"Why should we believe in real numbers, if most of them are uncomputable? Why should we believe in real numbers, if most of them, it turns out, are maximally unknowable like Omega?"
footnote with answer
"In spite of the fact that most individual real numbers will forever escape us, the notion of an arbitrary real has beautiful mathematical properties and is a concept that helps us to organize and understand the real world. Individual concepts in a theory do not need to have concrete meaning on their own; it is enough if the theory as a whole can be compared with the results of experiments."