This raises the question of what it means to "tell someone how big it is". Does it mean to write it using some particular notation (such as positional notation

This raises the question of what it means to "tell someone how big it is". Does it mean to write it using some particular notation (such as positional notation or exponentiation)? Does it mean to instill a satisfactorily good image in someone's head of how big it is? I mean, mathematically speaking, any definition of a number is as good as any other, and Graham's number can be defined perfectly well.