>However, at the end of the day, there is an input and output and compute and memory needed to run the thing and if we look at that we realize, we never actually left the bounded physical realm and we can still engineer software systems against real world constraints. We can judge its efficiency and breaking points.
This is a common sense view of computation that's unfortunately wrong.
The simplest counter example is the busy beaver program: with as little as 12 states we have saturated the computational capabilities of the universe, but it looks completely safe and sane for the first few states you would be testing against.
You may call it pathological, and you'd be right, but the point is that you never know under which rug a function that takes more computation than the universe can supply is hiding.
By comparison power electronics engineers don't have to formally prove that they didn't accidentally include a nuclear power plant in their e-scooter design.
I think you just made my point. If designing an eScooter you'd look at available power needed across the problem space. Even more so you might put in a safety features like a temperature monitor so electronic components don't fail because someone decided to go up a steep 12 mile mountain path and overheat the battery.
If I was designing a software system, I could introduce a time constraint. An imagined conversation:
"How long will it take to get an answer?
Between half a second and the heat death of the universe.
OK. Can we just issue a timeout error after 1 second?"
This is putting controls in place so the system doesn't exceed its constraints and although hypothetical it might be able to do a job for any input, it can't because we haven't been able to find a more efficient solution for certain known and unknown scenarios.
And then you quickly find out that the turing machine on your lap doesn't actually have infinite tape. Do you honestly believe that there's no other human endeavor where you can DoS yourself?
If on the other hand you're speaking of the theoretical computational needs of the program you just wrote, then your earlier dismissal of mathematics and its "even worse track record" is all the sillier.
This is a common sense view of computation that's unfortunately wrong.
The simplest counter example is the busy beaver program: with as little as 12 states we have saturated the computational capabilities of the universe, but it looks completely safe and sane for the first few states you would be testing against.
You may call it pathological, and you'd be right, but the point is that you never know under which rug a function that takes more computation than the universe can supply is hiding.
By comparison power electronics engineers don't have to formally prove that they didn't accidentally include a nuclear power plant in their e-scooter design.