odditudes-and-weirdities

Happy Interstellar Picard and Dathon at El-Adrel Day! This holiday celebrates one of the more interesting Star Trek TNG episodes . In it, the Enterprise meets the Tamarians, a race of people whose words translate well but without much meaning. The Tamarians employ a dangerous strategy to achieve a communications breakthrough; they transport Picard and their captain, Dathon, down to a planet where they'll need to coordinate together to survive against a dangerous predator. Picard eventually figures out that the Tamarians use allegory to express themselves, and if you don't know the allegorical references, their speech sounds like gibberish. Although the Tamarian captain dies, Picard's breakthrough in understanding the Tamarians allows the Federation to develop relations with them. The phrase "Picard and Dathon at El-Adrel" becomes a new allegory in the Tamarian language, presumably signifying a communications breakthrough or sudden understanding.

As I've (more or less) successfully managed yet another trip around the sun, so lets discuss what happened. This should be similar to what I did in 2022 and 2023 , so if those bored you nearly comatose you should be warned that this will be more of the same. Photographic evidence that I exist. (Almost certainly not an AI generated image of a random old guy.) Health : It wouldn't be a year in review without a passing mention about my left knee. Although I don't recall it swelling up like it used to do, these days I'll sometimes get a fairly sharp pain if I bend it weirdly (which is harder to avoid than you'd think it would be). Still, I go jogging most mornings ... so how bad can the knee really be? I hurt my back this summer. I attribute this to stupidity. At Duke Farms we were cutting down (mostly invasive) plants that were tangling into or just very close to some of their fencing. Since we were cutting on both sides of the fence but were only collecting the debri

Happy Semiperfect Numbers Day!  While perfect numbers are numbers that are equal to the sum of all their proper divisors, semiperfect numbers are equal to the sum of some of their proper divisors. (Yes, this means that all perfect numbers are also semiperfect numbers.) Similar to perfect numbers, semiperfect numbers don't seem to have a lot of application but are more of numerical oddities. Here are the smallest semiperfect numbers, including a couple that are also perfect numbers: And here's the arithmetic that shows why the smaller numbers are or are not semiperfect numbers. We celebrate Semiperfect Numbers Day on December 18 because 12/18 is the latest (American style) date that can be formed using consecutive semiperfect numbers.

Happy Deficient Numbers Day! Deficient numbers (aka defective numbers) are the somewhat disdainful name for the natural numbers that are the companions for the more prestigiously named perfect numbers and abundant numbers . They are numbers where the sum of their divisors is less than twice that number. The start of the deficient numbers is below. It's known that there are an infinite number of both even and odd deficient numbers. Though most odd numbers are deficient, there are exceptions; 945 is the smallest odd abundant number, and thus is the first odd number that's not deficient. Here is the classification the beginning of the natural numbers into deficient, abundant, and perfect numbers. (Some are also noted as semiperfect or almost perfect numbers .) We celebrate the deficient numbers today because the highest 2 consecutive deficient numbers that can form a date are 11 and 13: 11/13 or November 13.

Happy Prime Numbers Day! Prime numbers are quite possibly the favorite set of numbers in mathematics. They consist of natural numbers greater than 1 that are not a product of 2 or more smaller natural numbers. The table below shows the prime numbers less than 51. Interest in prime numbers goes back to ancient times. It's long been proven that there are an infinite number of prime numbers, for example. It's long been controversial whether the number 1 should be included in the primes. Though my initial instincts would be to include it, there are reasons to exclude it . If you want to pick a fight with a mathematician, refer to prime numbers in the past tense . We celebrate prime numbers today because the date can be represented as 11/13, the largest consecutive prime numbers that represent a valid date.  

I've recently completed yet another trip around the sun. While this would be extremely notable if I did it in a spaceship, I did it the easy way: I stayed home and let the Earth do the work of making the journey for me. Similar to last year , I figured I'd update people with the (modest) events of the preceding year. Caveats : Let me set expectations. I'm never going to be confused with that Dos Equis Most Interesting Man in the World . (I'm actually probably on the other side of the boring/interesting spectrum.) Health : Like most people who've been kicking around for 6 decades or so, it's always something . The foot problems that had troubled me in previous years didn't cause much in the way of problems last year, perhaps due to a simple foot-stretching exercise I started doing. On the other hand, my left knee got very achy late last winter. Sometimes it'd feel like my knee was going to buckle on me even doing fairly banal activities like walking down