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,California is the best state in the USA for rock climbing, and not just because I am biased. A guidebook for Joshua Tree National Park alone lists 3854 routes.
maybe in Harper's but I'm not sure)
The first climbing guidebook for the Owens Valley—published in 1988 and long since out of print—listed just ten routes in my neighborhood, dissed the area for having largely crummy rock, and called it a sort of "poor man's Joshua Tree". Well.
There are a lot more than ten routes in my neighborhood now. Fittingly, a few of them have names making reference to J-Tree route names. E.g., Real Hidden Valley. I say least because although IHV is in the latest guidebook, it's not popular and it doesn't turn up in a web search. Googling for the phrase returned only four results when I tried this evening, none of them referring to the climbing area. Google's helpful true‑enough count: "About 3 results".
Isaac Asimov told a story of having sat in on a sociology class where the professor classified mathematicians as mystics for believing in imaginary numbers. Asimov spoke up to defend them, and the prof said okay, hand me the square root of minus one pieces of chalk. The rest of the story can be found here.
Imaginary numbers don't come up in conversation often enough. It's been 31 years since the last time someone asked me what complex numbers are good for. Language stuff.
Yesterday, Mike Rogers (R-Alabama) stood by his claims that Edward Snowden is somehow in cahoots with Russian intelligence services. But from sentence to sentence, what Rogers claimed various unnamed officials think wobbled from "can't rule out" to "believe" to a thicket of overnegation:
We know today no counterintelligence official in the United States does not believe that Mr. Snowden, the NSA contractor, is not under the influence of Russian intelligence services.
A recent NY Times article discusses objections to the term "homosexual": it's outmoded, it's loaded, it can have a pejorative tone. It's a decent article as far as it goes, but it never mentions my favorite curious fact about homosexual, to wit: it's a hybrid word (homo from Greek, sexual from Latin).
I like how modern Greek has no truck with various hybrid words common in other European languages, preferring homegrown compounds instead. In Greece, a homosexual is an ομοφυλόφιλος (omofylófilos), an automobile is an αυτοκινήτων (af̱tokiní̱to̱n), and a television is a τηλεόραση (ti̱leórasi̱).
And for those who find typos in subheadlines amusing, I've saved one from the Times article in case they fix it. Goodyear has a new blimp1 and a name the blimp contest. The grand prize winner and up to five friends get to ride the blimp.
Contest rules include (italics mine):
Your Entry MUST2 meet the following qualifications, in the Sponsor's sole discretion:Okay then, I guess they mean it.
Most of my friends have deemed my nineteens to be insignificant and saw my interest in them as another of my quirks, if a fairly benign one. The only friend who understood had a recurring number of his own—1020—which impressed me because a number that large comes around less frequently than a small number like 19. When I did an experiment to test whether 19 came up more than other numbers, I chose a similarly sized number (17) as a control.
I was there to see some of my friend's 1020 instances firsthand and he told me about others, e.g.: