How to "gödelize" the number 11? I'm trying to understand the method Gödel described in his famous paper "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" and I don't understand many things about it right now, but the most prominent question on my mind is:
How to gödelize the number 11?
On page 11, he defines $R(x) \equiv 2^x$, for for example 100 can be formalized  as $2^{100}$. This is bijective. You can always get the 100 "back". I understand this as a special case of the more general function of gödelization:
$\text{prim}(\text{pos}_1)^{\text{number}_1} \times \text{prim}(\text{pos}_2)^{\text{number}_2} \times \text{prim}(\text{pos}_3)^{\text{number}_3} \times \dots $
where of course the position is 1 and therefore, $\text{prim}(1) = 2$, and the number in the special case of $R(x)$ being only 2, because there is only one position in the resulting formula.
Now my problem.
On page 8 he defines some "constants", e.g. 11 = "(", 13 = ")" etc. And he frequently uses these numbers, too. For example on page 11, § 10, where he says
$E(x) \equiv R(11) \times x \times R(13)$
which puts the number into brackets (11 and 13).
But how does he distinguish between the literal number 11 and a bracket, when "de-gödelizing" (e.g. interpretating) the number again?
This is very unclear to me and in the whole paper, I cannot find anything regarding this issue.
Is it that, as said in § 17, a number is not specified as a real "number", but more as "5 = fffff0", i.e. successions of the successor-function on 0?
(Remember: I am only a layman and this might very well be only my missunderstanding)
 A: Everything does indeed do double-duty (or more). A priori, "$11$" is (say) both a number and the code of some formula. But this isn't actually an issue: note that "the formula with Godel number $11$" makes perfect sense even if we have many different things we associate to $11$.
What we have to do is carefully reason about each "layer" of the translation. For example, when we say "the length function of formulas is representable in $T$" (where $T$ is our theory in question - originally PM, but in modern presentations PA or a variant) what we mean is that there is a formula $\varphi$ such that for every formula $\psi$ with Godel number $n$ and length $k$ we have 

$T$ proves $\forall x(\varphi(\underline{n},x)\iff x=\underline{k})$

(where "$\underline{i}$" is the numeral associated to the number $i$: e.g. $\underline{2}$ is the string of symbols "$S(S(0))$").

Note that this isn't actually weird at all. For example, a computer program (in your favorite language) "is" just a meaningless string of symbols, and we can talk about that string as just a string or as a program. In the same way, we can talk about a number as just a number or as a code for a formula. The whole idea of compiling relies on this semantic overloading, and indeed one of Godel's key insights was that this overloading isn't actually a problem.
