Why do we count in tens? Mathematicians generally agree that it is because we have ten fingers.
Can you imagine how we would count if we had twelve fingers, like Yoandri Hernandez Garrido from Cuba (pictured)? He belongs to a special group of polydactyl (many fingered) humans. Other people have oligodactyly (fewer fingers or toes) or ectrodactyly (‘two’ toes/fingers … actually a claw-shape due to missing digits). Granted, such conditions are a result of something going wrong genetically, but mathematicians wonder “What if?” What if humans naturally had only four digits on each hand (like cartoon characters)? How would our number system work then? How would we add, subtract, multiply and divide?
Although most cultures around the world developed counting based on the number ten (what we call the decimal system), some have based their number system on other numbers. The Babylonians used a base 60 system for counting, and we have remnants of that in our measurement of angles (360° in a revolution) and time (60 seconds in a minute and 60 minutes in an hour). The Maya in Central America are famous for their base 20 number system and even the French number system has some trace of a base 20 origin (the French for 90 is “quatre-vingt dix,” or four-twenties ten). Khmer and Roman numerals are partly based on the number five. Computers use a binary system (based on the number two), and computer code is often shown in hexadecimal code (base 16).
In time, I hope to share a little about all these systems. In the meantime, if you would like to read about these them (and the cultures that used them), visit the Wikipedia article about Positional Notation and look for the Positional Systems by Base section in the box at the right of the page. By clicking on the numbers in turn, you can read about the number systems, their uses and a little about the cultures that used them.
In this part of my website we will explore some of these number systems.
Our system of using just nine numerals (0,1,2,3,4,5,6,7,8, and 9) to write all our numbers is based on a very ancient tradition! Thousands of years ago, the Babylonians managed to write all their numbers with just TWO symbols! They were able to do this because they used 'place notation' ... that is, the VALUE of a number is determined by WHERE the numeral is written (i.e. in which column, or position).
Ultimately, all the better counting systems are based on this idea. Understanding it will help us understand how to add, subtract, multiply and divide our numbers ... and learn some short cuts as well!
In this video you will learn how to 'write' Babylonian numerals and how you STILL use this very old counting system every day of your life! I am confident that you will learn something new and interesting! You will also learn a little about our 'place notation' and we will follow up on this in subsequent videos.
By far the best educator I have been subject to in my schooling life. Apart from showing me with the utmost clarity the many concepts of mathematics, Graeme has inspired me to better myself in everything that I do in school and in my life. His dedication to his craft is truly admirable, and this level of dedication to helping the student achieve is something that is extremely hard to find. If you’d want anyone on your side during HSC mathematics, it’d be Graeme.
Harry B (student, 2012)