Although digital files are a modern phenomena, the concept of using numbers to describe things is much, much older. Counting, and its companion, numbering, are as old as humankind itself. Animal bones that date back to at least 15,000 BCE. have been found with notches in them, which are thought to be tally marks. These marks directly signify the things they represent: one mark for each bison, for example. Numbers, on the other hand, are an abstraction of these tally marks. Compare the number 5 to the five lines carved on a wall or a tree. Numbers are a precursor of the modern process of digitization: the description of concrete reality by abstract number.


Early numbering and calculating systems, such as those developed in Mesopotamia in the fourth millennium BCE, depended on direct physical analogs: one pebble for one sheep, two pebbles for two sheep. By the third millennium BCE, the Egyptians and the Sumerians had developed the written digit. Once numbers had entered the abstract world of writing and were independent of the objects they represented, they could be manipulated in new ways. Concepts of manipulating numbers developed into addition, subtraction, and so forth. In order to count, we must understand that things exist discretely from one another: an individual rock is complete in and of itself, and separate from the other rocks in a pile. Digital systems, those that rely on numbers or digits, are said to be discrete, such as whole numbers or integers. Analog systems are continuous and have no breaks or steps—just think of thermometers: an analog thermometer has a band of mercury that extends itself continuously as the temperature rises, whereas a digital thermometer shows a changing series of numbers.