What is Newcomb's Paradox?

Alright, no problem. Let's talk about this fascinating problem that has had philosophers and mathematicians arguing for decades.

What is Newcomb's Paradox? A Thought Experiment That Will Make Your Head Spin

Hey there, friend. Have you ever heard of a problem where no matter what you choose, you end up feeling like a fool? Newcomb's Paradox is exactly that kind of mind-bending phenomenon. It's not a simple riddle, but a serious thought experiment about "rational choice."

Let's use a story to make it clear.

The Scenario: A Super-Predictor from the Future

Imagine there's an incredibly powerful entity, let's call him the "Predictor." He might be an alien with super AI 👽, or perhaps a god who can see into the future. Either way, he knows more about you than you know about yourself. His predictions about your upcoming choices are accurate with a mind-boggling 99.9999% success rate.

One day, this Predictor approaches you, offering a chance to get rich. He presents two boxes:

Box A: This is a transparent glass box, clearly containing $1,000.
Box B: This is an opaque, mysterious box. You can't see what's inside, but it can only contain one of two things: either $1,000,000 or nothing.

The Predictor tells you the rules of the game:

“Before you arrived here, I made a prediction about you.

If I predicted that you would choose only Box B, I placed $1,000,000 in Box B.

If I predicted that you would choose both boxes (A and B), I left Box B empty.

My work is done. The prediction has been made, and the money in the boxes has already been placed (or not placed). Now, it's your turn. You can make your choice:

Option One: Take only Box B.

Option Two: Take both Box A and Box B.”

With that, the Predictor vanishes. Now, you stand before the two boxes. What will you choose?

Two Little Voices Start Battling in Your Head

At this point, two completely opposing, yet both seemingly very reasonable, ideas emerge in your mind.

Idea One: You Must Take Only Box B! (The "Trust the Predictor" Faction)

The logic behind this idea goes like this:

Unbeatable Historical Data: This Predictor is almost never wrong. Just look at everyone who has played this game before: all those who took only Box B became millionaires. And all those who greedily took both boxes ended up with only the measly $1,000 from Box A.
Your Choice Reflects Your "Type": Are you a "greedy person" or a "far-sighted person"? If you decide to take both boxes, it means you're the "greedy" type. The Predictor would have certainly seen through that, so he definitely wouldn't have put money in Box B. Conversely, if you decide to take only Box B, it means you're the "far-sighted" type, and the Predictor would have anticipated that, so Box B will contain $1,000,000.
Conclusion: To become a millionaire, I should act like someone who would choose Box B, which means... I should choose only Box B. Final Winnings: $1,000,000.

Idea Two: You Must Take Both! (The "Free Will" Faction)

The logic behind this idea is diametrically opposed:

The Past Cannot Be Changed: Listen, the Predictor has already done his part. He either put the money in Box B, or he didn't. That event has already occurred; it's in the past. Whatever you do now, you cannot travel back in time to change what's inside the boxes.
Analyze Both Scenarios: Let's analyze the two possible states of Box B when you make your choice:
1. Scenario One: Box B contains $1,000,000. This means the Predictor initially predicted you would take only B. But now, the money is already in there! If you take only B, you get $1,000,000. If you take both, you get $1,000,000 + $1,000 = $1,001,000. Taking both is better!
2. Scenario Two: Box B is empty. This means the Predictor initially predicted you would take both. The money is no longer in there. If you take only B, you get $0. If you take both, you at least get the $1,000 from Box A. Taking both is still better!
Conclusion: Regardless of whether Box B contains money or not, choosing both boxes always earns you an extra $1,000 compared to choosing only Box B. This $1,000 is like free money – you'd be foolish not to take it! Final Winnings: $1,001,000 or $1,000.

Where's the Paradox? 🤯

Feeling like your brain is tying itself in knots? That's the core of Newcomb's Paradox:

Logic One (Expected Utility Maximization) tells you that, based on the Predictor's astonishing accuracy, the expected payoff for taking only B is highest, close to $1,000,000.
Logic Two (Dominance Principle) tells you that, regardless of the circumstances, taking both boxes always yields an extra $1,000 compared to taking only one, making it the absolutely dominant strategy.

Two seemingly unassailable rational analyses lead to completely opposite conclusions. One strategy (taking only B) appears wise in terms of outcome but "irrational" at the moment of action; the other strategy (taking both) is absolutely "rational" at the moment of action but appears foolish in terms of outcome.

So, What's the Right Choice?

Friend, there is no standard answer. That's why it's called a "paradox." Philosophers, mathematicians, and decision theorists have argued over this question for decades.

Those who advocate taking only one box typically focus more on causality and the decision-maker's inherent 'type.' They see your decision type as the cause, and the money in the box as the effect.
Those who advocate taking both boxes are usually staunch "rationalists," believing that decisions should only be based on the currently observable, unchangeable situation. The past is the past, and there's no need to let what has already happened constrain your actions.

This paradox profoundly challenges our understanding of free will, causality, and "what constitutes rationality."

So, if it were you, what would you choose? Would you trust the Predictor's mysterious power, or the tangible logical reasoning right in front of you? 🤔