odditudes-and-weirdities

As I'm wont to do, here's another of my yearly reviews. It's at least a weak attempt to stay in touch with many of you that I rarely see in person. As I explain every year , the main downside is that I really don't do very much. And much of what I do is not particularly interesting. If any of you nod off during this, at your age you probably needed the rest anyway. If you're wondering, that's dinosaur ... wearing an Ankylosaurus hoodie Health : Barring a knee replacement, I can't imagine I'll ever have a truly healthy knee, though my impression is that it was somewhat less troublesome this year. I have 2 amateurish theories about that: Perhaps the collagen supplements I've been taking in recent years has mitigated the knee problems a bit. I've also wondered whether they've slowed down my hair loss a little. It's kind of hard to say. Maybe, just maybe, I've done a better job of backing off my morning jogging when the knee starts to bec...

Wrong Line Day - September 2 Have you ever filled out a form incorrectly by putting something on the wrong line? All it takes is a badly designed form or just being distracted to botch up a form, sometimes (especially on government forms) forcing you to go through the whole thing again. ( Murphy's Law ensures that you won't make or notice the mistake until you're nearly done with the form.) We celebrate Wrong Line Day on September 2 because of a potentially impactful signature that went on the wrong line in 1945. The Canadian representative signing the "Japanese Instrument of Surrender", documenting the end of WWII, signed on the wrong line . It's unclear how Colonel Lawrence Moore Cosgrove made this mistake, triggering every following signatory (France, Netherlands, and New Zealand) to also sign on incorrect lines. It sounds like the Japanese considered making a big deal out of this, but the instrument got hand-corrected country names before things went ove...

Happy Catalan Numbers Day! Catalan numbers are a sequence of numbers that represent the counts of several mathematical concepts. They're named after Eugene Charles Catalan , a French-Belgian mathematician who worked on number theory and combinatorics .  One of the things Catalan numbers count are the number of Dyck words, which are words consisting of X's and Y's which: Consist of an equal number of X's and Y's, And where all beginning sub-words have their number of X's greater than or equal to their number of Y's. For example, XYXY is a Dyck word because XYX, XY, and X are all beginning sub-words where there are at least as many X's as Y's. But XYYX is not a Dyck word because XYY is a beginning sub-word where there are more Y's than X's. Note that if you substitute "(" for X and ")" for Y, Dyck words constitute a valid sequence for arithmetic or regular expressions. Here are the smallest Dyck words. This video provides...

Another year, another boring summary of that year's trip around the sun. (For those struggling with insomnia, I have a series of these: 2024 , 2023 , 2022 .) Here's this year's picture, meant to suggest that it's been relatively cold here this winter. (I actually do dress like this on especially cold days; the key to staying warm is "layers, layers, layers".) Health : My knee and back continue to cause sporadic issues but they don't normally prevent me from doing much. I somehow managed to hurt my hip. I'm not sure how it happened; my best guesses are pulling stubborn weeds out of the ground or trying to open a sliding glass door that doesn't slide very well. On the bright side, staying away from the door and with no wintertime weed-pulling activities, the hip issue seems to have (temporarily?) gone away. As I'm wont to do, I got flu and COVID vaccinations in the autumn, and (thus far) I haven't gotten sick this season. (I do worry that thi...

Here's the Cornell Lab of Ornithology jigsaw puzzle I recently completed. Although there are 120 bird species in the picture, there are a few cases where, due to sexual dimorphism , they show a picture of both a male and a female, so there are over 120 birds pictured. It's a 1000 piece puzzle. The birds are all indigenous to eastern/central North America, though it's not a complete set.  Some of you have heard this before, so be prepared for a recap. Here are some observations: I don't really have the proper lighting for doing jigsaw puzzles in my apartment. I have those somewhat out-of-date "pig-tail fluorescent" light bulbs, which doesn't exactly emulate natural light all that well. And even during broad daylight my living room doesn't get the sunlight that would be helpful, especially in winter. A couple times I turned a flashlight on some pieces, detected some red or yellow feathering, and quickly found a spot for them. (The flashlight trick waned ...

On the eleventh day of the eleventh month we celebrate This One Goes to Eleven Day! Inspired by a Frazz cartoon , which was inspired by the This Is Spinal Tap movie, this day is about going beyond what conventionally would be a limit. (Admittedly in the movie they changed the labels more than extended their limits, but you've got an opportunity to do better than that!)

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 ...

Happy Moose Day! You'll find some references to this holiday on the web, but not much information about it. My hunch is that there's no strong reason to celebrate Moose on this particular day. The largest living species of deer is the Moose, and they are big dudes. Males are 5-7' tall at the shoulder and weight between 8-16 hundred pounds. Adults are too big for most predators, though the largest predators in an ecosystem will occasionally tangle with them. While most deer project classic good looks and gracefulness, the Moose could probably best be described as homely and ungainly. They're actually the most likely wild animal to injure someone in North America, though I suspect that's partly because they're more widespread than Grizzly Bears and Bison. The name "moose" is based on a Native American word for the animals. Confusingly the British call this animal an "elk", which here in North America refers to the Wapiti . I suppose if you...

