**Spoiler Alert, read at your own risk**

The major issue with Interstellar’s plot, the one all the critics can’t get over is that Cooper couldn’t have sent himself to NASA. It’s an ontological paradox. If Cooper gives the NASA coordinates to himself in the past, then where did the NASA coordinates come from?

On my first time through trying to make sense of all this, I’d found an interesting way out of the “Who sent the NASA coordinates?” causality paradox, only to get trapped inside a “Who created the wormhole?” causality paradox. On the second time through, I’d found a way out of both the first two causality paradoxes, only to find myself in a third causality paradox of “when was the secret NASA base built?”. Oh paradox my paradox! Solving one just creates another. “Hail Hydra!”

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That’s where I find myself now, but I’m comforted this is a paradox that goes away given one assumption: the Tesseract isn’t just a 3D box in 5D space built by 5D beings, it’s a really smart computer. If that’s true, there is a way around every other paradox in the movie, in such a way that aligns itself with the actual plot and quotes from the movie’s characters.

Please be patient with me, because I’m about to nerd out. Hard.

Here are some movie facts to consider:

  • NASA had known about the existence of the wormhole orbiting Saturn for 40 years prior to Cooper finding the secret NASA site.
  • NASA sent out the Lazarus missions 10 years prior to Cooper finding the secret NASA site.
  • NASA only created Plans A and B because they discovered Gargantua and the 12 worlds.
  • NASA only discovered Gargantua and the 12 worlds by means of the wormhole and the probes they sent through.
  • NASA knew about the gravitational anomalies, which had been happening for about 40 years, coinciding with the appearance of the wormhole.
  • A gravitational anomaly caused Cooper’s fly-by-wire to go out and his plane to crash, back when he was a NASA pilot.

As the movie is doing it’s best to align itself with the most modern understanding of physics (maybe not planetary science), here are some character observations that must be taken into account. This is what the characters believe about the universe they are in:

  • Brand says that you cannot physically go back in time, you can bend it and stretch it and compress it, but you can’t go back.
  • Brand says that the only thing that can cross dimensions is gravity. Insinuating that the only way to change the past is to create a gravitational anomaly in another time period.
  • Cooper says that the 5D beings are not aliens, they’re “us” meaning that they are highly evolved/transcendent humans from the future. Seeing as this revelation came during the climax of the film, we should take it as accurate.

So let’s make a few rock solid conclusions based on the above info:

  1. Cooper does not enter Gargantua or the Tesseract, unless the wormhole exists.
  2. Plan A, the giant rotating space station, does not exist unless the wormhole exists (remember, Plan A is the Secret NASA Base).
  3. Plan B, the plan to save humanity through frozen embryos does not exist, unless the wormhole exists.
  4. Cooper’s jet/craft never crashes, unless the wormhole exists (this happened back when he was a NASA pilot.
  5. The wormhole is the first change to the original timeline in which the wormhole never existed.

An explanation to the movie Interstellar has to answer the following questions:

  1. Who created the Tesseract?
  2. How does the timeline work?
  3. Who created the wormhole?
  4. Who sent the NASA coordinates to Cooper?

If you can answer those four questions without contradicting any of the movie facts, and without creating any new paradoxes; congratulations, you’ve made the movie make sense!

Who created the Tesseract?

They are 5th dimensional beings that built the Tesseract, and our protagonist believed they’re highly evolved or transcended human beings from the future. They are beings that have transcended time, and time for them is a physical dimension.

For them, the past might be a cavern they can walk into, or the future a mountain they can climb up. – Brand

This revelation is a big part of the mythology of the film. They don’t experience time linearly like, we, the audience does.

They are helping Cooper and humanity, and for a reason hidden from us, they want to save the people on Earth that died in the past. That’s the only part of the plot that really requires your faith. Whatever reason they have for wanting to go back and save everyone, it’d better be a good reason, because it will result in them being erased from existence.

