Doomsday Calendar, Part 3

In the process of looking up John Conway’s “Doomsday Algorithm” for figuring out what day of the week “any” date falls on, I came across Chamberlain Fong’s description of a simplification of Conway’s algorithm that he and Michael Walters came up with, which they describe in a paper on arxiv. (“Any” is in quotes for reasons explained in Part 2.)

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:

  1. Take the last two digits of the year.
  2. Is it odd? If so, add 11.
  3. Divide your number (which now must be even) by 2.
  4. Is your new number odd? If so, add 11 again.
  5. Reduce your number modulo 7.
  6. Subtract your number from 7 (“take the 7s complement”).
Continue reading “Doomsday Calendar, Part 3”

Doomsday Calendar, Part 2

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.

Continue reading “Doomsday Calendar, Part 2”

John Conway’s “Doomsday Calendar”

[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.

Photo by Denise Applewhite, Princeton University Office of Communications

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.

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Fixing Up My Virtual Garage

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.

The Archeology of Computer Programming

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.

Actually it all started when I read a post by Ben Orlin on his Math With Bad Drawings site about Evelyn Lamb‘s Page-a-Day Math Calendar, recently published by the AMS. One thing led to another, and my son Ben was kind enough to give me a copy for Christmas.

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Ultra-Brief Workouts: The Agony and The Satisfaction

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.

I seem to have an abiding interest in getting something for, well, if not nothing, then “as little as possible” (hence: short-term therapy, no-knead bread, and no doubt a number of other hyphen-bearing shortcuts). So when I started to hear about 20-minute workouts using high-intensity interval training, I got interested. [Spoiler alert: 20 minutes is way too long.]

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The Cubic Formula and Galois Theory

I read a couple of books fairly recently that discuss the cubic equation: Barry Mazur’s Imagining Numbers: (particularly the square root of minus fifteen) and William Dunham’s Journey through Genius. They got me interested in this formula, which had always been an afterthought (to the extent to which it had been a thought at all) in my mathematics education.

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.

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Errol Morris Resurfaces

Errol Morris, the noted documentary filmmaker, has recently published a book entitled, The Ashtray (Or the Man Who Denied Reality). It’s about my father, Thomas Kuhn, and the views on the history and philosophy of science that he initially set forth in his 1962 book, “The Structure of Scientific Revolutions.” As you might gather from the title, it is not a sympathetic account; the philosopher Philip Kitcher says, in his excellent review in the Los Angeles Review of Books, that “Morris disarmingly confesses [that] this book is a vendetta.”

Since the book’s publication, Morris has been appearing here and there on the radio, and friends have been asking me about my take on the book. Rather than saying the same thing over and over, I have decided to put my thoughts together in one place. I haven’t read Morris’s book, for reasons that will become clearer to those who read further, but I was a careful reader of his five-part 2011 series on the New York Times Opinionator website, which the book is based on. I find Morris’s reading of my father’s work a vast oversimplification, to the point where the straw man is easy to knock down. Many people have taken that approach over the years, but Morris has a higher profile than most. There are many people more qualified to deal with his criticisms on whatever merits they may have, and I will mostly leave it to them.  What impelled me to write this is my belief that the episode from which the book draws its title, in which my father supposedly threw an ashtray at Morris, never actually happened.

Is it important whether it happened or not? Everyone will have to come to their own conclusion on that. To be very clear up front: I would love to be wrong about this. I would love to hear from Morris’s classmates, family, or anyone else, that he told them that my father threw an ashtray at him at or close to the time that it allegedly happened. Because as misguided as I think his attacks on my father are intellectually, I believe that they come from a place of wanting to defend truthfulness. Defending truthfulness was important in 2011, and it is painfully obvious that it is more important than ever in 2018. I have great respect for Morris’s film work, and I think I share much of his political orientation. But just as the Buddha says hatred does not cease through hatred, falsehood does not cease through falsehood, and I believe that some of our current ills as a society stem from our delight in calling out falsehood among our opponents while ignoring it or even condoning it on “our team” and, more important, in ourselves. Continue reading “Errol Morris Resurfaces”

Links to writing on “Black Panther”

I’m not a big fan of superhero movies, and I generally find any efforts to appear “thought-provoking” are pretty tinny.

But  I would say that Ryan Coogler’s Black Panther is actually thought-provoking. Coogler and his cast and crew have accomplished so many things in this movie that it’s hard to know where to start. But one thing they’ve done is to evoke some basic moral/philosophical dilemmas and conversations in a way that doesn’t seem completely, uh, comic-book. Continue reading “Links to writing on “Black Panther””