I see no profit in believing things which cannot be demonstrated, proven, or otherwise shown to exist. I’m entirely open to new ideas

I should not do this, but those sentences tempt me to suggest a book to you. Unfortunately it's title is enough to make you sneer again: Dean Radin, "The Conscious Universe". As you will immediately see on Wikipedia Radin is highly controversial --- naturally, because his subject are psi phenomena, being the foremost scientist/charlatan in this area (I suggest to read the book first and then decide which term to use :)

What he does in this and his other books is presenting the scientific evidence, describing in detail his and other's experiments since the turn of the 20th century (Rhine's "Zener" cards etc.), the scientific evolvement of those experiments up to nowadays, and the statistical evaluation of each one (of special interest to me as since university I love statistics :)

But the book is about more. It's partly a history of physics, from Galileo to quantum mechanics in which Radin is extremely interested (later experimental setups are based on entanglement). It's also a brief of revolutions in physics and their reception in their respective aeras.

Would be interesting to hear what after reading it you'd think of his subject with respect to "demonstrated, proven, or otherwise shown to exist". I have it as ebook so if interested just shoot me an email. Even if you sneer every other page you'll probably find it well-written, absolutely not dry but often humorous and entertaining.