## Tags - Part of: [[Science]] - Related: [[Formal science]] [[Replication crisis]] [[Metascience]] - Includes: [[Scientific method]] - Additional: ## Definitions - One of the branches of [[Science]] concerned with the description, understanding, prediction and control and building of [[Physicalism|physical]] [[Process|processes]] based on [[Empiricism]] with [[Scientific method]]: observation, [[Hypothesis|hypotheses]], [[Theory|theories]], [[experimentation]], [[replication]], [[Meta-analysis|metaanalyses]]. - Using the tools of applied [[Mathematics]], mathematics constrained by making predictions about reality ## Main resources - [Natural science - Wikipedia](https://en.wikipedia.org/wiki/Natural_science) <iframe src="https://en.wikipedia.org/wiki/Natural_science" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [Search | MIT OpenCourseWare | Free Online Course Materials](https://ocw.mit.edu/search/) ## Landscapes - [Outline of natural science - Wikipedia](https://en.wikipedia.org/wiki/Outline_of_natural_science) - <iframe src="https://en.wikipedia.org/wiki/Outline_of_natural_science" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> - [[Physics#Landscapes]] - ![[Physics#Landscapes]] - [[Chemistry]] - [[Biology]] - [[Neuroscience]] - [[Psychology]] - [[Systems science]] - [[Systems theory]] - [[Earth science]], [[Astronomy]] - [[Transdisciplinarity]] - [[Biophysics]] - [[Neurophysics]] - [[Sociophysics]] - [[Omnidisciplinarity]] - [[Cognitive science]] ([[Artificial Intelligence]], [[Consciousness]], [[Linguistics]]) - [[Philosophy]] [[Mathematics]] [[Physics]] [[Computer science]] [[Dynamical systems]] [[Systems science]] [[Systems theory]] - [[Applied mathematics]] - [[Artificial intelligence x Science]] - [The Molecular Shape of You (Ed Sheeran Parody) | A Capella Science - YouTube](https://www.youtube.com/watch?v=f8FAJXPBdOg) ### Structure of reality from first principles Quantum fields, as described by the [[Standard Model of Particle Physics]], are fundamental to our current understanding of reality. While some theories like [[string theory]] or [[loop quantum gravity]] propose more fundamental structures, these remain speculative and unproven. Matter and forces are understood as excitations or quanta of these fields. The behavior of quantum systems is generally described by [[quantum mechanics]], with the Schrödinger equation being fundamental for non-relativistic systems. In [[quantum field theory]], relativistic equations such as the Klein-Gordon or Dirac equations are used. These fields exist within spacetime, and the curvature of spacetime due to matter and energy is described by Einstein's theory of [[general relativity]], with this curvature manifesting as gravity. Particles can exhibit quantum properties such as [[quantum superposition]] and [[quantum entanglement]]. As systems become more complex through the composition of these particles, systems of particles, and systems of systems, they can display varying degrees of quantum or classical behavior. When these systems interact with their environment, they undergo [[decoherence]] (best described by [[Quantum Darwinism]]), which tends to make them appear more classical. Generally, more complex systems that interact strongly with their environment tend to exhibit more classical behavior. Quantum computers are cooled such that the quantum effects are maintained. At larger scales, more complex systems give rise to [[Emergence|emergent]] phenomena described by higher-level laws. These include various branches of [[physics]], as well as [[chemistry]], [[biology]], [[ecology]], [[sociology]], [[astrophysics]], and other [[Natural science|natural sciences]]. While these emergent laws are ultimately based on the fundamental laws of physics, they often provide more practical descriptions of phenomena at their respective scales. The Standard Model describes three generations of matter particles: [[quarks]] and [[leptons]]. The six types of quarks are