I was really hoping that this was going to be some lively new way of thinking about or teaching big O notation, "Eulerian path runtime grows like the velocity of a car that drove off a cliff but Hamiltonian path runtime grows like the number of plague bacteria in a petry dish."
Big-O notation is a useful tool in a programmer's belt, knowing the math behind it in details is less useful. What's the problem? It's the same thing as not needing to know how an engine works to be able to use a car
That analogy does not really work. To use a modern car for transport, its power source can usually be treated as a black box, but if you don't know the math of Big-O, you don't understand it, and if you don't understand it, you may be unable to apply it in a situation where you have not rote-learned the answer, or, worse, misapply it without noticing. I have seen enough of this to know that it is a real problem.
What's next? Gradient decent with no gradients? Fourrier transform with no functions?
If math is do boring just skip the whole thing, don't try to kid yourself by saying you're not doing it when you are in fact doing it.
/rant