If they’re erased from existence, they never come up with a plan to save everyone. This is a grandfather paradox. This movie has a way around that paradox: Gargantua.

From here on out, I’ll refer to “the 5th dimensional beings” as “the beings”.

In all likelihood, the beings no longer existed the moment the wormhole was created because they changed their own past, but the Tesseract they built still existed at the beginning of the movie all the way until the end of the movie because it was built in a place of infinite time dilation, inside a singularity.

Why do the beings no longer exist?

For starters, nowhere in the entire movie does any human ever interact with the beings. The only moment we thought might have been an interaction turned out to just be Brand and future-Cooper shaking hands through a wormhole, unbeknownst to the spaceship’s crew at the time.

Secondly, if the beings are the descendants of humans, which the film is adamant that they are, then changing the history of humanity during the blight would affect their entire existence. Meaning changing the past would wipe themselves out of existence.

But if they don’t exist, how can the Tesseract they built exist?

Let’s address that now.

How does the timeline work?

This movie doesn’t address String Theory or the Multiverse, so for the sake of honoring the script, I’m assuming a single universe and a single, unalterable “cause and effect curve”, which I define as being different than a timeline.

In my infographic, a solid line represents the unalterable cause and effect curve, and a dotted line represents a timeline.

Like wormholes, time loops can’t happen by themselves. Like wormholes, they are unstable. Time loops are unstable due to contradictions, and infeasible due to the lack of a “beginning”. There needs to be an external first cause for a time loop, and there needs to be an exit.

That first cause is the beings, and Cooper is the exit.

If you were the beings, how would you create a non-contradictory time loop with a beginning? In this universe, it’s impossible to go back in time (according to Brand), but entirely possible to send messages back in time. The only way to send a message across dimensions is using gravity.

Remember inside the Tesseract when TARS said, “Coop, we’re not here to change the past”?

Well that was true. For Cooper in the Tesseract, he was looking at his own past, unaware that the Tesseract had already altered that past. Changing that past would keep him from ever leaving on the mission in the wormhole timeline, and would result in him undoing the already altered time stream he was in everywhere outside Gargantua. He was there to change what from his perspective would be the future of the humans remaining on Earth.

So, again, how would the beings create a non-contradictory time loop with a beginning and an exit?

Inside a black hole might be the only place in the entire universe that you could build something like a Tesseract, and then change your own past so that you never existed in the first place to build that Tesseract, but it still exists unaffected by your changes to your own timeline.

How?

I read once (in real life) that if you fell into a black hole, the time dilation would be so large, that you could turn around and watch the entire history of the universe unfold before your eyes in seconds. That’s right, you could watch the universe die, by going into a black hole backwards. From my very limited understanding of the mechanics of black holes, space-time folds over on itself, effectively removing yourself from time itself. This is how I use Gargantua to reconcile all the paradoxes.

Because of infinite time dilation, any changes in space-time would take an infinite amount of time to catch up with anything that exists inside the singularity. It’s like recursively walking half the distance between you and an object, you get close, but it’s impossible for you to actually touch the object if you did that.

So time is trying to catch up to the Tesseract to make it not exist anymore, but it will never catch up, because by being in a black hole, the Tesseract is effectively in a protected bubble outside of space-time.

The beings knew that, and that’s why they didn’t build the Tesseract and place it somewhere to be found in regular space-time. If they put it in regular space-time and then changed their past, it would instantly cease to exist, thus such an action would be impossible.

Basically there’s a new time travel rule: Timeline alteration in regular space-time is impossible, but time travel in a black hole is possible because you’re detached from the timeline. I’m only intuiting here, it makes gut-level sense to me, but I don’t have the expertise to work out the math.

This is movie closure we’re talking about here, not trying to win a Nobel Prize.

