It is a profoundly erroneous truism,
repeated by all copy-books and by eminent people when they are making
speeches, that we should cultivate the habit of thinking of what we
are doing. The precise opposite is the case, civilization advances by
extending the number of important operations which we can perform
without thinking about them. Operations of thought are like cavalry
charges in a battle - they are strictly limited in number, they
require fresh horses, and must only be made at decisive moments. — A. N. Whitehead, Introduction
to Mathematics, 1911
For this unit, work through the following preparatory
activities.