Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of $\Omega \Sigma K(\mathbb{Z}, 2d)$, and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same $n$-type problems and giving us an information about the rational homotopy equivalence.
During the last decades several studies in cognitive psychology have shown that many of our actions do not depend on the reasons that we adduce afterwards, when we have to account for them. Our decisions seem to be often influenced by normatively or explanatorily irrelevant features of the environment of which we are not aware, and the reasons we offer for those decisions are a posteriori rationalisations. But exactly what reasons has the psychological research uncovered? In philosophy, a distinction has been commonly made between normative and motivating reasons: normative reasons make an action right, whereas motivating reasons explain our behaviour. Recently, Maria Alvarez has argued that, apart from normative (or justifying) reasons, we should further distinguish between motivating and explanatory reasons. We have, then, three kinds of reasons, and it is not clear which of them have been revealed as the real reasons for our actions by the psychological research. The answer we give to this question will have important implications both for the validity of our classifications of reasons and for our understanding of human action.