Krazy Katie Kaboom!

DA-DA-LA DA-DA-LA DA-DA-LA DA-DA-LA THIS IS A KATIE UPDATE

Yes! Katie gets her very own update today! We just can't get over how much she's doing these days. Six months has really been the big one for her.

SIX MONTH OLD MIRACLE BABY WALKS
Well, not quite: but in one month she's gone from rolling back to front to almost crawling! I'm trying really hard (and failing spectacularly) not to compare the two girls, but I honestly don't remember Miriam getting this mobile this quickly. Maybe it's b/c Miriam spent so much time on her belly in the early months that it seemed to take her forever to do anything exciting -- with Katie it's hardly been 2 whole months that she's gotten any quality tummy time. But she's certainly made up for it! About a week or so ago she figured out how to spin in circles and wobble back & forth to reach for toys (it's hilarious to watch her), and then last week she started doing pushups (which I can't even do), although she kept scootching herself backwards! But then yesterday she figured out how to dig in her toes to push herself FORWARD. Dun dun duuuuuuuuuuhn! Today it took her about 5 minutes to wobble & scoot her way halfway across the living room... to reach all of big sister's brightly colored books, stacked so neatly on the shelf, of course! Also of course, this couldn't be tolerated, so I came on the scene to behold Miriam hauling books off the shelf, out of Katie's reach, telling her that NO, books were not for babies! Ahhh, and so it begins! All in all though, Miriam has been pretty good about sharing toys with Katie. She's such a devoted big sister that I think she really wants to make Katie happy. She seems to draw the line at books though. (I'm guessing she gets this from her mother's side of the family....) :)

Sooooo... this weekend I think we're going to be doing some extensive babyproofing and thorough vacuuming. Earlier today I caught Katie trying to finish off tortilla chip crumbs which Miriam had dropped on the floor. Okay, what is it with little kids and itty bitty things?? You know the joke: you give a kid a toy, they take the toy out of the box, play with it for 10 seconds, chuck it aside and then play with the box. Why is this funny? Because it's TRUE! WHY do we still insist on buying toys for our kids? I can surround Katie with half a dozen interesting toys, and she'll ignore them all to play with a tortilla chip crumb. Or a bran flake crumb. Or a tiny piece of crayon paper. Or the leg of the table. She'll also pull her toy basket over and spread the toys all around her,


Exhibit A

and then play with the wicker! I can always tell she's doing this because she'll get REALLY quiet. (it's also SO true that you get nervous and suspicious when your kids get quiet) She gets really focused, trying to pick up some microscopic piece of fuzz.

SIX MONTH OLD MIRACLE BABY SPEAKS
Here is a transcript of a conversation Katie recently had with her toes:
[brows drawn together in concentration] Aaaaaaahhhhhhthhhhhbbbbbbbttttmmmmmmmmm[toes now in mouth]mmmmmm thpppmmmm thmppppmmmmm[trying to blow raspberries w/toes still in mouth] thbbbbtaaaaahhhhhhhhhHHHHH [drool now running down both cheek and foot] MA-MA-MA-MA-BA-BAAA!! AA!! AA!! thbbbbbbbppppppttt... [etc. etc.]
She seems to be most eloquent between the hours of 2 and 5 am, while her diaper is being changed. We often wake up to her zrbtting out her pacifier in the wee hours. Speaking of the wee hours...

SIX MONTH OLD DEMON CHILD REFUSES TO SLEEP
Our angelic baby who used to sleep in until 8 or 9 has taken to waking up to eat at 4 or 5, and then NOT GOING BACK TO SLEEP!!! Needless to say, it's driving us batty. Mommy cannot live on 5 hours of sleep a night. Well, maybe she can live, but her children certainly won't for very much longer. Since Mr. Evil Sun has taken to rising at about the same time, we're going to try a couple different things to make the room darker in the morning, in the hopes that darkness will encourage her to sleep longer. (white blinds on our two big windows just ain't doin' it) If nothing works we'll move Katie's crib into the basement and invest in a couple pairs of earplugs. (ha ha, just kidding) (well, almost) It's a good thing she's so cute.


Exhibit B

Kids' cuteness is definitely a survival trait. And speaking of cuteness...

SIX MONTH OLD RAPUNZEL GETS FIRST HAIRCUT
Okay, so her hair isn't golden, but Katie's hair is definitely LONG -- almost as long as Miriam's was at her first birthday! I had to cut her bangs the other day b/c they kept getting in her eyes. I love her hair -- it's so soft and silky and thick -- it's gotten over the fuzzy stick-straight-up phase. She still gets some pretty awesome bedhead, though. (you can see a little remnant in Ex. B above) I'm sure both my girls will want to chop all their hair off when they're teenagers, so I'm enjoying their luxuriant tresses while they have them. :)

DA-DA-LA DA-DA-LA DA-DA-LA DA-DA-LA THIS HAS BEEN A KATIE UPDATE

I'm a Ravenclaw!

What House are you at Hogwarts? Harry Potter!
brought to you by Quizilla


I fell over laughing when I saw my results. It's too true! *sigh* I need more friends... (and more bookcases, come to think of it...)

