Numbers as realities misbehave. However, there is an ancient and innate sense in people that numbers ought not to misbehave. There is something clean and pure in the abstract notion of number, removed from counting beads, dialects, or clouds; and there ought to be a way of talking numbers without always having the silliness of reality come in and intrude.
Are numbers really as free as birds? Do they suffer as much from being crystallized into a rule-obeying system? Is there a magical transition region between numbers in reality and numbes on paper?
— Douglas F. Hofstadter. Gödel, Escher, Bach: An Eternal Golden Braid.