Mowing the Lawn in Spirals

Like a circle in a spiral / Like a wheel within a wheel / Never ending or beginning / On an ever-spinning reel. The Windmills Of Your Mind Broadly speaking, a spiral curve originates at a central point and gets further away (or closer) as it revolves around the point. Spirals abound in nature, being … Continue reading Mowing the Lawn in Spirals →

A Few Wild Functions

Sine Function: $latex {\mathbf{y=\sin x}}&fg=000000$ The function $latex {y=\sin x}&fg=000000$ is beautifully behaved, oscillating regularly along the entire real line $latex {\mathbb{R}}&fg=000000$ (it is also well-behaved for complex $latex {x}&fg=000000$ but we won't consider that here). Chirp Function: $latex {\mathbf{y=\sin x^2}}&fg=000000$ Now $latex {y=\sin x^2}&fg=000000$ is also well-behaved: its oscillations become more rapid as $latex … Continue reading A Few Wild Functions →

It’s a Small – Networked – World

Networks are everywhere in the modern world. They may be physical constructs, like the transport system or power grid, or more abstract entities like family trees or the World Wide Web. A network is a collection of nodes linked together, like cities connected by roads or people genetically related to each other. Such a system … Continue reading It’s a Small – Networked – World →

Which Way did the Bicycle Go?

``A bicycle, certainly, but not the bicycle," said Holmes. In Conan-Doyle's short story The Adventure of the Priory School Sherlock Holmes solved a mystery by deducing the direction of travel of a bicycle. His logic has been minutely examined in many studies, and it seems that in this case his reasoning fell below its normal … Continue reading Which Way did the Bicycle Go? →

New Tricks: No Clicks

The quality of music recordings on compact discs or CDs is excellent. In the age of vinyl records, irritating clicks resulting from surface scratches were almost impossible to avoid. Modern recording media are largely free from this shortcoming. But this is curious: there are many reasons why CD music can be contaminated: dirt on the … Continue reading New Tricks: No Clicks →