I'm just back from attending an Alex Bellos event as part of the Aye Write festival. Alex has spent the last few years traveling the world exploring how different cultures approach mathematics.
The talk covered an eclectic mix of topics ranging from the mathematical reasons for Puff Daddy becoming P Diddy to pre-electronic calculators designed to be used in rally cars.
I'm going to talk about the three parts of his talk that I found most interesting.
Tallying systems
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Tally marks are a form of numeral used for counting. They allow updating written intermediate results without erasing or discarding anything written down. The system Europeans are used to seeing is the 4 single 1s with a strike to represent a 5.
This system is pretty simple and often used:
However, in South America they use a system where you build a box:
And in China they use the 5 lines that make up the parts of their number 5:
I'm going to switch to using the the South American system!
Japanese Abacus counting system
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Alex also showed a video of some Japanese kids who excel at adding numbers together. They are using an abacus system in their mind which makes counting a visual rather than an arithmetic problem.
In this video the participants are playing a game called "Flash Anzan" where they have to add up numbers that are being momentarily displayed on a screen without the use of paper.
As if that wasn't scary enough, the abacus system doesn't use the part of the brain which we traditionally use for counting, meaning that we are free to use it to perform word games.
In this video the 10 year old girls are counting the numbers displayed to them while simultaneously performing a word game where you have to start a word with the last syllable used by the previous word.
Chimpanzee Math
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During the 1980s (in Japan again) they trained a few Chimpanzees to be able to recognise the numbers 1 to 9 and be able to answer questions about which one is higher and lower.
Then they decided to see if the chimps could remember sequences shown to them for a short period of time and then use a touch screen to select the numbers in order after they have disappeared. The scientists were suprised to see find that the chimps could perform to the same levels as humans in a control group.
Then they thought it would be interesting to reduce the time the numbers are shown from 0.6 seconds to 0.4. The human group only managed a 50% success ratio when shown the test. The chimps still managed 100%. Amazingly, they were able to reduce the time to 0.09 seconds and the chimps still have a 100% success rate.
Alex has a book about his discoveries if you would like to know more called "Alex's adventures in Numberland"