I want to make a prediction about you: by the end of this video, you won't know what to think. There's a paradox where you seem to have free will, while also seeming not to have free will: Newcomb's paradox. You may have heard about it in the Veritasium video on the paradox: a curious game-like scenario that splits real people roughly 50/50 into contradicting but apparently equally-valid strategies. Derek: Exactly! Henry: You don't want to buck the trend? Derek: You got me! I am a one-boxer, I will do it. The thing is, the Veritasium video and many other articles and papers on the paradox

mostly ignore two of the questions I had when I first heard the paradox, fundamental questions about the actual science (rather than just philosophy) underpinning the paradox: first, is the basic premise even physically possible? And if so… why does it feel so paradoxical? The answers will take us through casual calculus, quantum mechanics, chaos theory, and wondering if we in fact live in a simulation. First though, a recap of Newcomb's paradox: imagine something - a being, a supercomputer, or an algorithm - that's extremely good at

predicting people's behaviour, and it's just made a prediction about you. In a room with two boxes, one is open and has a thousand dollars inside, the other is a closed jackpot box that might contain a million dollars or might contain nothing. You are allowed to choose either just the jackpot box (worth either zero or a million dollars), or both boxes (together worth either a thousand dollars or a million plus a thousand dollars)… the catch is that the predictor-being-algorithm-thingy is set up in a way that penalizes being greedy, and before you entered the room, it only filled the jackpot with a million dollars if it predicted you'll choose only

the jackpot and not also the thousand dollars. If it predicted you were going to choose both the jackpot and the thousand dollar boxes, then the being left the jackpot box empty. The set of possible outcomes is this: if the being predicts you'll take just the jackpot box and so puts a million dollars in it, either you take just the jackpot and get a million dollars, or take both boxes, and get a million plus a thousand dollars. And if the being predicts you'll take both boxes and puts nothing in the jackpot, either you take just the jackpot and get nothing, or take

both and get a thousand dollars. But remember - the being is very good at predicting: it's made this same prediction many times before, with many different people, and is almost always right. The supposed reason it's a paradox is this: There are convincing arguments that tell you to take just one box, and to take two boxes. One-boxers say that if you choose two boxes, the prediction-being will have anticipated it, placed zero dollars in the jackpot box, and you'll end up with only a thousand dollars. And, their argument goes, if you choose just the jackpot box, the prediction being will have anticipated that, and put a

million dollars into it. One-boxers think you should choose just the jackpot box, and take a million dollars rather than a thousand dollars. Two-boxers say that once you're in the room and the game has begun, the being has already made its prediction and the money is already sitting there in the boxes. No matter what prediction the being made, whether it got it right or wrong - take two boxes and you will walk away with a thousand dollars more than if you took just the jackpot box. Two boxers think you should choose both boxes since that'll always get you an extra thousand dollars. You can watch Veritasium's video for some

of the usual discussion and arguments that surround the paradox, and maybe pause here to have a think about your own strategy. Lots of papers articles declare that these two analyses are more or less equally valid and focus on arguing which one is worth adhering to. But there are scientific tools that allow us to tell if the setup is even possible, and if it is, whether you should one-box or two-box. Causal calculus is one such tool. Causal calculus looks at statistics, not just to infer correlations between things - it looks at statistics combined with knowledge of the real world to infer causality. Here's how.

We know that the being's prediction and people's decisions are tightly correlated. This is clear because in the past, the being correctly predicted everyone's decision almost every time. Causal calculus tells us that a strong correlation like this can't occur by chance, and it means - causality wise - either the being's prediction must cause your decision, or your decision must cause the being's prediction, or they both must have a shared common cause. The timeline of the setup - which is that the being predicts, then you decide - tells causal

calculus that your decision can't directly cause the being's prediction, because that would require retrocausality, AKA time travel. And the being's prediction can't directly cause your choice, because after deciding whether or not to put the money in the jackpot box, the being is kept entirely isolated from you. Which leaves only one option: the being's prediction and your choice must have a shared common cause. Something both causes the being to place a million dollars in the jackpot box and causes you to choose just one box,

or it causes the being to place nothing in the box while causing you to choose both boxes. This simple causal calculus analysis tells you the best strategy is to take just one box, though it's also maybe not really your choice because something in the past (like, maybe, watching this video) convinced you it's the only way to get the jackpot, and the predictor knew that and therefore put the jackpot in the box. What makes Newcomb's paradox so bizarre and divisive is when you introduce another powerful tool of causal calculus: the power of intervention. Imagine a spectator sitting in the room with you who saw whether or

