In my experience teachers tend to only give examples of typical members of a category. I wish they’d also give examples along the category border, both positive and negative. Something like: “this seems to have nothing to do with quadratic equations, but it actually does, this is why” and “this problem looks like it can be solved using quadratic equations but this is misleading because XYZ”. This is obvious in subjects like geography, (when you want to describe where China is, don’t give a bunch of points around Beijing as examples, but instead draw the border and maybe tell about ongoing territorial conflicts) but for some reason less obvious in concept-heavy subjects like mathematics.
Another point on my wishlist: create sufficient room for ambition. Give bonus points for optional but hard exercises. Tell about some problems that even world’s top experts don’t know how to solve.
I tried to reason through the riddles, before reading the rest and I made the same mistake as the jester did. It is really obvious in hindsight; I thought about this concept earlier and I really thought I had understood it. Did not expect to make this mistake at all, damn.
I even invented some examples on my own, like in the programming language Python a statement like print(“Hello, World!”) is an instruction to print “Hello, World!” on the screen, but “print(\”Hello, World!\”)” is merely a string, that represents the first string, it’s completely inert. (in an interactive environment it would display “print(“Hello, World!”)” on the screen, but still not “Hello, World!”).
Edit: I think I understand what went wrong with my reasoning. Usually, distinguishing a statement from a representation of a statement is not difficult. To get a statement from a representation of a statement you must interpret the representation once. And this is rather easy, for example, when I’m reading these essays, I am well aware that the universe doesn’t just place these statements of truth into my mind, but instead, I’m reading what Eliezer wrote down and I must interpret it. It is always “Eliezer writes ‘X’”, and not just “X”.
But in this example, there were 2 different levels of representation. To get to the jester and the king I need to interpret the words once. But to get to the inscriptions, I must interpret the words twice. This is what went wrong. If I correctly understood the root of my mistake, then, if I was in jester’s shoes, I wouldn’t have made this mistake. Therefore, I think, my mistake is not the same as jester’s. Simultaneous interpretation of different levels of representation is something to be vigilant about.
C’est ne pas un pipe. This is not a picture of a pipe either, this is a picture of a picture of a pipe. Or is this a piece text, saying “this is a picture of a picture of a pipe”? Or is this a piece of text, saying “This is a piece of text, saying \”this is a picture… \”″… :-)