Computers are a “complete” system where everything they do is inspectable and, eventually, explainable, and I have observed that people who work with computers (myself included) over estimate their ability to interrogate and explain complex, emergent systems - economics, physics, etc. - which are not literally built on formal logic.
a single computer might be complete (even then, not everything is inspectable unless you have some very expensive equipment) but distributed systems are not.
There was an entire class of engineers at google- SREs- many of whom were previously physicists (or experts in some other quantitative field). A fraction of them (myself included) were "cluster whisperers"- able to take a collection of vague observations and build a testable hypothesis of why things were Fucked At Scale In Prod. Then come up with a way to fix it that didn't mess up the rest of the complete system.
Nothing- not even computers are truly built on formal logic. They are fundamentally physics-driven machines with statistical failure rates, etc. There's nothing quite like coming across a very expensive computer which occasionally calculates the equivalent of 1*1 = inf, simply because some physical gates have slightly more electrical charge on them due to RF from a power supply that's 2 feet away.
I think you're mixing up two different things: the challenges of building these systems at scale, and their fundamental properties. Take your example of the expensive computer returning 1*1 = inf because of a nearby power supply - that actually proves my point about computers being knowable systems. You were able to track down that specific environmental interference precisely because computers are built on logic with explicit rules and dependencies. When these types of errors are caught, we know because they do not conform to the rules of the system, which are explicitly defined, by us. We can measure and understand their failures exactly because we designed them.
Even massive distributed systems, while complex, still follow explicit rules for how they change state. Every bit of information exists in a measurable form somewhere. Sure, at Google scale we might not have tools to capture everything at once, and no single person could follow every step from electrical signal to final output. But it's theoretically possible - which is fundamentally different from natural systems.
You could argue the universe itself is deterministic (and philosophically, I agree), but in practice, the emergent systems we deal with - like biology or economics - follow rules we can't fully describe, using information we can't fully measure, where complete state capture isn't just impractical, it's impossible.
To simply illustrate your point: if you see a computer calculate 1*1=∞ occasionally, you know the computer is wrong and something is causing it to break.
If you see a particle accelerator occasionally make an observation that breaks the standard model, depending on what it is breaking you can be very confident that the observation is wrong, but you cannot know that with absolute certainty.