Katie's Theme Song

I think most of our loyal readers may be unaware that our little Catherine has a theme song. One of our friends (who also has a sister named Katie) started singing it to her on Easter, & it's been a popular song in our house ever since. And what is it? Why, K-K-K-Katy, that "Sensational Stammering Song Success Sung by the Soldiers and Sailors" of WWI, of course! According to Miriam, this is how it goes:

K-K-Katy, booful Katy,
you're da one-a ba-ba-baby I adore,
whe-hen the moon shines, over the cow shines,
I be waiting from da kitchen door!

Katie will smile any time one of us starts singing this song to her. She loves it.

Problems from the Graduate Student

There are many famous problems in probability. When the ideas and philosophy of probability began to develop in 1700’s, the ideas dealt mostly with how combinations and permuations related to specific problems. One such problem is the birthday problem.

What are these strange terms, and what do they mean? Like other topics in mathematics, most people understand and work with these ideas at some time in their life, but they may not understand the common lingo of mathematicians.

Both terms work with the idea of creating the total number of different lists. First think of the total number of outcomes after rolling 2 die. Let’s say that the first die rolled gives a 1. How many different outcomes exist given that the first die shows a 1? There are 6 different numbers on the second die, so the answer is 6. Now fix the first die to a 2, and repeat the process. Once again, you get 6 more outcomes to add to the first 6 outcomes. The total number of outcomes from rolling 2 die? 6x6 = 36. You simply take the total number of outcomes for each die and then multiply them (thus the name “multiplication rule”). Pretty simple.

Now think of a baseball team. There are 9 hitters on the team (not including the Yankee’s pitchers in the dugout who start fights. That’s a different type of hitter). How many ways can you arrange those hitters in the line up. For the 1^st position, you can choose from 9 players. For the 2^nd position you can choose 8 players, etc., etc. Continue this process until you reach the 9^th batting position, for which you can only choose 1 person. What’s total number of ways that you can arrange 9 hitters in a batting order? Following the example with the die we can use the multiplication rule which gives

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880.

This multiplication is known as factorial, and the shorthand for it is
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

If we shorten the number of batters to 5, then we follow the same ideas given above, except that we only list the first 5 numbers in sequence. With 9 total hitters and only 5 batters we have 9 x 8 x 7 x 6 x 5 = 15,120. This sequence is called a permutation of 9 objects choosing 5. It is written as ₉P₅.

Combinations are best described at a later date in another post, so I’ll just focus on the problem at hand: the “Birthday” Problem.

Here is the proposed question: how many people must be in a room until it is likely (greater than 50%) that two or more people share a birthday? The initial assumption might be 183, as 183/365 is greater than 50%. However, the required number is much lower than that.

To solve this problem it is easier to consider how many people will not share a birthday. To start off, if there is one person in the room then—duh!—that person won’t share a birthday with anybody else. Simple enough. If there are two people in the room, then the second person must have a birthday that is not the same as the 1^st persons birthday; hence, that person’s birthday must be on one of the 364 remaining days. For the 3^rd person, his birthday must be on one the remaining 363 days of the year. The pattern is similar to the baseball lineup mentioned before. When there are 5 people in the room, if nobody shares a birthday, then the number of different arrangements of birthdays is 365 x 364 x 363 x 362 x 361 = a really big number.

But how many total combinations of birthdays exist? To answer that question we look to the die rolling example. The 1^st person’s b-day can be on one of 365 days. The 2^nd persons b-day can be on one of any 365 days. Etc. For 5 people, the total permutations of birthdays is 365 x 365 x365 x 365x 365 = another big number.

A probability is given by taking the total subset of events (nobody shares a birthday) and dividing it by the total number of possible events (total outcomes). Given that there are 5 people in the room, the probability that 5 people do not share a birthday is

6.3 trillion

------------- = .97

6.47 trillion

and the probability that at least two people do share a b-day is 1 - .97 = .03, or 3%. This probability is pretty small, but as there are more people in the room the probability gets larger very quickly. Look at the following chart. Note that the horizontal axis only contains 60 days. As the number of days approaches 60, the probability of at least 2 people sharing a birthday is very close to 1. The initial guess of 183 was way off. If 183 people are in a room, then it is almost certain that at least two people share the same birthday. For our problem of when it will be more likely, the answer is 22, which is where the two dotted lines cross.

It's the sort solution that a person might at first find incredulous, but there is the answer. I hope you enjoyed this little aside into the world of probability. I'll hopefully include more interesting topics from that world at future dates.

Plot for B-day Problem

Hope they're still like this when they're teenagers...

...but I'm not holding my breath!

Miriam actually snuggled up next to Katie, put her arm around her and said,


"Look, Mommy, we're fwiends!"

How can that NOT melt a mother's heart?

Who would you be in 1400?

Pretty cool! Whether I actually AM this type, it's what I aspire to be.

The Prioress You scored 5% Cardinal, 74% Monk, 58% Lady, and 35% Knight!

You are a moral person and are also highly intellectual. You like your solitude but are also kind and helpful to those around you. Guided by a belief in the goodness of mankind you will likely be christened a saint after your life is over.

Link: The Who Would You Be in 1400 AD Test