I am happy to equate exploitation with understanding, but then I don’t see how you could possibly understand Mathematics without exploiting computation.
The pyramids were built at least 1000 years before Pythagoras was even born. If division and trigonometry was needed to build them then the Egyptians understood and exploited division trigonometry before Pythagoras invented the language to explain/teach division and trigonometry.
It is not at all surprising that nobody else could understand (exploit, compute with) a language Pythagoras made up, but eventually he taught (indoctrinated?) some students on how to use his invention.
To compute with; and exploit any language first you must comprehend its grammar and semantics.
Still! The Babylonians could compute the square root of 2 (in practical terms, obviously they didn’t call it “square root of 2”) to arbitrary precision even without having numbers in their Mathematics.
Overall I don’t think we are disagreeing over anything substantial either way. Computation is the controlled manipulation of matter. Manipulating symbols to do useful things is a form of computation.
A fly may have some knowledge sufficient to exploit nature in the moment, but it doesn’t have the knowledge necessary to encode and communicate its knowledge to its peers. And it certainly can’t communicate its knowledge to generations 2500 (or more) years into the future.