up, down, charm, strange, top, and bottom. The six leptons are the electron, muon, and tau, along with their corresponding neutrinos (electron neutrino, muon neutrino, and tau neutrino). Additionally, the model includes force-carrying particles: photons for the [[electromagnetism|electromagnetic]] force, gluons for the [[strong nuclear force]], and W and Z bosons for the [[weak nuclear force]]. The Higgs boson, discovered in 2012, completes the Standard Model and explains how other particles acquire mass through their interaction with the [[Higgs field]]. While the Standard Model successfully describes three of the four fundamental forces (strong nuclear, weak nuclear, and electromagnetic), it does not include [[gravity]]. The reconciliation of quantum mechanics with gravity remains an active area of research in theoretical [[physics]]. [[Images/80d7633c71319b05bb2717a1791dceef_MD5.gif|Open: 1_GptWg3QM1RtAZMBasNg_SA.gif]] ![[Images/80d7633c71319b05bb2717a1791dceef_MD5.gif]] ## Past and future [[Images/81337bf7083ae3d5700ee021c240ceb2_MD5.jpeg|Open: Pasted image 20240920040727.png]] ![[Images/81337bf7083ae3d5700ee021c240ceb2_MD5.jpeg]] [[Images/f278c2900dd0b614004184e2de311d95_MD5.jpeg|Open: Pasted image 20240920041037.png]] ![[Images/f278c2900dd0b614004184e2de311d95_MD5.jpeg]] - [[Computronium]] - From [The Singularity Is Nearer - Wikipedia](https://en.wikipedia.org/wiki/The_Singularity_Is_Nearer) by [[Ray Kurzweil]]: [[Images/4ee554bf075eb3a5879c61c1d14e1e51_MD5.jpeg|Open: Pasted image 20240919001041.png]] ![[Images/4ee554bf075eb3a5879c61c1d14e1e51_MD5.jpeg]] [4.5 Billion Years in 1 Hour - YouTube](https://www.youtube.com/watch?v=S7TUe5w6RHo) ### Let's build reality from first principles. I'll fix the factual errors in the text while retaining as much information as possible: Let's describe fundamental particles governed by quantum field theory and the Standard Model, and add gravity (which remains an unsolved problem mathematically in terms of unification with quantum theory) that together compose and give rise to equations of classical and statistical physics on higher levels, along with system theory equations, information theory, and computation theory. These interacting quantum fields with fundamental particles, in complex enough dynamics, give rise to the emergent equations of chemistry, which in turn compose to form biology, neuroscience, and social systems. We use many of these laws to engineer computers, artificial intelligence, and other technologies, which have various mathematical similarities and differences with biological systems. This allows for various types of compatibilities between biological and artificial systems that already enable us to better understand and engineer AI and upgrade ourselves with neurotechnology, and this progress is likely to continue. Planets, galaxies, and the whole universe operate under many approximately deterministic laws. We can predict fundamental particle behavior well, but there is inherent probabilistic nature in the quantum wave function. Since many nontrivial systems cannot be solved analytically, we have to approximate them with numerical methods. Chemistry and biology add numerous approximating equations because we cannot grasp all the variables in play for many cases, but we can simulate femtoseconds to picoseconds of simple chemical reactions using quantum mechanics on classical supercomputers and quantum computers in chemical physics. Societal complexity is very intractable, but we can apply some very general laws from physics statistics, game theory, evolutionary game theory, fluid dynamics, thermodynamics, network theory, and so on. The more macroscopic we go, the less fundamental quantum probabilities and fluctuations matter as they tend to average out, and we get more deterministic behavior, with higher-order dynamical complex systems made of subsystems with stochastic cybernetic controllers in nonequilibrium steady states forming nested hierarchies