When learning multiplication in the third grade, you are taught that "times is just repeated plus." So it is very natural to imagine that sometime in the fourth grade you will learn some new thing called "supermultiplication" that is "repeated times."
Unfortunately, multiplying repeatedly does not turn out to be nearly as beautiful as adding repeatedly, and so "supermultiplication" is never covered in fourth grade. Exponentiation behaves differently from other operations, because it is neither commutative nor associative.
But that seems a shame. Isn't it a blow to the beauty of mathematics that you can't just do the same thing again? Can't we have some sort of "supermultiplication" that is just as magic as multiplication itself, with commutative, associative, and distributive properties?
Of course you can!Continue reading "Supermultiplication"
American Home Mortgage is going out of business quickly now. Like their subprime customers, they can't meet their debt obligations.
Are we Americans just nuts for taking on all this debt? Or is it rational?Continue reading "Mortgages and Sauerkraut"
Yesterday I played with Mobius strips with my daugter.
But after a day of playing with the strips - cutting them in half, and in half again, and figuring out the knots that result - she asked me "what other knots can we play with?"
So yesterday evening I got a pencil and some string and a small drill bit, and recreated this classic Sam Lloyd puzzle.
It is a great puzzle.
You can see my father-in-law struggling with it on the right...Continue reading "Buttonholed!"
I'm saddened by the recent minor tragedy on Wall Street.
I'm not talking about last Thursday's market turmoil. I'm talking about this morning's WSJ Marketplace headline. The wry wit and quirky observation of the WSJ Marketplace writing staff has been replaced by this:Continue reading "Marketplace Ruined"
Mark the date!
According to VG Charts, the Wii has just exceeded the market share of the released-a-year-earlier Xbox 360. As of today, VG charts reports 10.57 million Wiis in the hands of consumers, compared to 10.51 million 360s.
My soon-to-be first-grader Piper has fallen in love with Google Earth. She has resolved to start every morning by exploring the planet. The other day she spent the afternoon exploring the new Google Sky feature.
"I discovered the Andromeda Galaxy," she explained.
In grown-up astronomy news today, Reuters is reporting on work by UMN astronomers Rudnick, Brown, and Williams that has detected "a gaping hole in the universe."
In Piper's spirit of naive exploration, let's take a look at where this hole is, and how big it is...Continue reading "Looking at the Sky"