N = 2N

The three-body problem of Russia, China, and the US has upended the rulebook on deterrence theory. The two-peer Russia vs. US landscape being long gone, the outdated Cold War model no longer aligns with a three-nuclear-peer world.

Oftentimes we lazily rely on anecdotes as the vehicle for our point. In the three-body problem anecdote, commentators borrow from physics the unstable gravitational system established by three celestial bodies orbiting one another. Unlike two-body problems (i.e., Russia versus the US), these problems require active stabilisation to prevent all-out collapse. The passive two-body model no longer guarantees stability.

That passive model included a nuclear arms race: Russia against the US.

This begs the question: what does a nuclear parity race look like under a three-body problem? Parity requires one party to match the power of all others. In truth, parity requires each party to have sufficient nuclear firepower to deter all other adversaries at once. For each party N:

N = 2N,

and so one party must match the strength of both others to approach parity. The US cannot match the combined nuclear strength of Russia and China (~6000 nukes) without having more than any one of Russia or China. Likewise for Russia. Likewise for China. Three-body-parity is inherently impossible.

Of course, this is an oversimplification. Parking parity for a second, the equation at its base becomes:

N1 = N2 + N3.

There are only two eventualities in which this equation holds true whilst retaining some semblance of parity:

1. N3 must equal zero. One of China, Russia, or the US must abandon its nuclear arsenal;

2. Or both sides of the equation approach infinity. China, Russia, and the US pursue a limitless nuclear arms race.