not the predictor-being put money into the jackpot box. From the spectator's perspective, it's an obvious choice: no matter what the predictor did, regardless of whether or not there's money in the jackpot box, there's still a thousand dollars in the other box and the spectator will be thinking to themself "I hope they take both boxes!" To take it further, if the spectator intervened and made you take two boxes/took the two boxes for you, you would always benefit, because you'd always get an extra thousand dollars. Causal calculus represents intervention by deleting

the causal relationship between the common cause (whatever it is) and the choice of boxes, which means that the box-choice is no longer correlated with the prediction about what you would choose - the intervener is now doing the choosing, and they're free to be as greedy as they want. This intervention argument has convinced adherents to causal calculus that the only rational decision is to choose two boxes, because, they say, once you're in the room, you are free to decide whatever you want - that's the whole point of free will! You can intervene in your own life.

But the intervention argument shouldn't convince you to take two boxes: because that would assume that you… are not you - the point is, if you've made up your mind, another person can intervene on your behalf, but YOU can't intervene on your own decision process. You ARE your own free decision process, and the being would supposedly have predicted that correctly. At least, according to the setup of the paradox. But that assumes the setup is even physically possible. We need to see what physics says about just how accurate a predictor-being could even be

in the real physical world: is perfect (or close to perfect) accuracy even possible? We've shown that there must be a common cause that results in both the being's prediction and also in your choice, and the most reasonable common cause is just the physical state of your past self: in addition to whatever else it knows, somehow the being must know enough about past you (and your environment) to predict what present-you will do. And while many aspects of how the brain works are still uncertain, we do know that decision making involves several cognitive processes occurring simultaneously via a complex web of billions of

neurons: so a small detail, influence, thought, memory, or timing difference could in principle tip you to change your mind, perhaps at the very last second. This complexity is a major problem for the existence of a predictor being, since it must therefore be able to instantiate an extraordinarily accurate copy of you (and your mind) in order to make reliable predictions. A similar problem arises when trying to predict the movement of a double pendulum: if you make a copy, the two pendulums may follow seemingly identical movements for a while,

until suddenly their motions diverge, because there was the tiniest error in the copy. The more accurately you copy the pendulum and starting conditions, the longer you can successfully predict the motion before it becomes unpredictable again, but eventually it will become unpredictable. And the brain is FAR more complex and unpredictable than a double pendulum. So the predictor-being would need an incredibly, incredibly, accurate copy or instantiation of you in order to predict your choice of boxes with great accuracy. And if the predictor-being's

copy of you is really so precise, then a bizarre reality arises: you can't actually know whether you are you or whether you are just the simulated experience of the copy, because the copy must be so accurate as to be essentially indistinguishable from you! And if you're the copy, your choice is clear: you should pick just the jackpot box, because that will put the million dollars in the real jackpot for the real you! In essence - there's a chance that your decision IS directly causing what's in the jackpot box, not by going back in time or anything, but because the decision made by a simulated

copy of you is the source of the predictor being's prediction - and you can't tell which you are. But creating a near-perfect physical simulation or copy of you is not just difficult in practice, it may be physically impossible even in principle. If the physical processes that go on in the brain rely on any inherently quantum features of matter - even just the butterfly effect perturbation from the underlying quantum fuzz of atoms - then the no cloning theorem (which is a physical law of our universe that means you can't make a perfect copy of a quantum

state without destroying the original) - the no cloning theorem prevents an accurate copy from being made, and so the predictor-being couldn't make an accurate enough prediction. So quantum mechanics destroys the setup of Newcomb's paradox. But it can also save the setup of the paradox! There's another quantum mechanism by which Newcomb's paradox could perhaps be physically possible, and which even provides an answer for the choice you should make: the mechanism is quantum entanglement. If, somehow, the predictor-being were able to quantum mechanically entangle your choice with the amount of money in the jackpot box, they could achieve perfect accuracy.

If (and it's a big if) they could put the quantum states of your choice and the contents of the box into a quantum superposition of "choose both boxes and the jackpot box is empty" and "choose one box and it has a million dollars", then, to an outside observer, the superposition must collapse into one of the two possibilities: either the player chose only the jackpot box and it has money in it, or they chose both boxes and the jackpot box is empty. Or if you subscribe to the many worlds interpretation, these two possibilities happen on different branches of the multiverse.

