Tag Archives: ordinal numbers


Parenting is a tremendous amount of work. Within that work are beautiful moments of love and joy. For Tabitha and me, these moments often involve music. We had an impromptu dance party in the kitchen the other night that began with my putting on some music to do dishes by.

When Griffin was born about 8 years ago, I began maintaining playlists. Each year, I collect songs that the kids liked, or that I was listening to, or that reminded me of them in some way. Some years I remember to burn these to CDs to share with family members. But I never delete them.

That first playlist is titled “Griffin year 1″.

Do you see the math here?

Tabitha (five): Are you done with my year 5 playlist yet?

Me: Yes. I finished that when you turned 5. Now I’m working on your year 6 playlist; I’m collecting a bunch of songs during the year and it will be done on your birthday.

T: Why isn’t this my year 5 playlist?

Me: Good question. Well…your first playlist I started before you turned one…

T: When I was zero years old.

Me: Right. Then when you turned one, I started your year 2 playlist. That’s what it means to be 1 year old; that your first year is over and you’re in your second year.

So when will I work on your year 10 playlist?

T: When I’m 9.

Me: How do you know that?

T: I don’t know. I just do…

So you’re working on Griffy’s year 9 playlist now? [Her brother Griffin is 8 years old]

Me: Yes. Nice. I was just about to ask you that, but you thought about it on your own. Good thinking.

T: Will you still be working on them when I’m an adult?

Me: I would gladly still work on them when you’re an adult. I don’t know if you’ll want me to at that point, but if you do, I will.

T: Oh, I will. Hey! Can you play my favorite song about the flower?

And so began the dance party.

What century is this?

At breakfast one morning, Griffin (7 years old) asked me,

Griffin: What century do you think this is? The 20th or the 21st?

Me: It’s the 21st century.

G: Oh darn. I was hoping you wouldn’t say that. I’ll have to ask Tabitha and Mommy and a bunch of other people this question.

At this point, I was thinking that he was feeling pretty smart for knowing that the year 2012 is the 21st century, even though there are only 20 sets of 100 in 2012. I was wrong. He was making the opposite argument-we should call the present century the 20th.

G: What about when you were born, in 1970? Was that the 20th century or the 19th century?

Me: It was the 20th century.

G: See, I don’t think that’s right. It should be the 19th century.

Me: Because it starts with a 19?

G: Yeah.

Me: I see. Well, what about the year 50? Not 1950, just the year 50? What century do you think that was?

G: Zero.

Me: Right. Well, we agreed that we would start counting with the first century instead of the zeroth century. So the year 50 was in the first century, and the year 150 would have been the second century.

G: Well, it shouldn’t be that way. I want to start counting at zero. So I’ll keep asking people and find people who agree with me.

A couple minutes later

G: So, have there only been people for 2000 years?

Griffin is an independent, contrarian thinker. If there is a way to think about something differently, or even a way to perform some physical deed differently, he’s all in. A critical thinker in the extreme, this boy never accepts “Because I said so” as an answer. This will serve him well in some areas of life and poorly in others. It makes parenting him a unique challenge.

From a mathematical perspective, it doesn’t matter at all whether Griffin thinks of this as the 20th or 21st century. Sooner or later he’ll give in to convention so that he can communicate with the rest of the population of the first world. The important mathematical thing is to explore the basis and the consequences of the argument he is making.

Is the basis of the argument purely the fact that 2012 begins with 20? Or is there an attention to place value? In other words, is he thinking about 2000 as 20 groups of 100, or just as beginning with 20? My question about the year 50 was intended to get at that. There is no beginning with in this case. He had no trouble, which suggests that he is thinking about groups of hundreds-there are no full groups of 100 in 50, so it should be the zeroth century according to his rule.

This is the consequence of his argument. If you’re going to argue that 2012 is part of the 20th century, you need to be ready to accept the idea of a 0th century.

What do video games have to do with cardinal numbers? I’m gonna find out!

Two gems from the excellent article on games in today’s New York Times Magazine.

First up is a dystopian take on gamification:

Gamification seeks to turn the world into one giant chore chart covered with achievement stickers

This is certainly my fear. And I hate that no one ever seems to observe that some people don’t want badges.

Second to the plate is the game Drop7. I was not at all interested in the game despite the author’s description of it as very addictive. But then (emphasis added):

Drop7 occupies a “hinge in the universe” that is at once mathematical (it allows you to play between the ordinal and cardinal meanings of a number) and spiritual: it holds you in a place between conscious problem-­solving and pure intoxication.

What?!? Cardinal and ordinal numbers in a video game? I’m in, baby!