A conversation and subsequent thoughts....

I had this conversation with one of my students today. I wish I could reveal his real name, as it is Super Awesome and I fully plan to put it in the running for the Baby Names Campaign (if and when I ever decide to finally settle down and let my uterus start calling the shots (Mom, Dad, I can FEEL you cringing from here)).

I digress.....

Allow me to first put it in context: the kiddos were working on a mini-project and I told them that they had four minutes left until we came back together for a group discussion. N. (age 8) gave a Scarlett O'Hara-eque sigh and the conversation proceeded from there:

Me: What's wrong?! Will four minutes not be enough time for you?
N.: No, it's not enough time. What is the maximum amount of time that you can give us?
Me: Um, I think maybe five minutes.
N.: Actually, the maximum amount of time that you would be able to give is infinity minutes.
Me: Well, in theory, yes.
N.: And the minimum amount of time would be point-infinity-zeros-one second. Um, one infinitieth of a second.
Me: That's much faster than we can blink or breathe or even think.
N.: Is infinity an even number or an odd number?
Me: Well, let's think of the number 5,018,903. Is that number odd or even?
N.: Odd.
Me: How do you know?
N.: You can look at the ones place.
Me: Well, since infinity goes on forever, it doesn't stop long enough to HAVE a ones place.
N.: So infinity can be BOTH even AND odd*.
[thoughtful pause, proceeds with coloring]
So it's both at the same time.
[thoughtful pause]
And it's neither at the same time.
Me: Wow, N. That's deep!
N.: Yes. I can be pretty deep sometimes.

We then calculated how many seconds are in a week, how many minutes are in a year (um, I knew that one off of the top of my head because I am a big, humongous Rent fan), and how many seconds are in a millennium. We also talked about they meanings of dec, cent, and milli as used in the words decade, century, and millennium. His mathematical curiosity sated for another day, he turned back to his mini-project.

N.: [Drawing a rabbit on his paper] Rabbits eat their own poop.

Never a dull moment.

*Alright, attention Math Nerds: I did a little bit of research on this topic after the conversation to make sure that I, y'know, did not pollute an Impressionable Young Mind by allowing him to think something that is erroneous. Infinity is definitely a very--dare I say it--spiritual concept. As one math nerd stated: "infinity is not a number, but a state..." Dude. It is therefore impossible to attempt to categorize it in any sort of manner, as it is outside of the realm of definition that language can give to fathomable concepts. However, another math nerd (on the same forum) was quite clear in stating that, while infinity is neither even nor odd, it certainly CAN'T be both at the same time, as even and odd are "mutually exclusive" descriptions. Some other websites seem to disagree with this statement by providing the explanation that if it is neither, it is also both**. Double dude. I am NOT a math person by any means. I DO, however, enjoy provocative (if a bit dorky) questions, especially when they are posed by eight-year-olds. Anyone care to tackle this one?? I've got my pocket protector ready.....

**Just a question: If something TRANSCENDS a certain boundary or definition (as infinity transcends odd and even), does it necessarily ENCOMPASS it as well?? Something that is transcendent is, by definition, BEYOND any sort of conceptualization or simple dyadic explanation (in other words, it is not something that can be defined by what it IS in part by stating what it IS NOT). At the same time, though, while infinity is neither odd nor even, isn't it also a manifestation of both? Or are the terms "odd" and "even" so rigid that they can only define a number whose boundary is completely firm, and therefore cannot be united in a single definition of "both"?? I have a headache....

Maybe N. will know the answer?