What is capable to make absurd meaningful?

Answer 1

Wisdom!

"Our two minds .... One is an act of the emotional
mind, the other of the rational mind. In a very real
sense we have two minds, one that thinks and one that
feels" (Daniel Goleman, Emotional Intelligence,
Bloomsbury Publishing, London, 1996, page 8).

The rational mind argues that some thing is absurd.
The emotional mind says that it may be meaningful.
The dichotamy is overcome by wisdom. That is what
is capable of showing many meanings to what is
argued as absurd by the rational mind. The rational
mind, which deals with logic and reason, has its
own limitations:

In the 1930s, Austrian mathematician Godel proved a
theorem which became the "Godel theorem" in cognition
theory. It states that any formalized 'logical' system
in principle cannot be complete in itself. It means
that a statement can always be found that can be
neither disproved nor proved using the means of that
particular system. To discuss about such a statement,
one must go beyond that very logic system; otherwise
nothing but a vicious circle will result. Psychologist
say that any experience is contingent - it's opposite
is logically possible and hence should not be treated
as contradictory.

Answer 2

I'm guessing what you meant to say was "what is capable of making the absurd meaningful?"

Self ultimately defines meaning
Absurdities are things which the self does not yet know how to identify unless they have identified absurdities in general.

So to give an absurdity meaning you would simply attach a value however you see fit.

Answer 3

Experience. What looks absurd suddenly becomes meaningful if we find ourselves immersed in it.

Answer 4

It's sounds corny but it's a little bit of love... Like Little Miss Sunshine. Their family is totally and absurdly out of whack but they love each other so it works.