Of all the paradigm shifts that science has muddled through, quantum mechanics has to rank as the most traumatic. It violates our common sense again and again, and then yet again in some completely new and unexpected way, constantly challenging rational, logical, fundamental assumptions about the nature of reality.

• It challenges taxonomies — is it particle or is it wave?
• It challenges observation — how can it possibly not have both position and momentum?
• It challenges continuity — how can it go from here to there yet never be anywhere in between?
• It challenges motion — what do you mean it took both paths?
• It challenges cause and effect — how can uncaused causes cause random effects?
• It challenges locality — how can something over there, spacelike separated, possibly affect something over here?
• It challenges measurement — don’t tell me it ain’t there until I look at it; what’s wrong with you?

How is it that our common sense feels violated by quantum systems? Why is it not a trustworthy source of intuition?

Apparently, nature has conned us. Sixty-five million years of evolution have programmed our instincts to be at odds with fundamental reality. Oh, they work great at the classical level (all we were missing was the calculus), but at the quantum level - at the quantum level, we are chumps.

So, we are naive about the nature of reality; challenge accepted.

Most quests begin with an epiphany, that Aha moment when the data lines up in a beautiful but unexpected way. This research stems from a pair of epiphanies; self-reference and games.

Self-reference lies at the heart of the major limit theorems of the last century - proofs that show where formal systems fail. Games are toy universes, perfect for building intuition through standard scientific reductionism. Together, they offer some hope of understanding quantum systems - not just computing them, not just predicting uncertain futures and fuzzy pasts, but actually developing an intuition about their nature.

It has been claimed that one should start at the beginning, but a paradigm shift is a gestalt phenomenon. It emerges as an integrated whole: no beginning, no ending, but rather an intricate structure in which every internal depends on other internals. You either see it, or you don’t - all at once, or not at all.

But a story, like a quest, has unavoidable linearity. It must be presented, and experienced, one stage at a time.

Paradigm of Paradox is an attempt to dive into the tangled morass with some guiderails. My hope is that you will find it an engaging and trustworthy guide — that after enough dives, that elusive Aha moment will arrive: the moment when the trauma of being lost in a jungle gives way to the relief of realizing you are actually in an orchard; ordered, regular, structured, even planned — each tree neatly laid out, forming a structure of sublime beauty.

If the obstacle is indeed a paradigm barrier, perhaps all that is required is a change in perspective.

Epiphanies are my great joy in life. It is my pleasure to share them with you.