The "Interstellar" Paradox is only a paradox if we believe Dr. Brand. And we shouldn't.

Warning: Spoilers to the movie Interstellar below.

I finally watched "Interstellar" and thought it was fantastic, even if there are some parts that don't make sense.  [Why did they have to send people to these planets, when they had such amazing robots? If some data (thumbs up, thumbs down) could be transmitted through the wormhole why can't they send more? Why does no Plan C seem to exist (more on this later)? etc...] But the biggest hole in the story is the central paradox. Namely, if humanity is going to die without the wormhole created by Future Humans, than how did Future Humans build the wormhole? [Update 1/18/2016 - Since writing this, someone has pointed out that perhaps humans don't survive. Instead robots with AI survive, and they continue to search for a way to save humanity, which is why they need Cooper to connect with Murph, because as robots they can't. Anyway, I really like this idea because it's more believable, but this obviously changes a lot below]

I think that I've worked out one possible, if absolutely incredible, way for that happen, and it starts with this: humanity doesn't need the wormhole to survive (Update: or at least for AI Robots to survive)

Dr. Branch tells us that humanity is doomed without Plan A (getting everyone off  Earth with an equation-powered spacecraft) or Plan B (Populating new planet with frozen embryos) working, but he later proves to be an unreliable source, he isn't likely to be privy to every plan by every nation and its a prediction about which he could just be wrong. In fact he has to be. If humanity can't survive without the wormhole, then there is no wormhole, so humanity must survive without it.

Below I attempt to work through the minimum number of timelines to get to what we see in the movie. One thing about influencing the past that I've assumed: each time that Future Humans influence the past, a new timeline is created from the point that they influenced and the current timeline ceases to exist (making any other influences impossible from that timeline). In that way a little information moves from one timeline to the next, but a lot of information is lost forever.

Timeline 1: No influence from the future.

Here we have the blight, the wars, the impending doom on Earth, but no wormhole, no Cooper crash, no ghost and no watch message. It's hard to say what happens, but clearly humanity won't just roll over and die. There are two survival techniques here. The first was hinted at in the movie - build an enclosed biosphere and try to survive on Earth despite the problems. We'll call that Plan C. The other is to build spaceships and send people out in the hopes of someday finding a habitable planet - a slowly moving biosphere. We'll call that Plan D. It's possible that both would be attempted. What's important is to accept that at least one of them worked. Humanity survived and evolved into 5-dimension Future Humans. Hooray!!

Considering all that happens afterward, and how much harder Plan D would be, it's easier to believe that Plan C works

Despite surviving and thriving even, Future Humans 1 don't like the outcome. Perhaps the dark times were very long and very miserable and Future Humans 1 would like to alleviate that suffering. Or perhaps they are now facing a new threat that's so dangerous that even they can't overcome it - but they calculate that if they had not wasted thousands of years drifting through space/living in a hole that they would have been more able to do so.

So they want to change the past, to shorten the dark ages and/or to save Future Humans from this unknown threat. Regardless of why, they decide to create the wormhole (perhaps at an exact point that Plan D survivors reached before they made it to Edmond's planet?) back in the past and wipe out their timeline.

Timeline 2: Wormhole

Now things become much more similar to the bulk of the movie. The wormhole appears and NASA sends people into it to save humanity. But in this timeline Cooper never crashes, there is no ghost and no watch message. This would mean that all the farm scenes don't happen, but we can assume that Cooper would pilot the same mission he does in the movie and that perhaps things continue as we saw in the film. Then either Plan B or Plan C succeeds, but Future Humans 2, still want to try and change the past. Again, I think it's cleaner if Plan C is what works (since it probably worked before) but it doesn't have to be C.

If they're  Plan C descendants, they still want to short circuit the dark ages just as Future Humans 1 did and so they want to make Plan A or B work. [if they're Plan B descendants, then perhaps they're motivated by the urge to save humans on Earth.]

Regardless, they try to communicate with humans to help and there are a lot of failed communication attempts (each one resulting in a new, very slightly changed timeline, so this is really Timeline 2 to Timeline N). These failed communication attempts are the other gravitational anomalies that NASA talks about with Cooper when he first arrives at NORAD. None of these failed attempts significantly changes the events on the timeline until they try to communicate with Cooper and cause the crash from his dream at the beginning of the movie and wipe out their timeline from the crash on.

