Since the excellent The Three-Body Problem book trilogy and the similarly great Netflix adaptation, I have been wondering why exactly is the name-giving physics/mathematics problem called the three-body problem considered unsolvable. Frustratingly, searching on Google didn’t let me find any good answers to my biggest question: given that the universe (erm, at least on a macro scale) is deterministic, isn’t it just a matter of refining our understanding of the rules (of physics)? Like, if we understood the exact rules, couldn’t we just build a computer simulation of a solar system with 3 suns and run it to get perfect predictions?

Finally, all these months later, I’ve stumbled upon this video from Up and Atom that has answered all my questions and more:

The gist of it is that yes, in principle if you understand all the rules, and you know the *exact* position, speed, direction, mass, rotation, etc. of *every* object in a system, then you can build a simulation and get perfect predictions. Unfortunately, in reality, for all practical purposes it is not possible to get exact measurements of all these properties, so we rely on approximations. For many things, approximations are good enough, and we will end up with a simulation or prediction that is going to be extremely close to the reality. This allowed us to get this far as a technological civilization.

Some things are not like that, and even a small inaccuracy in our measurement or approximation will yield a prediction dramatically different from the reality. This is called extreme sensitivity to initial conditions, and is one of the core ideas in chaos theory:

Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:

Chaos: When the present determines the future but the approximate present does not approximately determine the future.

The three-body problem happens to be an example of this.

I find these limits of knowability equally fascinating and horrifying. There are just things that we will never be able to do, no matter the knowledge, the understanding, or the resources we accumulate. Humans can thus never become gods.

Some additional examples are:

- The uncertainty principle, related to the three-body problem and chaos theory
- Gödel’s incompleteness theorems, which proves fundamental limits to any model or system
- Then of course there’s the entire field of quantum mechanics, with the central idea that at the heart of the universe it’s all just probabilities, which idea I just find viscerally disturbing.