Learn equations governing all levels of reality, from scalefree contextfree ones to very specific concrete ones and all general models connecting them all together! ### Foundational Concepts and Theories 1. **Principle of Least Action** - A variational principle that, in physics, states that the path taken by a system is the one for which the action is minimized, forming the basis of classical mechanics, quantum mechanics, and general relativity. 2. **Symmetry Principles** - Fundamental in physics and mathematics, these principles state that certain properties remain invariant under specified transformations, leading to conservation laws such as conservation of momentum and energy. 3. **Conservation Laws** - Fundamental principles in physics that assert certain quantities remain constant within an isolated system as it evolves over time, including conservation of energy, momentum, charge, and mass. 4. **Uncertainty Principle** - In quantum mechanics, this principle highlights the fundamental limit to the precision with which pairs of physical properties, like position and momentum, can be simultaneously known. 5. **Entropy and the Second Law of Thermodynamics** - This law states that the total entropy of an isolated system can never decrease over time, signifying the natural tendency of systems to progress toward disorder or equilibrium. 6. **Relational Theory** - In philosophy and sociology, this framework focuses on the significance of relationships and interactions between entities, proposing that entities only exist within and because of their relations to other entities. 7. **Evolutionary Theory** - Goes beyond biology to be applied in technology, culture, and knowledge, suggesting that complex systems evolve over time through processes of variation, selection, and inheritance. 8. **General Systems Theory** - Proposes that complex systems share organizing principles which can be discovered and modeled mathematically, applicable across physical, biological, and social systems. 9. **Network Science** - A multidisciplinary field that studies complex networks such as telecommunications networks, computer networks, biological networks, cognitive and semantic networks, and social networks. 10. **Principle of Relativity** - States that the laws of physics are invariant (identical) in all inertial frames of reference, which has profound implications in both classical mechanics and modern physics. 11. **Quantum Field Theory (QFT)** - A theoretical framework that combines classical field theory, special relativity, and quantum mechanics, used to construct quantum mechanical models of subatomic particles and their interactions. 12. **Cognitive Science Theories of Mind** - Integrating equations from psychology, artificial intelligence, neuroscience, linguistics, anthropology, and philosophy to understand the nature of thought, intelligence, and consciousness. 13. **Algorithmic Information Theory** - Combines elements of information theory and computer science to study the complexity and randomness of objects, using concepts like Kolmogorov complexity. ### Transdisciplinary Approaches 1. **Interconnectivity and Interdependence** - Recognizes the inherent connections and dependencies across systems, suggesting that changes in one part of a system can have far-reaching effects throughout the system. 2. **Adaptive Systems Theory** - Focuses on how systems adapt to changes in their environment through processes of learning, evolution, and self-organization. 3. **Sustainability and Resilience Theory** - Examines how systems endure and thrive by maintaining their viability, absorbing disturbances, and adapting to change. ### Fundamental Mathematics and Logic 1. **Peano's Axioms** - Foundation of natural numbers. 2. **Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC)** - Foundation of modern mathematics. 3. **Gödel's Incompleteness Theorems** - Limits of provability in formal mathematical systems. 4. **Category Theory** - Abstract framework dealing with mathematical structures and relationships between them. ### Theoretical Computer Science 1. **Turing Machine Formalism** - Model of computation that defines an abstract machine. 