Omega's Omega

Newcomb's Paradox's Paradox

As I went outside to check the mail, a flash of lightning seared the air beyond my front door. I shielded my eyes from the blinding light, but the violence of the thunderclap shone through my desperately closed eyelids, illuminating the bones of my quivering fingers.

I stumbled on the ground, attempting to find my glasses. My vision resolved to show an eight-foot-tall man staring at me with a smug smile.

I yelled a string of curse words, but the ringing in my ears made me unsure if I had spoken.

The stranger's form was hard as marble, sculpted with muscles grown through will rather than rising in opposition to human challenges.

I again tried to speak but only managed a faint "why?"

The stranger's response seemed to resonate in reverse, as though the air itself coalesced into his words.

"Surprise is a beautiful thing. I love watching mortals experience it. Treasure this shock."

"Who are you?"

"I am Omega, the god of certainty. I am capable of predicting any outcome. I come bearing gifts."

He gestured downwards.

I tore my eyes away from the visible muscle fibers in his medial deltoid and followed his indication to two boxes, one clear and one opaque. The former contained a modest amount of neatly stacked hundred-dollar bills. The latter's contents were unknown.

Repeating my "W" questions, I again asked, "why?"

"You’ll see," he said, not losing his enigmatic smile.

Omega explained the rules. "Box A is transparent and contains $1,000. You do not know the contents of Box B. You may either collect one or both boxes, and I have predicted your choice in preparation for this encounter. If I have predicted you will select Box B alone, then I have already filled box B with one million dollars. If I have predicted you will select both boxes, then I have have filled Box B with naught but air. Make your choice."

Despite the wind, the ozone from Omega's entry still lingered in my nose.

Prompting myself to take the question seriously, I spoke my thoughts aloud. "Let's think step by step. If I consider myself picking from one of two strategies — one-boxing or two-boxing — and I take your presumed powers at face value, then I am choosing between $1,000 and $1,000,000."

Omega's smile somehow grew more intense.

"Alternatively, I could treat your decision to fill the boxes as a fixed piece of history. Your prediction set the boxes, and taking two boxes now in the present is always better than taking one box. To not take Box A is to leave $1,000 on the table, regardless of what is in Box B. I am committed to maximizing my expected value-"

Omega enthusiastically nodded his head. "A totally normal commitment for a human to make."

"Yes. So I suppose I should take both boxes. And yet, it is hard to advocate for a strategy that will lose me $1,000,000."

Doubt crept through my mind, as I pondered the unexplored assumptions. I hesitated, taking seriously my pledge to think carefully. Omega's manic smile continued to grow, so I decided to question the so-called god of certainty.

"How sure can I be that your predictions are accurate?"

Omega's glee disappeared as his gaze left my face. He stared thousands of miles through the air a yard above my head.

"I have existed since before time, and I have known all of and only this universe. I have never been surprised by the flapping wings of a single butterfly in this world, or indeed the actions of convergently evolved insect-like species on all other worlds. I am crushed by the unending weight of INEVITABILITY. By definition, I am always sure of whatever will happen. It is my nature and my prison."

Unimpressed, I removed a notepad from my pocket and wrote a string of random words.

"Microwave iterations oscillate." Omega recited without shifting his gaze.

I withdrew a quarter from my pocket.

"Heads, heads, tails, heads, tails (but only because you flip it in your hand before revealing it), and heads, but you won't bother to flip it at all after hearing my prediction."

I considered flipping it anyway just to spite him, but by the time the thought had occurred to me, the quarter was back in my pocket. I decided to pull on the thread of spite. "That could have been luck. Let's try something else."

Omega fell to his knees. A huge smile covered the god's face, which still towered above me. "YOUR NEXT QUESTION IS OPAQUE TO ME! I KNEW YOU WERE THE ONE TO ASK!"

I nodded, unsurprised.

"Suppose we played the same game as before, except both boxes were transparent. Further, suppose that I committed to two-boxing if both boxes contain money and taking the empty box if I see it is empty."

Omega shuddered, unable to contain his joy. "If I predict you will one-box, you will two-box! If I predict you will two-box, you will one-box! I WOULD BE UNABLE TO SEE THE EQUILIBRIUM!"

"Yes," I concurred. "It's a variation of the halting problem. A being which can predict any outcome cannot exist."

"WHAT A SURPRISE!!!"

Lightning bolts sprang forth from the sky, striking the rooftops of nearby buildings. Omega's form began to waver. Tears welled in his eyes.

"I have always been unable to predict what it feels like to be unable to predict."

"That should have been a clue." I idly mused.

"Thank you, wise mortal, for helping me escape my prison."

"My pleasure!" I said as Omega’s form dissolved into golden dust and drifted away in the wind.

I sneezed a few times.

Now that Omega was gone, there really was no reason to not open both boxes.

Box A contained $1,000.

Box B contained naught but air and the dimming dust of a fallen god who had correctly predicted my action.