0-1

I just went to a meeting. I walked in with 1 piece of paper. I walked out with 4.

That, my friends, is what we call losing a meeting.

More books

I hadn't realized how far behind I'd gotten on my books.

Brisingr:  This book follows Eragon and Eldest, which I read recently.  I read those two (which I had read before) to remember what happened, so I could read the third and final book in the series and be done with it all.  But, as it turns out, this wasn't the final book as I had thought.  It was long and entertaining as the others were, and, I was glad to see that it provided some plot twists that I didn't see coming.  I remain curious to see how it all turns out.  Sometimes it is best to discover series' after they've all been written so you don't have to do the annoying part of waiting for the next book.

Six Easy Pieces by Richard Feynman:  In 35 years at Caltech, Feynmann was listed as teacher of record for 34 courses.  25 were graduate courses.  I guess when you're as big a name as Feynman, you can teach what whatever you want (or not teach, as the case may be).  But for two years, he taught a series of introductory physics courses.  The lectures were recorded and eventually edited and published as Feynman's Lectures on Physics.  The finished work is famous, among physicists at least, and anyone out there is welcome to buy it for me.  (It's 3 volumes, and not cheap.)  Until that day, I have 6 Easy Pieces, which are exerpts from the lectures.  They're interesting and are Feynman's attempts to collapse some big topics, like "Basic Physics" into a single lecture.

4 fluids

Julia is having a bit of a rough day.  Which of course means that we all are.  This afternoon she managed to get, more or less simultaneously, 4 different bodily fluids on my shirt: tears, slobber, boogers and poop.

I suppose that is better than if she had done it to four different shirts.

And, as I type this, she just got Shannon's pants.  (hint: not tears, slobber or boogers)

Her Parents Daughter

We've recently discovered a few traits that julia seems to have picked up from her parents.

From Shannon: Julia is a bottomless pit.  She would eat all day long if we would just be so kind as to keep feeding her.  Shannon likewise loves food.  One thing that Shannon loves about pregnancy and breast feeding is the ability to eat so much more.  "It's like a dream come true."  I've heard her say.  And now Julia is always hungry.  She at a full grilled cheese sandwhich today.  She went through two bottles just during church yesterday.  And she ate an hour before church started.  She knows a few signs.  "More" is made by touching all 10 of your fingers together infront of you.  "Eat" or "Food" is made by putting 5 fingers together and touching them to your lips.  Today she combined the two by bringing both hands to her mouth to sign for, what I can only imagine means "MORE FOOD NOW!"

From Clark:  When I got her home from church yesterday, I took off her shoes to find . . . sweaty feet.  I'm sorry Julia.  That's all I can say.  She might just be doomed to sweaty feed.  No matter how hot, no matter how cold, they just sweat.

Updump

Yes, here are some updates that really, are pretty dumpy.

1.  I read "Artemis Fowl: The Arctic Incident".  Yeah, it's a young-adult book.  The first one was interesting and mindless enough.  The second one made me realize that I didn't really remember much of the first one, even though it had only been a few months, and that neither one was really that good.  I don't plan on reading any more.

2.  I read "Clarks emails to Shannon May-Aug 2001".  Shannon printed out a collection of emails I wrote when we were first dating.  Let me sumarize: my job is boring.  There, I saved you a bunch of reading.  There were, of course, a few humorous nuggets, but man, did I just say the same things over and over again.

3.  Nothing quite so fun as holding your daughter and then realizing she's just peed all over you.  yay.

4.  Our garden isn't faring too well.  Nothing really seems to be growing, though most of the plants look ok.  Some, however, seem to be dead/disappeared, and are dying from North to South.  Perhaps a very, very, very slow moving plague?

5.  I've just about completely lost my voice over the last two days.  Now would not be the time to give me a call.

Boring tournament, Exciting math!

Yesterday, Brett started us down a dangerous path, but you'll be happy to know I saved us all from potential loss of sleep. I'll explain . . . . Brett was wondering, as I'm sure various of you were, what the results would be from a 64 team single elimination tournament in which there were no upsets and the positions of the teams are clearly defined and well known, but matchups are random. The tournament wouldn't be much good for setting contest up; we all know who the best team is, and they are guaranteed to win. However, there is an interesting question of who gets second place. Certainly, the #2 team has the best chance of getting second, but, if they meet the #1 team before the championship game, they are out of luck.

Brett started from a numerical approach, letting his computer set up 10,000 such tournaments, randomly placing the teams into brackets and seeing how it comes out, and intially supposed that team #2 has a 1/2 chance of 2nd place, #3 a 1/4 chance, #4 a 1/8 chance, and so on and so forth. The result isn't surprising. But quickly, we realized that this can't be correct. First off, it implies that all teams have a chance of winning, when they clearly don't. No team lower than the field size/2 + 1 can make the championship game. Also, that result can't be right because the probability of someone finishing in 2nd place only adds up to 1 if we sum forever, and we don't have infinitely many teams.

So, what is the probability? If you want to figure it out for yourself, quit reading now, because I'm about to tell you. Ok . . . I see that none of you have quit reading. (It's impressive that you've read this far.) After various attempts at finding a formula that fits, I present you with the formula for finding the probability of any team taking second place in such a tournament, generalized for any number of teams and any seed:
where f is the field size and s is the seed and a[s] represents the odds of the nth seed taking 2nd place, where 2 <> (f/2 +1). There, can't you rest easier this weekend now that this problem has been put to rest?