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Cantor's diagonal argument is a landmark math proof showing that there are more real numbers than integers even though there are infinitely many of either. But a similar argument can be used to count other things as well, e.g.—

How large is the set of all possible books that could be written using the English alphabet? If we define book as a sequence of letters, spaces, and punctuation characters, and if we require each book to be of finite length, then there are "only" ℵ0 possible books (i.e., as many books as there are integers). That follows from the fact that the books could be listed in sequence (roughly: sorted by length and by alphabetical order).

But if we drop the restriction that each book must be of finite length, the set of all possible books is a larger order of infinity: as many books as there are real numbers. Admittedly, we'd no longer be talking about books as we know them, as no book goes on forever (arguably a good thing).

A mathematician's Tao Te Ching could start with the line
There are only0 taos that can be spoken about.
flash paper
fire in the sky.
dry ice
smoke on the water.
Inyo mountains
snow on the mountains.
§The NY Times just announced a redesign of their Sunday magazine, including "the creation of an entire suite of typefaces". In case yesterday's posting wasn't sufficient evidence that I am hopelessly preoccupied with details, and in case a posting from last year didn't evince an alarming obsession with section signs, I note that the character shown to the right (from one of the magazine's new typefaces) is, to my eye, one of the strangest section signs I've ever seen.

That is all. makes me want to try laminating contrasting pieces of wood in a frameI've made more picture frames than any other woodworking project. They don't require much material, so if I have just a small piece of some type of wood on hand there's a good chance it will become a picture frame. Building frames has had the side effect of impelling me to inspect every frame I encounter. I pause DVDs to look at frames that appear on screen.

While at a friend's house for dinner last month I saw a painting on the wall that didn't look to be level. I had an immediate urge to rotate it but I didn't, partly as an exercise in resisting urges and partly because maybe my friend liked it just the way it was. Later that evening, looking at the frame from across the room, I saw that it was next to a corner that wasn't square to the ceiling.

The pic here is a still from a TV show. It cuts to a shot of three stacks of $100 bills. I sometimes pause to inspect details in scenes like that too, but no I don't have a hobby of printing banknotes. doughnut bokeh
Young jackrabbit
scratching himself
after sundown this evening.
DogAnimal psychologist Roger Mugford and his dog Bounce were guests on a recent BBC News programme. Dr. Mugford noted that dogs are good judges of character and suggested that people trust their dog's judgment when choosing a new partner. It goes without saying that this requires an in‑person evaluation. Grindr, Tinder, et al. don't convey scent and other important cues.
there are two bolted climbing routes on the rock faces under where the main rainbow hits
Water fell out of the sky this morning.
climbing partner.
He was described as ascetic, or as ascetic as someone in the habit of renting out entire hotels could be.
(from an obituary for King Abdullah)
It wasn't easy to find just what I wanted to say about Charlie Hebdo last week. I had the feeling that no matter what I said, I'd at some point need to go into more detail and address questions. This I now do.

I wrote
My sympathies are not with those who have presumed to tell Charlie Hebdo what they should and shouldn't publish, as did White House Press Secretary Jay Carney a couple years ago: "Well, we are aware that a French magazine published cartoons featuring a figure resembling the Prophet Muhammad, and obviously, we have questions about the judgment of publishing something like this."
A person having questions about the judgment doesn't bother me. But when someone talks that way in their official capacity as a White House spokesman, that's a step in the direction of government telling people what (not) to publish—people in another country, no less.

When Charlie Hebdo's staff was murdered, I wanted my response to be one of undiluted support. I wanted to avoid even hinting at ceding any ground to the killers. That may not be everyone's response, but it was my choice.

The New York Times, August 30, 1979 Religions—the Abrahamic monotheisms in particular—have a history of telling people what not to say, think, or read. This isn't an accident; authoritarianism is baked into any system that holds a scripture or a person to be authoritative. That is contrary to my own values, and I make no apology for saying so. I support asserting the right to be thoroughly critical of religion, especially given the history of religions to wish that their demands have the force of law. Note the statement quoted in the 1979 newspaper article excerpted here: a movie was called a crime against religion.

It touches a nerve with me when people try to suppress satire. Humor is an elegant and concise form of expression. I marvel at the effectiveness of the Tom Lehrer song I posted a link to yesterday. The lyrics don't argue against anything, nor do they reach for the coarseness used at times by Charlie Hebdo (or even Monty Python). And yet, as Mr. Lehrer recounted,
Many people over the years have said, "Oh, 'The Vatican Rag' changed my life." It's not that they were convinced of something they weren't convinced of before; it's just that now they realize it's okay to laugh.
There are times and places to show courtesy. I wouldn't mock someone's religion while I was a guest in their home. But consider what the pope said in the quote I posted yesterday: his vision for a better world is one where nobody makes fun of religion. That's not a free world. Jorge "Pope Francis" Bergoglio said
You cannot provoke. You cannot insult the faith of others. You cannot make fun of the faith of others.
Well, yes you can. I'll go farther and say that in the case of Mr. Bergoglio's organization, it's essential to do so. I defer to a satirist of great skill: Tom Lehrer, whose song The Vatican Rag is a gem, without which the world would be a poorer place.