@Piperbird, your findings are pretty much the same as mine. The aspirations it's possible to complete in this challenge are Painter Extraordinaire, Bestselling Author, Amateur Botanist, and Mansion Baron.
Now, if it's possible to play chess on the computer and have it count for the aspiration (and I don't think it actually is), then it would be possible to complete Nerd Brain, provided you don't mind your sim's living quarters being reduced to 3x8 to make room for a rocket.