Acausal (Atemporal) Negotiation and Interstellar

Interstellar, the sci-fi Nolan film about black holes has a lot of great ideas in it, and remains one of my favorite science fiction movies of all time. First off, its a visual treat, with its incredible cinematography, and it’s extremely detailed renderings of black hole geometry, for which Kip Thorne, Oliver James et al developed techniques to show how a black hole may look to an observer while approaching and falling in based on understanding at the time1. It’s also got some great acting by McConaughey and the supporting cast is excellent. And who doesn’t love the vision of AI it brings to the table with TARS and CASE. Yes, it rips the overdone folding paper and black hole analogy from Event Horizon, but if it ain’t broke don’t fix it I guess. To the nerds this is overplayed, but there are surprising many people who don’t know what black holes even are2, and it was certainly included in there for the crowd who would show up because Nolan made the Batman Trilogy, so this had to be at least somewhat good. They were correct. Sure, a planet with frozen clouds is unphysical, and McConaughey not getting turned into an atomic string by tidal forces when getting thrown into a black hole is also rather unlikely. But it’s a movie dear to my heart with many interesting ideas, made by an ambitious director. I love seeing big-budget non-action sci-fi whenever it comes out, so this was a welcome addition to that category of film like Contact or Arrival. Its success also allowed Hollywood to greenlight the Martian, which is another movie that I’ll get around to talking about in the beloved thematic genre of competence porn.

Okay, so what am I going to talk about right now, if not the specifics of the film? Well there’s been much keyboard hammering about how the ending of the movie is contrived, and the whole ‘love conquers all’ shtick is stupid. People also mention the movie is not as deep as it likes to think that it is. I’ll provide a defense for the movie’s premise from these accusations, because after chatting with a good friend (kzl, or @qephatziel on twitter) about acausal negotiation, I happened to watch Interstellar again afterwards, and whether or not Nolan and team were thinking about this, they ended up making an extremely interesting movie about decision theory and had some pretty cool insights. So, yes, this is more Interstellar apologia. The movie is much deeper than it expects itself to be. Let’s chat about it.

Setting the stage, acausal negotiation or acausal trading3 is a notion that was/is toyed around with and discussed often by LessWrongers and other rationalist cliques4. The topic is gaining some more attention because of alignment researchers in AI as well. A simple example, and possibly the canonical origin, of this type of coordination is during the Prisoner’s Dilemma, which I won’t recapitulate here. Basically, the notion of acausal negotiation is this dilemma, but a more extreme abstraction: “How do decisionmakers with no access to one another, who don’t even know if the others may exist, who cannot communicate any information between each other during the decision event, coordinate with one another to achieve a mutually beneficial goal?”

Interstellar not only poses this type of problem, but also gives a fascinating solution. In Interstellar, the first premise is as follows: “What would you do if you left Earth, had to give signals back about the viability of a planet, and had no idea who was coming behind to follow you, if anyone would get your signal, etc. How could you coordinate with them to make sure they come to the right planet?” The movie creates a one-shot version of this by creating the following resource constraint: because of relativity shenanigans, the cast don’t have enough fuel to visit both remaining candidate planets, they can only choose one. But wait, aren’t the signals coming from the planets violating that notion of no communication? No, since the planet they just visited also had good signals but those turned out to be an artifact. So, the signals are fundamentally unreliable. You have to make a choice based on something other than the signals, which are equally good, but are also basically equally uncertain. Now, you’ve got a choice you can only make once, coordinating with someone else, wherein the entire fate of humanity rests on your shoulders. Nice, we’ve got our first high-stakes one-shot acausal negotiation problem–and that’s right, there are two of them in the movie (actually there are a lot of them). Here are the two options for the first problem:

  1. The ‘rational’ option: Dr. Mark Watney, I mean, Dr. Mann is on one planet, and he’s as many of them say “the best of them”: the protégé of the leader of the missions and the resistance against entropy, Michael Caine’s Dr. John Brand, as well as the one who led the Lazarus missions and convinced 11 others to go into near-certain annihilation with him. This planet is still transmitting (though we’ve already seen that transmission of the signal is unreliable, spoilers, it’s a lot more unreliable than we think at this point in the film).

  2. The ‘irrational’ option: Dr. Wolf Edmunds planet, which transmitted a green go ahead signal, before it cut off. More importantly, Dr. Edmunds is whom Anne Hathaway’s Dr. Amelia Brand loves, and who loves her back before he left to save the world.

