1/7/08 - 1/13/08 Once a Runner, Twice the Nipple Chafing (325 minutes, one tempo run)

Sunday, January 13 (65 minutes)

Saturday, January 12 (6400m progression run)

I decided it was time to stop dicking around and go run at least some sort of workout. My goal was to hit a disciplined 6:00/5:50/5:40/5:30. Of course I did not. The first lap of the second mile was too fast, and after that the plan was about as effective at enforcing itself as the U.N.
As soon as I put a watch on, I go delusional and begin to think I'm not running a workout, but operating a ratchet. The pace cannot get slower. Even if you began by sprinting the first turn to impress the hot chick in short shorts, the pace cannot get slower. If you ever get slower in a workout you're training to get slower in a race.

I'd like to change the focus, and perhaps tell myself that running with discipline in a workout is training to run with discipline in a race. But that's a big cognitive leap when your manly honor is on the line.

The splits were 5:55, 5:37, 5:24, 5:19. Not too impressive, considering that I was working pretty hard by the end, but it's a decent starting point. And then afterwards I was walking past the start line for the hundred, and the sky was unusually black, the moon a small, sharply-focused crescent, the lanes seemed so immaculately clean and straight next to the green of the infield, and a bat was swooping around, and all this for some reason seemed absolutely perfect to me. I remember thinking that it was preposterous for anyone to have problems when the world could look like that, and that I couldn't understand how anyone could ever have a body and not want to run, gulping down this perfect air and circling the transparent darkness. That's an odd sort of scene to find inspiring, but there you have it.

Thursday, January 10 (70 minutes)
It's a problem you might have heard before, but I'll recap it anyway, since the makers of a BBC documentary about China seem to be confused.
In a certain country, every adult has a spouse, and every couple starts off having one child. If the child is a boy, they stop having children. If it is a girl, they have a second child, and if that one is a girl, a third, etc until they get a boy. What will the male/female ratio be in this country (assuming men and women live equal lifespans)? Also, what is its population growth per generation (assuming life expectancy does not change over time)?

At first brush, it might seem there will be more boys than girls, because every family has a boy, half the families don't have any girls. However, there will be some families with many girls and only one boy. These two effects cancel each other exactly, so that the male/female ratio is 50/50 (this also assumes male and female births are equally likely).

Simple proof: each child born has a 50/50 shot at either sex. Regardless of the couple's history, it's still a 50/50 shot for their next child, so there's no way around having a 50/50 split for the entire population. So the high boy/girl ratio in China (6:5) is due to illegal abortion of girls. Also for a 6:5 ratio of births, you'd need to abort one of every five girls. That's about two million black market abortions of girls every year.

Second part of the problem (population growth):
A family has a 1/2 chance of having just one child (first child boy), a 1/4 chance of having two children (first girl and second boy), a 1/8 chance of having three children, etc. To get the expected number of children per couple, we multiply the # children by the probability of getting that many, and sum.

I know two ways to do it. First, evaluate the sum explicitly. A good trick is to break the sum into a grand sum of easier sums, like this:
1/2 + 2/4 + 3/8 + 4/16 + 5/32 +...
= (1/2 + 1/4 + 1/8 + 1/16 +....) + (1/4 + 1/8 + 1/16 +...) + (1/8 + 1/16 + ...) + ...
These you probably recognize. You can solve them by multiplying by two, and seeing that you get the same sum back again, plus twice the first element. For example:
S = 1/2 + 1/4 + 1/8 + ...
2S = 1 + 1/2 + 1/4 + ... = 1 + S
S = 1

Using this result on the sum-of-sums, the grand sum simplifies to
1 + 1/2 + 1/4 + 1/8 +....
Which we now recognize to be 2. So in this scenario the population of the country remains stable. (In China, even without abortion, they officially don't go beyond 2 children, even if they're both girls. Also, not everyone marries and raises a family. Finally, you can also reduce the population significantly my marrying at an older age rather than having less children. That particular trick is a one-time shot though, and in the very long run population will start to rise again.)

There's a quicker way to get the answer than the sum-of-series. We already know there are just as many boys as girls. Further, every family has exactly one boy, so on average they must have one girl as well. That makes two.

Finally, the reason I'm watching documentaries about China and posting silly math problems related to their demographic regulations is that I'm pretty much decided to apply for the job in Beijing this summer. Anyone familiar with how to get a visa to visit China?

Also, I got an email today from Carlsbad describing the bib pick up instructions and free hotel accommodations arranged by the race. They never took my name off the list after I withdrew. But damn, if I'd known there was a free hotel room, course tour, special gear-stashing station, and free massages included in the deal I'd never have broken the arm to begin with.

Wednesday, January 9 (70 minutes)
I was relieved to wake up this morning (Thursday) and see that my foot was not covered in blood. Not my own, anyway. I feel like that's the sort of thing we all ought to check for once in a while. Wednesday afternoon I began running on the North Field, but was brought to a halt by a sharp but fairly inconsequential pain on the middle of the bottom of my left foot. When I looked at it it was actually bleeding. This was a relief.
The day before, I had been running barefoot on the south field, and cut the run short due to pain in the same spot. At the time I wasn't sure if it was a real injury or if I just stepped on some of the multifarious random crap that is strewn liberally across that field.
An injury is much worse, because it indicates something pernicious and possibly recurring, whereas stepping on something is a fluke. And at another level, an injury I psychologically perceive to be something wrong with me, and it casts a pall of weakness on my character. A fluke accident makes me a martyr, and allows me to complain indignantly to anyone foolish enough to stick around long enough to listen.

Tuesday, January 8 (40 minutes)
Stopped early, see above.

Monday, January 7 (30 minutes)
Stopped early. I was going out for a good long one, but my head felt weak and faint and I came back inside and slept all afternoon.