What is Spin? A More Simpler Explanation

The Copenhagen interpretation of quantum mechanics wasn't supposed to be mystical.  In fact, it was made precisely to avoid mysticism: "Shut up and calculate!" is probably the best summary of it possible.  Who cares what wavefunctions are or how they collapse, gimme the expectation value.  It's supposed to be practical, simple.  It's logical positivism at it's more rarified.

courtesy SMBC

Somehow, the refusal to address the complications of quantum and to just skate on by, has led to all sorts of weird mysticism stuff like quantum healing.  Today most non-physicists have misunderstandings of entanglement and many-worlds and why Schrodinger hated cats so much.  And very sadly, most physicists have no ability to correct them, as all they can do is draw squiggly tridents and funny S's and say "here is the answer".  That's all we're taught!  "It's a mystery, no one knows so shut up and calculate!"

The result is that no one really knows anything.  Physicists have a blackbox of expectation values and non-physicists have neat anecdotes for cocktail parties.

Zeno's Paradox and Why It Annoys Me

I have always been greatly annoyed by Zeno's paradoxes.

The reason why is due mostly to my stubborn pride at being ignored when I'm right.  When I was in 10th grade trig, we learned Zeno's paradox of Achilles and the Tortoise.  The problem so presented is an extremely simple algebraic equation, immediately solvable to anyone who has finished high school.

So in grade school, when I was taught this "paradox", I did solve it algebraically, almost before my teacher had finished reading it from the book, and I told her the answer, and she sort of gave me this exasperated smile and said "Yes, I know, but don't think about it that way."  And ever since, mention of this paradox as anything other than an ancient Greek misunderstanding of mathematics has infuriated me.

Basically, Zeno's paradox amounts to asserting that the geometric series cannot be summed.  Which is absurd; Archimedes was quite proficient at it, even in terms that Greeks would accept.  Some examples are below.  In terms of modern algebra, let $S$ be the sum of a geometric series; then
$$S = \sum_{n=0}^\infty a^n = 1+a+a^2+\cdots = 1+a\left(1+a+a^2+\cdots\right)=1+aS,$$
and rearranging, $S = \frac{1}{1-a},$ the formula you hopefully learned in high school.