Either way, entanglement means that from the player's point of view they can make their choice 100% freely, and the prediction can still be 100% correct. It's similar to how when you repeatedly measure pairs of entangled electrons, the first electron measured in each pair will appear to have randomly "chosen" to be spin up or down, and the second one will equally appear random, but when you compare the two, it turns out their spins were always the same. [Screen note: Quantum causality shows us that is doesn't matter which spin is measured first: they will appear

fundamentally random and always be correlated] In short, quantum entanglement is a viable way where a Newcomb-like setup can be achieved (albeit so far only with microscopic particles), and in this case, the only way to get a million dollars is to choose one box, because those two outcomes are entangled together - it's not causation, it's correlation. Well, actually physicists have proved that for quantum entanglements like the one we're discussing, the casual calculus analysis breaks down, and you need a quantum theory of causality! Which is too much for us to get into here.

Or maybe it's just impossible to set up entanglement between your brain and the contents of the jackpot box… So… what do I think? Is a game like this possible? I actually think it is, for reasons we've completely ignored until now: basic probability and human nature. A 100% accurate prediction of all participants is probably physically impossible, but a very good prediction seems totally reasonable. You don't need to be a magic-all-knowing-being to predict people with super high accuracy: you just need to get almost everyone to do the same thing.

Say I guess that a die roll will land on either a one, two, three, four, OR a five, then I'll be right around 83% of the time! It's a property of probabilities that if a thing is very likely, you don't have to be good at predictions: just choose the likely thing and your accuracy will be high, because it will be equal to the high probability of that likely thing. And that's where human nature comes in: we know that people can be primed or misdirected to make choices in one direction or another, maybe by the design of the game, the wording of the explanation, or even the color of the room they're in! Like,

imagine if the predictor is a five-year-old kid who predicts every time that people will take both boxes. Most people, when faced with real boxes containing real money, would guess that a five year old would be bad at predicting and likely doesn't have one million dollars to give away, so the vast majority people would choose two boxes, fulfilling the 5-year-old's prediction that they'll take two boxes, and making the 5-year-old a super-accurate-predictor-being! This is an implementation of Newcomb's paradox that has the same statistics but is much less paradoxical.

In short, I bet it would be quite easy to engineer a real-world scenario in which a majority of participants choose the same thing - not by accurately predicting the behavior of any individual, but by understanding human nature. And by getting a majority of participants to make the same choice, you can achieve falsely high accuracy just by always predicting the most common choice. So what should you do if you actually find yourself in the situation of Newcomb's paradox, choosing between the possibility of a million dollars or a thousand or both or none at all? If

the predictor being really is a vast intelligence capable of remarkable prediction, then causal calculus tells us that you should always pick one box, while an intervening observer should always pick two boxes on your behalf. Simulation theory says you should pick one box (because you might be in the simulation). Quantum no-cloning says that a perfect predictor-being is effectively impossible and maybe you should greedily pick two boxes, while quantum entanglement leaves open the door for perfect prediction, in which case you would pick one box. Whether entanglement like this

would be possible to set up is unclear, though. And if a random five-year-old is providing the money and doing the predicting, everyone should pick two boxes, which allows the five-year-old to falsely achieve incredible accuracy. So have you made up your mind about Newcomb's paradox? Would you choose one box, or two? Or are you still undecided? I predicted that by the end of this video, you wouldn't know what to think. So tell me - how accurate was my prediction? Derek: So here are some thoughts that I was scribbling down as I was watching… OK, so more from Derek in a second, but first,

instead of putting money into boxes for strangers - why not support the creation of more MinutePhysics videos like this one? If you've enjoyed watching my videos, please consider supporting me on Patreon and help make MinutePhysics sponsor free - thank you so much! And now back to Derek's thoughts. Derek: It is my experience with this problem that most people have a gut or instinctual response. And my sense is that they don't really change that over time. I'm such a one-oxer. I don't need to maximize every dollar. I don't need

to walk out of there with like, look, I got the most that possibly could have been got! The prize is the million, the thousand is the distraction. Maybe the prediction is much simpler than it's made out to be here in that you don't need a full simulacrum of them and their environment their experiences, which is obviously impossible, so maybe the question of, what are they going to do is actually way simpler than we think it is. Henry: Yeah, that's what that's literally what the next section of the video is about. Which I agree with. There is plenty of ways around

needing to perfectly clone somebody to predict. Derek: I do like the cleverness of bringing entanglement in there, which would perfectly determine the outcomes. Is the human brain a coherent quantum state? Like it probably isn't. And so that would be the problem. If all we were doing was treating electron states as choices or something, then obviously you could perfectly get this to work. Which is something interesting and I hadn't thought about that for sure.