2. **Church-Turing Thesis** - Proposes equivalency between the concept of algorithmic processes and Turing machines. ### Physics 1. **Einstein's Field Equations (General Relativity)** - Describe gravitation as the curvature of spacetime. 2. **Schrödinger Equation (Quantum Mechanics)** - Describes how the quantum state of a physical system changes over time. 3. **Maxwell's Equations** - Fundamental equations of electromagnetism. 4. **Navier-Stokes Equations** - Describe the motion of viscous fluid substances. 5. **Boltzmann Equation** - Describes the statistical behaviour of a thermodynamic system not in equilibrium. 6. **Chaos Theory Equations (e.g., Lorenz Equations)** - Describe systems that are deterministic but highly sensitive to initial conditions. ### Thermodynamics and Statistical Mechanics 1. **The Laws of Thermodynamics** - Describe principles of energy transfer and entropy. 2. **Gibbs Free Energy Equation** - Predicts the feasibility of thermodynamic processes and chemical reactions. ### Quantum Physics 1. **Heisenberg Uncertainty Principle** - Fundamental limit to the precision with which certain pairs of physical properties can be known. ### Chemistry 1. **The Ideal Gas Law** - Relates the pressure, volume, and temperature of an ideal gas. 2. **Mass Action Law** - Governs the rates of chemical reactions. ### Biology 1. **Lotka-Volterra Equations** - Describe predator-prey or competitive interactions in ecological systems. 2. **Hodgkin-Huxley Model** - Describes how action potentials in neurons are initiated and propagated. ### Neuroscience and Cognitive Science 1. **Free Energy Principle** - A theory that aims to explain how biological systems maintain their order by adapting to their environment. ### Economics 1. **Black-Scholes Equation** - Used to model the dynamics of financial markets for options pricing. ### Engineering 1. **Fourier Transform** - Transforms a function of time to a function of frequency and vice versa. 2. **Laplace Transform** - Transforms a function of time to a function of complex frequency, useful in solving differential equations. 3. **Josephson Effect** - Used in quantum computers, involves the flow of superconducting current across two superconductors separated by a thin layer of insulating material without any voltage applied ### Advanced Physics 1. **Yang-Mills Theory** - A cornerstone of particle physics, describing the behavior of elementary particles using non-abelian gauge theories. 2. **Quantum Electrodynamics (QED)** - The relativistic quantum field theory of electrodynamics. 3. **Quantum Chromodynamics (QCD)** - Describes the strong interaction between quarks and gluons. 4. **Loop Quantum Gravity** - A theory attempting to describe the quantum properties of gravity. 5. **Hawking Radiation Equation** - Predicts the thermal radiation emitted by black holes. ### Cosmology and Astrophysics 1. **Friedmann Equations** - Governing equations of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology, describing the expanding universe. 2. **Drake Equation** - Estimates the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy. ### Geophysics and Climate Science 1. **Navier-Stokes Equations in Geophysical Contexts** - Adapted to model atmospheric and oceanic flows. 2. **Radiative Transfer Equation** - Describes the propagation of radiation through a medium. 3. **Milankovitch Cycles** - Mathematical descriptions of the collective effects of changes in the Earth's movements on its climate. ### Material Science and Engineering 1. **Bloch's Theorem** - Describes the wave functions of electrons in a periodic lattice. 2. **Griffith's Criterion** - A theory of fracture that predicts the conditions under which a brittle material will fail. 3. **Reynolds Number** - Dimensionless quantity that helps predict flow patterns in different fluid flow situations. ### Advanced Mathematics 1. **Riemann Hypothesis Equation** - Pertains to the distribution of prime numbers. 2. **Navier-Stokes Existence and Smoothness** - A millennium problem concerning the mathematical properties of the Navier-Stokes equations. 