How old were you when you last used trigonometry?

My father was a civil rights lawyer, but among his many interests, he enjoyed recreational math, and he was never afraid of trig tables. Our family visited his mother's farm every summer, nestled in the Catskill mountains of New York, near the Ashokan reservoir. A beautiful bridged road called the "Reservoir Road" cuts across the Ashokan on its way to the reservoir ponds and the spellbinding aeration fountains. From that bridge, there's a prodigious view of the Catskills. Looking west you see a high, long ridge, and what looks like a "duckbill," the tip of a mountain peeking over that ridge. Everybody said that the duckbill was the top of Slide, the tallest mountain in the Catskills. We always enjoyed stopping to look at that ridge, along with the whole panoply of mountains surrounding the reservoir.

One day when I was about eleven, my father asked, "Is that really the tip of Slide Mountain?" Out came the topological maps and the trig tables, and my father began to plot triangles to calculate our line of sight. From the middle of the reservoir, the view west is toward the Friday Mountain/Cornell/Wittenberg Ridge (running north/south), about 3800 feet above sea level. Slide Mountain is set well back from the ridge, at a height of 4400'. If you look at a topo map like this one, it's hard to imagine what else the duckbill could be, but still, you have to do the math to see if Slide is visible over that ridge. We did the math, and sure enough it was. I can't convey to you how satisfying it was to know that the math proved that that duckbill was Slide.

IBMish Writing:

I'm going off half-cocked today, because I don't have a URL to point to, but I read somewhere that in Great Britain, schools are thinking about using computers to grade essay tests. Obvious jokes arise, as one thinks about how to pad a computer-read exercise to get higher grades. And what's the point in writing to a computer? They can't think.

However, I believe this is a good idea, up to a point. A computer can certainly try to check for proper spelling, punctuation and syntax. And a skilled writer, even in fourth grade, can learn how to avoid fancy writing constructions that a computer will fail to understand. It's all about technique, and everyone could use some practice in developing technique. As long as we don't trust a computer to decide whether the writer has actually answered a question.

Cancel a Mandatory Meeting:

I was invited to a mandatory meeting yesterday.

There's something wrong with that sentence, isn't there? We're not invited to mandatory meetings; we're told to come. To move our heaven and earth priorities, and to get there if we possibly can.

So I went.

This particular mandatory meeting was canceled. The cancellation notice went out an hour before the meeting, so several people – like me – didn't see it. But that's not the point.

I have deduced, in the course of my life, several rules by which a person may live better, and I have now deduced one more:

Do not cancel a mandatory meeting.

Look at it this way. When you cancel a mandatory meeting, you're saying: I'm scheduling this meeting, and you have to come. But I don't.

Now that Jay Leno's in Prime Time:

I Tivoed the second show so I could watch it later.

Bacteria! Infections! Shower heads! Never mind?

BBC News brings us the apparently useless news that showerheads can harbor dangerous bacteria. News sources are pretty good at misquoting their sources, but if this quote is accurate, I think we can forget about the whole thing:
Lead researcher Professor Norman Pace, said: "If you are getting a face full of water when you first turn your shower on, that means you are probably getting a particularly high load of Mycobacterium avium, which may not be too healthy."

Now when's the last time you turned your shower on, directly at your face? Didn't you let it run for a few seconds, or do you like to be frozen by cold tap water? I'm going to ignore this invaluable alert.

Accidental Ping!

I'm sure I once blogged about a clever tactic I used in my years of work at Exxon Office Systems. I had a reputation as a reliable hard worker. That meant that on rare occasions, I could accept an action item for something I hated to do, and then just not do it. I always got away with this, by the way. No one ever noticed; and if they had, I would have played for time by saying, “I sent you an email. Didn't you get it?”

Now I have discovered a vaguely similar tactic, but I have no use for it now. I hope it's helpful to some of you.

Let's suppose there's someone you need to contact by email. You tried twice (no response), and you fear trying again, because you don't want to seem to be bugging them. So you address them on some irrelevant email that was obviously intended for another person. There should be some name-similarity so that it will be obvious you just hit the wrong name in your address list.

After they send this irrelevant email back to you, telling you that you mis-addressed it: voila! You're in touch.

Chivalry?

I drove to the Post Office to ship a light package overseas. I parked to the right of a gas guzzler. A middle-aged woman struggled on my left to remove a large package from her car.

I decided that the right thing to do was to sit and wait for her. If I opened my car door, it would just get in her way. ... Five seconds later, I asked myself, What is she going to do with that package? Obviously, she was going to go into the P.O. and get on line, the same line I needed to get on. And she would be ahead of me.

Oh, no you don't!

I opened my door a tad, squeezed out and slipped past her, mumbling “Excuse me, excuse me,” and I hurried to the door.

And then my heart sank. Between me and the infernal clerk-line lay three heavy double doors. Here came that woman, struggling with her large package. And I knew what I had to do.

I opened the first double door so that she could enter ahead of me.

I opened the second double door so that she could enter ahead of me.

I opened the last double door so that she could enter ahead of me. She stepped in and said, “Go ahead, you go first.”

Chivalry.

Rare Earths:

The New York Times has a great article on the next world elemental scarcity: Rare Earths. Apparently, China mines the giant share of Rare Earth minerals. It is squeezing the world supply and persuading companies that they can get enough Rare Earths by building their factories in China. There's a lot of good background in this story, and a great chart on its second page (click where it says 'Multimedia').