ABSTRACT
Sir William Rowan Hamilton read a paper on ‘Algebra as the Science of Pure Time’ to the Royal Irish Academy in 1835. This was included in his long paper on ‘Algebraic Couples’ published in the Transactions of the Royal Irish Academy in 1837. There are at least three important observations to make on the summary of Hamilton’s concepts. First, algebra is not primarily a science of quantity. The numbers on the unidimensional line are real numbers, measure numbers. Secondly, the concept of order in progression means the numbers on the line are by their very nature ordinal numbers. This is very different from cardinal numbers, which have no ordinal character in themselves unless it is put there subsequently. Thirdly, the unidimensional line of time extends to infinity in both directions, forward and backward: this is the scale of numbers from plus infinity to minus infinity to which Hamilton gave the name scalar.