The critique Interstellar levies at cold scientific logic is at its premises of disposability, and its notion that scientific human actors are nobly scientific, rather than scientific rationality becoming another efficient justification for our innate drive for self-preservation. Cooper makes the call to go to Dr. Mann’s planet–the data looks better, it’s still coming in, and finally, the choice to pick the other planet simply doesn’t make rational sense. But let’s think about it. This is a two way coordination problem, so let’s simulate the others on the planet and try to make this decision in the context of an acausal negotiation problem.

Dr. Mann ends up on a new planet, and he has no ties to Earth or the people still living there. This is considered a strength, since he can make the decision rationally without emotional biases, but actually plays out as a deep weakness. Since he has no ties to the people still living on Earth, he can sacrifice them without remorse. Furthermore, the despair of Dr. John Brand’s inability to solve the gravity problem without data from the inside fuels him to only ever seriously consider that people will be coming to start the civilization over from scratch, without saving Earth and its citizens now. This is patently false, as mission lynchpin and ace pilot Cooper only agrees to the mission because he wants to save his family. Upon realizing the desolation of his world, he is unable to ‘nobly sacrifice himself for science’. Why? Simply because such an empty logical reason would render him just as disposable as the people on Earth, a subject of a cold and emotionless scientific rationality. It’s just not compelling enough of a reason to overcome something as fundamental as our biological need for self-preservation. Well what could be something that is strong enough?5

Interstellar provides the answer as love. Deep personal love provides the true impetus for people to coordinate, and that much is enough. To believe that the person you have to coordinate with loves you actually aligns them and you enough to make acausal negotiation possible. Dr. Wolf loves Amelia Brand, so even if he doesn’t know that she will be personally coming after him, he has someone on Earth at present that he wants to save. He can’t just throw humanity away. If he landed on the planet that Dr. Mann did and realized that there wasn’t a future for humanity there, I’m much more confident in saying that he wouldn’t lie about it. Why not? Because to do so would jeopardize the person he loves on Earth’s future. That is something that humans can nobly sacrifice themselves for. Dr. Amelia Brand’s instinct is proven correct–Dr. Wolf didn’t lie, maybe because he did know she was coming for him and wanted to see her again, or maybe he didn’t know and just wanted her to be safe. In any rate, love sufficiently aligned them to be able to coordinate acausally.

Now, there are some formulations of this problem that are even more extreme, those in which the agents making the decision have never met whatsoever. In those cases, appealing to concepts like love and rationality are difficult without making deep assumptions about the nature of the other agents6. But we do get an even more insane version of the problem in the latter half of the movie–when Cooper is in the black hole and has temporal access to every moment of Murph’s life in the bedroom, but cannot communicate except through very small bandwidth interactions (falling books, binary on a watchface, etc.)7. On the other end, we have adult Murph, played by Jessica Chastain, and young Murph, played by Mackenzie Foy, who does pretty well for a child actress. Now we have less of a traditional two-choice scenario. The adult Murph has every reason to believe that her father simply abandoned her; Dr. Brand on his deathbed essentially told her that his plan all along was to abandon Earth, she’s not received any communications from her father for decades, and her brother has also given up. She returns to the room with the gravitational anomaly, and recalls herself decoding the message ‘STAY’ from her Ghost. She’s sure there’s a clue here, but about what, and in what form it takes, she doesn’t know.

On the other side of space and literally beyond time, Cooper is in a multidimensional apparatus created by future humanity that spans a near infinity of moments of that very room. Here’s a third and fourth mini-coordination problem: Cooper coordinating himself, and the future entities coordinating Cooper. Cooper was the one that had to be there, because if Brand made the sacrifice to dive into the black hole and ended up in a tesseract with Murph’s childhood bedroom she wouldn’t have been very happy. So the future Cooper has to coordinate getting past Cooper to leave (leaving the coordinates the first time)8, and also the future entities had to have the following knowledge of Cooper: that absent the possibility of going home to his children, he would sacrifice himself in a surely suicidal attempt to transmit data from within the black hole after sending Brand to her lover’s planet. We don’t really see the other sides of these coordination problems, so I won’t spend too much time discussing them, but they’re still there, emphasizing my point about this movie actually being about decision theory and acausal negotiation style problems, just taking the black hole and planet stuff as a fantastical setting. Nolan is a filmmaker who loves dealing with these types of decision problems anyways, and if I get around to making a review of the Prestige or Tenet I’ll talk about that theme as it relates to his whole oeuvre more.

