You're right - we start with that analogy, presumably because it's more concrete. But I'd argue that basis is only popular by convention (and in any case, it br

You're right - we start with that analogy, presumably because it's more concrete. But I'd argue that basis is only popular by convention (and in any case, it breaks down soon enough) - SICP-like intro courses start at expressions combining, being abstracted, simplifying and evaluating, and steal intuition from (and here you're very right) math. They do just fine - I think that's just as accessible; it's just that the former is preferred because it's less abstract. (And, to be fair, I'd rather spend my time learning how programming a computer is different from what I already know - the point, in the end, is learn what programming is all about, and not just what it's like.) But what was the original point? Programming can be just as abstract or as nitty-gritty as you like, and I'd rather have a feel for the breadth of programming, and more bits and pieces in my toolkit of expression, than simply limiting myself just because I won't be earning big bucks directly from it.