of free energy minimizing complex Markov blankets (as Friston says [Friston's "Free Energy Principle" | The Most INTENSE Theory of Reality - YouTube](https://www.youtube.com/watch?v=uk4NZorRjCo) ) undergoing various phase shifts in the configuration space of functional architectures, like organisms and societies. Complexity grows as we go up the levels, with further tractable somewhat deterministic dynamics of planets, galaxies, and cosmology. We still have yet to discover and develop many better or new concepts, laws, frameworks, and technologies in all these fields and levels of analysis. The cosmological story of the universe, including why and how there is something rather than nothing, remains a mystery beyond our limited modeling, approximating, and compressing perspective, given our current data, time, and computational power. In its fullness, it's beyond our current comprehension. [https://twitter.com/burny_tech/status/1743851964163621190?t=U_HQh9x-BbQYDi19VT2qWg&s=19](https://twitter.com/burny_tech/status/1743851964163621190?t=U_HQh9x-BbQYDi19VT2qWg&s=19) [[bf8b4821f7ee855830505c37fb3db9e2_MD5.jpeg|Open: orders_of_magnitude_english_annotations_highres_horizontal_layout_25200x5760 (1).png]] ![[bf8b4821f7ee855830505c37fb3db9e2_MD5.jpeg]] At 10^-32m is thought to exist a foam of twisted spacetime (Quantum foam). 10^-24m cross section radius of 1 MeV neutrinos. 10^-22m Top Quark, the smallest quark. 10^-20m Bottom and Charm quarks. 10^-18m Up and Down quarks. 10^-16m Protons and Neutrons. 10^-14m Electrons and nuclei. 10^-12m Longest wavelength of gamma rays. 10^-11m Radius of hydrogen and helium atom. 10^-10m Radius of carbon atoms. 10^-9m Diameter of the DNA helix. 10^-8m Smallest virus (Porcine circovirus). 10^-7m Largest virus (Megavirus). 10^-6m X Chromosome. 10^-5m Typical size of a red blood cell. 0.1mm Width of human hair. 10mm Width of an adult human finger. 1m Height of an infant human being. 10m Argentinosaurus is the biggest dinosaur discovered yet (30 to 35 meters). Human figure is for comparison. In reality humans and dinosaurs didn't live at the same time. 1km Diameter of Barringer Crater in the northern Arizona desert (1186m). 100km Jamaica Island (235km long). 10000km Diameter of planet Earth (12,742 km). 10^8m Moon's orbit (770,000km). 10^9m Diameter of the Sun (1391400km). 10^11m Diameter of the inner Solar System. (600,000,000 km) 10^13m Diameter of the Solar System. 10^15m Outer limit of the Oort Cloud. 10^16m Distance to Alpha Centauri. 10^18m Messier 13 globular cluster. 10^20m Diameter of the Milky Way Galaxy. 10^22m Local Group of galaxies including Milky Way, M31(Andromeda), M33, SMC, LMC and smaller galaxies. 10^23m Typical galaxy cluster (2 to 10 Mpc). 10^24m Laniakea Supercluster of galaxies. (160 Mpc) 10^25m End of Greatness ("Cosmic web" structure). 10^26m Diameter of the observable universe sphere. The entire Universe is larger than 10^27m and possibly infinite. [Scale of the Universe](https://scaleofuniverse.com/en) ## Deep dives - [[Theory of Everything in Natural Sciences#Definitions]] - ![[Theory of Everything in Natural Sciences#Definitions]] - [[Metascience]] - ![[Metascience#Definitions]] ## Landscapes written by AI (may include factually incorrect information) ### Map # Giant Map of Natural Sciences Explore the vast landscape of natural sciences with this comprehensive map, encompassing numerous disciplines and their interconnections. This guide aims to provide an extensive overview of the fields that study the natural world, from the smallest particles to the largest cosmic structures. --- ### **A. Classical Physics** 1. **Mechanics** - Kinematics - Dynamics - Statics - Fluid Mechanics - Continuum Mechanics 2. **Thermodynamics** 3. **Electromagnetism** - Electrostatics - Magnetostatics - Electrodynamics 4. **Optics** - Geometrical Optics - Physical Optics 5. **Acoustics** ### **B. Modern Physics** 1. **Quantum Mechanics** - Quantum Field Theory - Quantum Information