How to Count the Grains of Sand

Abstract

For Archimedes’ investigations experiment and observation constituted a starting point, but it had to be experiment and observation of a very special kind. Only those properties of bodies that could be expressed in numbers attracted his attention. Once an experimental result has been expressed in mathematical language, the rest follows from the consequences of logic. It works through mathematical deduction. Some of the conclusions obtained with the help of this deduction can be experimentally checked. In this way, the truly scientific method was born. Three great traditions: Platonic, Aristotelian and Archimedean, have initiated different ways of thinking about nature and our efforts to resolve its mysteries.