Sunday, April 19, 2009

Y.D. on Infinity

Tonight at supper, Youngest Daughter (age 5 1/2) asked me, "What is the name of the biggest number?"

With some excitement, I told her, "There isn't one! If you name any number, there is always a bigger one." After talking about this for a while, and using the word "infinity" a few times, I asked her, "Do you understand?"

"No," she said, fairly cheerfully. End of subject for the time.

After supper, she got out a pencil and paper. "I'm writing the numbers up to infinity," she told me.

"But you can't!" I said. "It's not possible."

"Yes, I can," she insisted. "I have a paper and pencil, and I'm going to write them." A little later, she added, "I'm going to write the numbers up to 500."

"That's not infinity," I said. "Do you know what 'infinity' means?"


"If a thing goes on forever, that means it goes on to infinity. Numbers go on to infinity, and that means they never end."

A little later, she told me that she was trying to write, "The fact is that things go on forever. They never end." But, she added, she couldn't remember how to spell "things." I suggested that "numbers" is easier to spell than "things." We talked for a bit about how to spell "numbers."

Then I said, "Besides, it depends on what things you're talking about. Some things do come to an end, but others don't."

"Cups come to an end!" she said.

"That's right. Cups come to an end. But numbers don't."

Next stop: Actual and potential infinities.


william luse said...

And she hasn't even officially reached the age of reason. Boy are you going to have your hands full.

Lydia McGrew said...

She's a handful now and always has been. We call her the 2.0 version of her oldest sister, whom she closely resembles.

Anonymous said...

I've discussed a couple of times with Tim via e-mail and for a long time with Bill Vallicella at his weblog on the infinities, one or two years ago. I'm not sure there is no greatest (natural) number because I'm not sure whether I'm a realist about the series of numbers.


W. L. Craig and others about anti/realism and numbers:


Madeleine said...

She sounds like our 14 year old son at the same age. He was fascinated by infinity and asked all sorts of complex questions to try to get his head around it.

Whilst driving through thick and tricky traffic, he asked me to explain mass, why we don't go through some things and yet we can others. Rather tricky to explain to a 5 year old whilst driving a car!

Another time he was walking with Matt and jumping every few steps. When Matt asked him what was with the jumping he said you told me the earth is constantly spinning, I am trying to test it by seeing if I land in the same place when I jump.

Kids like this do your head in at times but they are a real reward! Have fun.

Anonymous said...

But I think the links have to do rather with the next stop (actual and potential infinity) and the stops after it. Nevermind, I just must remember she's 5 1/2.

SEP has an entry on the philosophy for children by a man at Tim's WMU department of philosophy.

Lydia McGrew said...

The thing is, Vlastimil, that if you're not a realist about numbers you have exactly the same questions to answer about the number 5 as about whether there is an infinite series. And if you can solve those questions, it seems to me that you have to be able to solve them in such a way that your non-realism is compatible with the argument that there is no greatest number. In other words, the non-realism has to fit with _all_ of mathematics or it fits with none of it. I've always wished there were some sort of numerical Aristotelianism rather than Platonism, but I've never been able to work out anything satisfactory!

Lydia McGrew said...

Madeleine, I promise I won't let her do it to me when I'm driving. :-) I'm too poor of a driver for that to be safe. Fortunately, she doesn't usually try it. (And I don't drive anywhere very challenging.) Where my kids usually try heavy conversations is at bedtime. Tucking in the little sweetheart, and suddenly it's, "Mom, I was wondering about God..." It's a pretty obvious delaying tactic, but I'm never sure quite what to do.

William Luse said...

"Mom, I was wondering about God..." It's a pretty obvious delaying tactic, but I'm never sure quite what to do.I'll bet you don't turn the lights out. They've got your "number."

Madeleine said...

The bedtime routine is a bit of a dilemma. Its like when you are trying to get them to catch the reading bug and then you find them with their light on deeply engrossed in a book...

Lydia McGrew said...

I'm a sucker for the bedtime theological questions, but if one of mine were trying to stay up reading, I'd probably tell them to get up early in the morning instead. Being a night owl myself, I don't understand the appeal of "permission" to get up early and read, but my older two seem to think that's cool.