Science - Quantum Optics 2. **Relativity** - Special Relativity - General Relativity 3. **Particle Physics** - High-Energy Physics - Standard Model 4. **Nuclear Physics** 5. **Condensed Matter Physics** - Solid-State Physics - Nanophysics - Superconductivity 6. **Atomic and Molecular Physics** 7. **Plasma Physics** ### **C. Applied Physics** 1. **Geophysics** 2. **Medical Physics** 3. **Engineering Physics** 4. **Photonics** 5. **Computational Physics** 6. **Biophysics** ### **D. Astrophysics** 1. **Stellar Astrophysics** 2. **Galactic Astronomy** 3. **Extragalactic Astronomy** 4. **Cosmology** 5. **Planetary Science** 6. **Space Physics** --- ### **A. Analytical Chemistry** - Spectroscopy - Chromatography - Mass Spectrometry - Electroanalytical Methods ### **B. Organic Chemistry** - Stereochemistry - Medicinal Chemistry - Polymer Chemistry - Petrochemistry ### **C. Inorganic Chemistry** - Bioinorganic Chemistry - Organometallic Chemistry - Solid-State Chemistry ### **D. Physical Chemistry** - Chemical Thermodynamics - Quantum Chemistry - Chemical Kinetics - Electrochemistry ### **E. Biochemistry** - Enzymology - Metabolism - Molecular Genetics ### **F. Theoretical and Computational Chemistry** ### **G. Nuclear Chemistry** ### **H. Environmental Chemistry** ### **I. Materials Chemistry** - Nanochemistry - Supramolecular Chemistry - Surface Chemistry ### **J. Green Chemistry** --- ### **A. Geology** 1. **Mineralogy** 2. **Petrology** - Igneous - Metamorphic - Sedimentary 3. **Structural Geology** 4. **Stratigraphy** 5. **Paleontology** - Paleobotany - Paleozoology 6. **Geomorphology** ### **B. Geophysics** 1. **Seismology** 2. **Volcanology** 3. **Geodesy** 4. **Magnetometry** 5. **Gravimetry** ### **C. Meteorology** - Climatology - Atmospheric Physics - Atmospheric Chemistry ### **D. Oceanography** 1. **Physical Oceanography** 2. **Chemical Oceanography** 3. **Biological Oceanography** 4. **Geological Oceanography** ### **E. Hydrology** - Hydrogeology - Limnology - Ecohydrology ### **F. Soil Science** - Pedology - Edaphology ### **G. Glaciology** ### **H. Environmental Science** - Environmental Chemistry - Environmental Geology - Environmental Physics ### **I. Remote Sensing** ### **J. Geoinformatics** --- #### **1. Botany** - Plant Anatomy - Plant Physiology - Plant Ecology - Plant Pathology - Phycology (Algae) - Bryology (Mosses) - Pteridology (Ferns) #### **2. Zoology** - Invertebrate Zoology - Vertebrate Zoology - Ichthyology (Fish) - Herpetology (Reptiles & Amphibians) - Ornithology (Birds) - Mammalogy (Mammals) - Entomology (Insects) - Arachnology (Spiders) - Malacology (Mollusks) - Parasitology #### **3. Microbiology** - Bacteriology - Virology - Mycology (Fungi) - Protozoology - Phycology (Algae) #### **4. Genetics** - Classical Genetics - Molecular Genetics - Population Genetics - Genomics - Epigenetics #### **5. Cell Biology** - Cytology - Cellular Physiology #### **6. Molecular Biology** #### **7. Biochemistry** #### **8. Ecology** - Behavioral Ecology - Population Ecology - Community Ecology - Ecosystem Ecology - Landscape Ecology - Conservation Ecology #### **9. Evolutionary Biology** - Evolutionary Developmental Biology - Phylogenetics #### **10. Physiology** - Comparative Physiology - Human Physiology - Plant Physiology #### **11. Anatomy** - Comparative Anatomy - Human Anatomy #### **12. Neuroscience** - Neuroanatomy - Neurophysiology - Cognitive Neuroscience - Computational Neuroscience - Neurobiology #### **13. Developmental Biology** - Embryology #### **14. Immunology** #### **15. Endocrinology** #### **16. Epidemiology** #### **17. Ethology (Animal Behavior)** ### **B. Biotechnology** - Genetic Engineering - Synthetic Biology - Cell Culture Technologies ### **C. Bioinformatics** ### **D. Biophysics** ### **E. Systems Biology** ### **F. Biostatistics** ### **G. Pharmacology** ### **H. Toxicology** ### **I. Biomedical Sciences** --- ### **A. Astrobiology** ### **B. Biochemistry** ### **C. Biophysics** ### **D. Chemical