Numerical notation systems, like the Roman numerals or our own (Hindu-Arabic, or Western, numerals) are frequently evaluated on the basis of how efficient they are perceived to be for arithmetical computation. From this, it is concluded that the present ubiquity of our numerals is due to their superiority for calculation. However, computation is not the most important function for which numerical notation is used. Numbers are used to denote far more often than they are to reckon, even in our highly numerical society, and this was doubly true in pre-industrial contexts. In many ancient societies, numerals were never manipulated in order to do arithmetic. Instead, a variety of non-numeral techniques such as abaci, counting-boards, and finger-computing were used where we would use written numerals. While modern arithmetical techniques have depended on manipulating written numerals for several centuries, this is a historical contingency, not an inevitability. The efficiency of numerical notation systems should not be evaluated in the abstract, but only in the context of the purposes for which they were developed and used.