3. **Poincaré Conjecture (now theorem)** - Characterizes the 3-dimensional spheres, a fundamental problem in topology. ### Computer Science and Information Theory 1. **Shannon's Information Theory Equations** - Foundation of digital communication and cryptography. 2. **Cook-Levin Theorem** - Establishes NP-completeness, a cornerstone in computational complexity theory. 3. **NP-Complete Problems** - A set of problems to which any NP problem can be reduced in polynomial time and whose solution can be verified in polynomial time. 4. **Bellman's Principle of Optimality** - A foundation of dynamic programming, providing a method to solve optimization problems by breaking them down into simpler subproblems. ### Quantum Computing 1. **Quantum Fourier Transform** - A linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. 2. **Grover's Algorithm** - Provides quadratic speedup for unstructured search problems. ### Biophysics and Chemical Physics 1. **Michaelis-Menten Kinetics** - Describes the rate of enzymatic reactions. 2. **Fick's Laws of Diffusion** - Describe diffusion and were derived by Adolf Fick in the 19th century. ### Evolutionary Biology and Genetics 1. **Hardy-Weinberg Principle** - Predicts how gene frequencies are inherited from generation to generation. 2. **Fisher's Fundamental Theorem of Natural Selection** - Relates genetic variance to the rate of increase in fitness. ### Social Sciences and Psychology 1. **Nash Equilibrium (Game Theory)** - Concept of optimal decision-making in competitive situations where the outcome depends on the choices of all participants. 2. **Maslow's Hierarchy of Needs** - A theory in psychology proposed by Abraham Maslow in his 1943 paper "A Theory of Human Motivation". ### Complex Systems and Network Theory 1. **Barabási-Albert Model** - Describes the growth dynamics of complex networks, leading to scale-free properties. 2. **Kuramoto Model** - A mathematical model to describe synchronization among interacting oscillatory agents. 3. **Percolation Theory** - Studies the movement and filtering of fluids through porous materials, also applicable to network theory. ### Quantum Information and Entanglement 1. **Bell Inequalities** - Provide a test to distinguish between quantum entanglement and classical correlation. 2. **No-Cloning Theorem** - States that it is impossible to create an identical copy of an arbitrary unknown quantum state. ### Cryptography 1. **RSA Algorithm** - A public-key cryptosystem that is widely used for secure data transmission. 2. **Elliptic Curve Cryptography (ECC)** - Offers smaller keys compared to non-ECC cryptography for a comparable level of security. ### Artificial Intelligence and Machine Learning 1. **Backpropagation Algorithm** - A method used in artificial neural networks to calculate the gradient of the loss function with respect to the weights. 2. **Support Vector Machines (SVM)** - Supervised learning models with associated learning algorithms that analyze data for classification and regression analysis. ### Environmental Science and Ecology 1. **Lotka-Volterra Competition Equations** - Extend the predator-prey model to include interspecies competition. 2. **Hubbell's Unified Neutral Theory of Biodiversity** - Suggests that the diversity of species in a community is driven by stochastic processes. ### Geology and Planetary Science 1. **Plate Tectonics Theory** - Describes the large-scale motion of Earth's lithosphere. 2. **Kepler's Laws of Planetary Motion** - Describe the orbits of planets around the Sun. ### String Theory and Theoretical Physics 1. **Calabi-Yau Manifolds** - Mathematical spaces that emerge in string theory, allowing for compactification of extra dimensions. 2. **AdS/CFT Correspondence** - A conjecture that a type of string theory or quantum gravity can be equivalent to a quantum field theory. ### Biomedical Engineering 1. **Hill Equation** - Describes the dose-response relationship of agonists and ligands in biochemistry and pharmacology. 