Biology** ### **E. Geochemistry** ### **F. Geobiology** ### **G. Biogeochemistry** ### **H. Nanoscience and Nanotechnology** ### **I. Materials Science** ### **J. Environmental Science** ### **K. Computational Biology** ### **L. Systems Biology** ### **M. Quantum Biology** ### **N. Mathematical Biology** ### **O. Medical Physics** ### **P. Bioengineering** ### **Q. Biomaterials** --- #### **1. Observational Astronomy** - Radio Astronomy - Infrared Astronomy - Optical Astronomy - Ultraviolet Astronomy - X-ray Astronomy - Gamma-ray Astronomy ### **B. Astrophysics** - Stellar Astrophysics - Galactic Astrophysics - Extragalactic Astrophysics - Cosmology - Physical Cosmology - Observational Cosmology - Computational Cosmology - High-Energy Astrophysics - Particle Astrophysics ### **C. Planetary Science** - Planetary Geology - Planetary Atmospheres - Exoplanetary Science ### **D. Space Science** - Space Physics - Solar Physics - Space Weather - Heliospheric Physics ### **E. Astrobiology** ### **F. Astrochemistry** --- ### **A. Environmental Biology** - Conservation Biology - Restoration Ecology - Landscape Ecology - Population Ecology ### **B. Environmental Chemistry** ### **C. Environmental Physics** ### **D. Environmental Geology** ### **E. Environmental Engineering** ### **F. Climate Science** ### **G. Atmospheric Sciences** ### **H. Earth System Science** ### **I. Sustainability Science** ### **J. Ecotoxicology** --- ### **A. Computational Physics** ### **B. Computational Chemistry** ### **C. Computational Biology** ### **D. Bioinformatics** ### **E. Geoinformatics** ### **F. Computational Neuroscience** ### **G. Scientific Computing** ### **H. Data Science** ### **I. Artificial Intelligence Applications** --- ### **A. Applied Mathematics** ### **B. Mathematical Physics** ### **C. Mathematical Biology** ### **D. Mathematical Chemistry** ### **E. Biostatistics** ### **F. Statistical Mechanics** ### **G. Dynamical Systems** ### **H. Nonlinear Dynamics** ### **I. Chaos Theory** ### **J. Computational Mathematics** --- ### **A. Planetary Geology** ### **B. Planetary Atmospheres** ### **C. Astrogeology** ### **D. Exobiology** ### **E. Space Weather** ### **F. Helioseismology** ### **G. Planetary Magnetism** ### **H. Cosmic Mineralogy** --- ### **A. Anatomy** ### **B. Physiology** ### **C. Pathology** ### **D. Pharmacology** ### **E. Neuroscience** ### **F. Immunology** ### **G. Epidemiology** ### **H. Genetics** ### **I. Microbiology** ### **J. Virology** ### **K. Biomedical Engineering** --- ### **A. Cognitive Neuroscience** ### **B. Neurobiology** ### **C. Psychobiology** ### **D. Neuropsychology** --- ### **A. Agronomy** ### **B. Horticulture** ### **C. Plant Breeding** ### **D. Plant Pathology** ### **E. Entomology** ### **F. Soil Science** ### **G. Forestry** ### **H. Agroecology** ### **I. Animal Science** --- ### **A. Marine Biology** ### **B. Marine Chemistry** ### **C. Marine Geology** ### **D. Marine Ecology** ### **E. Physical Oceanography** ### **F. Biological Oceanography** ### **G. Chemical Oceanography** ### **H. Geological Oceanography** --- ### **A. Meteorology** ### **B. Climatology** ### **C. Atmospheric Chemistry** ### **D. Atmospheric Physics** ### **E. Aeronomy** --- ## **XVI. Earth System Science** - Integrated Study of Earth as a System - Earth Observation - Geomatics --- ### **A. Physical Geography** - Geomorphology - Biogeography - Climatology - Hydrology - Pedology ### **B. Geographic Information Systems (GIS)** --- ### **A. Toxicology** ### **B. Occupational Health** ### **C. Environmental Epidemiology** ### **D. Environmental Risk Assessment** --- ### **A. Archaeometry** ### **B. Geoarchaeology** ### **C. Bioarchaeology** ### **D. Paleoanthropology** --- ### **A. Glaciology** ### **B. Snow Science** ### **C. Sea Ice Studies** ### **D. Permafrost Studies** --- ### **A. Solar Physics** ### **B. Magnetospheric Physics** ### **C. Ionospheric Physics** ### **D. Heliospheric