ESLII confusion about splines regression In elements of statistical learning, beginning of chapter 5.2 they state ‘we assume X is one dimensional’.
I understand this as meaning X has one feature and N samples. 
However in chapter 5.2.2(extract below) 

they present an example where, to my understanding, X is no more one dimensional since there are X1, X2,... 
Am I correct or not?
Then in chapter 5.7 (extract below)

they present how to handle splines to handle multidimensional X. But isn’t it exactly what has already been done in Chapter 5.2.2 using other notations?
 A: No, there is a difference that is not merely notational.
In the first case we are dealing with $p$ one-dimensional $X_i$, each expanded into its own spline basis $h_i(X_i)$.  From the point of view of the spline, each input is one-dimensional ($X_i$ is one-dimensional); we don't need any other $X_j, j\neq i$ in order to calculate the spline basis $h_i(\cdot)$ for $X_i$.  
Somewhat confusingly, each of these $X_i$ in this section corresponds to $X$ in the "we assume $X$ is one-dimensional" statement.  The upside is that when describing the algorithm the notation is simpler, because you don't need to carry around subscripts all the time that might needlessly add to subscript complexity when combined with subscripts used within the algorithm and cause confusion that way.
In the second case we are dealing with a multi-dimensional $X$ expanded into a single, joint spline basis.  With respect to the specific example, the tensor product basis, each basis function of the joint spline is the product of two basis functions of $X_i$-specific splines (two because we are assuming that $X$ is two-dimensional, i.e., that $p=2$.)  From the point of view of the spline calculation, we need both $X_1$ and $X_2$ as inputs in order to calculate the basis functions $g_{jk}(X)$.
From an application perspective, the former does not allow for interactions between the various $X_i$, but the latter does.
You sometimes have to be a little careful about when $X$ refers to all the data, e.g., $X = [X_1 | X_2 | \dots | X_p]$ or when $X$ is just being used as a placeholder for purposes of explaining a particular algorithm, in which case there's sort of a "local" definition of $X$ and a "global" definition of $X$ to keep track of.  I've fallen into that particular trap myself!