Remember when Cooper said to Brand, “I don’t think either of us has time to worry about Relativity anymore”? He said that because their mission was in shambles, and time was dilated too much by them getting too close to the event horizon. Basically at that point in time, they could consider everyone on Earth dead already.

Cooper’s only chance to save Earth, would be to go into the Tesseract and make the one final change that the Tesseract had planned for him to make.

Who created the wormhole?

The dialogue and actions in the film gives us a few clues:

  • Stable wormholes are not natural.
  • The beings built the Tesseract in 5 dimensional space so humans could interact with time as a physical dimension.
  • TARS knew a lot more about the Tesseract than he should have, hinting that the Tesseract may have been communicating with him.
  • The Tesseract knew when Cooper was done sending the Quantum data to Murphy.
  • The Tesseract sent Cooper and TARS back through the same wormhole they went through in the beginning.
  • The Tesseract disassembled itself.

What does that tell us?

First, it gives us a clue that the wormhole is somehow connected to the black hole and the Tesseract. Wormholes like the one depicted in the film aren’t natural phenomena. They have to be manmade because they’re so unstable. Furthermore, wormholes need a massive energy source to stay open. It didn’t just turn on and off like a Stargate either, it was on for a good 40 years. I present to you: Gargantua, the wormhole’s power source.

Second, because the Tesseract was able to instantaneously send Cooper and TARS back through the wormhole to safety once the data transfer was complete, I propose that besides just being the power source, the Tesseract has control over the wormhole. I present to you: the Tesseract, the wormhole’s controller.

Third, because of the intelligence and programming exhibited by the Tesseract, in being able to “catch” Cooper and TARS, wait for them to finish the data transfer, send them through the wormhole, and then disassemble itself afterwards, I propose that the Tesseract isn’t just a box. It’s a smart box. Like AI smart. I present to you: the Tesseract, the wormhole’s creator.

Any task intelligent beings (future humans) can do themselves, they’re smart enough to program a machine to do. So if the 5 dimensional beings have the technology to create a wormhole in the past, they can program a Tesseract to do it too.

The Tesseract is a giant AI construct built by the 5 dimensional beings for the sole purpose of changing the history of mankind to a version where many more humans survive than in the original timeline. If the blighted humans could build TARS, imagine the kind of AI that the beings could create. The Tesseract is exactly that kind of AI.

In the new wormhole timeline, created by the Tesseract, NASA builds out Plan A and Plan B. Plan A is a lie, but not if the Tesseract can choose someone to help it alter this new timeline by providing Earthlings with the solution to the gravity problem. The Tesseract looks through the new timeline and “chooses” Cooper and Murphy as the two most likely humans to help it succeed.

Remember when Cooper discovered NASA and Professor Brand insisted he be the pilot for the mission? Cooper said, “I’ve got kids, professor. Why do you need me? As of yesterday, you were going to go anyway.” The professor said he was a good last minute addition to the team because he (an ex NASA pilot) was the only pilot alive that had actual flight experience outside a simulator.

So in the wormhole timeline, before the Tesseract decided to choose Cooper and Murphy, Professor Brand had launched the mission without Cooper, and Plan B may have worked (from the audience’s perspective).

When Cooper decoded the binary coordinates in the beginning of the movie, he thought they chose him. They weren’t the beings, “they” was the Tesseract. Later inside the Tesseract, looking back at his past, he realized they didn’t choose him, they chose Murphy, but he was a necessary part of their plan.

What does the cause and effect curve look like so far?

The first cause was the beings; they created the Tesseract. The second cause was the Tesseract, it created the wormhole. The third cause was the new timeline resulting from the creation of the wormhole. The new timeline presented the Tesseract with new information on how to improve the situation of humanity beyond Plan B.

Who sent the NASA coordinates to Cooper?

Cooper giving himself the coordinates to NASA as the first cause is untenable, because he’d never have gotten the coordinates if he didn’t send them himself in the first place. It’s a loop that has no beginning, which is nonsensical unless there is a “first cause”. But that’s not exactly what happened, is it?

