tl;dr After the NY Times purged some solutions and available guesses back in February, they quietly reintroduced them as available guesses, and they also shuffled around some of the solutions, without eliminating any.
Wordle was born on June 19, 2021. Perhaps Josh Wardle wanted to celebrate the birth, because the first answer was “cigar.” Being birthed of a nerd, this was known as “Wordle 0.”
Joy often comes with pain, and Wordle is no exception. Wordle was pre-programmed with 2315 answers, so the last Wordle was to have been Wordle 2314, on October 20, 2027. (If you’re into spoilers, you can find all of them here.)
Around Feb 15, 2022, shortly after the New York Times purchased Wordle, they eliminated some words that they felt were obscure or offensive. People noticed because some folks had the original version in their browser cache, and they got a different answer (“agora”) from the folks who wound up with the revised NYT version (“aroma”). “Agora” was the first of six solutions that were eliminated. The other five were “pupal,” “lynch,” “fibre,” “slave,” and “wench.” With 6 fewer words, Wordle will draw its last breath on October 14, 2027.
If you’re a psychiatrist (or psychiatric RNCS) in the US reading this, you are almost certainly aware that all of our billing codes changed on Jan 1, 2013. If you are like most of the psychiatrists I know—at least in private practice—you are at least somewhat freaked out by this. If so, keep reading. If not—for example, if you’re not a psychiatrist in the US—stop reading this immediately and go do something more interesting, like… well, like just about anything other than memorizing a phone book. (There used to be things called phone books… never mind.)
Unlike 2013, the billing codes themselves have not changed, but as of January 1, 2021, the documentation requirements for these codes have gotten significantly less complex and onerous. Like then, this post should be of no interest to you if your are not a US psychiatrist or psychiatric nurse. But if you are—and especially if a significant portion of your practice is psychotherapy—the situation is very different from 2013 because these changes are:
What does the Fong/Walters algorithm do differently? Let’s note what’s the same. Conway’s scheme of “Doomsdays” is still in place, and you still need to know the Doomsday for the start of the century. The difference is in computing the offset. There is no dividing by 12, remembering the quotient, dividing the remainder by 4, etc. (Apparently that part of the method was due to Lewis Carroll, as explained in Part 2 or in Fong’s Scientific American blog post.)
How does the alternate method , which they call “odd+11” work? If you love flowcharts, look here. But it’s pretty simple:
Take the last two digits of the year.
Is it odd? If so, add 11.
Divide your number (which now must be even) by 2.
Is your new number odd? If so, add 11 again.
Reduce your number modulo 7.
Subtract your number from 7 (“take the 7s complement”).
This internet thing, though. It seems to be all rabbit holes, all the way down. In my previous post, I wrote about John Conway’s “Doomsday Algorithm” for figuring out what day of the way “any” day falls on. It seems that there are quite a few people who have spent a lot more time thinking about calendars in general, and mental calendars in particular, than I have. Most of what’s in this post is based on this excellent piece by Chamberlain Fong.
The first helpful thing Fong does is to give some history. Conway’s method has two parts: the identification of particular days of the year as “Doomsdays,” which all fall on the same day of the week. Once you know what day of the week any give year’s Doomsdays fall on, it is easy to figure out the day of the week of an arbitrary date. The other part is to figure out what day of the week the given year’s Doomsdays fall on.
The first part of the algorithm seems to be entirely due to Conway. The second part, interestingly, was apparently worked out by Lewis Carroll—one of the few people in the orbit of mathematicians who may have been more playful that Conway. Martin Gardner, the legendary author of Scientific American’s Mathematical Games column, was a serious student of Carroll, and when he came across Carroll’s work on perpetual calendars, challenged Conway to come up with something simpler.
[This wound up being Part 1 of 3. You can find Part 2 here, and Part 3 here. You don’t need to read all three parts, but Part 3 does actually describe a significantly simpler algorithm than the one Conway used.]
John Horton Conway, a great mathematician of unmatched playfulness, died recently at age 82 of Covid-19. His biographer, Siobhan Roberts, wrote an excellent New York Times obituary. Conway was something of a showman, in a good way, so I should give a spoiler alert up front, especially these days, that this has nothing to do with Doomsday as in the end of the world.
I never met Conway, but in the mid-70s my math camp buddy Rob Indik had a summer in which he commuted to the UI Chicago campus “with Vera [Pless] driving, Conway in front, and me riding in the back and trying to ride along with Conway’s free flow of ideas.” I remember Rob regretting that he couldn’t remember a mental “perpetual calendar” that Conway had taught him. In the computer age we have no call for perpetual calendars, but back when dinosaurs roamed the earth they were novelty items: a small object with a few dials, which would let you figure out what day of the week any date falls on. A mental one sounded like fun, and I occasionally thought—not very hard—about how you might go about it. I never got very far. [I see that this is not the definition of “perpetual calendar” favored by Wikipedia, but that the American Heritage Dictionary has me covered.]
With Conway’s death, I decided to look it up, and found that it’s around the web in several places, but without a very clear explanation of why it works. So I thought I would explain both how it works and why it works.
In my last post, I told the story of reviving a moribund computer program from 15+ years ago.
In the process, I revisited my stash of moribund computer programs, including a little web page with links to some of them. It was dusty and pathetic and pretty much nothing worked. So I rolled up my sleeves and prettied it up, and if you want to look any of it, you can find it here.
TL;DR You can skip any time to the 20-second movie at the bottom of the post. Spoiler alert: the video will eventually reveal the solution to the puzzle.
Happy New Year! I just returned from a quick family trip to Seattle, and you would think that this post would be about my visit to the Living Computer Museum with my cousin Eric, and programming adventures now 50+ years ago in the RESISTORS. But it’s not, as worthy as those topics are.
The New York Times has come up with a new puzzle, called “Spelling Bee.” (Sorry, to use that link you apparently need a Times Crossword subscription, which comes bundled with many of their plans.) The idea is simple: they give you 7 letters, with one in the center. Here is today’s.
To say I have a love-hate relationship with exercise would be too strong. But I’ve never truly enjoyed it, and for the relatively small fraction of my life when I’ve done it regularly, it has been at best a chore.
One of those times was in medical school. For a quarter or two, I went to the pool regularly. After a vacation, I returned to the pool and ran into my friend Brad. When I asked how his vacation was, he said, “Great!” and proceeded to tell me about biking a century or maybe two, hiking, running. I realized that there two kinds of people in the world: the ones who exercise more when they’re on vacation, and the ones who exercise less. Both kinds were represented in that conversation, and you can see which I was.
The cubic and quartic formulas were perhaps the greatest accomplishments of Renaissance mathematics, and they were a key spur to Evariste Galois’ beautiful study of the symmetry inherent in polynomial equations. Yet I got a PhD in mathematics without knowing much more than the bare fact that such formulas exist. It should certainly be possible to understand these formulas in light of Galois theory, but such explanations are not easy to find.
I wrote this paper to pass on what I learned about the cubic equation, and how it can be derived in the context of Galois theory.