‘Irrational’ and ‘real’ are not incompatible in mathematics or life ..and ‘nonsense’ is either merely pejorative or an assertion that a proposition is meaningless as in ‘lightning runs faster than gravity’; most of these theories/beliefs are not meaningless in this sense. Nevertheless an amusing chart and I assume its title is self-referential.
Wittgenstein has some interesting things to say about ‘nonsense’.
In Ludwig Wittgenstein’s writings, the word “nonsense” carries a special technical meaning which differs significantly from the normal use of the word. In this sense, “nonsense” does not refer to meaningless gibberish, but rather to the lack of sense in the context of sense and reference. In this context, logical tautologies, and purely mathematical propositions may be regarded as “nonsense”. For example, “1+1=2” is a nonsensical proposition.