Most popular posts of 2024

The time it takes earth to orbit the sun is not a simple multiple of the time it takes earth to rotate on its axis. The ratio isn’t even constant. The time it takes earth to circle the sun wobbles a bit, and the rotation of the earth is slowing down slightly. The ratio is […] The post Unix Time and a Modest Proposal first appeared on John D. Cook.

Stirling’s asymptotic series for the gamma function is Now suppose you’d like to find an asymptotic series for the function 1/Γ(z). Since the series for Γ has the form f(z) times an infinite sum, it would make sense to look for a series for 1/Γ of the form 1/f(z) times an infinite sum. The hard […] The post Series for the reciprocal of the gamma...

My nephew recently told me about being on a camping trip and seeing a long line of lights in the sky. The lights turned out to be Starlink satellites. It’s fairly common for people report seeing lines of these satellites. Why would the satellites be in a line? Wouldn’t it be much more efficient to […] The post Starlink configurations first...

I’ve been playing around with Grok today, logging into some of my X accounts and trying out the prompt “Draw an image of me based on my posts.” [1] In most cases Grok returned a graphic, but sometimes it would respond with a text description. In the latter case asking for a photorealistic image made […] The post Putting a face on a faceless...

OpenAI has just released its full o1 model—a new kind of model that is more capable of multi-step reasoning than previous models. Anthropic, Google and others are no doubt working on similar products. At the same time, it’s hotly debated in many quarters whether AI models actually “reason” in a way similar to humans. Emily […] The post Can AI...