19+ hour, 1+ min ago  (240+ words) Last week I wrote about the orbit of Artemis II. The orbit of Artemis I was much more interesting. Because Artemis I was unmanned, it could spend a lot more time in orbit. The Artemis I mission took 25 days while Artemis…...

18+ hour, 12+ min ago  (94+ words) I recently found out about Andrica's conjecture: the square roots of consecutive primes are less than 1 apart. In symbols, Andrica's conjecture says that if pn and pn+1 are consecutive prime numbers, then "pn+1 " "pn < 1. This has been empirically verified for…...

2+ day, 17+ hour ago  (343+ words) Landauer's principle gives a lower bound on the amount of energy it takes to erase one bit of information: E " log(2) k B T where k B is the Boltzmann constant and T is the ambient temperature in Kelvin. The…...

3+ day, 19+ hour ago  (571+ words) The best way to run AI and remain HIPAA compliant is to run it locally on your own hardware, instead of transferring protected health information (PHI) to a remote server by using a cloud-hosted service like Chat GPT or Claude....

5+ day, 3+ hour ago  (289+ words) This post will look at the problem of updating an average grade as a very simple special case of Bayesian statistics and of Kalman filtering. Suppose you're keeping up with your average grade in a class, and you know your…...

6+ day, 1+ hour ago  (269+ words) I used the term perilune in yesterday's post about the flight path of Artemis II. When Artemis is'closest to the moon it will be furthest from earth because its closest approach to the moon, its perilune, is on the side of…...

6+ day, 16+ hour ago  (279+ words) I was looking through an old geometry book [1] and saw a hyperbolic analog of Napier's mnemonic for spherical trigonometry. In hindsight of course there's a hyperbolic analog: there's a hyperbolic analog of everything. But I was surprised because I'd never…...

1+ week, 4+ hour ago  (336+ words) The Artemis II mission launched yesterday. Much like the Apollo 8 mission in 1968, the goal is to go around the moon in preparation for a future mission that will land on the moon. And like Apollo 13, the mission will swing around…...

1+ week, 1+ day ago  (105+ words) You can take the diagram that illustrates the'nth pentagonal number and warp it into the base of the image that illustrates the (2n " 1)st triangular number. If you added a diagram for the (n " 1)st triangular number to the bottom of…...

1+ week, 2+ day ago  (350+ words) I'm skeptical that quantum computing will become practical in the next 100 years. However, if it does become practical and we don't prepare, the world's financial system could collapse. Everyone agrees we should prepare for quantum computing, even those of us…...