Wednesday, 25 July 2012

Alex's Adventures in Numberland - Chapter 0

In the introduction to Alex's Adventures in Numberland, Alex Bellos explains that he has a degree in mathematics and philosophy. He entered into journalism to continue with philosophy and abandon his mathematics. While working as a journalist though, he was surprised by how innumerate most journalists are. After a few years, Alex was trying to find what he wanted to do, when he delved back into the world of mathematics. As an adult, he wasn't looking at exam maths, but anything that he found interesting and curious. This is where he got the inspiration to write this book.

The book starts at chapter 0, to emphasise that the content covered in the chapter is pre-mathematics, how numbers emerged. In the contents page, the chapter is described as follows:

A Head For Numbers - In which the author tries to find out where numbers come from, since they haven't been around that long. He meets a man who had lived in the jungle and a chimpanzee who has always lived in the city.

Basically, the chapter is talking about number instinct. Do people everywhere have the same instincts when it comes to numbers? What about babies? Animals? Reading the chapter, I have learned some interesting things.


There is an interesting case about a horse called Clever Hans, who was thought to be able to perform simple arithmetic by stamping out the correct answer with his hoof. A committee of scientists investigated the horse to see if the act was just a trick, but decided that the horse was in fact doing the maths. However, a psychologist also investigated the horse, and noticed that he reacted to slight changes in his trainer's face as he reached the correct answer. The trainer wasn't even aware that this was happening, but the horse was very sensitive to facial changes. So the horse wasn't doing arithmetic, but I still think it was incredibly clever for the horse to be able read these changes.

In Japan, they wanted to test the mathematical abilities of animals without the chances of human cues, intentional or not. This is where Ai came in. Ai is a chimpanzee from West Africa, brought over to Japan in the late 1970s. The aim was to teach Ai to count without human interaction, but using touch screens and apple cube treats. Ai became the first non-human to count with Arabic numerals (1, 2, 3, etc.) In order to count, you need to understand two concepts about numbers, which are quantity (cardinality) and order (ordinality). Ai grasped these concepts fairly quickly, and so they tested her (and her son) with flash memory tests. The numbers 1-5 were arranged randomly on screen for just over half a second, and then covered so that Ai had to tap the numbers in order from memory. Compared to a sample group of Japanese children, the chimpanzees continued to perform well when the time the numbers were visible dropped, whereas the children dropped below 50% success rate. This showed that the chimpanzees have an incredible photographic memory, which could be down to having to make snap decisions in the wild about things like the number of foe there are.


Other tests have been conducted to find out what instinctual maths abilities babies might have. To start with a puppet is placed on a stage. Then a screen is placed in front of the puppet. Another puppet is shown to be placed behind the screen. When the screen is removed, either 1, 2 or 3 puppets will be revealed. It was found that babies stared longer at the puppets when the maths didn't add up, suggesting they were expecting only 2, which in turn suggests they have some basic understanding of numbers. This is backed up by the fact that they didn't stare for longer if the puppets had changed completely, only if there were the wrong numbers. Obviously it is difficult to tell for sure if this is because of a basic grasp for numbers, because you can't just ask a baby, but the research has shown some interesting results.

There are loads more examples of comparisons between maths you learn and maths you are born knowing in the chapter. For example, it talks about tribes that only have numbers for 1, 2, 3 and many. It is really interesting to see how maths is thought about and used by other cultures and creatures and I recommend reading it. Being written by a journalist for people other than mathematicians, it is very easy to read and understand. It isn't so much about how maths works, but how people use it.

Here is the Amazon link for it.

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