It's 2021! Is Groupon dead yet?
Graphiviz is useful graph- and network-layout software. You give it a description of a graph, as on the left:
and it produces a drawing of a graph as on the right. The first line says that node A is connected to B, which is connected to C. The second line says that B is also connected to D and F, but the edges should be dotted. The third line says that D is also connected to F, which is connected to E, which is connected to C.
Graphviz has several layout engines, which try to optimize layouts for
different kinds of properties. The example above uses the
I built a Graphiviz configuration file for the graph of U.S. state boundaries and put it in to see what would come out. The graph is naturally planar, and it will be interesting to see if the layout algorithms can detect that.
Here's what the U.S. actually looks like. (Source: Wikimedia Commons)
This is the output of Graphviz's default layout engine,
(Nodes here are labeled with their standard postal abbreviations. When you hover your pointer over a state name or other gegraphical designations in this article, the corresponding abbreviation will pop up. For example, New York should pop up a box with “NY”.)
The Mid-Atlantic, South Atlantic and Pacific coasts are clearly visible, Florida is dangling off the bottom, as it does. It's pretty amazing. The fact that the map is oriented correctly is a bonus. There are a few oddities: New England is where it should be, but Vermont should be switched with Connecticut and Rhode Island. South Carolina is sticking out into the Atlantic Ocean.
There is only one planarity failure, resulting from the inadvertent flipping of New England. The apparent crossing edge between Minnesota and Michigan is illusory; the edge could have been curved around Wisconsin with no trouble. (The real border between Minnesota and Michigan is a bit of an oddity, occurring in Lake Superior, and it really does leap over the head of Wisconsin that way.)
It has New England flipped over like
Now we move on to the odd ones. The
The geography is still correct here, more or less, with South at the top and East on the left. That puts Florida in the upper left and Washington in the lower right. But in between it's unexpectedly tangled. The central column states, ND-SD-NE-KS-OK-TX are all over the place.
So many questions here. What the heck is going on with Ohio and Michigan? And Illinois and
This reminds me a little of the time I had to explain to someone on Math Stack Exchange why every function is onto its range.
And by “the Michigan Supreme Court” I meant “the Wisconsin Supreme Court”.
Q: What do you call a centipede after you've stepped on it?
A: A nillipede.
Ms. 16 drove me to Valley Forge today. Perhaps you have heard that Washington was grievously injured at Valley Forge. He was struck by a small cannon ball, and his skull was fractured in three places.
Implementing your own authentication system is like getting involved in a land war in Asia.
The losers who moderate Reddit's r/math forum have deleted this brilliant post, Petition to create new flat-earther groups.
Check it out.
On Saturday when I woke up Lorrie said I had awakened her in the night, and asked me what I had been saying. It had woken me up too, and I remembered.
I had been dreaming that I was at some sort of a conference, and at the start of a conference session, everyone in the audience stood up, put their hands on their hearts, and sand The Star-Spangled Banner.
In the dream, I sang also, and when the song ended, I shouted “PLAY BALL!”
Python code I wrote today:
Larry Wall says that a successful program is one that does its job before your boss fires you. Somehow I don't imagine Guido being as lenient.
Suppose you have available an evil necromantic spell that turns humans into mindless zombies. (Whether the humans are required to be dead or alive is not important for this inquiry.)
What happens if you cast this spell on starfish instead, turning them into mindless zombie starfish?
Today I had a cream cheese and cashew nut sandwich. It was pretty good.
It was inspired by the “nutted cheese” sandwich found at Chock full o'Nuts lunch counters long ago. (Theirs had walnuts, not cashews, and was served on dark raisin bread. When I have the ingredients handy I sometimes make the walnut and raisin bread version, which I recommend.)
These days Chock full o'Nuts exists primarily as a supermarket coffee brand. I'm so old I can remember actually eating a chicken salad sandwich at one of the lunch counters.
Thinking on this a little more, I think you have to make Ringo d'Artagnan, and play up his country-bumpkin-ness.
Then George is Aramis (obviously) and Paul is Athos, so that makes John Porthos.
I am having a lot of trouble picturing this. Which Beatle is which Musketeer? There is no Porthos in the Beatles. There is no Ringo in the Musketeers.
The script was written by George MacDonald Fraser, creator of Harry Flashman.
I would watch a Flashman movie. The likelihood of there being a Flashman movie for me to watch, in the next twenty or thirty years, seems close to zero.
Aha, but there is already a Flashman movie, directed by the same Richard Lester who directed The Three Musketeers. Malcolm McDowell plays Flashy. And Oliver Reed, who played Porthos, returns in Royal Flash as Otto von Bismarck. How about that?
Etsy search for “not a place of honor” produces nothing relevant. This is a hundred-dollar-bill on the sidewalk, waiting to be picked up.
I want it on a doormat.
Tootsie Pops! New Himalayan pink salt flavor.
Though rarely seen, the Siberian Snow Camel is a majestic beast, with its splayed hooves and shaggy white fur. Modern populations of Snow Camels are believed to be remnants of the great herds that crossed the land bridge during the last ice age and whose descendants evolved into the bison of the North American plains.