On the side of number we have another test of the power of abstraction; and while the lower races show lack of practice in this, they show no lack of power. It is true that tribes have been found with no names for numbers beyond two, three, or five; but these are isolated groups, like the Veddahs and Bushmen, who have no trade or commerce, and lead a miserable existence, with little or nothing to count. The directions of attention and the simplicity or complexity of mental processes depend on the character of the external situation which the mind has to manipulate. If the activities are simple, the mind is simple, and if the activities were nil, the mind would be nil. The mind is nothing but a means of manipulating the outside world. Number, time, and space conceptions and systems become more complex and accurate, not as the human mind grows in capacity, but as activities become more varied and call for more extended and accurate systems of notation and measurement. Trade and commerce, machinery and manufacture, and all the processes of civilization involve specialization in the apprehension of series as such. Under these conditions the number technique becomes elaborate and requires time and instruction for its mastery. The advance which mathematics has made within a brief historical time is strikingly illustrated by the words with which the celebrated mathematician, Sir Henry Savile, who died in 1662, closed his career as a professor at Oxford: By the grace of God, gentlemen hearers, I have performed my promise. I have redeemed my pledge. I have explained, according to my ability, the definitions, postulates, axioms, and the first eight propositions of the _Elements_ of Euclid. Here, sinking under the weight of years, I lay down my art and my instruments.[260] From the standpoint of modern mathematics, Sir Henry Savile and the Bushman are both woefully backward; and in both cases the backwardness is not a matter of mental incapacity, but of the state of the science.