V_3_15 — Functional Analysis: Infinite-Dimensional Spaces and Operators

Functional analysis — the study of infinite-dimensional vector spaces (function spaces) and the linear operators acting on them — is one of the great unifying frameworks of 20th-century mathematics. It provides the rigor

V_2_22 — Imaginary Numbers: From "Truly Imaginary" to Physically Necessary

In 1545, the Italian mathematician Girolamo Cardano encountered expressions involving the square root of a negative number while solving cubic equations in his Ars Magna. He used the expression — computed with it, obtain

K_0_00 — Consciousness & Mind: Section Summary

K_1_00 — Theories Frameworks: Subfolder Summary

Q_1_00 — Foundations Cosmological Models: Subfolder Summary

Q_4_32 — The Fundamental Constants: Physics, Life, and Mathematics

The universe runs on numbers — and not arbitrary ones. A small set of fundamental constants, mostly dimensionless, determines every property of matter, energy, space, and time. Change any of them by a fraction and atoms

Q_4_00 — Physics Methods: Subfolder Summary

Q_2_20 — Black Hole Information Paradox & Hawking Radiation

The black hole information paradox is arguably the deepest unsolved problem in theoretical physics, lying at the intersection of general relativity, quantum mechanics, and thermodynamics. In 1974, Stephen Hawking showed

Q_0_00 — Cosmology & Astrophysics: Section Summary

ZD_1_00 — Foundations Theory: Subfolder Summary

ZD_0_00 — Information & Computation: Section Summary

ZD_4_00 — Applied Interdisciplinary: Subfolder Summary

S_5_00 — Society Infrastructure: Subfolder Summary

ZA_2_00 — Gravity Spacetime Cosmology: Subfolder Summary

ZA_5_03 — Infrasound — Physics, Biological Effects, and Anomalous Phenomena

Infrasound — sound below the conventional human hearing threshold of ~20 Hz — is a pervasive physical phenomenon generated by natural sources (wind, ocean waves, volcanic eruptions, earthquakes, thunderstorms, animal voc

ZA_5_19 — Bekenstein Bound: Information Limits and the Physics of Black Holes

The Bekenstein bound — proposed by Jacob Bekenstein in 1981 — establishes a fundamental upper limit on the amount of information (entropy) that can be contained within a given region of space with a given amount of energ

ZA_5_22 — Ionizing Radiation: Physics, Biological Effects, and Applications

Ionizing radiation — electromagnetic waves or particles with sufficient energy (>10 eV) to remove electrons from atoms — was discovered in the final years of the 19th century through a rapid sequence of breakthroughs: Wi

ZA_4_00 — Condensed Matter Thermodynamics: Subfolder Summary

ZA_4_22 — Superconductivity: BCS Theory to High-Temperature

Superconductivity — the complete vanishing of electrical resistance and the expulsion of magnetic fields below a critical temperature — was discovered by Heike Kamerlingh Onnes on April 8, 1911, in mercury at 4.2 K. The

ZA_4_11 — Time Crystals and Discrete Time Symmetry Breaking

A time crystal is a phase of matter that spontaneously breaks time-translation symmetry — the fundamental physical principle that the laws of physics are the same at all times (which, via Noether's theorem, is linked to