Mathematics allows for no hypocrisy and no vagueness



Babylonian 60

Today we count in base ten, but the ancient Babylonians counted in base 60 (sexagesimal), because they could count to 60 using their hands. They counted the three bones of each finger on one hand using the thumb on the same hand (start at the top of your little finger and count down the bones 1... 2... 3. then move on to the next finger 4... 5... 6... and so on). Having got to 12 you count this off as one '12' on the other hand and go back to the beginning. You can do this five times, with twelve bones per time and thus count to 60 on two hands without having to write anything down.

This Babylonian numbering system is the reason behind 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day. Also 12 inches in a foot, 360 degrees in a circle and any number of other imperial measurements. Also, numbers which are multiples of 12 (such as 24, 60, and 144) are all also divisible by 2, 3, 4, and 6, whereas 10 is only divisible by 2 and 5 - so it's easier to count halves, quarters and thirds in a base 12 system. 


Anyone can count to 99 on their fingers using a Korean system called ‘chisanbop’ which means ‘finger calculation' (chi ‘finger’ + sanp·p ‘calculation’). Chisanbop turns the fingers into a form of abacus and was created in the 1940s by Sung Jin Pai. Since the ‘70s it has been widely used in the US to help teach basic maths skills. It can even be used to perform calculations. You use your right hand for 1-9 and the left for tens (10, 20, 30, etc)

The right hand works like this: 
Index finger out = 1 Thumb and index finger = 6 Two fingers out = 2 Thumb and two fingers =7 Three fingers out = 3 Thumb and three fingers = 8 Four fingers out = 4 Thumb and four fingers = 9 Fingers in, thumb out = 5

Finger counting systems are nothing new. The Venerable Bede could count up to a million, apparently, by 'moving his hands up and down his body'. 

LORD BYRON (1788-1824)

I have imbibed such a love for money that I keep some sequins in a drawer to count, and cry over them once a week.

MARK TWAIN (1835-1910)

In the Spring, I have counted 136 different kinds of weather inside of 24 hours.

Animals Can Count

Almost all animals have a sense of number, in some cases comparable to our own. Pigeons, parrots, raccoons, ferrets, rats, salamanders, honeybees, monkeys and apes have been shown to count, add and subtract.

Rhesus monkeys at Colombia University have shown they can arrange groups of up to nine objects in the correct numerical sequence. Similar experiments have shown crows and parrots can count up to five or six.

Cormorants seem to be able to count to seven: used for centuries in China to catch fish, fishermen rewarded the birds by allowing them to eat every eighth fish. The result was that after they caught their seventh, they refused to move from their perch until their neck ring was loosened so they would be able to swallow the next fish they caught. 

How Many Fish?

A 2008 Italian study demonstrated that even fish can count. The experiment used mosquitofish, a kind of carp from North America. The study turned on the fact that a female, harassed by a male, will bolt to the largest nearby shoal for cover. The researchers showed that the fish could distinguish between shoals containing one and two fish, two and three fish and three and four fish. They could not tell the difference between shoals of four and five. With larger numbers, the difference between the shoals had to be big enough for the fish to make a meaningful choice - such as the difference between eight and 16 fish in a shoal. At smaller differentials, such as 12 and 16, the fish did not show a preference. 

The female mosquitofish’s numerical nervousness might be related to the fact that the males have huge penises, equipped with four grappling hooks. When fully extended, they can reach 70 per cent of body size, making them the best endowed of all fish species. Although females are ‘attracted’ to the better-endowed males, the males suffer for it: their swimming is hampered by the oversized tackle, making them more vulnerable to predators. 

When counting in Japanese, different words are used depending on what shape the objects being counted are.

You can tell the age of a fish by counting the annual growth rings in its otoliths (the bones in its ear).

In 1999, working in pairs to minimise errors, British govern-ment ornithological surveyors counted all 64,842 pairs of fulmar on St Kilda.

The Incas used intricate knotted bits of string called QUIPU to write down their numbers. Zero was a space.

Coots can count their own eggs, even in the presence of eggs laid by other birds.

At one rather dreary meeting at the Royal Geographical Society, Francis Galton made a boredom chart, log-ging the total number of fidgets per minute.