Yes, that's exactly what I'm doing. This proves that random sequences don't necessarily contain all finite sequences.

Not at all. The sequence is no longer random when you remove all of the 1s from it. It's akin to flipping a coin an infinite number of times, and removing all of the times heads came up leaving you with an infinite sequence of tails. That is not random.

My example proves your intuition wrong. It doesn't prove that pi fails to contain the encoding for every song. But it does prove that irrationality is not sufficient to support that claim.

Your example is flawed.

I don't think your analogy works the way you think it does. When you drop all the 1's from the sequence, you are limiting in scope (for lack of a better term) the subset of possible sequences so that they no longer have 1 in them. This doesn't prove the impossibility of containing every possible pattern when you similarly apply the same condition (ie, every pattern that doesn't contain a 1). Because Pi is irrational, my intuition tells me it would contain the encoding for every song.

Long time lurker, had to create an account to post on this one. Wasn't this the whole premise behind the space shuttle...a reusable craft to ferry people to/from the ISS? And didn't this fail because of the extreme abuse the shuttle suffered upon re-entering the atmosphere? And unless he's planning on mining for fuel on Mars, there is going to be the cost of ferrying the fuel to Mars in the first place, regardless of whether or not you are on that ferry...