Rational numbers are rather simple quantities, being describable and understood in simple finite terms; yet they can be used to specify distances that are as small as we please or as large as we please. If all geometry could be done with rationals, then this would make things relatively simple and easily comprehensible. The notion of an ‘irrational’ number, on the other hand, requires infinite processes, and this had presented considerable difficulties for the ancients (and with good reason).
