>Tesler's Law, also known as The Law of Conservation of Complexity, states that for any system there is a certain amount of complexity which cannot be reduced.
I take this more to mean that the logic you're trying to implement has a fixed, non-zero level of complexity (sometimes called "essential" or "inherent" complexity), which forms the complexity floor of your application. On top of that, your implementation adds additional complexity (sometimes called "accidental" or "incidental" complexity), which is not-zero but not fixed.
So, my reading is that in saying "every application has an inherent amount of complexity that cannot be removed or hidden", the law is referring to the essential complexity. Meaning, the law says "some of the complexity is unavoidable in every application" vs. "the amount of complexity is fixed in every application". I do think the name of the law is a little weird, as it implies the latter meaning.
This isn't a dichotomy. My point is that there are clear examples of situations where you aren't just pushing complexity around, but actually achieving great simplifications.
No it wouldn't. The complexity of a pattern can usually be conserved while reducing its length, but for each pattern there is a limit. This is the entire concept behind the Kolmogorov complexity of a system and any patterns that cannot be reduced any further without removing complexity are at their limit already.
This is also related to the idea that you cannot have a universal compression algorithm.
Unless there is one system to rule them all, configured exactly the way it is needed out the box.