standing math. Researchers in human development have confirmed the existence of an inherent "mechanism devoted to quantifying discrete entities" through studies of the arithmetical awareness of infants as young as five months (Bower 132). Tests were conducted on infants with objects placed behind pairs of screens. One object is revealed, for example, and then screened, and a second object is revealed and screened with the second screen, but when the two screens are removed only one object is visible, thus implying 1 + 1 = 1. Surprised by these 'incorrect' solutions, babies were found to look "markedly longer at new or unexpected stimuli" (Bower 132). The effect disappeared, however, when numbers over 2 were used--indicating that babies' extremely limited short-term memory was exerting a limiting effect. But mathematical reasoning--or, at least, some "general quantity judgment" clearly exists almost at birth (Bower 132).
Practical applications of the discoveries of mathematicians--who rate practicality very low on their scale of interests--are increasingly important in the modern world. Even the field of statistics--which seems so familiar in everything from public opinion polls to social science methodology--extends beyond those uses characterized by British Prime Minister Benjamin Dsiraeli who said that "there are lies, damned lies, and statistics" (quoted in Trefil 66). Since probability and statistics, by their very nature, deal with "situations where certain knowledge is impossible" they have broad practical applications (Trefil 66). A good example is the use of mathematical statistics in epidemiology.
It had previously been thought that nearly 100 percent vaccination of the population of Papua New Guinea would be necessary to control malaria--a serious problem since the "cost of a programme goes up disproportionately as one tries to get near 100 percent" ("Medicine" 94). Malaria control is complicated by different...