The problem with saying that "a thing a becomes meaningful only if it is connected to something else b that is meaningful" is that some things turn out to be meaningful on this definition, whereas in reality all things are meaningful to an equal degree.

This is a true statement. To a degree, everything has the same level of meaning: it becomes a matter of differentiating it out only through the perception of the person who attaches the idea of "meaning" to the stimulus. While some people might find a stimulus meaningless, that same bit of information might be life changing to another person because of the experiences they have had in the past.