“Have you ever wondered why clouds behave in such familiar ways when each specimen is so unique? Or why the energy exchange market is so unpredictable? In the coming age we must develop and apply nonlinear mathematical models to real world phenomena. We shall seek, and find, the hidden fractal keys which can unravel the chaos around us.”
— Academician Prokhor Zakharov, University Commencement
Quantum Labs require the eleventh-tier Quantum Power technology to construct, logically enough. They serve as a multiplier building for raw energy sent to either the general economy or the labs. From the gameplay perspective, these facilities are best seen as upgrades to the previous Fusion Labs for the late-game.
And, as before, this bonus is quite good. This is mostly because typical multiplier buildings force the player to choose between cash and research. But since these labs provide an equal benefit both ways, it means that the player will get a significant benefit no matter how the player has geared his economy.
The accompanying quote is pretty straightforward given this context. The Quantum Lab is a place where these nonlinear mathematical models actually get tested and their predictions replicated. From the name and the description, it would seem that the key to accurately predicting these types of complex, chaotic phenomena is to break everything down to the smallest level and derive the outcome from there.
This is a pretty dramatic break from the way people generally do science and engineering nowadays. Most everyone agrees in principle that higher-level physical phenomena are fundamentally based on the low-level physics. People might hold out for some non-materialist explanations when it comes to human behavior, but most everybody is convinced that clouds are fundamentally explicable by known physics. And yet, in practice, work only gets done because higher-level models are able to assume that much of the complexity at the lower layers largely cancels out.
For instance, someone designing a typical circuit doesn’t need to carefully model the path and energy of each electron in the system. He just needs a few general rules of thumb – like, say, Ohm’s Law – and some macro properties of any various components to successfully get a working product. Essentially, the detailed state of each electron is made practically insignificant by the simple rules that govern how lots and lots of electrons will behave in a typical circuit scenario.
When this underlying complexity doesn’t cancel out well enough, like in clouds and market prices, you get chaos. Strictly, a chaotic model is one in which the outcome is overly dependent on tiny perturbations in the initial conditions fed into the model. This is generally a bad sign for a model that intends to explain long-running systems, because chances are you won’t actually get a wildly different outcome in real life if you had started the clock a couple of seconds before or after.
It’s quite interesting to note that this effort is only being embarked upon now, in the late game. Nonlinear Mathematics, the technology that presumably underlies the models Zakharov references, came about in the years just after Planetfall. And the last word in theoretical physics was a mid-game tech. So why did it take so much longer to put them together?
The answer is likely pretty mundane: it’s a lot of work for not a lot of gain. The brilliant theoretical breakthroughs led to the plucking of the low-hanging fruit. All that’s left for the scientific project now is the brute-force effort of working from the theoretical predictions to settle the remaining edge cases and, thus, place all human understanding on a solid foundation.