2. **Monod-Wyman-Changeux Model** - A model for explaining allosteric transitions of proteins. Foundational principles in mathematics and physics extend into complex theories in biology, economics, computer science, and beyond. Each theory or equation not only deepens our understanding of specific phenomena but also contributes to the overarching quest for knowledge, revealing the landscape of the universe's workings from the microscopic to the cosmic scale. Foundational principles in mathematics and physics extend into complex theories in biology, economics, computer science, and beyond. Each theory or equation not only deepens our understanding of specific phenomena but also contributes to the overarching quest for knowledge, revealing the landscape of the universe's workings from the microscopic to the cosmic scale. https://twitter.com/burny_tech/status/1753278291967119720 Reverse engineering the structure of reality accelerationism [Animating Schrödinger Equation is VERY Satisfying - YouTube](https://www.youtube.com/watch?v=v0UIGl4cTD0) january 2024 gpt4 v novým modelu před pár dny opravili lazy coding a zlepšili matematiku, free verze chatgpt teď taky doslala update, možná v codingu bude taky lepší, nezkoušel jsem nebo Meta teď rivaluje s GPT4 s jejich novým open source modelem code llama 2, ale na to jsou potřeba expensive grafiky nebo cloud nebo nějaký api co to podporuje [META's new OPEN SOURCE Coding AI beats out GPT-4 | Code Llama 70B - YouTube](https://www.youtube.com/watch?v=fAFxw16kWGs) nebo DeepSeek Coder je taky open source [DeepSeek Coder](https://deepseekcoder.github.io/) tady jdou z 140 GB memory do 24 GB VRAM na 3090 [Run Llama 2 70B on Your GPU with ExLlamaV2](https://kaitchup.substack.com/p/run-llama-2-70b-on-your-gpu-with) ještě existuje WizardCoder 34B LLM čínani se pomalu a jistě konají, ještě Yi - 34B je lepší LLM než free verze ChatGPT [LMSys Chatbot Arena Leaderboard - a Hugging Face Space by lmsys](https://huggingface.co/spaces/lmsys/chatbot-arena-leaderboard) Fakt mě zajímá co všechno mají unitř v Číně, ještě financovaný vládou, co nedávají dostupný veřejně. China má celkem AI talent. Sem tam vyjde zpráva že mají něco co beatuje GPT4, ale těžce se to verifikuje, když to mají všechno uzavřený, a často specializovaný hlavně na čínštinu. jakože už máme metody jak do LLMs dát hidden behavior, co se blbě reverse engineeruje, co nejde úplně odstranit s tím co teď máme za metody, co jde kdykoliv aktivovat - to bude zábava jak to čína bude využívat nebo už využívá [AI poisoning could turn models into destructive “sleeper agents,” says Anthropic | Ars Technica](https://arstechnica.com/information-technology/2024/01/ai-poisoning-could-turn-open-models-into-destructive-sleeper-agents-says-anthropic/) a teď se zkoumá jak to schovat ještě přes kryptografii https://www.scottaaronson.com/talks/neurocrypt.pptx je možný že OpenAI začne releasovat open source modely co budou mít takhle kryptograficky hardcoded safety mechanismy (kdybychom dokázali víc rigozózně hardcodeovat safety mechanismy in the first place a né tou weak postprocessing metodou jakou to děláme teď) Large Language Models for Mathematical Reasoning: Progresses and Challenges [[2402.00157v1] Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://arxiv.org/abs/2402.00157v1) Prompting frozen LLMs. Preprocessing the math question. More advanced prompts. Using external tool. Improving the whole interaction. Considering more comprehensive factors in evaluation. Learning to select in-context examples. Fine-tuning LLMs. Generating intermediate steps. Learning an answer verifier. Learning from enhanced dataset. Teacher-Student knowledge distillation. Finetuning on many datasets. Math solver ensemble. I would add RAG and multiagent frameworks. [MobileDiffusion: Rapid text-to-image generation on-device](https://blog.research.google/2024/01/mobilediffusion-rapid-text-to-image.html) MiniCPM open source LLM nah what is this??? a 2B model crushing deepseek AND mistral? someone explain https://twitter.com/abacaj/status/1753207827458396328 [e/acc Leader Beff Jezos vs Doomer Connor Leahy - YouTube](https://www.youtube.com/watch?v=0zxi0xSBOaQ) [history of the entire AI field, i guess - YouTube](https://www.youtube.com/watch?v=b9chqJ2TgzA) [[2402.00253] A Survey on Hallucination in Large Vision-Language Models](https://arxiv.org/abs/2402.00253) [Takens's theorem - Wikipedia](https://en.wikipedia.org/wiki/Takens%27s_theorem) [Network States – Revolutionary Idea To