I suggest that much of Australia's good performance will turn out to have been a bit illusory. We were extremely lucky to experience a significant terms of trade increase from ~2003 onwards, as world iron ore and coal prices increased.
Unfortunately for us, we pissed all that windfall up against a wall. I don't think we posted a current account surplus at all throughout the resources boom years. Instead, Australian banks borrowed money from overseas to lend to Australians so they could sell houses to each other for ever increasing amounts every year. The Australian economy grew because we borrowed from overseas. Existing property owners got to feel richer. As soon as we start to pay back all the debt in a significant way, our economy will shrink. Just as the dependent to worker ratio has peaked. We will have nothing to show for it. Certainly not fast internets.
>Australian banks borrowed money from overseas to lend to Australians so they could sell houses to each other for ever increasing amounts every year. The Australian economy grew because we borrowed from overseas. Existing property owners got to feel richer. As soon as we start to pay back all the debt in a significant way, our economy will shrink.
Sounds like the exact same finance became dominant in every other Western economy.
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.
You could just simulate a run of your algorithm against all the possible configurations left. Even with the segmenting trick from the article, this will sometimes be far too slow; but e.g. trying it for 10 seconds before terminating the computation may help.
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.
