The maximum price that people are willing to pay isn't "dependent on" demand, it is demand. In particular, it has nothing to do with supply; if something is available for much less than the maximum price someone is willing to pay, then that just means that they get it for a lot less, it doesn't change how much they are willing to pay in principle.
(There are a few subtleties here, such as that willingness to pay should be measured in terms of opportunity costs rather than dollars, but all this stuff can be found in an economics textbook.)
Nice algorithm. That's pretty close to optimal. There is one improvement you missed, though it's not obvious how to implement it and I'm not sure how helpful it would be. When you aren't sure what to do, you assign probabilities in order to guess which square to click, but you could also estimate how useful each square would be.
There might be one square that's unlikely to contain a mine, but also unlikely to help much in solving the rest of the board. You might even be able to infer exactly what it will be before you click on it. Then, if there is another square that's a bit more likely to have a mine but also more likely to help, you can click on that one instead.
Well they would be mostly actual votes, but it causes Obama voters on Twitter to be more likely to mention having voted than Romney voters. You'd probably get more accurate results if you eliminated all these.
This fits with things other people who have worked with 3D printers have told me. I would have liked to see longer timescales described though. How many of these points are going to change soon or not-so-soon? I've heard that prices aren't going down quickly enough to make it economical for everyone to have a 3D printer in their homes in the near future, but it would be nice to see what other people think and to know about other issues blocking widespread adoption.
Undecidability is about the impossibility of predicting what programs will do. You have proven that there are functions from integers to integers that we cannot program, but that is not at all the same thing. Deciding whether a Turing machine will halt is one of these functions, but proving that is different than just proving that such functions exist.
Your proof that there are unprovable statements also doesn't work, as can be seen from the fact that some theories are decidable, such as Presburger arithmetic, which is the theory of the natural numbers without multiplication. The flaw here is your correspondence between propositions about naturals and functions from the naturals to the booleans. It's not clear how you want to set up this bijection, but there is actually no way of doing so, as the set of propositions about the naturals expressible in any alphabet is the same size as the naturals, by the same argument you use in your second paragraph. It therefore must be smaller, rather than the same size as, the set of functions from ℕ to the booleans.