Three-Body Problem

Ever since Newton, one would think that the position of any planet can be predicted for all time. Except that one would be wrong! Just having 3 objects in the scenario makes calculations very tough! That’s the (in)famous “three-body problem”. (And in case you wondered, yes, the first three-body problem people tried to solve involved the sun, earth and moon).

You might be thinking if it’s so tough for humans, why not just throw a computer at the problem? Aha, but the point is in this line from Wikipedia:
“There is no general closed form solution for every condition.”
Put simply, the problem is that, for almost all starting positions, there is no equation into which you plug in the masses, coordinates and velocities at time zero and then find where they’ll be at all instants in the future. Sure, you can calculate positions instant by instant, but that still means we don’t the answer for all time. For example, consider the more general form the problem, the n-body problem (where “n” is the number of bodies): is the solar system “stable”? Or will the planets escape the solar system? Or slam into each other? Or fall into the sun? The answer: nobody knows. Sure, we’ve done instant by instant calculations to know the status at those times, but we can’t know for all time.

Cixin Liu wrote a best-selling sci-fi book in Chinese titled (what else?) Three-Body Problem (Yes, it’s been translated into English). The book involves so many things: a virtual reality game that helps people experience the three-body problem, search for extra-terrestrial life, and the reactions of different groups on earth once contact is made. Plus, it has lots of twists and turns.

So where does three-body problem come into all this? Turns out the aliens live on a planet that orbits 3 suns. They can’t predict their planet’s orbit (and thus the climate) because… the three-body problem! An unpredictable orbit means the climate can change from freezing cold to boiling hot with cozy periods thrown in… but it’s all unpredictable.

Where the book is different from most other books/shows is that it also looks at contact from the aliens’ perspective! So having discovered us, thanks to those radio messages we broadcast into space, here’s how they think about the prospect of making contact face-to-(alien)face:
-         Will we be peaceful or violent when we interact with them? What would be the outcome of such an encounter?
-         If we learn to co-exist or the aliens win, what would be the economic consequences for the aliens themselves? If they can enslave us, how many aliens would lose their jobs? Will the resources they find on earth disrupt their economy and way of life radically?
-         Are we technologically more advanced than them? What are our capabilities?
-         What is the rate at which we evolve technologically? This is their take:
“This (earthly) civilization possesses the terrifying ability to accelerate their progress.”
(100,00 years from Hunter-Gatherer Age to Agricultural Age; from Agriculture Age to Industrial Age in a few thousand years; from Industrial Age to Atomic Age in 200 years; and from there, to enter the Information Age took just decades!).
-         The above question on the rate of progress is critical. Why? After detecting our existence via speed of light transmission of radio waves, it would take much longer for people and aliens to meet up at the much slower speeds of their space crafts. Since that time would run into centuries or more, how best to use that time to be prepared for the eventual face-to-face? And to do that, they need to estimate how much we’d have progressed by then.
-         Even if the aliens don’t want to meet face-to-face feeling it’s too risky, can they be sure we won’t be coming to them?
-         And in this case, do the aliens even have a choice? Their own planet is in that crazy three-body orbit, highly unconducive to life. So whatever the risks of coming to earth, they must take the chance because staying put in their there-body world is not really an option!

Few sci-fi books or movies look at things from an alien’s perspective. And boy, this book does a good job of that. Like I said, it’s a good read, especially if you like sci-fi and think about such questions.

Comments

  1. Ramiah KumarJanuary 29, 2018 at 10:28 PM

    Very interesting. I too like the idea of aliens puzzling out the three body problem.

    I recall this detail about the three body problem. Euler is the top mathematician of the world arguably, with one other contender for the same honor - the great Gauss. Migrating from France, he did most work in Russia, where the queen took care of his needs. One day he got a request from another country (England, if I remember correct) to provide them a means to that the sailors could know the tide locations with fair accuracy. There was the risk of their hitting the ground unexpectedly due to the unpredictability of tides.

    This is a three body problem, a nightmare for mathematicians, even for those who wish to sleep with mathematics! Earth's, moon's and sun's gravitational effects had their say in the tides. All these are mobile, which enormously complicated the even-otherwise complex maths challenger. Further, the tides arise due to center to center pull effect as well as compression in the perpendicular direction. Is your mind boggling?

    Euler, quire surprisingly, invented a method called 'algorithm'. By repetitively performing, ordinary arithmetic which is within the know of sailors, with each step refining the accuracy, the sailors can get a fair idea about tide at a chosen place at a chosen time. Five to six rounds of repetitive calculation would meet their requirement.

    Euler got his paltry reward of course. Had he patented 'algorithm method', by now he would be worth millions! Euler's mathematical glory is still sung high, with his crowning achievement through the simple yet profound equation: 'e power i pi = minus one'!

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