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@fried
From my intuition, no idea if proper, a set of programs differentiated by their exact computational cost, which must each over some set of inputs compute the exactly same values as all other programs from this set, should be the models of the algorithms, which for us represent understanding at some level of a concept.
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This means that a simple model of a boat is something that gets you from A to B and floats on water. A nautical engineer has a different idea of it however, maybe he sees it as a composition of different faring components, and in much more detail most likely.
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So then, you must necessarily understand at least one of the nested subsets of the starting infinitely complex superset to be able to produce exact output to some testing function verifying whether you understand the concept at all. Otherwise you are going to have an error rate, maybe calling a fish a boat or something
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Not only that, but all algorithms of subsets are going to have an error rate other than algorithms of infinite complexity. If the transition is in fact continuous, then you should be able to progressively get better at understanding the pure, infinitely complex concept.
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I'm misusing a lot of math terms and probably reinventing the wheel, but essentially, depending on how we 2 people understand a boat, the intersection of the resulting sets is going to be the concept. The interval is 1 (ONE archetype) to INF (if a boat is inaccurately enough defined, everything is a boat).
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So, the main point, from understanding testing does not necessarily follow, testing can confirm the validity of understanding some group concept against some reference, understanding strives towards the archrtype.
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Though, understanding an archetype should be an automatic test and pass, because all of the information necessary is self contained and self proving, meaning that "you know if you know".
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So TL;DR you can't test against something you don't understand, only others that understand can test against it, that is the ptoblem with the human brain. In programming settings we write down and test already understood concepts!
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This makes sense — what are you testing against, if you, yourself, do not “know” the concept? You need “knowledge” to reference against.
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