My favorite little girl in the world just asked me yesterday, “When you were negative infinity years old, were you happy?” She’s fascinated with negative numbers now, what you get when you subtract a larger number from a smaller one, say, five from two, and she’s also fascinated with infinity – so NEGATIVE infinity, less than any number, must be doubly fascinating.

Earlier the same day, she asked me, “What do you get when you add infinity and negative infinity together?” Does she have any idea how complex the answers to her simple questions are? I told her you can get anything – from negative infinity to zero, to positive infinity, and anything in between. I was preparing to explain why, but she was already aware of many strange properties of infinity, and was thus willing, for the time being, to take this one on faith. Instead, she asked, “What’s positive infinity?” so I had to explain that this is just another way of saying infinity, that positive meant “not negative”.

She has established in her mind that “there’s no number past infinity”, but I had to clarify that there are different sized infinities. So far, she hasn’t asked for an explanation of this, but I fear I’ll soon have to start figuring out how to explain Cantorian set theory to a six-year-old. How will I approach the diagonal argument before she understands infinite decimals – or is that the next step? Will I have to discuss non-Cantorian set theory, so we can talk about whether or not there are infinities between Aleph Naught and the Continuum? It seems to me she’s dangerously close to asking questions like that – and, if she gets any further, I’ll have to study just to keep up.

So, back to her question, she was reasoning that, since everyone is older than negative infinity, everyone must have been negative infinity at one time – just like every child in her school is older than one, and each was one year old at some point in the past. I guess the concept is that, infinity years ago, we were all negative infinity years old, and we all passed through our negative years, getting older and older, until we were zero, and were born.

I answered that I don’t know if I was happy, but I don’t think I existed infinity years ago. “Was the earth invented infinity years ago?” (She seemed to have made the conceptual shift between an age of negative infinity and “infinity years ago” rather seamlessly.)

“No, the earth wasn’t there infinity years ago.” (I opted not to get into who might have invented the earth.)

“Was NOTHING there infinity years ago?”

“I think that infinity years ago was so long ago, that not even NOTHING was there.”

“Whoa.” Her mind seemed sufficiently blown, and we moved on to a different topic.

I’m flattered that she thinks about my happiness over an infinite expanse of time. Was I happy forever ago? I hope I was. I hope she was, too. And I hope we will be happy forever from now, too. At least I know I’m happy now. How could I have a discussion like that, and not be?

This entry was posted on Tuesday, May 4th, 2010 at 3:59 PM and is filed under Adoption, Steve Thinks. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.