A Story of Numbers
This chapter travels through time instead of through formulas. Its driving question is a simple one, how did people ever learn to write numbers down?, and chasing the answer takes us across tens of thousands of years and several continents. We open with Anaya puzzling over an old rubbing covered in odd wedge-shaped dents, then step back to the Stone Age to ask why anyone needed to count in the first place. Along the route we meet notched bones older than agriculture, body-part counting from the Pacific, the Roman numerals of old Europe, the Egyptian scheme that first stumbled onto the idea of a base, the Mesopotamian, Mayan and Chinese schemes that worked out place value, and at last the Indian (Hindu) system whose treatment of zero as a number reshaped mathematics. By the close you will recognise the four great ideas, grouping, landmark numbers, base, and place value, tucked silently inside every number you write.
Learning Outcomes
By the end of this chapter, you will be able to:
- say why early people needed to count, and describe one-to-one mapping as the engine that makes counting work;
- describe several early schemes, tally marks, body-part counting, counting in twos, and Roman numerals, and the ideas each introduced;
- explain what landmark numbers are, and how the Egyptian scheme used powers of 10;
- define a base-n number system and list the landmark numbers of any base;
- explain the idea of place value and the decisive role of zero as a placeholder and as a number, as worked out by the Mesopotamian, Mayan, Chinese and Indian peoples;
- convert small numbers between base 10 and other bases (base 2, 6, 8), and appreciate why the Indian system spread across the entire world.