Saturday  28 Feb 2015           comment?

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

Thursday  26 Feb 2015           2 comments

Wednesday  25 Feb 2015           1 comment

Tuesday  24 Feb 2015           1 comment

Saturday  21 Feb 2015           comment?

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.

Friday  20 Feb 2015           1 comment

I'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.

Wednesday  18 Feb 2015           1 comment

Sunday  15 Feb 2015           1 comment

Animal 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.

Saturday  07 Feb 2015           1 comment