The mathematical concept of “Lyapunov time” is essentially the span in which it is possible to predict the state of a chaotic system. Though incomputable for human events, the idea of a forecasted horizon at which predictability fails is useful in assessing these aforementioned events — like the current war.

I hope, then, too, that our mathematicians forgive the appropriation of the term. For Europe is fast approaching its Lyapunov horizon. As Ukraine continues to fight, prewar certainties are fast dissipating — first among them, the belief that Europe would watch as Ukraine fell.

It has not. Nearly all European countries are sending arms, ammunition, and funding. Some are also sending fighters. Governments in Denmark and Latvia are allowing their citizens to join the new International Legion of the Territorial Defense of Ukraine announced by President Zelensky on Sunday.

Some American and British special force veterans have also joined. For the first time, too, the European Union is financing the purchase and delivery of equipment into a conflict. Europe, it seems, has awoken to the realities of power politics. Even Germany has shed its tendency to dither on wartime assistance efforts.

Suddenly, Berlin has transitioned from decades spent as a pacifist laggard — understandably so — to committing more than two percent of its gross domestic product to its defenses. It will be Europe’s largest defense spender. President Putin’s war has accomplished what three consecutive American presidents failed to do.

Sweden and Switzerland have, at least at the moment, forsaken their neutrality to side with Europe against Moscow, Britain has achieved a breakout from its post-Brexit isolation, and Russia has been all but disconnected from the West. Its economy is in tatters.

Inside Russia, too, growing discontent among citizens, celebrities, and even some oligarchs suggests an increasingly destabilized country. The potential for upheaval cannot be discounted – the gravity of such an event, should it happen, even less so.  

It is tempting to enthusiastically cheer some of these developments. Yet we must also be mindful. For they are injecting much chaos into an already dynamic system. Europe – and with it likely the global order – is being pushed past that Lyapunov marker — the edge of predictability.

While it is a time for action, it is also a time for tempered prudence. For what could it mean if foreign fighters can take up arms in Ukraine? Already, far-right European militias and Muslim militias from the Middle East are readying for combat. Could Europe face at home the foreign fighter problem it sought to avoid with Syria?

Or what of Switzerland’s ostensible bygone neutrality? Might future peace negotiations be challenged absent impartial grounds on which warring factions can meet? How might a well-armed Germany alter European geopolitics? If Ukraine manages to hold out, could a destabilized Russia yet prove to be Europe’s biggest crisis?

For the West, the war will not be a passing storm or a calamity after which things return to normal. A new era is being written. Along with ending the horrors in Ukraine, then, decisions now being made should also aim to maintain a degree of predictability – to extend Europe’s Lyapunov horizon.