Category Archives: science

Wheels that are not circles

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Triangle-Wheeled Bike Gives New Meaning to ‘Tricycle’. The inventors

… went back to the drawing board to see if they could come up with a bike design featuring triangular wheels. They succeeded, and unlike the square-wheeled bike, these triangular wheels actually roll like round ones.

This is known as the Reuleaux triangle. I first ran across it in Poul Anderson’s 1963 SF story The Three Cornered Wheel, which I read sometime in high school (1964-68). A stranded spaceship crew needs to transport a heavy object over land. Unfortunately, the use of anything circular for mundane purposes is forbidden by the religion of the natives. However, the use of a curve of up to 1/3 of a circle is allowed for a sufficiently important cause. The young hero figures out that using such a “three cornered wheel” will solve the crew’s problem without offending the religious authorities.

Seeing Stars on the Moon

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Why don’t moon photos show stars?. Specifically, why can’t we see the stars in the photographs of the Apollo Astronauts on the moon? As the article clearly explains, all of the pictures were taken during lunar daylight, during which the lunar surface is well illuminated by the sun. This completely washes out the light from the stars. If you made a long enough exposure to catch the stars, the lunar surface, the astronauts and their gear, and the lunar lander would be grossly overexposed. This would defeat the purpose of documenting human activity on the moon.

In fact, this issue was anticipated by Arthur C. Clarke in his classic science fiction novel A Fall of Moondust, first published in 1961, eight years before the first Apollo expedition landed on the moon. Continue reading →

Electrons and Positrons

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I have known about Electron–positron annihilation for at least 52 years, from my course in Atomic and Nuclear Physics at Carleton College in the spring of 1970 if not before. The reaction is

e– + e+ → γ + γ

I had always assumed that the inverse reaction

γ + γ → e– + e+

was also possible because of time reversal symmetry. Apparently so had everyone else, but it has only recently been observed: Matter arises from light? We finally know the answer to this question!. Even now there is a caveat about “virtual” as opposed to “real” photons.

Black Hole Lifetimes

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Black holes are not totally black! They will evaporate by Hawking radiation. This is required by Thermodynamics and Quantum Mechanics. All properties of a Schwarzschild Black are determined by its mass, so if you know the mass the lifetime and other properties follow automatcally. Or you can start with the lifetime and determine the initial mass. Or the Schwarzschild radius, or the temperature, or the entropy, etc. For black holes comparable in mass to “normal” astronomical objects this lifetime is much longer than the current age of the universe. Viktor Toth’s Hawking radiation calculator is a convenient tool for such calculations. Here are some results:

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UFOs? OK. Alien Spacecraft? No so fast.

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I found How Washington Got Hooked on Flying Saucers to be fascinating if somewhat depressing. “There is nothing new under the sun.”

This is a subject I have been watching from a safe distance for well over half a century, when I first read Martin Gardner’s Fads and Fallacies in the Name of Science (Few books have influenced me more than this one).

I met J. Allen Hynek in my last year of high school, 1967-68, when I was a student in the Astro-Science Workshop (Still around although in a different format) at Chicago’s Adler Planetarium. This program was organized and run by Hynek. Hynek was a pleasant and interesting speaker, and a good teacher, but he never spoke to us kids about UFOs.

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My First Peek at Renormalization

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I have vaguely known about renormalization since the 1970’s, but had never seriously studied it. Out of curiosity I watched Renormalization and envelopes on YouTube Thursday evening. This was the final lecture of the Asymptotics and perturbation methods course by Prof. Steven Strogatz of Cornell University. I had watched the first two lectures of the course, but none of the others until this one. Fortunately, there were relatively few explicit dependencies on them, so I was able to follow this quite well. Here is the description:

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