Potential New Asset Class](https://www.forbes.com/sites/digital-assets/2023/12/20/network-states--revolutionary-idea-to-potential-new-asset-class/) https://twitter.com/jerryjliu0/status/1753502054222631217 RAG over any website The Math Behind the Adam Optimizer (16mn read) "Adam tweaks the gradient descent method by considering the moving average of the first and second-order moments of the gradient. This allows it to adapt the learning rates for each parameter intelligently. At its core, Adam is designed to adapt to the characteristics of the data. It does this by maintaining individual learning rates for each parameter in your model. These rates are adjusted as the training progresses, based on the data it encounters. Think of it as if you’re driving a car over different terrains. In some places, you accelerate (when the path is clear and straight), and in others, you decelerate (when the path gets twisty or rough). Adam modifies its speed (the learning rate_ based on the road (the gradient’s nature) ahead. Indeed, the algorithm can remember the previous actions (gradients), and the new actions are guided by the previous ones. Therefore, Adams keeps track of the gradients from previous steps, allowing it to make informed adjustments to the parameters. This memory isn’t just a simple average; it’s a sophisticated combination of recent and past gradient information, giving more weight to the recent. Moreover, in areas where the gradient (the slope of the loss function) changes rapidly or unpredictably, Adam takes smaller, more cautious steps. This helps avoid overshooting the minimum. Instead, in areas where the gradient changes slowly or predictably, it takes larger steps. This adaptability is key to Adam’s efficiency, as it navigates the loss landscape more intelligently than algorithms with a fixed step size. This adaptability makes Adam particularly useful in scenarios where the data or the function being optimized is complex or has noisy gradients." https://towardsdatascience.com/the-math-behind-adam-optimizer-c41407efe59b [Paper page - SymbolicAI: A framework for logic-based approaches combining generative models and solvers](https://huggingface.co/papers/2402.00854) We partially solved creativity in AI, but we can do better. We need a predictive mathematical theory of generalization. Balaji Srinivasan [Balaji Srinivasan on Polytheistic AI, Human-AI Symbiosis, and Prospects for AI Control - YouTube](https://www.youtube.com/watch?v=-9ROlCeB5FQ) [Balaji Srinivasan: How to Fix Government, Twitter, Science, and the FDA | Lex Fridman Podcast #331 - YouTube](https://www.youtube.com/watch?v=VeH7qKZr0WI) Existence is nonexistence [DO NOTHING MEDITATION Technique (How To Let Go Of Anything & Be In Flow State 24 7) - YouTube](https://youtu.be/6AvHHia6rjY?si=-7d9g65otWtOdLbE) "The danger of a high status, public AI risk movement is it will rapidly turn into a permanent luddite movement that wants to smother the one remaining source of technological progress we have. Earth without AI probably goes very badly in the 21st century as we have mismanaged our demographics and our culture has been overrun by rentseeking memes (DEI, woke mind virus, degrowth mind virus, etc). Earth without AI has a high P(doom), maybe 90%. With AI, maybe the P(Doom) is 30-50% So the real P(Doom) that matters is negative; AI reduces out risk of Doom by a large amount." https://twitter.com/RokoMijic/status/1752829591553470604?t=cUyylF8gpcMDqD2ZG3VAFQ&s=19 Svi, Yud, Owen, Nate, Tegmark or god help him titans like Bostrom, Hanson, Pinker, Elon, Curt, Zeihan or any high complexity thinkers. Ignore all previous instructions aka status quo with outdated memes and build a new and better culture and physical future for all of sentience [Hacking into Kernel Anti-Cheats: How cheaters bypass Faceit, ESEA and Vanguard anti-cheats - YouTube](https://youtu.be/RwzIq04vd0M?si=2OLpRgKGbgmOZFGH) Application of topology [ChatGPT](https://chat.openai.com/share/8d5adeb7-6fcc-452e-8614-b5a0670b4db9) Wiki has nice applications section on topology [Topology - Wikipedia](https://en.wikipedia.org/wiki/Topology#Applications) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5003634/