Funbers 10, 11 and 12
The fun facts about numbers that you didn’t realise you’ve secretly always wanted to know…
10 — TEN
We did it! We finally reached double figures! The fact that 10 is the first number in our system of counting that has two digits tells us that we count in base ten. We start with 0, 1, 2, … and keep going until we reach 9. If we add one more then we have one full set (the 1 in the first column) and have to start counting again from the beginning (the 0 in the second column). When we move to three digits it’s because we have ten sets of ten, and so we need a new way of keeping track of ten ten’s, which we call one hundred. Same with one thousand, ten thousand, one hundred thousand, one million… You’ll notice that once we reach 9 in a column, we then add a new column to the left that allows us to keep counting higher.
The fact that we count in base 10 is likely to do with our hands, or specifically the number of fingers on our hands. I recently interviewed Professor Ian Stewart about this very subject (check it out here) and he made the interesting observation that if aliens were to visit us on earth, it is very likely that they would not count in base ten as we do. If you’re an alien with seven tentacles, why would you count in tens? You’d probably use sevens. So their version of eleven, one full set of seven plus one extra, would actually be the same as our number eight. We can count in any base we want, as long as we know the rules. For example, computers count in base 2, which is why the data contained in a computer is often displayed as a string of 1’s and 0’s — in base two they are the only digits available!
11 — ELEVEN
The number 11 has quite the infamous history, both good and bad. The end of World War I, the armistice, was marked by the signing of a peace treaty on the eleventh hour of the eleventh day of the eleventh month, and we still use this time — 11am November 11th — to pay our respects to those that lost their lives with a minute’s silence. The actual treaty was signed at 5am on November 11th 1918 on board the private railway carriage of French Allied Supreme Commander Ferdinand Foch, but didn’t come into force until six hours later. In 1940, Adolf Hitler forced the French to sign a peace deal in the exact same train carriage… I think he was trying to make a point.
September 11th is of course the date in 2001 when the twin towers in New York were destroyed in a terrorist attack, claiming the lives of 2996 people. The plane that crashed into the North tower was American Airlines flight 11 and many conspiracy theorists claim that the number 11 is a symbol of the two towers. Speaking of conspiracies, the first moon landing of 1969 was completed by the spacecraft Apollo 11, unless of course you believe that it was all filmed in a Hollywood studio, in which case JFK was probably hit with 11 bullets and Area 51 contains 11 alien specimens (unverified information).
12 — TWELVE
Twelve is the last number that we learn in our times tables at school, which is probably because we used to have a base twelve system for currency in the UK until 1971. Decimalisation was first introduced by Russia in 1710 when the Ruble was set at 100 kopecks (yes it is a real word) and most other countries have since followed suit. While the USA still refuse to accept the metric system of measurements (what on earth is a 12 fluid ounce can), they did convert to the decimal currency system in 1792 with the introduction of the dollar.
Twelve is also big in the calendar — there are twelve months of the year and similar to the days of the week they have names that are heavily influenced by the Romans. January is named after Janus, the Roman God of gates and doorways (I guess all the good ones were taken). February is named after Februa, the Roman festival of purification. March is for the Roman God of War, Mars (a month and a planet, someone’s doing well…). April is known as Aphrodite’s month — I assume because that’s when all the babies are born and Aphrodite is the Greek Goddess of love and beauty. (May and June aren’t very exciting so I’m going to skip them). July is named after Julius Caesar, the former emperor of Rome, who reformulated the calendar and obviously thought it only fair to name a month after himself. His adoptive son, Augustus Caesar finished the reformulation and following in his Father’s footsteps he too named a month after himself — August. September, October, November, December are all named as the seventh, eighth, ninth and tenth months in Latin, which means that clearly someone was very bad at counting… I’m looking at you Caesar.
The ultimate reason that we have twelve months is in fact a mathematical one. The solar orbit of 365.24 days (the time taken for the Earth to complete one full orbit of the Sun) divided by the lunar orbit of 29.53 days (the time taken for the Moon to complete one orbit of the Earth) gives you about 12, plus some change. This meant that 12 became a significant number for the Sumerians who liked it so much that they also divided the night into twelve stages according to when certain stars appeared. The Romans jumped on the bandwagon and divided the day into twelve parts as well, thus forming the beginnings of the 12-hour clock we use today. Two sets of twelve rather than one lot of 24 also meant that clock faces could be smaller and therefore contain more intricate patterns. In other words, without 12-hour clocks we would have no Swiss cuckoos, and that is not a world that I want to live in...
Author
The Funbers series is written and presented by Dr Tom Crawford and is broadcast weekly on BBC radio. For more maths fun check out Tom’s website tomrocksmaths.com and follow him on Twitter, Facebook, Instagram and YouTube @tomrocksmaths.
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