At first, I was thrown for a loop because the information for the NASA coordinates does have a beginning. TARS is a NASA robot, so he would have the coordinates. So the origin of the NASA coordinates is NASA, not Cooper.

So it’s not the coordinates you need to find a beginning for, it’s Cooper and TARS friendship that needs a beginning. Cooper was with TARS in the Tesseract, and asked TARS for the coordinates in binary to send to his past self. So TARS is part of the NASA Coordinates timeloop too. TARS is the source of the coordinates, but TARS would not be with Cooper in the Tesseract in the first place, unless Cooper and TARS went on a mission together in the first place, and they never would have gone on a mission in the first place unless they were both in the Tesseract and sent past-Cooper the NASA coordinates. The ontological paradox is the origin of their friendship.

So who started this friendship? The Tesseract did. The Tesseract sent the NASA coordinates to Cooper the very first time, which led to the events where they found themselves in the Tesseract. Remember, the Tesseract is an AI built with the purpose of making small changes to the timeline of the beings, in order to save humanity from the future that the beings once occupied.

Having chosen Cooper and Murphy, the Tesseract sends the first NASA coordinates to Cooper. The coordinates given to Cooper by the Tesseract changed humanity’s timeline a second time (the wormhole was the first change) and made Cooper go on the mission with NASA.

A bunch of emotional stuff happens: heroes and villains and action sequences; and then we get back to the plot…

TARS is ejected from the ship into the black hole in order to gather Quantum data that will help the physicists on earth reconcile Relativity and Quantum mechanics, if it could just be broadcasted out somehow (it can’t, it’s a black hole, no wavelength of light can escape).

Also, Cooper pretends that ejecting TARS will give them enough momentum to make it to Edmund’s world, but it’s a lie.

Remember, we agreed. Ninety percent. – Cooper

At the last moment, to save Brand and Plan B, the apparent last hope of humanity, Cooper detaches from the ship.

Having nothing better to do than die of suffocation, Coop decides to go into the black hole, little did he know that the Tesseract brought him here, and planned for this meeting.

Once Cooper found himself inside the Tesseract with TARS, he was able to divine the knowledge of his purpose, which was to make one last change to fix the timeline.

That last change was to get Murphy the Quantum data she needed to solve gravity.

The cause and effect curve (detailed)

  1. The beings build the Tesseract in the original timeline.
  2. The Tesseract builds the wormhole, which erases the beings from existence. This creates a new space-time in which the wormhole exists in orbit around Saturn. The wormhole timeline.
  3. The Tesseract inspects this new timeline for any new ways to improve humanity’s situation.
  4. The Tesseract becomes aware of NASA’s Plan A and Plan B (because the Tesseract created, powers, and controls the wormhole that the NASA probes and Lazarus Missions went through).
  5. (Movie starts here) Plan B is likely to work without any more changes by the Tesseract, but the Tesseract decides to help the humans accomplish both Plan A and B. The Tesseract, using it’s access to the new timeline, chooses Cooper and Murph out of all the humans on Earth as the two most likely to save the planet.
  6. The Tesseract sends the initial NASA coordinates to Cooper, who thinks “they” have chosen him.
  7. Cooper goes to NASA and becomes the mission’s pilot.
  8. Stuff happens, heroes and villains, people die, Plan A was a lie.
  9. Cooper sends TARS inside the black hole to gather quantum data.
  10. Cooper detaches from Brand to save her and Plan B.
  11. Cooper enters the black hole, because “Why not?”
  12. Cooper makes it to the Tesseract, which gives him access to his daughter’s bedroom.
  13. Cooper freaks out and tries to communicate with 10 year old Murphy. TARS helps him realize that only gravity can transfer between dimensions. His first message to his past self is “STAY”.
  14. After a few tears, and the “Make him stay, Murph!” TARS lets him know that he’s not there to “change the past” (i.e. his past in the wormhole timeline), but to change the future of humanity (i.e. his future in the wormhole timeline). How a robot figures this out without help is beyond me, but it’s TARS so I suspend my disbelief.
  15. Cooper then realizes that in order to not change the past, he needs to send the coordinates to NASA to himself in binary. TARS provides the data for him.
  16. Now that Cooper has kept his past intact in the new timeline, he gracefully exits the loop. He and TARS figure out a way to use gravity to send the Quantum data to his daughter Murphy (final timeline).
  17. He decides a wristwatch he gave her is the best bet, and Morse code though the second hand will be the language he sends the quantum data in.
  18. Murphy uses this data to solve the other half of the gravity equation, making Plan A feasible.
  19. The Tesseract disassembles and sends Cooper and TARS through the original wormhole out to Saturn. Cooper shakes hands with Brand on the way back through the wormhole, then blacks out.
  20. Cooper learns that Murphy solved gravity, puts TARS back together, steals a ship and goes to tell Brand the good news. (Movie ends here)

