i = i+1 :)

I think that most people would happily go through their lives not thinking about this stuff at all. Most people don’t even realise that math has a relevance to music, nor do they have a clue at the engineering, modelling and math that goes on behind the scenes with something as “simple” as a screw, nut or wrench is produced.

Consumers are often mindless when it comes to this kind of thing.

Would I want to buy something that wasn’t properly tested and modelled? Absolutely not. But I think the vast majority wouldn’t think twice about it unless they knew that the models existed.

Actual software engineering involves the same sorts of things that any other form of engineering does, just in forms that are applicable to the domain. Things such as studying existing software to find its structure, then extrapolating from available data what the likely failure points are going to be when it is put under loads of various sorts.

That requires a deep enough understanding of the algorithms and fundamental math to have a solid grasp on what is going on, but also having the knowledge of how actual systems “in reality” — as opposed to a in a pure model — behave, including nasty little problems that pure math tends to hand-wave such as “you ran into an I/O bottleneck”.

The goal of all of that being the ability to answer questions such as “how gracefully does it degrade under load?”, “are there any severe inflection points in the curve?”, and “at what point does it just fall over and die (for any practical purpose)?”