Studying the fundamentals of circuit theory, I was reading the Wikipedia article on the Passive Sign Convention and found out about the Active Sign Convention (ASC). After searching many introductory circuit theory books - such as Nilsson's and Dorf's ones -,I realized that almost none of them mentions "Active Sign Convention". When some circuit element is with the current entering in the negative terminal, they say something like "the current and voltage reference directions are not in conform to the passive sign convention", as shown in the pictures below:
Searching more about the ASC, I have found these lecture notes that states (page 6):
Also, what's with the "Not Passive Sign Convention"? In general, circuit elements that absorb power (like resistors) are called passive elements, and circuit elements that supply power (to the circuit!) are called active elements. But for some reason, the opposite of the passive sign convention is not called the active sign convention. (Of course, people use the term active sign convention, but they are not supposed to. If you want to be an alpha geek, find out why and go around correcting them!) Instead, the awkward term "Not passive sign convention" is used. Actually, the full blown correct expression is "The element does not conform to the passive sign convention." But that's way too long to say or write (unless you are being the alpha geek).
So, my question is: Why "the opposite of the passive sign convention is not called the active sign convention"? Why they use "the current and voltage reference directions are not in passive sign convention" instead of "the current and voltage reference directions are in the active sign convention"?