The Million dimensional Fed Ex problem

After your recent upgrade from a 3-Dimensional being to a million dimensional super-being, you become faced with the problem of shipping a ball. In particular you want to ship a unit ball via Fed Ex. THey provide two forms of shipping, one is the Fed Ex box, which is very expensive and the other is the fed Ex envelope, which is very cheap.

So the questions is, can you fit a unit ball into a fed ex envelope? We will assume that the envelope actually allows a 1/50 unit of width. Unfortunately, your ball has a diameter of 1 unit. So some shaving will be required to fit it into the envelope. In our traditional 3 dimensinal space, you would have to shave off about 98% of the ball before you could fit it into the envelope. How about in the million dimensional space?

The amount you have to remove would be 1 part in a googol. In other words, if 1 part in 10100. If the ball were made up of more atom than exist in our pathetic 3-D universe, you would have to remove less than one atom to get it to fit.

The Fed Ex tube

As one might expect, if you shaved in two different directions you could fit the ball into a tube that was 1/50 of a unit in diameter. You now would have to remove about 2 in a googol particles to do this.