The rationalization of this ring can be understood in a very nice way, as follows. Suppose for simplicity that $X$ is simply connected. Then we can define its rational homotopy groups

$$\pi_n(X, \mathbb{Q}) \cong \pi_n(X) \otimes \mathbb{Q}.$$

What can we say about their structure? One observation is that $\pi_n(X) \cong \pi_{n-1}(\Omega X)$, and $\Omega X$ has a loop space structure. This means that the rational homology $H_{\bullet}(\Omega X, \mathbb{Q})$ has the structure of a graded Hopf algebra, with product given by the Pontryagin product. Furthermore, there is a rational Hurewicz map

$$\pi_{n+1}(X, \mathbb{Q}) \cong \pi_n(\Omega X, \mathbb{Q}) \to H_n(\Omega X, \mathbb{Q}).$$

> **Theorem 1:** These maps are injective.

> **Theorem 2:** The image of the rational Hurewicz map consists precisely of the primitive elements in the Hopf algebra $H_{\bullet}(\Omega X, \mathbb{Q})$.

As in the ungraded case, the primitive elements of a (graded) Hopf algebra naturally have the structure of a (graded) Lie algebra, under the commutator bracket. This is precisely (the rationalization of) the Whitehead bracket. Furthermore: 

> **Theorem 3:** $H_{\bullet}(\Omega X, \mathbb{Q})$ is the (graded) universal enveloping algebra of the (graded) Lie algebra $\pi_{\bullet}(\Omega X, \mathbb{Q}) \cong \pi_{\bullet-1}(X, \mathbb{Q})$.

This is one way to think about the shift in degree necessary to define the Whitehead bracket. 

These theorems have many nice applications. For example, you can use them to compute the rational homotopy groups of spheres, by computing the rational homology groups of the based loop spaces of spheres. 

There is also a nice connection to Koszul duality; the fact that the rational homotopy groups form a graded Lie algebra while the rational cohomology groups form a graded commutative ring reflects the fact that the Lie operad is Koszul dual to the commutative operad.