The same could be said of any Turing-complete language (though I'll admit Scheme's macro system gives it a leg up when it comes to implementing new features.) But given that Scheme's syntax encourages thinking in terms of mathematical recursion, it seems silly that (a) I can't write something so simple as the Fibonacci function by using its traditional mathematical recursive definition, and that (b) SICP encourages the use of Scheme to solve problems which require thinking in terms of iteration and mutation -- this is a pedagogical faux pas.
The difference between Scheme and any "Turing complete language", is the philosophy behind it, which is one of minimalism. That's why memoization isn't implemented for you.
Scheme was also designed to encourage implementing non-recursive control structures, as well as programming with side effects. Scheme isn't supposed to be totally pure. If you encounter a problem that requires mutation, you're supposed to try to abstract away from the mutation, if possible, and it gives you the tools to do that. (first class functions, macros, continuations, etc. are all very effective tools for abstraction, once you learn them.)
I recommend that you use SICP to learn Scheme, as it will make more sense when you actually know how to use it. It's an incredibly elegant and beautiful language, and it's certainly still relevant.
P.S. If you're thinking of those problems in terms of iteration and mutation, you're probably doing it wrong :). Think more functionally.
>I recommend that you use SICP to learn Scheme, as it will make more sense when you actually know how to use it.
I used it my entire graduate career, under an advisor who is part of the inner circle of PLT/Racket. I'm quite familiar with it.
> P.S. If you're thinking of those problems in terms of iteration and mutation, you're probably doing it wrong :). Think more functionally.
I primarily program in Mercury and Coq (languages which are both purely functional). I can promise you I have no problem "thinking functionally". The solution presented in SICP is not structurally recursive (while the "naïve" solution is) but rather relies on an accumulator, tail calls, and a measure to terminate recursion... this is much closer in spirit to an iterative algorithm than a recursive one.
