But there's still a lot to be done here. I do think some future automated scientist architecture will merge Cholletian neurosymbolic program synthesis in Popperian/Kuhnian/Quineian/Feyerabendian scientific method loop, with Stanleyian/Clunian divergent open-ended search that never stops accumulating information, and Suttonian reinforcement learning. And mixing these approaches, depending on the task. Sometimes you want to climb clear mountains of verification signals or mountains of abstractions. Sometimes you want to divergently explore the novel unknown without any concrete goal in mind. Sometimes you want neural/statistical, in big part black box, models. Sometimes you want symbolic white box models. Sometimes hybrids. Sometimes symbolic models are too rigid, but sometimes they predict better, are simpler, have better explanatory power, and generalize and adapt better (lots of physics). Sometimes neural models are too brittle, but sometimes they predict better, are simpler, have better explanatory power (sometimes after reverse engineering maybe), and generalize and adapt better (classifying certain images). Sometimes something combining those in the middle gets you to better local minima (some physics models). " The more we can expand the scope, diversity and scale of intelligence, the better we can understand what questions to ask about the universe, platonic realm and overall reality, to understand the nature of it all, with more predictive and explanatory power