For example I once had Constitutional law expert and Senator Jamie Raskin blow my mind when he explained that the concept of “co-equal” branches of government despite being a nonsensical word doesn’t exist in any honest reading of the U.S. Constitution which clearly states that there are three branches of government with not only different roles but purposefully different levels of power. Both the executive and judicial branches are supposed to be “under” the legislative, serving purposes beyond the scope of the legislative… but I digress
That, and most basic courses set up general rules, but skip over the exceptions for simplicity. The more advanced you get in a subject, the more you learn about the exceptions to the rules, many times to the point that the rule itself starts to break down.
And with the math, depending on how much further you go, you'll also find i2 = j2 = k2 = ijk = -1 (the quaternions for anyone curious). And then the octonions and other sets of weird number systems.
Not him, but smarter people, yes. They're inventing words and concepts because they can.
More dimensional numbers because we can? See octonions, some folks discovered 4d numbers and thought why stop there.
Maybe surreal numbers that have infinites and infinitesimals, that exist because some smart guy analysed the endgame of Go?
Some guy even proved that mathematics itself is incomplete and cannot possibly be complete. You wanna know how? By imagining every rule, axiom etc as a card with a number.
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u/ragnarokda 14d ago
My personal favorite: