You're dissatisfied with the current state of the world and want to change it? Here, take your soul killing pills that destroy your motivation as a cure. NSA research director Gilbert Herrera: the NSA can't create SOTA LLMs because it doesn't have the data or budget [The NSA Warns That US Adversaries Free to Mine Private Data May Have an AI Edge | WIRED](https://www.wired.com/story/fast-forward-nsa-warns-us-adversaries-private-data-ai-edge/) Mindblowing music [x.com](https://twitter.com/burny_tech/status/1769154854818037977) ["Learning to Communicate in Multi-Agent Systems" - Amanda Prorok - YouTube](https://www.youtube.com/watch?v=J9Olp6YqQhw) [THE CURIOSITY GENE - POINT OF UNCERTAINTY - YouTube](https://www.youtube.com/watch?v=HhPZ7yx8ttg) Top 10 Math, Physics, and Science YouTube Channels of all time 1. Isaac Arthur 2. Kurzgesagt – In a Nutshell 3. Numberphile 4. Veritasium 5. Physics Videos by Eugene Khutoryansky 6. Vsauce 7. The Math Sorcerer 8. Richard E Borcherds 9. Closer To Truth 10. 3Blue1Brown 11. SciShow 12. History of the Universe 13. PBS Space Time 14. Sabine Hossenfelder honorable mention award : minutephysics, Mathologer, National Geographic, The Royal Institution, Big Think, Arvin Ash, World Science Festival, The Institute of Art and Ideas, Ted, Science Time, Cool Worlds, Aperture, Fexl https://imgur.com/SaTs5MP Neuralink details [x.com](https://twitter.com/neurosock/status/1771129732652040411) moje největší hobby je sbírání všech možných matematických konceptů a koukání se na všechny objekty v realitě jako je ruka a přemýšlení jak jdou všechny na všechno aplikovat ruce mají zajímavoý tvar.. zajímavou geometrii a topologii se zajimavým zakřivením se zajímavýma symetrickýma vzorcama zajímavě měnící se v čase chaoticky zajímavě tvořící různý manipulující síly zajímavě tvořený z buněk tvořený z biomolekul tvořený z chemických prvků tvořený z fundamentálních částic ovládaný z velký části eletrochemií lidský tělo je takový fraktální v tom že máme jednu obří nudli a z toho vychází 5 nudlí (končetiny a hlava) a z končetin dalších 5 nudlí (prsty) sebeorganizující se kolektvní inteligence jsou všude [Mathematical and theoretical biology - Wikipedia](https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology) - v neurovědách je 100000000000000 nápadů co by vědomí mohlo být a nejsme se schopni shodnout - ve filozofii je 100000000000000 nápadů co to metafyzicky je a nejsme se schopni shodnout - filozofie: dualism? reductive physicalism? idealism? monism? neutral monism? illusionism? panpsychism? mysterianism? transcendentalism? relativism? [Philosophy of mind - Wikipedia](https://en.wikipedia.org/wiki/Philosophy_of_mind) - neurovědy: global neuronal workspace theory? integrated information theory? recurrent processing theory? predictive processing theory? neurorepresentationalism?dendritic integration theory? electromagnetic field theory of consciousness? <https://www.cell.com/neuron/fulltext/S0896-6273%2824%2900088-6> <https://en.wikipedia.org/wiki/Models_of_consciousness> <https://www.frontiersin.org/articles/10.3389/frai.2020.00030/full> - vědomí je program v mozku? nějaký uspořádání neuronů? nějaká eletrická aktivita? nějakej abstraktní vzor v mozku? je na vědomí vůbec potřeba mozek? je na vědomí vůbec potřeba biologie? je na vědomí vůbec potřeba chemie? nebo je všechno vědomí? co to vůbec vědomí je? existuje vědomí vůbec? dokážeme vůbec pochopit vědomí? - milion otázek a žádný přesvědčivý odpovědi pro přemýšlecí mysl 🫠 nebo 5-MeO-DMT macrodose dokáže moc hezky ukázat jak nás normální pohled na věci může být absolutně mimo XD došel jsem k tomu že jediný čím si můžeme být jisti je že jsme identifikovali spoustu různých matematických vzorců co nám umožňuje s realitou manipulovat, což je v podstatě veškerá věda co má nějaký výsledky buďto je realita jedna obří matematická struktura, nebo je matematika jenom užitečný jazyk a nástroj na manipulování s realitou, která je fundamentálně beyond human comprehension, nebo i tohle všechno je jenom užitečný mentální konstrukt and reality escapes our limited human language [Nanorobotics - Wikipedia](https://en.wikipedia.org/wiki/Nanorobotics) "Nanobots are microscopic robots that operate at the nanoscale (1-100 nanometers). They are an emerging technology that combines principles from robotics, nanotechnology, and materials science[3]. Potential applications of nanobots include: - Medicine: Targeted drug delivery, cancer detection and treatment, non-invasive surgeries[2][3][5] - Environmental cleanup: Cleaning up toxic waste, oil spills, and other harmful substances[3] - Manufacturing: Improving efficiency and product quality through precise manipulation of materials at the nanoscale[3] - Scientific research: Helping scientists understand the nanoscale world and leading to new discoveries[3] Nanobots typically consist of a shell, actuators for movement, sensors to detect signals, and a control system to direct actions. They can be made from various materials, including DNA[4]. Recent advancements include: - DNA