Content-Type: text/shitpost

Last night I dreamt that I was explaining to someone how to solve a certain math problem. I said you shouldn't consider the situation as an ongoing process, but instead imagine it as a fully-realized decision tree, and then apply the Davis-Putnam algorithm. In the dream someone spoke up from across the room: “You mean the Davis-Putnam-Brown algorithm.”

“What??” I exclaimed in mock surprise. “Next you are going to tell me that Bunyakovsky discovered the Cauchy-Schwarz inequality!”

Tell me, Dr. Freud, what does this mean?

It's not enough to make the coffee, you also have to drink it.

In many Christian communities, it is traditional to eat cheese on Holy Saturday, to commemorate the day Jesus spent ripening in a cave.

As far as I can tell there are no octahedral cathedrals. Why not?

Google search produces several claimed examples, such as the Cathedral of San Flaviano in Giulianova. But photographs make clear that this is actually an octagonal cathedral, actually an octagonal prism surmounted by a dome. Similarly, St. Basil's cathedral in Moscow has a floor plan with a roughly eightfold symmetry, but is not octahedral in any way.

Polyhedral buildings are common, but the space is dominated by cuboids. Even the Kaaba in Mecca, despite its name (“cube” in Arabic) and its enormous religious significance, is only approximately cubical, visibly irregular.

The Egyptians famously made pyramids but they are all pentahedral. none is a tetrahedron, much less a regular tetrahedron. A regular tetrahedron is too steep for practical construction anyway; the Egyptians had bad experiences with overly-steep pyramids.

It should not be too hard to make a building in the shape of a regular octahedron, considered as a triangular antiprism. I would be surprised if there weren't one somewhere. When I am King of the World, there will be an octahedral cathedral or someone will have brief but very uncomfortable conversation with me about their failure.

Also, where the hell is my Sonar Taxlaw fanfic?

[ This had been sitting unpublished on the other blog for six months. It has now been weighed in the balanc e and found wanting. ]

If a billion is a thousand millions, and a trillion is a million millions, how much is a pavillion?

Surely someone must already have discussed the Brazilian cotillion in the vermillion pavilion, it's too hard to miss.

(There is a joke about how George W. Bush, upon learning that four Brazilian miners were trapped underground, asked how many a Brazilian was.)

[ Previously ]

If the laws of physics are time-symmetric, why do I always have to preheat the oven, and never postheat it?

Sid Vicious, clearly.

In fact I think I'd be comfortable nominating the Sex Pistols as the worst band, overall. The world is full of obnoxious and incompetent bands. What gives the Pistols the prize is their insistence that they represented authenticity — maybe they hated you, but at least you knew it. This insistence, though, was itself nothing but a pose, manufactured by them and Malcolm MacLaren.

It's 2022! Is Groupon dead yet?

Pretty pleased with myself today for spelling “Aung San Suu Kyi” without having to look it up.

Previously, I had some suggestions.

Since then, Aung San Suu Kyi has been looking like a good choice.

Also, since they apparently gave Obama the prize for not being George Bush, they should give Joe Biden two prizes for not being Donald Trump.

Suppose !!\mathcal L!! is a regular language and there is some string !!t!! that is a substring of every element of !!\mathcal L!!.

Is it necessarily the case that there must exist regular languages !!A!! and !!B!! such that $$\mathcal L = A t B?$$

Fuck, Marry, Kill, except it's Rum, Sodomy, and the Lash.

• The first musical instrument [Roy] Clark ever played was a four-string cigar box with a ukulele neck attached to it.

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:

    graph "example" {
        A -- B -- C
        B -- D, F [style="dotted"]
        D -- F -- E -- C
    }

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 neato layout engine, which tries for a generally compact layout. The example below gives the same input to the dot engine, which is intended more for directed graphs and which tries to emphasize hierarchies or flows among the nodes.

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, neato, which has done a great job of inferring the actual shape of the United States!

(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.)

Here's fdp, which uses a similar approach to neato: a “spring” model where it imagines the nodes are connected by springs and tries to minimize the energy. It produces a very similar result:

It has New England flipped over like neato does. I wonder why that happened? And Washington is embedded in Northern California for some reason.

The sfdp engine is a variation on fdp which “uses a multi-scale approach to produce layouts of large graphs in a reasonably short time”. The map it produces has south at the top and east on the left, but otherwise looks pretty much like the fdp one. I'm pretty sure that by graphviz standards this is not a “large” graph:

Now we move on to the odd ones. The dot engine I mentioned before tries to maintain the hierarchy, to the extent that there is one.

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

[ Note: this is where I lost interest and stopped writing. ]

• Cincinnatus’ name means “curly-haired”.

• The namesake of the chlamydia infection (and also the less well-known Chlamys, a bivalve mollusc) is the Chlamys, a short cloak worn by the ancient Greeks, and most notably Hermes.

• You should never go swimming with a kangaroo; it will attempt to drown you.

• Dr. Spock ran for president in 1972 against Richard Nixon and George McGovern. He received around 0.1% of the vote.

• McGovern, the losing major-party candidate, was utterly flattened by Nixon, who won over 60% of the popular vote and 520/538 electoral votes. Nixon, of course, resigned in disgrace in August 1974.

Today the School District of Philadelphia informs me:

All children are capable of reaching their fullest potential

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”.

• Six of the seven justices of the Michigan Supreme Court are women.

• Catalonian nativity scenes traditionally include El Caganer, a figure of a guy pooping with his pants down.

• Another Catalonian Christmas tradition is Tió de Nadal, the Christmast Log. This is a small log with a happy face and a red hat, propped up on legs. In the run-up to Christmas, the kids feed the log daily, and then on Christmas Day it magically poops out nougats, hazelnuts, or other plausible log poop objects such as dried figs.

• To make Tió de Nadal defecate, one puts its end into the fireplace, or, if no fireplace is available, beats it with sticks.

• Tió (“trunk”) should not be confused with tío (“uncle”).

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.