# Tag Archives: logic

## The oldest man in the world

Tabitha (six years old) and Griffin (on the cusp of nine) are attending a three-hour soccer camp in the neighborhood every afternoon this week. Furthermore, she has been begging to come to Tuesday night Ultimate Frisbee with me this summer. This week was the first opportunity for her to come along. It’s about a half hour ride up to Blaine so we had time to chat in the car.

Tabitha (6 years old): My group is 6 and under, but everyone is 6.

Me: Interesting.

T: Yeah. Six and under, so even a zero-year-old could play.

Me: I suppose so. But everyone is six, so there are no “unders”.

T: Daddy, everyone is under something.

Me: Huh?

T: Like you. You’re under 100.

Me: I suppose so. But then everyone you know is under 100.

T: Not the famous guy.

Me: What famous guy?

T: The oldest man in the world. He’s not under 100.

Me: No he’s not. But you don’t know him either.

Feeling smug for having won this round, Tabitha sits in silence for a moment.

T: Are his mom and dad still alive?

T: The oldest man in the world.

Me: Let’s see if you can work this out yourself.

T: Oh! They’re not alive.

Me: How do you know?

T: Well, his mom and dad are older than him. So if they were alive, they would be the oldest people in the world.

Pause.

T: Or, they could be alive, but younger than him.

### Postscript

Quick plug: Tony Sanneh is evidently from Minnesota. He has a foundation that, among other things, offers free soccer camps in Minneapolis and St Paul recreation centers. They seem to be really positive, well run affairs drawing kids of diverse economic and cultural backgrounds. From what I can tell, they are doing lovely work that we should applaud.

## A five-year old explores infinite loops

I’m doing the dishes on a Thursday evening, Griffin is doing his homework. Tabitha is playing quietly with her plastic ponies on the living room floor, talking softly to herself as she likes to do.

She calls me in from the kitchen.

Tabitha: Daddy, why did you tell me skin is made of layers of skin?

Me: Huh?

T: When I was three or four, you told me that skin is made of layers of skin. But then that skin is made of skin, and that’s made of skin… Why did you give me that bad answer?

Me: I don’t remember that, but you have a good point. That was a crummy answer wasn’t it? If skin is made of skin, then what’s that skin made of? Must be skin. And that doesn’t answer your question at all.

Me: I don’t know. But you know what that’s called? That’s an infinite loop. Skin is made of skin, which is made of skin, which is made of skin. It never ends.

[pause]

Me: Did you realize that was a bad answer at the time I gave it, or were you thinking about it now and noticed it?

T: Oh, I was just thinking about that stuff. Like a light bulb in a light bulb in a light bulb.

Me: Huh?

T: Like a light bulb has a light bulb in it, and then a light bulb in that one.

Me: Wait. I don’t get it. Were you thinking about where the light in a light bulb comes from?

T: Yeah.

Me: And light comes from light bulbs, so you thought there must be a light bulb inside the light bulb for the light to come from?

T: Yeah.

Me: Wow. So that’s like my skin answer because each light bulb needs another light bulb inside it to give off light, and that never ends. It’s another infinite loop.

T: Right.

## 4-year old logic again

Tabitha was telling me about the Muppets, which she and her brother saw without me recently.

I’ll spare you her lengthy plot summary. But if you haven’t seen the movie, the plot surrounds a boy born into a human family, but who is, in fact, a Muppet. Fish out of water. Happy ending.

Here's the guy.

So I ask Tabitha (who, recall is 4 years old and will soon be 5) a question.

Me: Is it possible that you’re a Muppet?

Tabitha: Dad! No! I don’t look like a cartoon.

This is great, right? All Muppets look like cartoons. I don’t look like a cartoon. Therefore I am not a Muppet.

In formal logic,

$A \longrightarrow B \Longleftrightarrow \sim{B} \longrightarrow \sim{A}$

Ever the teacher, I want to assess.

Me: Nice. Are all cartoons Muppets?

Tabitha: Sheep in WordWorld isn’t a Muppet. Clifford’s not.

Sheep from WordWorld (on PBS)

$A \longrightarrow B \not \Longrightarrow B \longrightarrow A$

Me: One more question. If you’re not a Muppet, does that mean you don’t look like a cartoon?

$A \longrightarrow B \Longrightarrow \sim{A} \longrightarrow \sim{B}$

She thinks for a while. Finally.

Tabitha: Dad! Clifford’s not a Muppet, but he looks like a cartoon!

So not only is it:
$A \longrightarrow B \not \Longleftrightarrow \sim{A} \longrightarrow \sim{B}$

She also seems frustrated by the obviousness of my question, given that:

$B \longrightarrow A \Longleftrightarrow \sim{A} \longrightarrow \sim{B}$

## Further adventures in 4-year old logic

I was having a little quality time with my favorite 4-year old the other day over quesadillas in the kitchen.

Tabitha: What is an umbrella bird?

Me: I don’t know. I’ve never heard of one before. Did you hear about umbrella birds somewhere?

Tabitha: No.

Me: Did you make it up?

Tabitha: (casually) No.

Four-year olds don’t concern themselves with the law of the excluded middle.