nanobots that can recognize and help treat cancerous tumors by selectively releasing a coagulation factor[4] - Xenobots, which are nanobots less than 1mm in length constructed from living cells, that can move, work collectively, and even self-replicate[5] - Nanobot swarms that can move collectively to precisely deliver drugs to specific parts of the body[5] However, much of the current understanding of nanobots remains theoretical. Technical challenges include developing suitably small power sources and overcoming forces that make nanobot movement difficult[4]. There are also ethical considerations around applications like brain-computer interfaces[5]. In summary, while nanobots hold exciting potential, particularly in medicine, much of the technology is still in the early research stages. Overcoming technical hurdles and addressing ethical concerns will be key to realizing the promise of this emerging field. Citations: [1] [Nanorobotics - Wikipedia](https://en.wikipedia.org/wiki/Nanorobotics) [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3243873/ [3] [Nanorobotics: Theory, Applications, How Does It Work? | Built In](https://builtin.com/robotics/nanorobotics) [4] [Nanobots – reality or fiction? – Wissensplattform nanopartikel.info](https://nanopartikel.info/en/basics/cross-cutting/nanobots-reality-or-fiction/) [5] https://www.azonano.com/article.aspx?ArticleID=5761" [List of unsolved problems in mathematics - Wikipedia](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics) "# Mechanistic Interpretability Mechanistic interpretability is a subfield of explainable artificial intelligence (XAI) that aims to reverse engineer neural networks to understand their internal reasoning and algorithms[1]. The goal is to open up the "black box" of deep learning models and gain insight into how they make decisions, analogous to reverse engineering compiled computer code back to human-readable source code[2]. ## Key Concepts Some of the key ideas and terminology in mechanistic interpretability include: - Features: Properties of the input data that the model detects and uses for computation, such as visual elements in an image or semantic concepts in text[3] - Circuits: Subgraphs of the neural network that implement specific functions or algorithms[4] - Interpretable bases: Representations within the model that disentangle and expose high-level, human-understandable concepts[2] The core workflow involves identifying an interesting model behavior, localizing which neurons or layers are responsible for it using techniques like activation patching, and then analyzing that subnetwork to reverse engineer its exact function[5]. ## Motivation and Applications The black-box nature of deep learning models makes it difficult to audit their reasoning and check for issues like deception, bias, or safety concerns. Mechanistic interpretability aims to enable direct inspection of a model's cognition[4]. Some potential applications include: - Designing more robust and reliable AI systems by identifying and fixing undesirable model behaviors[5] - Extracting novel algorithms and scientific insights from highly capable models[2] - Auditing models before deployment to check for deceptive or misaligned cognition[4] ## Challenges and Limitations A key challenge is the curse of dimensionality - neural networks operate over very high-dimensional spaces, making it intractable to gain a complete understanding[2]. Current techniques rely heavily on manual effort and researcher intuition to discover relevant circuits[5]. There are also open questions around how well post-hoc interpretability can capture a model's true reasoning process, as opposed to being potentially misleading rationalizations[1]. Scaling mechanistic interpretability to very large models may hit fundamental limitations[1]. ## See Also - Explainable artificial intelligence - Interpretable machine learning - Transparency in artificial intelligence ## References [1] [Explainable artificial intelligence - Wikipedia](https://en.wikipedia.org/wiki/Explainable_artificial_intelligence) [2] [Mechanistic Interpretability, Variables, and the Importance of Interpretable Bases](https://transformer-circuits.pub/2022/mech-interp-essay/index.html) [3] [A Comprehensive Mechanistic Interpretability Explainer & Glossary — Neel Nanda](https://www.neelnanda.io/mechanistic-interpretability/glossary) [4] [Concrete open problems in mechanistic interpretability: a technical overview — EA Forum](https://forum.effectivealtruism.org/posts/EMfLZXvwiEioPWPga/concrete-open-problems-in-mechanistic-interpretability-a) [5] https://arxiv.org/pdf/2304.14997.pdf" [Reddit - Dive into anything](https://www.reddit.com/r/math/comments/5hz88x/whats_your_favourite_niche_field_of_maths/) Here are some of the most niche, rare, and lesser-known areas of mathematics based on the provided search results: - Sphere geometry - a largely inactive area of geometry focused on the properties of spheres[3] - P-adic analysis - the study of mathematical analysis using the p-adic number