Timeline 3: Failed Communication/ Crash over the Straights

This is where things start to get hairy. The plot remains much the same as the movie, except that Cooper almost surely stays on the farm. There is no ghost and no co-ordinates so Cooper never goes to NORAD or rejoins NASA. The mission with TARS, Amelia Brand and others has a different unknown pilot (although it is possible that Cooper is recruited anyway, but that requires a big leap and the next steps make less sense if so). Perhaps Mann is successful in his plan to force them to take him to Edmond's planet. Perhaps not. It's all kind of irrelevant, what matters is that either Plan B or Plan C succeeds, but Future Humans 3,  still want to try and change the past - and that the change they want is to get Cooper back into the mission.

Future Humans 3 can probably figure out that humans on another timeline built the wormhole, and that they tried, unsuccessfully, to communicate with humans causing Cooper's crash. And they also know about Plan A and why it's doomed - Brand and Murph need data from inside the black hole.

As is suggested in the film, love plays some sort of roll in the communication from within the Tesseract and so Future Humans 3 (again, perhaps after numerous loops and attempts with other combinations. This is a loop that has to happen but it need not be the 3rd one. This is really Timeline N+1 to N+n) decide they need Cooper so that he can communicate with his daughter who they know is working on the math (which only works if they're Plan C descendants). They hatch a plan to get him.

Future Humans 3 figure that Cooper needs the time with Murph on the farm so that the bond between them can grow. And that if there is no crash and he's focused on flying for NASA that may not happen. So, they choose a time after the crash to get him back on track. THEY are the ones who initially intervene with the binary message of dust on the floor, choosing a moment that gives Cooper enough time on the farm to build the necessary bond, but leaves enough time before the mission for NASA to feel comfortable sending him. This wipes out their timeline from the dust storm on.

Timeline 4: Dust message and Tesseract

Finally we're getting to a timeline that looks almost identical to the one in the film. We have blight, wormhole, crash, binary dust message to Cooper, Cooper goes to NORAD and then flies mission exactly as we see it and falls into the black hole with Amelia going on to Edmond's planet.

What we don't have are all the ghost manifestations, the "STAY" message or the watch.

But Cooper falls into the black hole and time for him slows down, considerably. Humanity survives and evolves into 5-dimensional beings who eventually figure out that  humans on another timeline built the wormhole, and that they tried, unsuccessfully, to communicate with humans causing Cooper's crash, and that they sent him a message to get him back into the mission. And they also know about Plan A and why it's doomed - Brand and Murph need data from inside the black hole.

Finally,  they realize that Cooper and TARS are still alive and still falling into the black hole. Time for Cooper and TARS has slowed down so much that humanity is able to evolve into 5 dimensional beings before they're killed/destroyed. But of course to them it seems only like seconds.

So Future Humans 4 build the Tesseract as a way for Cooper to transmit the data gleaned from within the blackhole back to Murph. While in the tesseract, Cooper behaves exactly as we see. He knocks books off the shelves, sends the "STAY" message, creates the co-ordinates dust message (incorrectly believing that he had done that before) and transmits the data to the watch. This is why the dust message is the only one in binary - because Cooper is replicating what Future Humans 3 did, not initiating his own communication. This may take several loops, with him wiping out his timeline and then repeating behavior over and over until he does all of these things. But when he sends the watch data, then he's done.

Timeline 5: Plan A - The movie

Now everything is in place. We have blight, wormhole, crash, ghost, binary dust message to Cooper, Cooper goes to NORAD, Murph gets the "STAY" message and Cooper flies mission exactly as we see it and falls into the black hole with Amelia going on to Edmond's planet.

Once done,  Future Humans 5 - who are now definitely not descendants of Plan C - put together all of the pieces of what has happened, find Cooper and TARS in the wormhole, build the Tesseract for them, pull them out of the black hole and back through the wormhole to be found by space station Cooper, with no more interference in the past necessary.

It's convoluted and unlikely, but it works.