Ever feel like the universe is out to get you? Well, it is. Here's the proof:
- NP-complete Problems
- There are problems that you'd like to know the answer to, but it takes too long to figure them out! The frustrating part is that if you had some hint telling you what the solution could be, then you could quickly check it and know for sure if it was the right one -- but God ain't giving out any hints.
- Undecidable Problems
- Okay, fine. Suppose you could build an arbitrarily fast computer! Then surely you could solve all problems, right? Oops, except that there are problems which cannot be solved in all cases, because any algorithm which purported to do so would contradict itself! Crazy stuff.
- Very well, then, this just means you need a magic box that is able to solve any problem we pose for it! Then mastery of the universe will be yours, right? Well... except there's this little thing called chaos, which says that you can't screw up the question you ask your box even a little or it might give you a completely different answer. This isn't the box's fault, but a fault of the problem itself: tiny changes to how you start a chaotic system result in hugely different outcomes. So if you can't measure everything perfectly, then you can't get the right answer because you can't ask the right question!
- Uncertainty Principle
- All right, fair enough! This just means you need to invent a perfect measuring device that will allow you to know the exact position and velocity of every particle in the Universe, and then you will be able to ask your box perfect questions! Brilliant plan... except for the fact that particles don't have an exact position and momentum, so even your imagination can't invent a device to measure them perfectly.
- No-cloning Theorem (i.e., quantum indeterminacy)
- Okay, so particles might not have an exact position and momentum, but they do have an exact wave function, so you're going to measure that! Then you can fed it along with Schrodinger's Equation into your box, and you will become omniscient! But no, sadly, it doesn't work that way. Quantum information can't be copied on account of the No-cloning Theorem, so that means it is never possible for you to measure a wave function since that is a form of copying. If you try anyway, nature will punish you by collapsing the wave function so that you get a random result. Some mother she is.
Man, just thinking about these things makes my blood boil...