we know that simply observing an experiment can change the outcome. We don't know why that is either, AFAIK
We most certainly *do* know why observation affects an experiment. It's the Heisenberg uncertainty principle in action - if you make a measurement of the state of a system, that variable is known to some degree of precision. Its conjugate variable is thus made uncertain to a degree prescribed by the uncertainty principle. This has nothing to do with consciousness or a living observer.
A simple double-slit experiment works because of the uncertainty in the position of the particle. The wavefunction interferes with itself as it comes out of both slits and affects the possible positions it can be observed at on the detector. If you measure whether the particle passes through one of the slits, it's position is no longer uncertain, the wavefunction changes, and the experiment reflects that. This is well-understood quantum mechanics, although the popular press likes to pretend we don't know anything about it. And yes, IAAP (I am a physicist).
I can second the recommendation for Hartle (the title is Gravity: an Introduction to Einstein's General Relativity). It's a great introduction that I used as an undergrad, but be warned - it's still pretty complicated, even as an introduction. The nice part about it is that it develops the concepts of curved spacetime as you need them to investigate interesting physical systems, like the geometrized version of Special Relativity (which gets you time dilation and the Twin Paradox) or Schwarzschild black holes. My favorite section is where it discusses the metric of the entire universe, which describe the expansion of space and what happens to spacetime in the distant future.
As to Misner, Thorne, and Wheeler - avoid it until you've gone through some more introductory texts. It's really easy to get in over your head and get discouraged in that text, as they dive in head-first with hard-core math.
1 = 0! Holy shit!
The irony here is that 0!=1 is a true statement. And yes, I do think factorials are exciting.
The generation of random numbers is too important to be left to chance.