The Perfect Shape
GeekPress is back, and linking to a fascinating article on squaring circles. I love that we live in a time when a solution has been found to such stubborn old problem. Interestingly, it proved much easier to make a cube out of a sphere than it did a square out of a circle. The article explains:
In the previous year, Tarski and Stefan Banach (1892–1945) had proved a remarkable analog of the same conjecture in three dimensions, showing paradoxically that a sphere can be cut up into a finite number of pieces and rearranged not only into a cube of the same volume but also into a cube of twice the volume. In fact, a sphere sliced up in just the right way could be rearranged into virtually any shape of any size. [Emphasis added.]
This
suggets to me that a sphere might be an excellent default shape for a multi-purpose
robot (made up of trillions of nanobots) designed to assume whatever shape is
necessary for the task at hand. So you've got this sphere that you carry around
in your backpack, or that rolls along with you as you go. It starts raining
out and poof! The sphere is now an umbrella. You stroll along until the
rain stops and poof! The umbrella is a sphere again. You decide that
you'd rather be biking than walking, and poof! You get the idea.
There's something charming, very Harry Potter, about this image of a world in which everybody has a magic sphere ready to do their bidding. Somehow, the whole thing sounds less appealing if the default shape is a cube or even an amorphous cloud.
But, hey, that's probably just me.