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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.

The trouble with Tesler's Law is that it's often difficult to distinguish between essential complexity and incidental complexity. When I face a UX problem that seems like an insurmountable barrier, if I step back and consider many perspectives, I often find a way to change the context so that the problem becomes easy to solve. What feels like essential complexity is often surprisingly incidental.

What I'm objecting to is the notion that there is a "fixed, non-zero level of complexity." Often real innovations in organization and structure allow for fundamentally simpler implementations. I'm reminded of physics: there's an inherent complexity in solving a rotational problem. But introduce polar coordinates and you fundamentally change the game, removing a dimension from your analysis for some problems, and making the solution trivial.

In this case your original estimate of the complexity was high due to a choice of coordinates increasing the incidental complexity of the solution

If it was objectively not true, then you could have infinite compression and any program could be reduced to a single bit.

If "conservation of complexity" were universally true then ANY compression would be impossible.

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.

>If "conservation of complexity" were universally true then ANY compression would be impossible.

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.

I don’t see how your example makes it false.