Cardinal Virtues

Riding the ski lifts with my kids has the virtue of being uninterrupted time which opens the door to many fascinating conversations. Barnacle Boy enjoys numbers. He checks out how many chairs are on each lift, and then generally ruminates on interesting properties of that number. There were 173 chairs on the lift we were riding up the other day, which led to...

"Is 173 prime or composite, Mom?"

"Prime, I think."

This conversation quickly led us to think about whether there are more even or odd integers. One theory developed about half-way up the mountain: if the positive and negative odds and evens are paired up, there are equal numbers of each; now throw zero into the mix, which is even. In this way you would conclude that there are more even integers than odd. Given that we have an expert in the house, we consulted Math Man at dinner, who told us that we have Cantor to thank for the solution to this problem of the cardinality or countability of the integers (and other infinite sets of numbers). The set of of even numbers is exactly the same size as the set of odds. The notion is that if you can map one set onto the other, they have to have the same number of members. He then said, there are the same number of even integers as there are integers divisible evenly by 10. This boggles the mind!

The explanation? If you can write a bijective function (that is one that matches each member of set A with a member of set B and vice versa) that connects one set to the other, they have the same number of elements. For example, the set of squares of the integers is not the same size as the set of integers because while you can write a function that takes one member of the set of integers to one and only one member of the set of squares you can't write a function that goes the other way. Each square matches with two possible integers (the positive one and the negative one). The square of 5 is always 25, while the square root of 25 could be either 5 or -5. In Math Man's terms: you can write an injective relationship, but not a surjective one. Hence, the relationship is not bijective! I understand, but I'm still not sure I believe!

Ornamemories

In what was (for me at least) a huge departure from tradition, we decorated the Christmas tree the day before Christmas Eve. More and more, the incursion of secular Christmas into the ecclesial season of Advent feels awkward to me, like I'm continually crossing some weird international date line. B101 is playing Christmas music, while I'm listening to the messianic passages from Isaiah on my iPod. As soon as Christmas arrives on my internal calendar, the Christmas music vanishes from the airwaves and Christmas trees appear at the curb, ready to be turned into mulch. Is it Christmas or not?

The short Advent season this year meant that the celebration of the 4th Sunday of Advent overlapped with the Vigil of Christmas, and I was responsible for proclaiming 3 different psalms at four Masses over three days. So, if the tree were going to be decorated, it was going to have to happen before the liturgical quadrille began. Barnacle Boy and Crash are now full participants in this hallowed event. The Boy enjoyed pulling ornaments and recalling the stories associated with each one. "Here is the one Aunt Barbara made for my first Christmas!" "Oh, Dad, this is your beautiful one from Vienna..." He enjoyed hearing the story of the foil bell which hangs from a black thread that you wrap around the branch. My mother made these for her first married Christmas. She and my dad were grad students, and expecting a baby in few months (me!), so funds for decorations were non-existent.

Chris pulled out an elaborate pink Victorian ornament and demanded its story from Victor. "I don't know that one. Ask your Mother..." Waving the ornament in my direction, I told him that was an ornament without a story...at least until now.

And the blind will see

I spent a couple of weeks recently as a pedestrian after my Mini's clutch failed catastrophically. The weather was thankfully ideal for walking - that crisp, sunny, energizing fall weather, the sort that makes you want to jump into a pile of leaves. In the middle of just such an afternoon, I was walking down a street that winds through a neighborhood of large, elegant homes, on my way to pick up my car at long last. There, in the middle of the sidewalk, sat a pair of glasses. No one in sight, just the glasses laying there, as yet unscathed. I started to walk past, thinking there would be no way for me to find the owner, so what would I do with them if I picked them up? But I couldn't help but think that someone would need these, and perhaps I could do something to help their owner see clearly again! I bent down and scooped up the spectacles, and tucked them into my bag, still wondering just what I could do that would offer even the remotest hope of reunion. About two minutes later, a gardener driving a golf cart turned out from one of the driveways. As he paused to let me past, I asked him if the glasses were his. At his enthusiastic and surprised, "Yes!", I handed the glasses over and continued on my way.

We often despair of making a difference in the world. We long to change the world, to see miracles happen. Sometimes I wonder if we miss the miracles, and our chances to make them happen, by stepping over and around the little things left on the sidewalk. We want to do big things, to see big miracles - so we skip over the trifles. Or else we worry that any thing we can do is but a drop in the bucket, we have no faith that our efforts will change anything at all - and leave the insignificant bits behind. I'm not Christ, healing the blind man along the road, but in this one thing not overlooked on the sidewalk, I could abet a small miracle. What were the odds of my ever finding the owner of the glasses? Small to none. Yet someone sees more clearly because I was willing to take on - in faith - the negligible burden of picking up the glasses.

One Liners

Crash Kid is the master of the one liners.

"Did I say that out loud? I'm sorry, when I'm stressed, sometimes my sub-text becomes text."

"Who are you, and what have you done with my mother?"

And of course, "Neat." Which can be inflected to mean anything from "awesome" to "and tell me again why I should care?"

A Kid'll Eat the Middle of an Oreo First

...and save the chocolate cookie outside for last!" So goes the jingle from MY childhood. I must admit, I never liked the chocolate cookie part of an Oreo much, and if left to my own devices would eat the white stuff in the middle and leave the chocolate cookie outside for someone else entirely. With four brothers, finding someone to consume my chocolate remains, licked clean or not, was rarely a problem.

The other day Barnacle Boy appeared with an impish grin and a plate of white discs -- guess what he saves for last! Those creamy white insides. This must say something about our respective psychologies, if only I could figure out what.