Author Archives: 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 … Continue reading &… Continue reading →

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 … Continue … Continue reading →

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, t… Continue reading →

Up before dawn this morning to watch 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 … Continue reading &… Continue reading →

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 no… Continue reading →

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 gravi… Continue reading →

After the conference in Switzerland, I stopped in Tübingen to visit Otto Rössler. Nearly everyone who learned about nonlinear systems knows the nowadays named Rössler attractor and his work in chaos theory in the 1970s. For the last four years … … Continue reading →

As a kid, pouring over the Guinness Book of World Records, I was struck by the longest flight; instead of lasting hours, as I would have guessed, it lasted more than two months! Nearly 66 years later, it remains one … Continue reading → Continue reading →

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 relatively bright lunar or space station surfaces and consequently unde… Continue reading →

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 … Co… Continue reading →