Author: John F. Lindner

  • Spinors

    John F. Lindner

    Fermions like electrons, protons, and neutrons inhabit a 720° world: 360° rotations negate their quantum states, but 720° rotations restore them. A simple macroscopic model of such spinors is an arrow translating on a Möbius strip: as the center circle rotates, the attached arrow flips after 360° but flips back after 720°. In Dirac notation but…

  • Squares & Cubes

    John F. Lindner

    Marvelously, the square of the sum of natural numbers is the sum of their cubes! Equivalently, the sum of their cubes is the square of their sum. This mathematical gem is attributed to Nicomachus of Gerasa who lived almost 2000 years ago. For example, More generally, or The accompanying animation illustrates the identity, where the cubes…

  • Transition

    John F. Lindner

    As I transition to emeritus status tomorrow, I reflect on 33 years at Wooster. I am thankful for the freedom I’ve had to design my own courses, including eight first-year seminars; for the flexibility to explore a wide range of research topics, from celestial mechanics to biophysics to dancing in reduced gravity; and for six…

  • Archimedes & Euler

    John F. Lindner

    A complex function that is its own derivative normalized to one at zero implicitly defines the famous Archimedean and Euler constants of circular motion and exponential growth. Even in a world of strong gravity, where the ratio of a circle’s circumference to its diameter noticeably varied from place to place, this exponential function and the axioms of mathematics…

  • Free-Fall Spinning Tunnels

    John F. Lindner

    Jump into an evacuated hole drilled straight through a uniform, static Earth-like sphere. Accelerate to 7.9 km/s (or 18 000 m.p.h.) at the center, then decelerate back to zero at the antipodes 42 minutes later! Step out of the hole upside down — or return 84 minutes after you left. Last fall, as part of his senior thesis,…

  • Geographic Tongue

    John F. Lindner

    The improbable email was from a pre-dental math major asking about physics research projects combining math and dentistry, but my reaction was, “Yes — only at Wooster!”. Like animated tattoos, the surface patterns of benign migratory glossitis slowly move on the human tongue. I knew my colleague Niklas Manz was working with my dentist to model…

  • Mars Sky Crane

    John F. Lindner

    At the NASA press conference today, chief engineer Adam Steltzner presented three iconic images of the space age: Armstrong’s photo of Aldrin on the lunar surface, Voyager 1’s photo of Saturn and its rings from above the ecliptic, the Hubble Space Telescope’s photo of the Eagle Nebula’s “Pillars of Creation” star-forming region. And then he…

  • Nightfall

    John F. Lindner

    NASA’s Transiting Exoplanet Survey Satellite (TESS) has discovered a sextuply-eclipsing sextuple star system. I think of “Nightfall”. The six stars of TCY 7037-89-I orbit each other in three binary pairs, as in the schematic. The primaries are slightly larger and hotter than our sun and the secondaries are about a half as large and a…

  • Chemical Clock

    John F. Lindner

    Wooster’s summer 2019 Sherman-Fairchild group just published, “Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles”, in Physica A. Working with Fish Yu ’21, Chase Fuller ’19, Margaret McGuire ’20, and Niklas Manz (Physics) was wonderful. Extending previous work with Reba Glaser (SUNY Geneseo)’19 and Nate Smith ’18, we wrote computer…

  • Dragon Eye

    John F. Lindner

    “Resilience rises! Not even gravity contains humanity when we explore as one for all.” My eyes were glued to NASA-TV last weekend as I followed the flight of the SpaceX Dragon “Resilience” to the International Space Station. Ferrying a diverse Crew 1 of Mike Hopkins, Victor Glover, Shannon Walker, and Soichi Noguchi for a six-month…

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