Category: Mathematics

Although almost all ordinary mass effectively arises from the kinetic and binding energy of quarks and gluons bound to protons and neutrons in atomic nuclei, the Higgs mechanism does endow some particles like quarks and weakons with intrinsic masses. Here I gently introduce the Higgs mechanism without using loose analogies like vacuum field viscosity. Stationary…

A vector is the sum of its components, a mechanical vibration is a combination of its normal mode motions, a quantum state is a superposition of its eigenstates, and any “nice” function is a Fourier sum of real or complex sinusoids, . The animation below traces the Wooster W in epicycles of 100 circles-moving-on-circles in the…

Despite growing up in three dimensions, as a kid I did not recognize one of 3D’s deep and subtle properties: full rotations tangle, but double rotations untangle! Following physicist Paul Dirac, twist a belt one full turn about its length. The 360° single twist cannot be undone without changing the belt buckles’ orientations, although the twist…

In quantum electrodynamics, the bare charge of an electron is infinite, but the renormalized dressed charge is finite. The bare electron shields itself by polarizing the virtual electron-positron pairs of the nearby quantum vacuum to reduce its coupling at large distances to in natural units, where the “I” decorating the equals sign denotes an informal relationship. Renormalization techniques help…

I just bought a new calculator. New to me, that is, but older than me. Inspired by the 1600s Gottfried Leibniz stepped cylinder and the 1800s Thomas de Colmar arithmometer, the Curta mechanical calculator design was developed by Curt Herzstark while imprisoned in the Buchenwald concentration camp during World War II. Curta calculators were manufactured between…