What is the three-body problem?

Knowing three orbital positions of a planet’s orbit, Sir Isaac Newton was able to produce an equation that predicted a planet’s motion; i.e., to give its orbital properties: position, orbital diameter, period and orbital velocity. Years later however, Newton and other astronomers discovered that the equation wasn’t particularly accurate. Newton realised that this was because of the multiple gravitational interactions that take place once you introduce a third body:

“And hence it is that the attractive force is found in both bodies. The Sun attracts Jupiter and the other planets, Jupiter attracts its satellites and similarly the satellites act on one another.”

The three-body problem is part of a broader group of problems in physics called “n-body problems”. Systems for which n ≥ 3 may appear random, but they are actually chaotic. According to Wikipedia chaos is defined as “underlying patterns, constant feedback loops, repetition, self-similarity, fractals, self-organisation, and reliance on programming at the initial point known as sensitive dependence on initial conditions.”

What does any of this have to do with commodity markets?

Well, the three-body problem demonstrates why it is a mistake to think in simple terms of supply and demand – anchoring your thinking based on historical relationships is not always going to work.

As the GIF above shows, chaotic systems are extremely sensitive to changes in the initial conditions. In the real world this can take the form of a technological innovation that disrupts existing supply or demand patterns, an adverse weather event, a political and social revolt against the status quo, and so on.

These are perhaps the obvious examples. Many more will fly under the surface and only really be observable after the fact, except perhaps to the most astute observer. That’s why it’s important to think in terms of nth order impacts, unintended consequences, and try to understand things from a non-linear perspective where the outcome from an event might be exponential times greater than the input.

Adding additional factors into an already chaotic system moves that system even further from how it looked in the past. Commodity markets are a chaotic system, and that degree of chaos has only become more unstable over the past twenty years.

The first factor driving this change is that commodity markets have become increasingly financialised, and so investor behaviour and macro factors play a much larger role. Second, technological innovation and algorithmic trading means that markets tend to be governed by non-fundamental factors in the short-term, exaggerating the impact of capital flows driven by macro factors.

A third factor is globalisation, which means that commodity markets are increasingly interconnected, and so also interrelated by their “gravitational pull”. It is no longer possible to analyse a commodity market in isolation. Instead, as Newton found out, the push and pull of Jupiter, its moons and the Sun made a mockery of his formula. Commodity markets will increasingly be driven by other factors, things that won’t appear in a model. Those things might be bitcoin and other digital assets, state and central bank intervention, climate change or something else. Whatever it is, throwing out the formulas of yesteryear is the only way to avoid not seeing what is coming over the horizon.

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