How do you get two passengers to a colony 89 years away within their lifespans?

At the end of Passengers, Jim and Aurora (played respectively by Chris Pratt and Jennifer Lawrence) are fated to be alone on the colony ship Aurora until it reaches its destination in another 89 years. The other 5000 passengers and crew on the ship won’t be awakened until four months before they reach their destination. To borrow an analogy that the film itself uses at one point, Jim and Aurora are effectively stranded on a desert island with zero chance of rescue or human contact. The nature of the human lifespan makes it almost certain neither of them can live for the duration of the journey.

As hopeless fates go, this could still be worse. The ship is designed with all the amenities that one could want. The private rooms are comparable to a very nice futuristic hotel, meals are provided, and there’s a recreation deck and a bar staffed by a friendly robotic bartender. A lifetime of limited human contact is certainly its own hell, but at least you won’t starve or be killed by the elements.

Oh, and they also have a medical pod that is capable of putting one – and only one – of them to sleep. It’s not precisely a hibernation pod, but it’s close enough that Jim suggests to Aurora that she could use it and still continue her journey much as she intended. As we see, Aurora rejects this solution, and proceeds to live out the rest of her life by taking the journey with Jim. The film had charted the course of their relationship from strangers, to lovers, to estrangement when Aurora learns Jim deliberately woke her up. That tension is resolved by the end of the film, at least to the point where Aurora can’t bear to condemn Jim to a lifetime of solitude.

Jim has endured a year on his own already, and that form of solitary confinement drove him extremely close to suicide. Thus, even if you were to ignore any romantic reading of Aurora’s self-sacrifice, there’s clearly compassion motivating her choice. An easy out for her likely means a slow, emotionally painful death for Jim. The film treats this dilemma as an either/or: she goes back to sleep, or she stays with Jim.

But is it really that simple? I can’t help but think of the old “river crossing puzzles” that we often were given in school. My personal favorite of these is the “Missionaries and Cannibals Problem,” where three missionaries and three cannibals have to get across the river, but are only able to travel two at a time. The complication is that at no point can the cannibals on one bank outnumber the missionaries on the same bank. Thus, getting everyone over safely requires problem solving more complex than just taking people across sequentially.

Kids, we’re gonna science the shit out of this problem.

We have a life pod that only one person can use, and two people who need to use it. There is also the complication that too much time in isolation could drive the awake passenger to madness. (So it’s not as simple as “You sleep 45 years and then we can trade places.”) And we have 89 years until they reach port. How do we get both of them to the colony within their lifespan?

My solution would be to take turns in this fashion: Aurora sleeps for a year. Then he wakes up and she and Jim spend a year together, after which, he sleeps for a year. Essentially, it’s a three-year round robin. After twelve years of objective time, Jim and Aurora will each have only aged 9 years.

In other words, they will have slowed down their aging by 25%. That would mean that in 89 years, they will have only aged about 67 years. Let’s assume they’re both about 30 when this starts. That would get them to 97 by the time they reached the planet. Considering the resources of the ship and future medical advancements with regard to human lifespan, they might have decent odds of seeing their destination.

If you buy into that, what if we threw a different factor into this equation? Part of why no one should be left on their own for more than a year is the fear of what isolation will do to them if they are left alone any longer. What if that wasn’t a factor? What if they could sleep for a year and a half, be together for six months and then the other person sleeps?

How would you accomplish this? By having a baby. If the lone parent has a child for companionship, it would make longer periods without the other more bearable. Thus, the hibernations could be longer, and the periods where all three are awake could be shorter. For the sake of this scenario, we’ll posit that each hibernator will spend a year and a half asleep and then the entire family will only all be awake for six months before the other parent goes to sleep for a year and a half.

What that would mean is that for every four years, Jim and Aurora would have only aged 2.5 years. That works out to 62.5% of aging relative to objective time.

So let’s say that the main body of Passengers takes place in the year 3000, just to give us some round numbers to work with. Let’s also assume Jim and Aurora are 30, just to make the math easier. On January 1, 3001, Aurora goes to sleep and they begin the first plan. One year asleep, one year together, one year alone. After two cycles of this, they are both 35 as the year 3006 ends and Aurora gives birth, having gotten pregnant during their “together” year of 3006.

The timeline would then look something like this:

3007 — Jim and Aurora turn 36, Baby turns 1.

3008 — Jim sleeps, Aurora turns 37, Baby turns 2.

3009 – “Together Year.” Jim turns 37, Aurora turns 38, Baby turns 3.

3010 – Aurora sleeps, Jim turns 38. Baby turns 4.

3011 – “Together year.” Jim and Aurora both turn 39. Baby turns 5.

At 3012 is when the “Baby” is old enough that Jim and Aurora take longer naps of a year and a half and are together less time, only 6 months. This gives us our 62.5% aging figure. Conveniently, that means they age only 15 years over 24 years objective time. Therefore, in 3035, Jim and Aurora will be 54, while their child will be 29.

There’s still 54 years left on the trip. If they stop sleeping now, Jim and Aurora will arrive at their destination at the age of 108 and the child will be 83. But, if they go in a straight round robin, with one of them always asleep, each of them will age only two years for every three years. Therefore, in 54 years, each one will only gain 36 years of age.

Jim and Aurora make it to the colony at age 90, with their child at age 65.

I thought about working out the math for how it would go if they had two children, but at that point, it seemed it would take an interesting intellectual exercise into pure pedantry. I’m curious if anyone else worked out their own figures on how Jim and Aurora might survive their journey.