No Fooling, a Really Cute Story Based on Infinity
This happened a while ago. I kept meaning to blog it, mainly to economize on my telling it to relatives, but better late than never. My son Clark is 6. Here is our exchange:
Clark: Daddy why can’t there be a biggest number?
Bob: Because no matter how big a number is, there is always a bigger number.
Clark (puzzled): Why?
Bob: OK, let’s say a guy comes up to me and says, “Hey, I know the biggest number!” Then I would say, “Oh yeah, what is it?” And the guy would tell me, “It’s a billion billion.” But then I would just add 1 to it, and say, “A ha, a billion billion and 1 is a bigger number. So you made a mistake when you said you thought of the biggest number.”
Clark (after a pause): What guy are you talking about?
Bob: Just any guy. I’m saying, if anybody tries to think of the biggest number, I’ll always be able to do that trick–where I add 1 to it–so they can’t do it. They’ll always lose.
Clark: What if a girl asks you?
[I ran through the same thing with a girl asking me…]
Clark: OK I want to tell the story!
Bob: Sure go ahead.
Clark: So what if a guy came up to me and said, “Hey Clark, I know the biggest number! It’s 100 billion!” Then I would say, “No, 100 billion and 1 is bigger! You’re wrong!”
Bob: Right, good job. So he didn’t really think of the biggest number after all, did he?
Clark: No.
Bob: And you can always do that.
Clark: OK let me tell it again with Sam [name possibly changed–a kid from his class].
Bob: OK.
Clark: So what if Sam came up to me and said, “Hey Clark, I know the biggest number. It’s 50 googol.” But I would say, “No Sam you’re wrong! 50 googol and 1 is bigger!” But Sam gets mad so he would start shouting and say, “I DID TOO THINK OF THE BIGGEST NUMBER CLARK!!”
Somehow, I don’t think my attempts at an abstract proof worked. Join us next week when I describe the awkward moment in a parent/teacher conference when I had to explain to the math teacher that Clark’s “imaginary numbers” were based on the square root of -1, not numbers who were his invisible friends.
Well he seems to have gotten the logic of the proof fine.
What Clark seems to have caught on to (and perhaps supersedes his dad on – although I don’t know how methodologically rigid of an Austrian you are) is the insight that human behavior and reality more broadly doesn’t have the same a prioristic foundations that math or logic does. So while – given a set of axioms – we can build up a mathematical superstructure with deduction, we simply can’t do that in predicting his classmate Sam’s reactions. Deduction isn’t useless, of course – but it can’t be relied on exclusively to scientifically study human behavior.
Hmm, should I start an argument over praxeology with Daniel in this thread? Nope.
Dude – you’re just coming back from Auburn. You’re likely to kick my ass.
Looks like you failed to properly predict my actions.
Win
This is too funny. Clark asks great questions … was he proving that the debt ceiling needs a new roof?
I guess you already tried explaining to Clark that the cardinality of the natural numbers is invariant under transformations of largest number proponent?
Well they already covered that in Blue’s Clues.
You taught your 6 year old child the complex plane of numbers? Who are you? And are you trying to say that your son isn’t friends with numbers just because they are products of negative one? These are the typical “Absolute Values” you christian have these days.
I now have a personal goal that all of my children will know what a googol is by age 6.
I nearly spit out my coffee while laughing. Great story.