[ThenAsNow]

> That is clearly wrong if one is willing to take a moment to stop gazing at the wonder of pure mathematics and look at the outside world. There is no notion of "correctness" for the pyramids of Egypt, the dykes of the Netherlands, Milan Cathedral, or the world economy and yet those huge-scale systems all function.

Wow, couldn't disagree with this more, at least on your examples of civil engineering (buildings, dikes). There are testable, comprehensive physical principles that govern whether any of these engineered products function in their most fundamentally-intended ways. This is the reason most buildings are resilient and don't collapse under load, or that dams keep water from flowing uncontrolled. You can debate "correctness" in the sense of the purpose the product serves, but there is the principle of correctness of construction which your civil engineering examples (and anything truly engineered) satisfy. Correctness in construction is not subjective.

[raiph]

> Correctness in construction is not subjective.

Perhaps, but it's never certain. So things that are "correct" can still be wrong.

Here's how Einstein expressed his disagreement with what you are saying:

> As far as the laws of mathematics are certain, they do not refer to reality, and as far as they refer to reality, they are not certain.

Nothing in physics (or any other science) is certain. All one can do in science (other than mathematics) is disprove. One cannot prove.

To prove you would have to be all knowing. You would have to have taken into account all relevant aspects of all physical characteristics. For example, all known aspects of quantum mechanics, including the uncertainty principle, AND all relevant unknown aspects of quantum mechanics, which is guaranteed to be hit and miss, and can rationally be expected to contain an unknown number of misses that isn't zero.

It's the human propensity to ignore these fundamentals that leads to things like the Tacoma Bridge collapse.[0]

[0] https://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)

[munificent]

> There are testable, comprehensive physical principles that govern whether any of these engineered products function in their most fundamentally-intended ways.

These are statistical engineering tests of the probability of failure under certain conditions. That is not at all what Dijkstra would consider to be "correctness". Dijkstra is talking about mathematical proof. In mathematics, one does not say "1 + 2 = 3 plus or minus 0.1 with a safety factor of 2".

[ThenAsNow]

When we determine if an aircraft trims, or a boat floats, it is not correct to say it is statistical engineering test of the probability of failure. You formalize the properties the system must have in order to not fail, and you use conservation equations to ultimately compute whether or not the system satisfies those properties. Margins are used to account for parameters that have uncertainty attached. All of these elements are subject to symbolic mathematical formalism. One can quite clearly state the inequalities that must be satisfied to be, e.g., controllable.

It's unclear how this would be any different than mathematically formalizing a distributed system, identifying the properties that constitute correctness of operation of that distributed system, and symbolically proving that subject to certain assumptions, the distributed system model does or does not satisfy those properties. This would presumably be consistent with the Dijkstra view of mathematical correctness.