Author: John F. Lindner

  • Relaxing Fermat

    John F. Lindner

    In 1637, while reading a copy of Diophantus’s Arithmetica, Pierre de Fermat famously scribbled “Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.” which roughly translates to “It…

  • Stainless Steel Starship

    John F. Lindner

    Welders in a Texas swamp have built a starship. But don’t bet against SpaceX. Starship is a prototype upper stage for a next-generation, fully reusable, two-stage-to-orbit launch vehicle designed to enable the human exploration of the solar system and the colonization of Mars. It’s made from stainless steel. (A little carbon converts iron to hard steel;…

  • After the Moonwalk

    John F. Lindner

    Iconic is Neil Armstrong’s photograph of Buzz Aldrin during the first moon walk, with Armstrong reflected in Aldrin’s visor. Much less well-known is this pair of photographs taken just after the moon walk. To my eyes, Armstrong seems exhausted but happy; Aldrin seems satisfied … and over his shoulder, almost casually, is a window, and…

  • “Contact Light”

    John F. Lindner

    Our TV is broken, so Aunt Nora invites us to her apartment. (Aunt Nora isn’t really our aunt, but she introduced our parents to each other, so that’s what we call her.) My brother Jim and I lie on the floor close to the TV, while the adults sit on the couch. We watch NBC…

  • Wooster Epicycles

    John F. Lindner

    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…

  • Redefining SI

    John F. Lindner

    Today the SI (Système international d’unités) base units are redefined. The following are now exact. Memorize these numbers! Cs-133 transition frequency constant  defines the second. Then light speed constant  defines the meter. Then Planck’s constant  defines the kilogram. Then electron charge constant  defines the Ampere. Then Boltzmann’s constant  defines the Kelvin. And Avogadro’s constant  defines the mole. And luminous efficacy constant  defines…

  • Black Hole Radii

    John F. Lindner

    I set the alarm for 8:55 AM. Brutal, but I wanted to watch live the National Science Foundation Event Horizon Telescope news conference. I was expecting the first image of a black hole, and the EHT team did not disappoint. But the black hole was not the Milky Way’s Sgr A*, but M87*, a thousand…

  • The Longest Day

    John F. Lindner

    The December solstice is the longest day of the year, despite being the northern hemisphere’s shortest daylight. Earth’s sidereal day is the time to rotate 360° with respect to distant stars, about 23 hours and 56 minutes, and its solar day is the time between successive noons, about 24 hours. Earth’s obliquity (tilt) and revolution (orbit) require…

  • Relativistic Colors

    John F. Lindner

    Metallium, Inc. is attempting to manufacture coins made from as many different metals (and elements) as possible, typically 99 to 99.9% pure. My Metallium coin collection currently includes aluminum, titanium, iron, nickel, copper, zinc, silver, tin, and gold coins. Most metals are silvery gray because they absorb ultraviolet light and reflect visible light. However, relativistic…

  • 720° untangles 360° tangles

    John F. Lindner

    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…

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