(Written: Wednesday, August 6, 2014)
West on Amtrak
Ok. So Marja and I are traveling by train across the plains of North Dakota on our way from DC to Seattle to go hiking and to see our West Coast children. We see a large wind farm, the blades revolving so slowly that Marja wonders out-loud why they sometimes kill migrating birds. I think, well, the ends of the blades are probably moving more quickly than they seem. How fast, I wonder?
There being nothing better to do after staring out the window at corn and grass and sky for a couple of hours, I decide to figure it out. (For those of you who don’t care how fast they’re going or don’t follow math easily, you might skip to the last four paragraphs.)
I google the size of a wind-turbine blade: 116 feet long (Holy smokes! I thought maybe 40 feet long). I time one revolution of the blades: six seconds.
(Five years ago I could have gone from here and figured the speed of the tips in my head, but I can’t come close now, so I take a scrap piece of paper and write each step down.)
I’m happy that I remember from my basic geometry that the circumference of a circle is πr (pi [3.14] times the radius), so I calculate that the distance the tip travels in one revolution is 364 feet. Now I need to translate the feet into miles. I dig out from my memory that one mile is 5280 feet; so the number of miles traveled in one revolution is 364 divided by 5280 (364/5280). Since there are 60 seconds to a minute and 60 minutes to an hour, there are 3600 seconds in every hour. So the time of one revolution per hour is 6 divided by 3600 (6/3600). Therefore, the speed in miles per hour is the result of 364/5280 (the distance expressed in miles) divided by the result of 6/3600 (the time expressed as a fraction of an hour).
Now I realize that this may sound complicated when you read it. If you write out the numbers and if you know basic geometry and algebra, however, it’s really pretty straightforward.
(It would have been a whole lot simpler, of course, if I’d done the long division of each of the separate fractions into their decimal equivalents before proceeding, but in my confusion I didn’t see that until I’m writing this blog post and checking it over several times.)
The answer as a complex fraction is 364/5280 divided by 6/3600. This should not be difficult for a high-school valedictorian, Yale-graduate physician, whose best subject was math. But I can’t do it, even on paper. The source of my problem is a usual one for me: it’s a multistep process. I should translate the feet traveled into miles traveled; translate the time of one revolution per second to the time per hour; make them into a complex fraction; and do the arithmetic. But by the time I finish with the first step and begin the second, I’m already confused about where I am in the process. I keep flipping each of the fractions, multiplying and dividing and getting thoroughly confused. My scrap paper is covered with the four numbers (364, 5280, 6 and 3600) in various combinations plus others I can’t remember the source of.
So I finally remember to calculate the decimal equivalents by dividing the fraction in the numerator (364/5280) into its decimal equivalent, but I get confused even doing that. (Divide the numerator by the denominator, right? Or is it the other way around? How do I do the long division of 364 divided by 5280? C’mon, David; long division is elementary school arithmetic!) I figure out one of the decimals and now I can’t remember where I am in the process, which of the fractions on the paper means what? My brain feels parboiled.
Finally, I have either to give up or “cheat” using the calculator on my phone. I calculate the 364/5280 into a decimal (0.069 of a mile) and write it down on a fresh piece of paper. Then I calculate the 6/3600 into its decimal form (0.00166) hour and write that down. Finally, I divide the nominator decimal by the denominator decimal and get 43 mph.
I then decide that you might be interested in reading the whole debacle. But as I write the fifth paragraph above about my calculations, I notice that in my first step I used the wrong formula: The circumference is supposed to be pi times the diameter and not pi times the radius. Does that make my result twice as large or half as large? I have to work that out on paper, too. And now I can’t remember what my initial result was nor can I find it in the jungle of numbers on the papers, so I recalculate the whole thing on my calculator, getting confused again along the way. I make so many mistakes that it takes me perhaps twenty minutes just to repeat the simple process. And checking all the calculations again takes me another half an hour, and I’m still not sure I’m right. So far, I’ve gotten three different answers, but the final one seems right.
To those of you who wisely jumped here after the third paragraph or tried and didn’t make it through the preceding paragraphs, I don’t mean to imply that anyone should be able to figure this out easily. The point is that I used to be able to get an approximate answer to something like this in less than a minute in my head; With pencil and paper I could get the exact answer in two or three minutes. And now it takes me well over an hour and the use of a calculator to work out an answer I’m only shakily confident in.
If ever I need clear demonstration of my decline, something like this is it. I have no idea why my decline on cognitive testing, but the reality is obvious.
For about a minute I notice myself getting depressed about it, but that lifts pretty quickly. I already know that I’m cognitively impaired. Do I really care how fast the tips of the propellers are moving? No, I don’t. (It’s 83 miles an hour if you’re interested, probably fast enough to clobber a goose who’s blindly following the goose in front of him while daydreaming about his mate and not paying enough attention to the blades.) Perhaps I used to care about impressing and amazing my friends by figuring out the approximate answer in less than a minute, but I’m actually happier now not being so hooked on the need to be superior.
Values change. I enjoy most of my new values better than the ones they’ve replaced. I’ll put up with the occasional confusion.