So in this case, Cooper has to somehow provide his adult daughter whom he doesn’t really know 9, with complex quantum information through some artifact that exists within the room. Could he have made more gravitational slices like he did before? Sure, that possibility exists. But to emphasize the movie’s thematic point about love being a great option for acausal alignment, he chooses the watch that he gave her before he left. She also thinks about the watch, and contrary to all reason, all possibility, she realizes that indeed the twitching of the watch hands is actually binary code for quantum information that her father must be sending her. This is an incredulous leap in logic, and could not have been reproduced by anyone in that position except her. She wants to believe in her dad because she loves him, she knows him to be the unstoppable force of exploration and perseverance that he is–if anyone would have found a way to solve the deepest problem she had at the moment, it would be her father who didn’t go off and abandon her, or die in vain somewhere, but somehow, figured something out. This type of irrational belief in one another is obviously difficult to quantify, but humorously, the bandwidth is extremely high if we consider exactly how much information she used to make that decision. She had to, at least:

  1. Believe her father was alive and didn’t abandon her and humanity to their fate.

  2. Able to survive the journey itself.

  3. Not only survive the journey, but somehow acquire black hole data, which can only be obtained from within the black hole–a known impossibility.

  4. Not only somehow acquire black hole data, but somehow enter into a space where he’s able to change the gravity in the room itself, communicating to her as her ‘Ghost’ through time and space.

  5. Also transmit the black hole data to her through the watch that he left behind using said gravity mechanism.

The first is a test of character, the second is a measure of belief in capability, and if you already believed 1-4, then the 5th is easy enough to believe. The real insane information to coordinate is 3 and 4. The point the movie was trying to make, that “love is the only thing that humans can perceive that transcends the boundaries of time and space” while initially seeing a lot of eyerolls and mockery, I hope now comes through a lot clearer. Maybe the movie is a bit contrived, but all thought experiments are. I think Interstellar does an incredible job making an impassioned argument about coordination problems, and how loving the other person you need to coordinate with can allow for incredible amounts of information to be transmitted between two people. Only through love alone could the points 3 and 4 be communicated–only because Murph loved her father, believing that he had to have had a role in trying to help her even now. She could only have linked the gravitational phenomena and her father because the Ghost reflected what she wished her father was thinking in his innermost heart (she wanted him to want himself to stay). These lay the breadcrumbs for her to be able to link her father to the Ghost, and if he’s the Ghost, then he has somehow acquired the means to coordinate through time and space by the way of gravity. If that’s possible for him to do, then it’s not only possible for him to have also acquired black hole data, but it’s extremely likely. Why would he have even been paying attention to black hole data? Because as scientists working on the same problem, or at least Cooper being in proximity to the scientist working on the problem like Romilly10, they would both know that the information from within a black hole would be the lynchpin to creating the gravity drives that humanity needs to escape Earth.

I’ll leave these thoughts with probably my favorite exchange in any movie I’ve seen, and definitely my favorite line from a big budget blockbuster like this one.

“It’s not possible.” “No. It’s necessary.”

Absolute kino. Great film.

  1. See https://arxiv.org/abs/1502.03808 ↩

  2. I remember being on a plane once, reading a book about black hole geometry and I was blown away by some random point about Kerr black holes having white holes that exist infinitely far in the past, corresponding to the singularity existing infinitely far into the future according to an exterior observer, whereas the interior observer would reach these surfaces in finite time on their own watch, and thereby traverse time in extremely bizarre ways (maybe this is not even true, I don’t know anything about black hole physics, it was sometime in high school I was reading this). The notions of elsewhere, other universes to be ejected out of, the ring structure of the Kerr black hole singularity implying that you can ‘miss’ hitting it, and sail out of the white hole into another universe entirely, were spinning through my head. I was unable to contain my excitement, so I turned to the poor woman next to me to try and explain what I had just read. (yes, cringe, I know. But I am a cringe person, and it has been a very fruitful and entertaining experience thus far, and so I am unlikely to change.) She looked me dead in the eyes and asked “Oh that’s interesting, honey. What is a black hole?”. I was stunned–unexpected token sequence, response generation delayed 50 sec. If only I had a sheet of paper with me. ↩