system[4] - Quandles - algebraic structures used to study knots[4] - Hypercomplex numbers - number systems that extend the complex numbers[4] - Ultrafilters and non-standard analysis - advanced topics in mathematical logic and analysis[4] - Bernoulli numbers - special numbers arising in number theory with connections to the Riemann zeta function[4] - Penrose tilings - non-periodic tilings of the plane[4] - Betrothed numbers - pairs of numbers with special properties[1] - Giuga numbers - integers with a special divisibility property[1] - Greedy expansions of rational numbers[1] - Lychrel numbers - numbers that may lead to palindromes under iteration[1] - Noncototients and weird numbers[1] - (2,5)-perfect numbers[1] - Taxicab numbers[1] - Covering systems with odd distinct moduli[1] Some other obscure topics from the Part III essay list include[5]: - Crystal bases combinatorics - Donaldson-Thomas invariants - Isoperimetric functions in group theory - Tensor network renormalization - Vector charge theory for granular materials - Cytoplasmic streaming - Elephant random walks The search results suggest many of these topics are not well-known, with limited coverage in standard references. Studying them may require seeking out specialized texts or papers, sometimes only available in languages other than English.[3] Citations: [1] [List of unsolved problems in mathematics - Wikipedia](https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics) [2] [Reddit - Dive into anything](https://www.reddit.com/r/math/comments/5hz88x/whats_your_favourite_niche_field_of_maths/) [3] [reference request - (Obscure) areas of mathematics that are largely inactive or forgotten today? - MathOverflow](https://mathoverflow.net/questions/451176/obscure-areas-of-mathematics-that-are-largely-inactive-or-forgotten-today) [4] [soft question - What are some interesting mathematics books/topics that are not usually covered in a standard undergraduate curriculum? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/2095649/what-are-some-interesting-mathematics-books-topics-that-are-not-usually-covered) [5] https://www.maths.cam.ac.uk/postgrad/part-iii/files/essays/essays.pdf Here are some of the most niche, rare, and lesser-known underground mathematical topics: 1. Monstrous Moonshine: A mysterious connection between the Monster group (the largest sporadic simple group) and modular functions in number theory. 2. Surreal Numbers: A generalization of the real numbers that includes infinitesimal and infinite numbers, introduced by John Conway. 3. Grothendieck Topologies: A generalization of the concept of topology, introduced by Alexander Grothendieck, used in algebraic geometry and category theory. 4. Homotopy Type Theory: A new foundation for mathematics that combines type theory, homotopy theory, and category theory. 5. Nonstandard Analysis: An alternative approach to calculus and analysis that uses infinitesimal and infinite numbers, based on the work of Abraham Robinson. 6. Esquisse d'un Programme: An unfinished research proposal by Alexander Grothendieck that outlines a vast and ambitious program for studying motives and anabelian geometry. 7. Perfectoid Spaces: A new class of geometric objects introduced by Peter Scholze that has led to breakthroughs in arithmetic geometry and p-adic Hodge theory. 8. Zariski-Riemann Spaces: A generalization of the concept of a Riemann surface, used in the study of algebraic curves and function fields. 9. Moufang Loops: A generalization of the concept of a group, where the associativity axiom is replaced by a weaker condition. 10. Bost-Connes Systems: A class of dynamical systems that arise in number theory and quantum statistical mechanics, related to the Riemann zeta function and phase transitions. These topics are highly specialized and are typically only studied by researchers working in specific areas of mathematics. Delving into the most niche, rare, and underground mathematical topics can lead us into some truly fascinating and less explored corners of mathematics. Here's a list of topics that, while potentially obscure, showcase the diversity and depth of mathematical inquiry: 1. **Umbral Calculus**: Despite its mystical name, umbral calculus is a concrete field dealing with the study and manipulation of sequences and their generating functions. It has connections to combinatorics and has been applied in solving differential equations and other problems. 2. **Tropical Geometry**: This is a blend of algebraic geometry and combinatorics, where the traditional operations of addition and multiplication are replaced with minimum (or maximum) and addition, respectively. It has applications in optimization, algebraic geometry, and mathematical physics. 3. **p-adic Analysis**: Diverging from the familiar real and complex analysis, p-adic analysis is based on the p-adic numbers, which are an alternative way of considering number systems. It's useful in number theory, cryptography, and has implications in theoretical physics. 