Physics** --- ### **A. Seismology** ### **B. Tectonophysics** ### **C. Volcanology** --- ### **A. Marine Biology** ### **B. Freshwater Biology** ### **C. Planktonology** ### **D. Marine Ecology** --- ### **A. Radiobiology** ### **B. Radiation Chemistry** ### **C. Radiation Physics** --- ### **A. Optical Physics** ### **B. Quantum Optics** ### **C. Laser Physics** ### **D. Nonlinear Optics** ### **E. Fiber Optics** --- ### **A. Protein Crystallography** ### **B. NMR Spectroscopy** ### **C. Cryo-Electron Microscopy** ### **D. Computational Structural Biology** --- ### **A. Functional Genomics** ### **B. Comparative Genomics** ### **C. Transcriptomics** ### **D. Proteomics** ### **E. Metabolomics** --- ### **A. Evolutionary Biology** ### **B. Evolutionary Developmental Biology (Evo-Devo)** ### **C. Phylogenetics** ### **D. Paleobiology** --- ### **A. Ethology** ### **B. Behavioral Ecology** ### **C. Sociobiology** ### **D. Neuroethology** --- ### **A. Kinesiology** ### **B. Comparative Biomechanics** ### **C. Cellular Biomechanics** ### **D. Biofluid Mechanics** --- ### **A. Physical Biochemistry** ### **B. Structural Biology** ### **C. Biophysical Methods** --- ### **A. Bioinformatics** ### **B. Cheminformatics** ### **C. Geoinformatics** ### **D. Medical Informatics** ### **E. Computational Physics** ### **F. Data Science** --- ### **A. Cosmic Ray Physics** ### **B. Neutrino Astronomy** ### **C. Gamma-Ray Astronomy** ### **D. Dark Matter Studies** ### **E. Gravitational Wave Astronomy** --- ### **A. Molecular Biology** ### **B. Molecular Genetics** ### **C. Molecular Ecology** ### **D. Molecular Evolution** ### **E. Molecular Medicine** --- ### **A. Surface Chemistry** ### **B. Surface Physics** ### **C. Tribology** --- ### **A. Comparative Planetology** ### **B. Atmospheric Chemistry** ### **C. Atmospheric Dynamics** --- ### **A. Exoplanet Detection** ### **B. Exoplanet Characterization** ### **C. Habitability Studies** --- This map illustrates the interwoven nature of natural sciences, highlighting the vast array of disciplines dedicated to understanding the natural world. Each field contributes unique insights, and their overlaps foster interdisciplinary research, driving scientific discovery forward. #### List The natural sciences encompass a broad range of fields that study the natural world. Here is a comprehensive list, including various sub-disciplines and specializations: ### 1. [[Physics]] - Classical Mechanics - Quantum Mechanics - Thermodynamics - Electromagnetism - Optics - Astrophysics - Cosmology - Particle Physics - Nuclear Physics - Plasma Physics - Field Theory - Condensed Matter Physics - Acoustics - Computational Physics - Experimental Physics - Theoretical Physics - Biophysics - Geophysics - Materials Science - Quantum Field Theory - Relativity ### 2. Chemistry - Organic Chemistry - Inorganic Chemistry - Physical Chemistry - Analytical Chemistry - Biochemistry - Environmental Chemistry - Industrial Chemistry - Theoretical Chemistry - Pharmacology - Materials Chemistry - Nuclear Chemistry - Medicinal Chemistry - Polymer Chemistry - Electrochemistry - Photochemistry - Quantum Chemistry - Computational Chemistry - Spectroscopy - Thermochemistry - Chemical Kinetics ### 3. Biology - Molecular Biology - Microbiology - Zoology - Botany - Ecology - Genetics - Evolutionary Biology - Cell Biology - Anatomy - Physiology - Developmental Biology - Biotechnology - Bioinformatics - Biophysics - Marine Biology - Environmental Biology - Conservation Biology - Ethology (Animal Behavior) - Paleobiology - Neurobiology - Virology - Mycology (Study of Fungi) - Phycology (Study of Algae) - Parasitology - Pathology ### 4. Earth Sciences - Geology - Meteorology - Oceanography - Geophysics - Atmospheric Sciences - Hydrology - Soil Science - Paleontology - Mineralogy - Petrology - Glaciology - Volcanology - Seismology - Climatology - Environmental Science - Geochemistry - Planetary Geology - Sedimentology - Geodesy - Earth