This is a not-very-Christmas-y post I published a couple of weeks ago at does this make sense? I still like the ideas about infinity; I'm feeling more upbeat these days, though.

How do you understand infinity? An infinite amount of time, an infinitely large space, or an infinite number of objects... Infinity is a strange concept. It's more than just a very large number.

David Hilbert, a German mathematician, gives a marvelous example. Imagine the Grand Hotel, which has an infinite number of rooms. You arrive late one rainy night and ask for a room.

"The hotel is entirely full," says the clerk at the front desk.

"But you have an infinite number of rooms," you say.

"I'm sorry, but tonight we also have an infinite number of guests. All mathematicians. Room 1 is occupied, and Room 2, and Room 3... A guest is in every single room."

You sigh. "Is there nothing you can do?"

The clerk thinks for a moment. "There is. It will take some cooperation, but everyone should be accommodating. I'll ask the person in Room 1 to move to Room 2, and the person in Room 2 to move to Room 3, and so forth. That will open up Room 1 for you."

"Will that work?"

The clerk shrugs. "Everyone will need to move to the room next door, but as you know, we never run out of rooms."

 The concept of infinity doesn't match our everyday intuitions. For example, if we imagined that the infinite number of mathematicians in the Grand Hotel all had the ability to shrink themselves down to an infinitely small size, they'd all fit in one room--even a closet, a medicine cabinet, or a pill bottle.

My ruminations about infinity are sparked by articles you'll find online about the true meaning of Christmas. Some mention that Jesus came to Earth to save us from the "consequences of sin".  What are those consequences? Here's a traditional Christian view:

But he that shall blaspheme against the Holy Ghost hath never forgiveness, but is in danger of eternal damnation.

Not all Christians see damnation as being an eternity of hellfire, but it's a common enough view. This is a consequence of one particular sin: an infinity of punishment. This outcome doesn't seem physically impossible, as with our mathematician examples, but it does bump up against some of our other intuitions, those we have about fairness and proportionality. In our human systems of justice, we prefer to have the punishment fit the crime. Minor violations of the law produce a slap on the wrist (fortunately, that's only a metaphor), while major violations lead to execution, sometimes called the ultimate punishment. Is it really the ultimate punishment, though, in principle? We can imagine worse--an infinity of punishment...

Scary. I suppose that's the point. If you design a belief system to seriously discourage some kinds of thoughts or behaviors, you don't want people thinking too hard about tradeoffs. So you put an infinite weight on one side of the scales.

But let's come back to the real world. What is the true meaning of Christmas? I like the idea that it's about joy, love, and peace. Goodwill toward men. I'd be happy if we could have those in infinite amounts. Lacking that, though, a modicum will do.