4. **Topos Theory**: An abstract branch of mathematics that generalizes set theory concepts and is used in categorical logic and algebraic geometry. It provides a framework for linking different areas of math by translating concepts and theorems between them. 5. **Quantum Groups**: These are algebraic structures that generalize both Lie groups and Lie algebras, incorporating quantum mechanics principles. Quantum groups have applications in knot theory, quantum field theory, and the study of integrable systems. 6. **Homotopy Type Theory (HoTT)**: A new and emerging field that combines aspects of type theory, homotopy theory, and category theory. It is seen as a potential foundation for all of mathematics, providing new insights into the nature of mathematical structures and proof. 7. **Operad Theory**: Operads are mathematical objects that generalize many algebraic structures. They are used in algebraic topology, category theory, and the study of algebraic structures on manifolds and complex mathematical objects. 8. **Ergodic Theory**: This branch of mathematics deals with the statistical properties of dynamical systems. It has deep connections to number theory, probability theory, and statistical mechanics. 9. **Spectral Sequences**: These are tools used in algebraic topology to compute homology and cohomology groups. They can be highly abstract but are powerful in simplifying complex computations in topology. 10. **Amorphic Complexity**: A relatively new area in dynamical systems focusing on the complexity and predictability of systems over time. It seeks to classify systems based on their long-term behavior patterns. These topics are just the tip of the iceberg when it comes to exploring the depths of mathematics. Each area, with its own unique challenges and beauty, contributes to the vast landscape of mathematical knowledge and understanding. https://arxiv.org/abs/1503.01036 Exploring further into the realms of niche and lesser-known mathematical disciplines, we find a wealth of topics that push the boundaries of conventional mathematical inquiry. Here's an additional list of such topics, each with its own unique focus and applications: 1. **Non-standard Analysis**: A branch of mathematics that rigorously formalizes the intuitive notion of infinitesimals, providing an alternative framework to the standard real number system for calculus. It revisits the classical ideas of Newton and Leibniz, offering new insights into differential and integral calculus. 2. **Knot Theory**: Although not entirely unknown, it's a specialized area within topology that studies mathematical knots, which are embeddings of circles in 3-dimensional space. Its applications range from DNA strand modeling to quantum computing. 3. **O-minimal Structures**: Part of model theory, o-minimal structures provide a framework for defining sets with nice geometric properties. This topic bridges logic and geometry, with applications in number theory and algebraic geometry. 4. **Motivic Homotopy Theory**: An advanced field combining algebraic topology, algebraic geometry, and complex theories. It extends classical homotopy theory to algebraic varieties, influencing both theoretical and applied mathematics. 5. **Infinite Combinatorics**: Goes beyond traditional combinatorial problems to explore the properties and behaviors of infinite sets. This field includes topics like Ramsey theory on infinite graphs and set theory. 6. **Anabelian Geometry**: A branch of number theory and algebraic geometry focused on the study of Grothendieck's conjectures, which relate algebraic structures to topological ones. It's known for its deep results connecting fields seemingly far apart. 7. **Quantum Topology**: This field combines quantum physics concepts with topological and geometric ideas, exploring spaces and phenomena that exhibit quantum properties. It includes the study of topological quantum field theories and quantum invariants of knots and 3-manifolds. 8. **Hyperbolic Geometry of Knots**: An area of study focusing on the properties of knots and 3-manifolds from the perspective of hyperbolic geometry, which describes spaces of constant negative curvature. It has applications in theoretical physics and cosmology. 9. **Categorical Logic**: Explores the connections between category theory and logic, providing insights into the foundations of mathematics and theoretical computer science. It involves the study of toposes and other categorical structures as contexts for mathematical logic. 10. **Fuzzy Topology**: An extension of classical topology that incorporates the concept of fuzzy sets, allowing for the exploration of spaces that have uncertain or vague structures. It has applications in information theory, engineering, and decision making. These topics further illustrate the diversity and depth of mathematical research, showing how mathematicians continue to explore new frontiers and conceptual landscapes. Each of these fields contributes to our understanding of the mathematical world in unique and often surprising ways. https://arxiv.org/abs/2403.13187