There's a thin line between crazy people and the rest of us.
On the drive home the other day, the following train of thought occupied my mind.
Take a ball of rubber bands, one produced in mass quantity and sold through a popular office-supply store. It's composed of rubber bands of four different colors in seemingly equal proportion. Now, take ten of them, take them apart, and reconstitute the resultant pile-o'-bands into four balls, each of a single color. How large will those four balls be? Well, each ball will have a volume 2.5 (10/4) times the volume of one of the original balls. Since the volume of a sphere is dependent on the cube of the radius (4/3πr³, to be exact, the anti-derivative of the formula for the surface area, 4πr²), spheres whose volumes differ by a factor of 2.5 have radii that differ by a factor of the cube root of 2.5. What's the cube root of 2.5? It's about 1.35 (the calculator tells me it's 1.357). So the radius of one of the four final single-color balls should be about 1.35 times the radius of one of the original ten four-color balls. Simple.
And then I realized I was almost home. And this is part of why I don't want to drive, to be in full control of moving myself across a city all the time. I'd feel better about living inside my head on a train. Then, of course, I went to the Office Max web site and ordered 10 rubber-band balls for delivery. They arrived yesterday, but I'm so far stymied on starting the project. Early tomorrow morning, I have to drive my father to the airport for his two-week trip to Israel, and I am not a morning person at all. I am so far away from being a morning person that I can wake up in the afternoon and still be annoyed for my first two hours or so of consciousness. So why not stay up all night, take him, and then go to sleep? What a great plan. And since I'm staying up one night of the weekend, why not do it for both? And why not get the office an hour after they close (at one! They close at one in the afternoon! Lazy bums.) and be unable to pick up the package, meaning I am now searching for something else to do.
This is reminiscent of when I was laid off and made a level-2 Menger Sponge out of business cards. I think it was 208 cards total, but that's pretty simple to recalculate. If I cared to. [Edit: Being bored lends itself to recalculation. The actual number is 192, and it should've been obvious that 208 is wrong, what with it not being evenly divisible by 6.]
There's always reading.
Take a ball of rubber bands, one produced in mass quantity and sold through a popular office-supply store. It's composed of rubber bands of four different colors in seemingly equal proportion. Now, take ten of them, take them apart, and reconstitute the resultant pile-o'-bands into four balls, each of a single color. How large will those four balls be? Well, each ball will have a volume 2.5 (10/4) times the volume of one of the original balls. Since the volume of a sphere is dependent on the cube of the radius (4/3πr³, to be exact, the anti-derivative of the formula for the surface area, 4πr²), spheres whose volumes differ by a factor of 2.5 have radii that differ by a factor of the cube root of 2.5. What's the cube root of 2.5? It's about 1.35 (the calculator tells me it's 1.357). So the radius of one of the four final single-color balls should be about 1.35 times the radius of one of the original ten four-color balls. Simple.
And then I realized I was almost home. And this is part of why I don't want to drive, to be in full control of moving myself across a city all the time. I'd feel better about living inside my head on a train. Then, of course, I went to the Office Max web site and ordered 10 rubber-band balls for delivery. They arrived yesterday, but I'm so far stymied on starting the project. Early tomorrow morning, I have to drive my father to the airport for his two-week trip to Israel, and I am not a morning person at all. I am so far away from being a morning person that I can wake up in the afternoon and still be annoyed for my first two hours or so of consciousness. So why not stay up all night, take him, and then go to sleep? What a great plan. And since I'm staying up one night of the weekend, why not do it for both? And why not get the office an hour after they close (at one! They close at one in the afternoon! Lazy bums.) and be unable to pick up the package, meaning I am now searching for something else to do.
This is reminiscent of when I was laid off and made a level-2 Menger Sponge out of business cards. I think it was 208 cards total, but that's pretty simple to recalculate. If I cared to. [Edit: Being bored lends itself to recalculation. The actual number is 192, and it should've been obvious that 208 is wrong, what with it not being evenly divisible by 6.]
There's always reading.