Really? Care to give an example on the second one? Sounds like a lot of hand-waving to me.

Obviously, if no one finds out about what you did, no one will know about you. If you're doing something truly extraordinary an old diary, some notes in the margin, or just visible side-effects are enough.

This kind of over-simplification doesn't say much at all. If you're finding the cure for death people will find out eventually, and if you're someone who accidentally got famous (catastrophe survivors, some TV-personalities) you don't have to do anything to get lucky.

EDIT: Replace cure for death with say - trading strategy that makes you insanely rich, or some software which helps you do x much faster than anyone else, or anything really which carries the original signal forward. It was just an extreme (and silly) illustrative example.