  3. Okay a bit of a misnomer here since there is causality at play, the better name for it would be atemporal negotiation since the agents are divorced in time, unable to communicate, not divorced in causality since even in the prisoner’s dilemma, they are following the cause and effect relation of ‘being arrested’ and ‘have to coordinate now that they’re arrested’. ↩

  4. See https://www.lesswrong.com/w/acausal-trade. Not the only discussion, but a good one. References some cool decision theory. ↩

  5. Also brilliant casting of Matt Damon as Dr. Mann, whose normal repertoire would make us believe in him immediately as a heroic type, and not someone who would do the things he ends up doing. A very empathetic, but cowardly person, whose cowardice we can deeply understand. I also love how he justifies his cowardice with the trappings of scientific rationality, self-sacrifice, and nobility. Just adds a lot of richness to the thematic conflict between love/romantic science and this notion of noble science without emotions or sentimentality. ↩

  6. Though if you know that they’re part of the same philosophical or religious framework as you, and that framework requires a deeply inculcated worldview, like some type of esoteric number system, or way of viewing the world etc. then there are possible strategies that you can derive because of how much shared information and values you have between you. Still, this violates the most extreme type of coordination problem, where the agents have zero information about one another, and can assume nothing about one another. It’s another post to discuss these scenarios, which are also interesting. ↩

  7. Could Cooper have found a better way to communicate, given access to every moment, or even a regularly spaced set of moments of this room with Murph? Was there a higher bandwidth object he could have used to communicate with her? Higher bandwidth encoding means that the decoding on Murph’s side would have been less intuitive, after all, binary is pretty simple to guess, and is kinda the least risky. If Cooper had been overclever and coded more information into morse code hexadecimals, then maybe everyone would have died. If Murph had been overclever and interpreted the binary as Morse, and upon seeing nonsense, gotten disheartened and quit, then everyone would have died. Simplest is easier to coordinate upon, and it’s possible that Cooper himself taught Murph what binary was, or at least spoke about it. Then again, it may have also been possible that Cooper taught her morse, which has a higher bit rate (encoding an alphabet rather than two digits means more info, also morse is ternary: dot, dash, and null representing the space between words). Then again, morse code has its own issues…anyways this is completely off the topic now, but something I was musing on while thinking of this scenario. ↩

  8. Cooper leaving the coordinates for himself is like a cool self-coordination problem atemporally. He knows that simply leaving the coordinates in a gravitational anomaly in the childhood bedroom of Murph is enough to get him to find NASA, and that the ball would roll forever forward from that part onwards. Of course, he could have sabotaged himself, and he slightly attempts to in a panic by telling Murph to make him stay, but he also knows deeply that if he had successfully done so, Earth would be doomed. So once he gains some handle on the situation, he doesn’t spend the rest of his time trying to convince himself not to go, but rather to try and convince Murph that he’s still there and that he has the black hole information. ↩

  9. Eh, kindof. She only spoke one to him through the messages he received, although her not talking to him, and only mentioning his failure to show up when she was his age does give information to him that she’s still mad, and she still loves him enough to be deeply hurt ↩

  10. I love this character. The interaction between him and Coop where he receives the ambient storm sounds is quite profound and beautiful. He’s also one of the most tragic characters–he stays up waiting for his comrades in a ship he’s scared of being on for decades, only for them to return down one member, and tell him that the next planet is the last try. Then they choose the next planet upon which he lands, begins to unravel Mann’s conspiracy, and is killed. Romilly is also the one that informs Coop that the secret to the equation lies within the black hole itself. Great character, and extremely well acted by David Gyasi, with a reserved confusion about things, and a calm pensive demeanor only broken by his moment of passionate anxiety when divulging to Cooper that he hates being out in space with just a few inches protecting him. Another point about Romilly that’s incredible is that he stayed on the ship alone for 23 years, and was willing to go even further. Most of that time he doesn’t spend in hypersleep. Compare that with Dr. Mann’s decades on the planet with Mann staying in hypersleep for most of it. It illustrates the difference a tangible and perceived connection makes in the strength of character human beings can exhibit. Rom knows that if he cuts the cord, his team members who counted on him will be let down. Mann remarks about how nobody else has been tested like he had been, but Romilly literally just had. He and Dr. Mann are great foils–rational people who are simply built differently. Granted, Mann faced guaranteed death, as once he knew his planet was bad, he had to make the choice to die. Still, Rom reveals his character as deeply courageous in a very subtle way. ↩