[eightysixfour]

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.

[Vegenoid]

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.

[eightysixfour]

Great explanation, thank you.