Oooh, are we allowed to answer these? I'll bite:
Schrodinger's cat is just a thought experiment: a cat is left in a box with a device that may or may not kill it. And until you open the box, you have no way of knowing whether the cat is alive or dead. That's it. At it's core, the idea is literally that simple.
Of course, as with all science, they take the analogy a step further in order to describe an abstract phenomenon: until you open the box, for all intents and purposes the cat exists in both states at once-- alive AND dead-- because both are equally likely.
And this is serves as an introduction to the idea of particles whose states can't be known until they are observed, and that the act of observation ('opening the box') automatically 'chooses' a state to observe.
If you mean stuff like x+x^2, there are plenty of ways to deal with those...mostly just involving breaking up x^2 into the smaller exponents that it must contain. As an adult, I don't think it has to 'stick'; you just have to know enough to quickly re-teach yourself how to use them again when the opportunity arises.
If you mean binary code, though...your guess is as good as mine. ^^;
I've never heard of this experiment, but I think it's meant to be a classic example of psychosomatics (I think there's a better word, but I don't remember what it is...basically, how your mind can influence your body's immune response and perception of pain).
Just like people can have real auto-immune responses brought on by stress, I think it's possible that the anticipation of intense pain accompanied by a real stimulus (even if it's not the "right" one) can provoke a physical response. Maybe not the actual cell death that results from a true burn (unless that rod was REALLY cold), but they could easily have swelling and redness in the area of the "burn".
What makes me skeptical about this, though, is the threatening nature of the experiment (and the fact that participants DID come away with some form of injury)...I'm not sure that would be allowed today. ^^; Maybe 50 years ago or earlier, when regulations were looser (or nonexistent)...
Anyway, here's some things that confuse me. If anyone wants to pop in and try to explain any of 'em, I welcome it:
Cell differentiation
Basically, how does an embryo form and grow? Like, how...do the cells know what to do? How do they know where to go?? How do they become the correct shape???
Mind you, I am a biochemistry student, so I am supposed to know how to answer this. And I guess I do...but only up to a certain point.
Like, I know DNA->mRNA->Protein...but I don't get how that works on the macroscopic scale. Like, between a certain protein being made and cells assembling themselves into a beating heart, what the f*ck is going on in there?? I just don't get it...
The Discovery of Mathematics
I can deal with math that exists: it may make my brain hurt, but at least everything can be explained...it has to; that's kind of the point. ^^;
Math that doesn't exist yet, though...that, I can't comprehend.
It just never ceases to amaze me that math is just...not real. It's not; it's wholly and completely a human construct. So all these rules and equations that we're exposed to throughout school, from the streamlined and elegant to the nasty and horrible: someone had to invent them.
And someone had to invent whatever they were based on...at some point, someone had to think of numbers as more than a mnemonic device to help you keep track of how many things you have, and as an entity of their own that could be manipulated in the abstract...what a place the inside of their head must have been. '_' I don't think I could do that.
Consciousness
Once I heard that butterflies (or some kind of bug that goes through metamorphosis) can retain memories from before, when they were caterpillars. As in, their whole body liquefies and is rebuilt from the ground up, and somehow, someway, their conscious experiences survive the process.
That was a pretty mind-blowing day for me. Like, Big Bang level mind explosion...
I...just don't even know how to deal with that, if it's true. I feel like maybe there are three possible explanations:
1) The bugs don't completely liquefy; there's some brain remnant floating in the goop that we've just overlooked
2) CONSCIOUSNESS IS NOT A TRUE GESTALT SITUATION; IF THE PARTS ARE THERE, WE CAN BRING IT BACK FROM DEATH AND BEYOND...MOTHER NATURE ALREADY KNOWS HOW; WE JUST HAVE TO FIGURE IT OUT
3) Bugs have souls?? Idk