I know calculus. Not enough to enjoy looking at the harmonic equation though.

It's a shame I never took a class on Quantum Mechanics. Most descriptions I've heard of it, even from professors, are indistinguishable from magical thinking.

I didn't come up with it. It's called the EPR Paradox.

If you have a set of entangled particles, would it not be possible to measure one aspect of each particle in the set, and thus achieve a fully accurate observation?

The Pythagorean Theorem is just a special case of the magnitude of a vector, aka the Euclidean Norm. Though, I wouldn't be able to derive that if that were deleted from my brain.

When I click that link, my browser downloads a file called redirect.php.

At some point, the answer may become "we cannot know". For example, in quantum mechanics, the uncertainty principle tells us that there is a limit to the accuracy of our measurements, and once we hit that limit, attaining more accuracy is impossible. The big bang is similar -- if time makes no sense in a singularity, perhaps we can't know what happens before that point. Maybe at some point we will find a way around these limitations, in which case it was just another instance of hitting Explain and letting science grind along, but it could be that we have already reached the ultimate limit, and no more explanations will ever come.