Regarding his example with the scissors, I would think there are three distinct ways to loop the string through: each of the two he showed, plus a loop that goe

Regarding his example with the scissors, I would think there are three distinct ways to loop the string through: each of the two he showed, plus a loop that goes through both handles. And I think by mushing the volume of the scissors a bit, you could show that all three of those are exactly equivalent. And then we might say that the number of ways you can loop a string is actually equal to how many distinct pairs of a holes an object has. It just happens to turn out that three distinct things allow three distinct pairings, whereas two distinct things (ie the two "holes" in a straw) allow only one distinct pairing. Working backward one step further, this does lead to the slightly unsettling idea that a simple solid object like a ball may have one hole in it. But I can actually get behind that. All the rest of the space not part of the ball is the hole in the ball.