Tuesday, February 3, 2009

The 162nd Carnival of Homeschooling is Up!

Yes, it has now reached the noteworthy milestone of 162. That's a seriously important milestone.

What's that, you say? 162? What could possibly be special about that number? It's just a normal number, right? Nothing interesting there.

Ah, but there you're wrong. There's something interesting about every number (at least, every non-negative integer). I can prove it mathematically.

But first, the Carnival, which is almost as interesting as my proof. :-) It's being hosted over at Dewey's Treehouse this week. Alas, I didn't submit anything this week (although I did for the last two carnivals), but there are a number of good posts in there. Here are a few I liked.

Over at Mother by Nature there is a post in which a mother shares a spontaneous conversation she had with her son about money. The kid was doing a math problem (trying to figure out sales tax), and then... started asking the economic equivalent of existential questions. What is money? Where does it come from? Why does it have any value at all? Personally, I think this is good stuff. These are not necessarily easy questions at all. After all, the green stuff in your pocket is little more than ink on paper. Why do we value it so much? And I'm not asking this as some anti-materialist rhetorical question; I mean it. Can you explain where its value comes from? I think the mother in this post did a really good job, and I'm not sure I would have done as well under similar circumstances. Just like when I took Combinatorics in college and discovered that counting is one of the hardest things to do in math, sometimes these seemingly easy questions are the hardest, when you start to pull at all their little threads....

And then there's this fun post from The Reluctant Homeschooler, who happens to be married to a somewhat old-world Ukranian. More power to them! The thing is, though, when their kids get it into their heads that they'd like to raise livestock in their suburban backyard, Daddy agrees quite enthusiatically with them, and Mommy is left to ponder questions like, "but who's going to learn to skin and cook all the rabbits?" Right now, the kids are weighing the pros and cons (mostly the pros) of keeping a pair of goats around. Mommy is, somewhat amusedly, bracing herself....

Then over at the Five J's, we have this post in which the homeschooling mother has gone through all the Dr. Seuss (and similar) books in their personal library, and figured out which ones are good for teaching which first-grade grammar lessons. For example, if you want to learn about prepositions, Green Eggs and Ham is excellent. ("And I would eat them in the rain, and in the house, and on the train....) Likewise, for numbers you could use Bears on Wheels, and for (my favorite) Onomatopoeia, there's Mr. Brown Can Moo, Can You?

There are plenty of good selections this week, so check it out.


And now, for my assertion that there's some interesting fact about every non-negative integer. Yes, this assertion is provable mathematically.

Start by assuming the opposite. There is some non-empty set of uninteresting numbers, U. By construction, no interesting fact exists about any of the elements of U. Well, since these are all non-negative integers, we can say that one such number N, element of set U, has the lowest value of any member of set U. (That is, for all other members M of set U, N is less than M). Note that this is an interesting fact about N! N is the smallest number about which no interesting fact exists. That fact, in and of itself, is interesting.

But! We have just arrived at a contradiction. N, by construction, has no interesting facts about it; but we just gave precisely such an interesting fact.

Therefore, we must conclude that our initial assumption, that the set of uninteresting numbers is non-empty, is false; and the opposite of our initial assumption is true. Every non-negative number therefore has some interesting fact about it. Quod Erat Demonstratum.

Determining what's so interesting about the number 162 is left as an exercise to the reader. ;-)


Roger Z said...

uh, I think you have a sleight-of-hand with the word "interesting" going on there???

motherbynature said...

Hi! I'm the 'mother' at Mother By Nature, thanks so much for your kind words about how well I handled my son's currency questions. I feel appreciated. :)

And LOL I love your reasoning there about interesting numbers. What's interesting about 162? Let's see... it's double 81, which is the square of 9. The 6 in the tens place is double 1+2 from the hundreds and ones places. It's one less than 163, which is the 38th prime number.

Yeah, I'm a math geek.