The cause and effect curve (simple)

To understand this, don’t think of a timeline, think of it as cause and effect curve.

  1. The beings create the Tesseract.
  2. The Tesseract creates the wormhole (the first change). Plan B is likely to work without further intervention by the Tesseract.
  3. The Tesseract sends the NASA coordinates to Cooper (the second change).
  4. Most of the movie happens here.
  5. Cooper sacrifices himself to save Brand and Plan B.
  6. Cooper and TARS re-send the NASA coordinates to past-Cooper to exit the loop. If he doesn’t do this, he can never leave the black hole, because his timeline will cease to exist.
  7. Cooper and TARS send the quantum data to alive Murphy (because Murphy is already dead as far as Cooper is concerned), accomplishing the will of the Tesseract (the third change).
  8. Murphy solves gravity and Plan A works.
  9. We find out that Plan B works too, because #5.

Is that the actual plot in the minds of the creators of Interstellar? Probably not. But it’s one way for it to all work out in a single universe, without contradiction, and with a beginning.

The movie provides emotional closure, but if you’re looking for nerd closure, there you go.

Fun Q&A

Q: Is that the only way for the plot to make sense?

A: No. There are other much simpler ways for the story to work out logically, like the addition of benevolent and contemporary aliens, but that contradicts with the actual plot of the movie, because there are no aliens in the movie.

The wormhole could have been natural, and not manmade, but that also contradicts with the actual plot.

Q: Why would the Tesseract place a wormhole in orbit around Saturn, and not the Earth?

A: Because Christopher Nolan wanted to make a space epic filmed on 65mm film to be released in IMAX. Saturn is pretty. It has rings that are also pretty. It looks great on 65mm film. Also, because ‘merica.

Q: But wouldn’t placing the wormhole in low earth orbit (LEO) would eliminate the need to solve gravity since getting people in LEO is pretty routine?

A: Yes, but solving gravity is much cooler than that. LEO has already been done. You don’t win an Oscar by copying last year’s movie.

Q: Why not find a way to stop the blight in the past, that way no one has to leave Earth in the first place?

A: They’ve already done that movie, it’s called 12 Monkeys. It wasn’t as good.

Q: How did TARS figure out the purpose of the Tesseract?

A: By being awesome.

Q: What if Cooper failed?

A: The Tesseract could just try again, with slightly different parameters. What if the Coop that succeeded wasn’t the first Coop to try, like the Matrix?

Q: Why did he have to use gravity to communicate with Murphy?

A: Because the only thing that can travel across dimensions is gravity. So you can’t write a note, or yell through the Tesseract. But you can digitize gravity, just like you can digitize anything, so you can communicate.

Q: How do you digitize gravity?

A: Make one thing represent 0 and a slightly different thing represent 1. Since 1 > 0, it’d be more intuitive to make a thick line equal one, and a thin line equal 0 since thick > thin.

