Author: John F. Lindner

  • Outer Planet Cloud Colors

    John F. Lindner

    From my teens to my twenties, from junior high school to graduate school to young professor, I excitingly followed the first reconnaissance of the outer solar system by the Pioneer and Voyager spacecraft. But the exploration isn’t over. For the last decade, the Hubble Space Telescope has been systematically observing the colors and dynamics of…

  • Sum of Reciprocals

    John F. Lindner

    The sum of the reciprocals of the natural numbers diverges, but slowly, like the logarithm of the number of terms. The sum of the reciprocals of the prime numbers also diverges, but even more slowly, like the logarithm of the logarithm of the number of terms, as the primes are sparse in the naturals! Here…

  • There and Back Again

    John F. Lindner

    I awoke yesterday at dawn in a log cabin in Vermont. Fortunately, the wifi was good. Each successive test of the SpaceX Superheavy Starship has been a significant improvement over the previous one, and test five was no exception, with both the booster and the ship demonstrating soft pinpoint landings — except this time, the…

  • Rey’s Theme

    John F. Lindner

    Yesterday, as part of the Polaris Dawn mission, SpaceX engineer Sarah Gillis became the youngest person to walk in space. Today, on a space-qualified violin, she performed Rey’s Theme, composed by John Williams as the musical leitmotif for Rey, the central character in the Star Wars movie The Force Awakens. The performance audio and video…

  • Skywalker

    John F. Lindner

    Up before dawn this morning for the Polaris Dawn space walk, the first commercial space walk and the furthest from Earth since the Apollo program over half a century ago. After stalling for so long, human space flight is again advancing. Polaris Dawn’s Commander Jared Isaacman, Pilot Scott “Kidd” Poteet, Mission Specialist Sarah Gillis, and…

  • An academic in industry

    John F. Lindner

    Recently, with members of NCSU’s Nonlinear Artificial Intelligence Lab, I completed a 3.5-year project as a subcontractor working on an industrial project. As an academic, this was a novel experience. Unlike most of my research, this work will not result in a journal article or conference presentation, although it might one day contribute to an…

  • Does a charge in gravity radiate?

    John F. Lindner

    Caltech, Saturday night, grad student pizza. The conversation turns to a famous general relativity puzzle: does an electric charge at rest in a gravitational field radiate? According to Einstein’s equivalence principle, a static homogeneous gravitational field is indistinguishable from constant acceleration in empty space, and as is well known, accelerating charges radiate. Does that mean…

  • The Longest Flight

    John F. Lindner

    As a kid pouring over the Guinness Book of World Records, I was astonished by the record longest flight, which lasted not just a few hours – as I would have guessed – but more than two months! Today, nearly 65 years later, that amazing achievement remains one of aviation’s most enduring records. For over…

  • Where Are the Stars?

    John F. Lindner

    When viewing space photography, such as Apollo or International Space Station photos, people often ask, “Where are the stars?” Typically such photos properly expose the bright lunar or space station surfaces and consequently underexpose the dim background stars, rendering space as featureless black. Current ISS astronaut Matthew Dominick has been experimenting with photography, and his…

  • Bertrand’s Postulate

    John F. Lindner

    When searching for prime numbers, the next prime number is no larger than twice the current number. Postulated by Joseph Bertrand, first proved by Pafnuty Chebyshev, I present an elementary proof based on one by the teenage Paul Erdős. Erdős was one of the most prolific twentieth century mathematicians, publishing about 1500 articles with more…

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