Happy Newt Years Day! You may have a bunch of people wishing you a Happy Newt Year today, though many of them fail to pronounce the last "t" of "newt" [1]. Still, you have to give them credit for their enthusiasm about newts. Newts are a set of semiaquatic salamanders , and thus are amphibians . Despite a superficial resemblance to lizards, they are much more closely related to frogs and toads. Check here to find out if your salamander buddy is also a newt. Though I haven't taken a picture of a newt myself, I do have a picture of one of their salamander cousins . This Eastern Newt from iNaturalist shows just how photogenic they can be though. July 19, 2011 Photo 249874612, (c) litt10, some rights reserved (CC BY-NC) [1] Perhaps this is similar to Stephen Colbert, where the family doesn't pronounce the last "t" either.

Happy Look and Say Day! It celebrates an especially tricky sequence of numbers, the Look and Say Sequence. Look and Say Day is about the following sequence of numbers: 1 11 21 1211 111221 312211 13112221 etc Simply seeing this sequence, the average person probably wouldn't figure out the next numbers (1113213211 and 31131211131221, FWIW) ... but since I told you this is Look and Say Day, you may have already figured it out. Starting with a "seed number" of 1, each subsequent number is basically the pronunciation of like digits: 1 (one 1) 11 (two 1s) 21  (one 2, two 1s) 1211  (one 1, one 2, two 1s) 111221 (three 1s, two 2s, one 1) 312211 This turns out to be a fairly easy (if lengthy) sequence to derive. (It might be one of those puzzles that a child is more likely to resolve than an adult, since they'll spend less time going down incorrect paths.) There's a video on the Look and Say Sequence here . We celebrate Look and Say Day on December 11 (or 12/11) because 12...

Happy Semiprime Numbers Day! Semiprime numbers are the product of exactly 2 prime numbers , so 4 (2 X 2) and 6 (2 X 3) are semiprimes, but 8 (2 X 2 X 2) and 30 (2 X 3 X 5) are not. More examples are here: Public key cryptography depends on the difficulty of factoring very large semiprime numbers for its effectiveness. Semiprime Numbers Day is celebrated on the date 10/14, or October 14, since 10 and 14 are the largest consecutive semiprime numbers forming a valid date.

Happy Powerful Numbers Day! Powerful numbers  (aka squareful numbers) are ones such that for every number dividing it that is prime or 1, the square of the divisor is also a divisor. Powerful numbers are basically a subset of the composite numbers in addition to the number 1, and contain the square numbers as a subset. Here's some of the arithmetic that determines powerful numbers. We celebrate Powerful Numbers Day today because 9 and 27 are the largest powerful numbers that form a valid date: 9/27 or September 27.

Happy Square Numbers Day! Square numbers are the numbers formed when you square a positive integer, making them a fairly easy concept to grasp. Here is the beginning of the sequence: While triangular numbers are the integers representing the number of objects needed to form equilateral triangles, square numbers similarly form squares of different sizes. They are also a subset of the powerful numbers . We celebrate today as Square Numbers Day because the 2 largest consecutive square numbers that form a date are 9 and 16: 9/16 or September 16.

Happy World Goat Day! This is another holiday where the webpage I used to use for it disappeared so I'm writing one to replace it. As is often the case I don't know why today was selected for World Goat Day. As a species that was domesticated back in prehistoric times, today's date is unlikely to denote some milestone in human-goat relations. Regardless of why today's date is World Goat Day, goats have been important livestock for an estimated 10,000 years. But I don't think today is supposed to be about the domesticated goat in particular; since the original webpage I had for it was for a zoo, I suspect today is about celebrating all the animals in the goat genus . This includes guys like the Markhor (the world's largest goat), various ibexes like the Alpine Ibex , domesticated goats, et al. (Sorry Mountain Goat , but unfortunately you're not considered to be a true goat, though clearly a goat relative.) Further up the taxonomy hierarchy, goats are in the...

Happy Almost Perfect Numbers Day! Today we celebrate numbers that aren't perfect numbers but are almost perfect numbers  (aka slightly deficient numbers aka least defective numbers). Perfect numbers (in case you've forgotten) are the numbers such that if you sum up their divisors the result is 2 times the number itself. For example, the divisors of 6 are 1, 2, 3, and 6, and if you sum them up you get 1+2+3+6=12, which is also 2 x 6. Almost perfect numbers are numbers where the sum of the divisors is 1 less than 2 times the number. For example, the divisors of 4 are 1, 2, and 4, and the sum of them is 1+2+4 = 7, which is 1 less than 2 x 4. All the known almost perfect numbers are powers of 2, like 2x2 = 4, 2x2x2 = 8, 2x2x2x2 = 16, etc. It hasn't been proven that every almost perfect number is of this form, though given the computational power we have today, if other forms exist, they must be very large almost perfect numbers. Here is the beginning of the almost perfect numb...