Mr. North uses the term singularity within the context of dynamical systems. A mathematical field, a singularity is a point that determines the behavior of the points around it. (Within the field and related areas, singularities may be called attractors, nodes, fixed/periodic points, sinks/sources/saddle points/centers.) Since Mr. North is a systems analyst who uses predictive models, it is all too natural for him to use the term singularity. When creating a prediction based on a system model, only two things matter: the singularities of the system and where we start. Singularities completely control the outcomes of their systems. We only care about the starting point because it determines which singularity we will be governed by.
When two singularities compete for a single space, different areas of space will fall into one or the other singularity’s influence. On the boundary, there may be rather erratic and unpredictable behavior. In this case, mission completion and the fate of individual pilots, Oured, etc. are near the boundary. Since we can’t be totally sure which side of the boundary each item will actually fall, we cannot predict their ultimate fate. Mission success means enough key points fall into Trigger’s region, while failure is the same but with Torres.
If Trigger is the only singularity, Osean victory is guaranteed. If Torres is the only singularity, he will win. The difficulty is in their interaction and, since Alex didn’t have much data to study how the two singularities would interact while in the same space, it’s only natural for the AI to deny the request.
Now, through most of DLC missions 1-3, the term could be replaced with any phrase meaning [something influential]. However, Alex’s justification for keeping Trigger alive points directly to Trigger’s effect on battlefields, which are dreadfully complicated systems (and, if Trigger weren’t a supernatural pilot with even more supernatural weapons carrying capacity, filled with countless and unknown singularities). Despite all the competing influences in Trigger’s battles, he always increases survival rate. Nothing short of a singularity is that consistent. Beyond Alex, at the very end of mission 3, Mr. North speaks in strongly dynamical terms: Torres brought those in his orbit to destruction, while Trigger brings those around him into security (which Alex emphasizes: Stick with trigger, and you’ll make it). Singularities don’t just influence those around them, singularities determine their fate.
Some interesting references:
Depiction of how changing a single parameter in a system can cause the number of singularities to go from 1 to infinity: https://ars.els-cdn.com/content/image/3-s2.0-B9780128158388000091-f09-14-9780128158388.jpg?_
Relevant wikipedia article. I’d point you to the image that provides a nice rundown of singularity classifications in 2 dimensions. https://en.wikipedia.org/wiki/Stability_theory
Chaos (in the mathematical sense) is a result of an infinite number of singularities operating over a space. Weather prediction happens to be a chaotic system, which is why weather estimates only go out 10 days. https://en.wikipedia.org/wiki/Lorenz_system
When chaos exists, if our initial measurements/evaluation of the situation is not perfectly correct, then our predictions will be wrong no matter how small the error, as demonstrated in the following video: https://www.youtube.com/watch?v=5xu-9D4ahVU
[Originally for r/acecombat]