System Science - Paleoclimatology - Limnology (Study of Inland Waters) ### 5. Astronomy and Space Sciences - Observational Astronomy - Theoretical Astronomy - Astrophysics - Cosmology - Planetary Science - Stellar Astronomy - Galactic Astronomy - Extragalactic Astronomy - Solar Astronomy - Space Exploration - Astrobiology - Astronomical Instrumentation - Celestial Mechanics - Astrophysical Data Analysis ### 6. Interdisciplinary Fields - Environmental Science - Biogeochemistry - Systems Biology - Astrochemistry - Physical Oceanography - Geoinformatics - Ecotoxicology - Paleogeography - Geobiology - Quantum Biology - Neuroethology This list, while extensive, is not exhaustive. The natural sciences are constantly evolving, with new sub-disciplines emerging as science advances and as interdisciplinary fields grow. Each of these branches can be further divided into more specialized areas, reflecting the depth and complexity of the natural world. #### Applied mathematics The mathematics underpinning our universe spans multiple scales and scientific fields, from the quantum realm to cosmic structures. At the smallest scales, quantum mechanics describes particle behavior using complex-valued wave functions governed by the Schrödinger equation, with operators representing observables like position and momentum. The uncertainty principle, expressed mathematically as ΔxΔp ≥ ħ/2, limits simultaneous knowledge of conjugate variables. Quantum field theory extends this framework, treating particles as excitations of underlying fields, with the Standard Model using gauge theories based on SU(3) × SU(2) × U(1) symmetry groups to describe fundamental forces. At larger scales, classical mechanics emerges, with Newton's laws of motion and universal gravitation describing macroscopic object interactions. These laws can be reformulated using the principle of least action, leading to Lagrangian and Hamiltonian mechanics. Electromagnetic phenomena are described by Maxwell's equations, unifying electricity and magnetism. Einstein's special relativity introduces Lorentz transformations and the famous equation E = mc², while general relativity describes gravity as spacetime curvature using tensor calculus and differential geometry, with the Einstein field equations relating matter distribution to spacetime geometry. In thermodynamics and statistical mechanics, concepts like entropy and free energy are formulated using probability theory and combinatorics, with the laws of thermodynamics governing energy transformations. Fluid dynamics employs vector calculus and partial differential equations like the Navier-Stokes equations to model fluid behavior. In astronomy and cosmology, the Friedmann equations, derived from general relativity, describe the universe's expansion, while models of stellar evolution use nuclear physics and hydrostatic equilibrium equations. Chaos theory and nonlinear dynamics, utilizing concepts from topology and differential equations, explain complex systems' behavior across various fields. Information theory, founded on Claude Shannon's work, quantifies information content and transmission, finding applications in fields from communications to biology. Group theory and symmetry principles underlie various physical laws and conservation rules. Computational methods, including numerical analysis and Monte Carlo simulations, are crucial for modeling complex systems in fields ranging from climate science to materials engineering. Chemistry leverages quantum mechanics for understanding molecular structure and bonding, using the Born-Oppenheimer approximation to simplify the Schrödinger equation for molecules. Chemical kinetics uses rate laws, often expressed as differential equations, to describe reaction rates. Statistical thermodynamics bridges microscopic and macroscopic properties using partition functions and the Boltzmann distribution. In biology, population genetics uses the Hardy-Weinberg principle, expressed as p² + 2pq + q² = 1, to model allele frequencies in populations. Ecological interactions are often described using Lotka-Volterra equations, a system of nonlinear differential equations modeling predator-prey dynamics. In neuroscience, the Hodgkin-Huxley model, a set of nonlinear differential equations, describes action potential propagation in neurons. Systems biology employs graph theory and network analysis to study complex biological interactions. In earth sciences, geophysics uses partial differential equations like the heat equation to model Earth's internal processes. Plate tectonics is described using vector calculus for plate motions. Climate models employ complex systems of differential equations, incorporating fluid dynamics and thermodynamics to simulate global climate patterns. In materials science, crystal structures are analyzed using group theory and Bravais lattices. The behavior of materials under stress is modeled using tensors in continuum mechanics. Solid-state physics employs band theory, using Bloch's theorem and the Schrödinger equation to describe electron behavior in periodic potentials. Computer science fundamentals rest on discrete mathematics, including graph theory, combinatorics, and formal logic. Algorithm analysis uses Big O notation to describe computational complexity. Cryptography employs number theory, particularly modular arithmetic and prime factorization. In economics, game theory uses mathematical models to analyze strategic interactions, with concepts like Nash equilibria described using systems of equations. Financial mathematics employs stochastic calculus, with the Black-Scholes equation modeling option pricing. Linguistics uses formal language theory, employing concepts from automata theory to describe grammar structures. Information theory quantifies language complexity and efficiency. Psychology and cognitive science use Bayesian inference to model perception and decision-making, with Bayes' theorem providing a mathematical framework for updating beliefs based on evidence. In acoustics, the wave equation describes sound propagation, while Fourier analysis is used to decompose complex sounds into frequency components. Optics uses ray tracing and wave optics, with Maxwell's equations describing electromagnetic wave propagation and phenomena like diffraction and interference. Machine learning's mathematical foundation integrates multiple disciplines. Linear algebra provides the framework for data and parameter representation through vectors and matrices. Calculus, especially gradient descent, drives optimization in model training. Probability theory and statistics underpin data analysis and model evaluation. Information theory contributes concepts like entropy for decision-making in algorithms. Functional analysis supports kernel methods in SVMs. Neural networks leverage calculus for backpropagation, while deep learning extends this to complex architectures. Optimization theory guides the training process across various models. Quantum computing extends classical computation using quantum superposition and entanglement, with quantum algorithms expressed in terms of unitary transformations on qubit states. Astrophysics employs nuclear physics to model stellar evolution, using the Saha ionization equation and equations of state under extreme conditions. Gravitational wave detection relies on solutions to Einstein's field equations for binary systems. This vast mathematical framework, encompassing linear algebra, calculus, geometry, topology, and more, forms the language through which we understand and describe the universe's fundamental workings across all scales and scientific disciplines. [[Images/624bf71f6436af4a5d39614bf7476943_MD5.webp|Open: DALL·E 2024-06-24 03.47.15 - A comprehensive visual representation of the mathematics underpinning our universe, spanning multiple scales and scientific fields. At the smallest sc.webp]] ![[Images/624bf71f6436af4a5d39614bf7476943_MD5.webp]]