Yes, that Scott Aaronson paper was an eye opener for me.
It wasn't because of the correspondence between Godel's theorems and the halting problem, although for a computer programmer Aaronson's formulation turns Godel's inscrutable theorem into something easily accessible. (Oh, and for the curious, the reason Godel's theorem is so hard to understand is he needed a computer programming language for his proof but there were none lying around back then, so he invented his own. I strongly suspect he wasn't thinking of it as a series of executable steps, let alone a programming language whose most important property is to be readable. As a consequence it's bloody terrible.)
No, it was because it Aaronson made it plain both the halting problem and Godel's theorem are really statements about the difficulty of reasoning about infinities. The infinities are really well hidden in both approaches, but once you uncover them it's like seeing the elephant in the room - it all becomes obvious. And it also becomes evident they aren't particularly relevant to anything you are likely to encounter here on earth. That's because there are no infinities in our corner of the universe. And, there there is no halting problem for finite, bounded systems. For some reason, no one ever tells you that.
This paper, listed here on HN recently, explains it much better than I can:
It wasn't because of the correspondence between Godel's theorems and the halting problem, although for a computer programmer Aaronson's formulation turns Godel's inscrutable theorem into something easily accessible. (Oh, and for the curious, the reason Godel's theorem is so hard to understand is he needed a computer programming language for his proof but there were none lying around back then, so he invented his own. I strongly suspect he wasn't thinking of it as a series of executable steps, let alone a programming language whose most important property is to be readable. As a consequence it's bloody terrible.)
No, it was because it Aaronson made it plain both the halting problem and Godel's theorem are really statements about the difficulty of reasoning about infinities. The infinities are really well hidden in both approaches, but once you uncover them it's like seeing the elephant in the room - it all becomes obvious. And it also becomes evident they aren't particularly relevant to anything you are likely to encounter here on earth. That's because there are no infinities in our corner of the universe. And, there there is no halting problem for finite, bounded systems. For some reason, no one ever tells you that.
This paper, listed here on HN recently, explains it much better than I can:
https://arxiv.org/abs/math/0411418