Before the advent of the Internet, going to bars was one of the better ways to meet gay people. But when I reached drinking age (18 in New York at the time) I didn't like alcohol and pretty much every bar played disco. I didn't go to bars until I discovered one that I had fun at: it played rock and roll and it had a pool table.
I like playing pool, and this place had good players that I learned stuff from. One guy made shots I've never been able to duplicate. He ultimately got thrown out of the bar for playing too well. Well, also for being unfriendly—but it was his beating everyone at pool that was the last straw. Or maybe he wasn't buying any drinks.
As bar pool table protocol lets you play as long as you keep winning (at least if you're gracious about it), and as playing pool is one of few things I can enjoy doing in a bar, I had incentive to improve my game. From 1981‑82 I lived in an apartment complex with pool tables and I learned a bit just by experimenting. I discovered that some complicated shots were not as hard as they looked. I never got to be a great player but I had a lot of fun.
I don't think Confucius had billiards in mind, but he was right when he said (Analects, 1.1.1):
To study, and when the occasion arises to put what one has learned into practice—is that not deeply satisfying?
From the NY Times web site this afternoon. It was reworded after about 90 minutes.(thanks Sasha for finding this) When taking pics of the sun or moon near the horizon, it helps to know how much time it takes for objects to rise or set. If you can remember that the apparent diameter of the moon or sun is about ½ of a degree of arc, calculating the rate they set at is easy.
A day is a turn of 360 degrees. Rising-setting motion is 360 ÷ ½ = 720 moon‑or‑sun diameters in a day, or 30 diameters in an hour. So the moon or sun takes roughly two minutes to rise or set the distance of its own diameter.
Roughly. The moon's orbital motion makes it set about 3% more slowly than the sun does, if that matters.
And speaking of orbital motion, sometimes the moon will be approaching a star or planet and I'll want to estimate when it'll be in the spot I want for a pic. If you can remember how many days are in a month, that's about how much slower the moon's motion relative to the stars is than its rising-setting motion. The moon orbits in somewhat less than 30 days so it takes a little less than 30 × 2 minutes = one hour to move a distance of its own diameter.
Last night's eclipse reminded me of all this. The total phase of a lunar eclipse begins a little less than an hour after the start of the umbral phase.
Mr. Bush has an uncanny ability to translate photographs into more awkward images enlivened by distortions and slightly ham-handed brushwork.
These empty headed daubs look the work of someone you wouldn't trust to mow a lawn without cutting someone's foot off.(NY Times and The Guardian, respectively) Assuming that
there are intelligent extraterrestrials, andI once said I'd be curious to see what symbol an alien culture used for π, and a friend asked, "How do you know they would have a π in their mathematics?"
they write (with symbols on two-dimensional surfaces),
My friend knew how ubiquitous π is, not just in geometry/trig but in every branch of mathematics. He just liked to ask questions that made you consider anything you might be overlooking.
Funny thing is, that conversation didn't lead to what I now see as the elephant in the room—namely that it's better to have a symbol for the ratio of a circle's circumference to its radius rather than its diameter. The appearance of 2π in so many formulas in math and physics (e.g., angular frequency is 2πf ) is a hint that 2π is more fundamental. The case for 2π is laid out in detail in Michael Hartl's The Tau Manifesto, whose arguments I find compelling. Were I designing math nomenclature from scratch, I would so define a symbol for 6.28318... instead of 3.14159... .
Will the world see the light? The weight of literature and tradition behind our definition of π is huge. We're stuck with it like we're stuck with the QWERTY keyboard. As much as I'd like to see the movement to ditch π in favor of τ (=2π) succeed, I think it's a longshot to get much traction in my lifetime. But I'd bet you a nickel that if we ever compare notes with extraterrestrials, they'll have a symbol for τ instead of π.
(recreation of a cartoon I saw years ago,
maybe in Harper's but I'm not sure)