(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
doesn’t show up
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.