I’ve always been blessed/cursed with a moderate amount of nerdulence. I like computers and gadgets and Star Trek, for example. And it turns out, that I like (some) math, too. Those who know me well may laugh at that as I am notoriously bad at math. It’s hard! But that doesn’t mean I can’t appreciate what others are able to do. Specifically, I like real-world applications and the more unusual, the better.
For example, the Monty Hall Problem. If you’ve seen the movie 21, then you know this one. It goes like this: Suppose you’re on a game show and the host tells you that there are three doors and behind one of them is a new car and behind the other two is a goat. And you get to pick one door. After picking one, the host (who knows what is behind each one), opens one of the other two doors to reveal a goat. He then asks you if you’d like to switch your selection, or keep the one you made previously.
Most people would claim that there is still a 1 in 3 chance of getting the car no matter what, but they would be wrong! Others would say that, since one door/goat has been eliminated, you now have a 50-50 chance of getting the car no matter what, and they are also wrong. It turns out, and this can be proven mathematically, that you have a 2/3 chance of getting the car if you switch your choice and only a 1/3 chance of winning if you don’t. Weird, right? But it works out in the math. Wikipedia spells it all out.
Then there is the Missing Dollar Riddle. I’ve loved this one for years, but it’s not so much a math problem as it is a riddle; in other words a trick question. It goes like this: Three guests check into a hotel room and the clerk tells them that the room will be $30, so they each give the clerk a $10 dollar bill. The clerk then realizes that they are eligible for a discount and the room will only be $25. So he gives them back five $1 dollar bills. They each keep one dollar and tip the bell hop $2.
So, they each paid $10, but then got a dollar back. So now they’ve each paid $9. That nine dollars multiplied by the three guests is $27. Add that to the $2 they tipped the bell hop and you get $29. Where did the other dollar go?
As I said, it’s a trick and Wikipedia has the answer
On a more serious math note, I’ve always found the Fibonacci Sequence of numbers fascinating. That sequence is the set of numbers that are the sum of the previous two numbers in the sequence. For example:
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
and so on, so the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377 …
Where it starts to get cool is that if you divide any of the numbers in the sequence by the number immediately before it, you get a number very close to the Golden Mean (aka Golden Ratio) of 1.618. The higher the numbers, the closer you get to the mean. And this is where it gets cool, because that Golden Mean is used all over the place in nature. Here’s a neat video which shows some of it:
Wikipedia has good articles on both the Fibonacci Sequence and the Golden Mean.
As long as I’m in supernerd mode, I should also mention a couple of my favorite scientific problems / paradoxes.
The first is Fermi’s Paradox, which is pretty well known. Fermi wondered why, given the size and age of the universe, and if Earth is typical, then shouldn’t extraterrestrial life be common? If so, why have we not detected any at all? No radio or light waves or any sign of intelligence anywhere else. Projects like SETI are designed to try to figure this one out. Here’s the Wikipedia link.
And finally, a fun one: Olbers’ Paradox. I especially like this one. It supposes, if the universe infinite and static, then why wouldn’t every spot of the night sky be filled with a star? How can there be any black/empty parts of the sky? Shouldn’t it be white all over? If there are that many stars, one would expect to see one in any direction one looked. It is solved best, I think, by the theory of the Big Bang and an expanding universe. Wikipedia link.
Ok, enough. I’m going to go pretend I’m cool and coach Owen’s baseball game.