“There are two kinds of scientific progress: the methodical experimentation and categorization which gradually extend the boundaries of knowledge, and the revolutionary leap of genius which redefines and transcends those boundaries. Acknowledging our debt to the former, we yearn nonetheless for the latter.”

— Academician Prokhor Zakharov, “Address to the Faculty”

Nonlinear Mathematics is one of those technologies that seems pretty odd at first sight. It’s a second-tier technology (requiring both Applied Physics and Information Networks to research) that is coded as a military technology, instead of a pure science discovery as you might naively expect. And, in game, this makes a lot of sense, as this technology opens up the critical early-game railgun tech (referred to as “impact” weaponry in the designer). This technology is really important: it’s the first weapons tech that gives you a decent chance of conquering another faction. As such, among experienced players, the early game is sometimes referred to as the “Impact Rover” era.

That’s all well and good. But why is that crucial technology an application of a mathematical discovery? And that is where the quote comes in. Zakharov speaks of two fundamentally different kinds of approach to the scientific endeavor.

The first is what virtually every working scientist would see as the real experience of the job. In that role, you work and slave for years to set up an experiment whose results hopefully add some weight to the best prevailing theory of how algae grows in a pond or to find out what horrible side effects a proposed drug candidate might have in monkeys. Good work. Honorable – even noble – in its way. But it’s not inspirational.

That’s the domain of the second. Think of all the great scientists we know from the past. Newton, Maxwell, Einstein: we remember them all as scientists in a particular heroic mold. In this model, it’s fundamentally one man’s mind set against the mysteries of nature. And when the man leaves the figurative cage with the crucial insight that overturns everything we thought we knew about a key problem, that’s the heart of his contribution. All the work that goes into establishing it and proving it is work that anybody could do.

So, by extension, Nonlinear Mathematics is one of those latter ones. A breakthrough along the lines of an Einstein. Which is a pretty inspired place to put a near-futuristic scientific breakthrough, if you think about it. Right now, there are lots of phenomena that we have a really hard time modeling because the relationships among them aren’t linear. Often, we have to use numerical methods or simulation to come up with the answers; we can’t solve them analytically. Imagine if we were just one lightning-flash of insight away from a solid resolution to all of these problems. That’s the magic of Nonlinear Mathematics.

It just so happens that the first application of this is in making practical, large magnetic field generators that can be used to throw chunks of metal at one’s enemies. It’s always nice when things work out so neatly.