Q: Why were the NASA coordinates sent in binary and not Morse?

A: You could send the latitude and longitude data as two six digit integers, respectively, parsing out every two digits in the string to be degrees, minutes, and seconds but that would be harder to decipher than using a standardized method that an engineer might be familiar with. The receiver would then have to be clever insane enough to decipher that those integer numbers are in fact coordinates.

What might be easier for an engineer to interpret is if you send in two 32-bit numbers (at least) in a Q15.16 format (1 sign bit, 15 integer bits, 16 fractional bits). The 32-bit number might clue in the observer that this is computer binary encoding and not just jargon and that it might be a fixed point 2’s complement number. 2’s complement is a mathematical operation applied to binary numbers so they can represent both positive and negative numbers. You need negative numbers in a geographical coordinate system with the smallest being -180 and the most being 180 (for longitude).

33.310681 and -111.888477 are the lat/long coordinates to a Chick-Fil-A. They’d be 00000000001000010100111110001001 and 11111111100100000001110010001101 in Q15.16 binary. Any engineer that saw those two numbers written in binary in grains of well organized dust particles and light, might clue in to that being a message because of the statistical unlikelihood of so many leading ones and zeros.

That’s pretty complicated already, but morse code would be much longer, and Morse isn’t as good as binary for static visual cues of numerical data.

Q: Why was the Quantum data sent in Morse and not Binary?

A: Because it’s likely a ton of data. That would be better off being punched into the second hand of a watch than being scattered throughout the very limited space of Murphy’s bedroom. I’m guessing there’s more quantum data than could fit into her room in an organized fashion.

Also the quantum data would have to be on a loop in Morse, because you never know when she’ll start writing it down. Binary data would take much longer for Cooper to punch out, even if he was being read out the data by TARS in 1s and 0s. Binary is very efficient computer to computer, but not human to human, so that’s why Coop used Morse code. That’s why the military uses Morse code.

100101101 is 300 in binary, but adding letters and negative numbers to your message make it more complex. To transfer over letters, you’d need to use some sort of defined binary language, like ASCII or Unicode. To represent negative and positive numbers you’d have to use 2’s complement binary. If you allow off = dot and on = dash,  300 in Morse code is “00011” [3 unit pause] “11111” [3 unit pause] “11111”.

Also Morse code doesn’t take as much deciphering because of it’s ubiquity. Technically, you could memorize the most common ASCII characters to achieve a higher throughput than Morse (you don’t have to pause), but nobody memorizes ASCII, and you’d have memorized a language that few people on the entire planet could understand. Anyone that has ASCII memorized either did it by accident because they’re a genius/savant, or on purpose because of work (assembly language) or they’re a weirdo.

Tens of millions of people worldwide understand Morse code, as part of their job. Any NASA pilot, or anyone in the military, would learn Morse code during training.

Either way, sending the quantum data, would have been impossible without TARS there to facilitate.

Q: How long would it take to transfer quantum data readings through binary?

A: A long ass time. Longer than Morse. Lets not forget that humans make mistakes. “Oh, sorry, did you say 1011? I punched in 1101.” He’d have to notate any errors.

If it was TARS on one end and CASE on the other, they could transfer all the info in binary through a wristwatch very quickly, and without mistakes. Orders of magnitude faster than Cooper could (depending on the mechanical limitations of the watch), even though they’re using the same medium of communication.

Q: How did Cooper survive the black hole?

A: Magic. In real life he’d be ripped apart. That’s not actually the question you should be asking though.

Q: How did Cooper and everyone even survive in the same solar system as the black hole, wouldn’t it be spewing out enormous amounts of radiation, like Gamma radiation?

A: Exactly. Their goose would be cooked, as it were.

Update 11/24/14:

The original draft is on the left, and the final is on the right.

The original draft is on the left, and the final is on the right.