Let's be specific: Before the AGI goes FOOM and takes over human society, where will its increases in computing power come from? Why won't achieving those gains require solving computationally hard problems?
Your examples about wonder technologies like converting Mercury into computron and solving fusion are plausible acts for a post-FOOM AGI, not a pre-FOOM AGI. I'm asserting that the path from one to the other leads through computationally hard problems. For example, a pre-FOOM AGI is likely to want to decrypt something protected by a 512-bit key, right?
The first 3 among those are a few decades to centuries out of our own reach. We wouldn't use Mercury to build a Dyson Sphere/ring, because we need the sunlight. But we're actively working on building more and better processors and attempting to turn fusion into a viable technology.
Also, have you heard of lead pipe cryptanalysis? Decrypting a 512 bit key is doing things the hard way. Putting up a million dollar bounty for anyone who determines the content of the message is the easy way.
I was very interested in the discussions and opinions that grew out of the last time this was played, but find digging through 800+ comments for a new game to start on the same thread annoying. I also don't want this game ruined by a potential sock puppet (whom ever it may be). So here's a non-sockpuppetiered Irrationality Game, if there's still interest. If there isn't, downvote to oblivion!
The original rules:
Enjoy!