**Maths and Language - Aliens, Belgium and Coloured Numbers**

25th January 2018

We tend to think of maths as a pure, universally understood language. Numbers and quantities, functions and symbols essentially mean the same thing no matter what the language being used to process them. Indeed many scientists have suggested that the best way for us to communicate with any type of alien life would be through the language of mathematics.

However other experts have pointed out that there could still be major differences in how we interpret the various realities that make up our understanding of a range of mathematical concepts, such as physics.

Carl DeVito, an emeritus faculty in the mathematics department at the University of Arizona in Tucson, has proposed a language based on plausibly universal scientific concepts and has published his ideas in the book "Science, SETI, and Mathematics" (2014).

There are many potential problems to be considered though as he explains.

‘An alien race might start with a different geometry and derive its laws of motion in that geometry… Therefore, the results might be very different from the formulation of the laws that are familiar to us.”

"The mathematics of motion is differential calculus. Can we assume that an alien race shares this with us? Differential and integral calculus are so fundamental in so many areas of science that it is hard to imagine a science without them," DeVito said. "But this is, perhaps, a human bias."

DeVito also ponders such questions as whether an alien society would have the equivalent of Euclidean geometry.

"We, of course, can't know, but we must be aware that the physics of an alien race, even in a fundamental area like mechanics, might differ in subtle but important ways from our own."

This is just the tip of the iceberg when it comes to predicting potential problems when we consider how to communicate with extra-terrestrial life, they would likely have understanding of much higher mathematics than we can currently comprehend, and they may also express these ideas completely differently.

For example people with the ‘condition’ Grapheme-color synaesthesia experience different numbers through different colours thus giving an extra-sensory level to their perception of numbers. Some even report numbers as having different tastes and smells! Studies of the brains of such people are fascinating, the area of the brain where word, letter, and color processing are located, V4a showing the most differences in make up to ‘neurologically normal’ people.

Fun fact - the character Dr Sheldon Cooper from the hit comedy show 'The Big Bang Theory' probably also has synaesthesia as he tells another character that he automatically sees prime numbers as red and that twin primes appear pink and smell like gasoline.

So it is entirely possible that alien species might experience and express mathematical ideas in a different way. It’s a fascinating area of theoretical science to explore, one which we’re sure would make for some lively debate in the classroom!

But what about on earth? Despite the existence of synthsetes we all seem to calculate mathematical concepts in the same way, and seeing numbers as different colours doesn’t change the answers they arrive at when making calculations.

However an interesting study recently showed that there are observable differences in how the brains of bilingual people process arithmetic, and these are not neccesarily explained by any process of automatic translation.

Researchers at the University of Luxembourg recruited students whose native language was Luxembourgish which is essentially a German language but who were also fluent in French having studied in the bilingual country of Belgium.

They gave the participants simple arithmetic problems first in their mother tongue of ‘German’ and then in French and found very little difference in the time and accuracy of their responses. They also scanned their brain activity using Magnetic Resonance Imaging (MRI) and noted that areas in the temporal lobe commonly associated with speech were seen to be slightly more active when simple arithmetic was presented in German.

Not much else was different until the problems became more complex. Then the participants took a little longer to reach their answers when the problem was presented in French and they made more mistakes.

When they compared the MRI activity they found that when solving problems in French several areas of the brain were activated which were not activated when the problem was presented in German. Most notably areas associated with visuo-spatial processing which the researchers concluded was not a result of having to automatically translate the problems from German to French.

This suggests the participants were ‘summoning mental images of symbols, perhaps visualising the numerals, in order to compensate for differences between the languages.’

So language and maths have a much more complex relationship than previously thought and this should be considered when teaching students maths in a language which is not their mother tongue. Other studies have shown that students do struggle when learning maths in a secondary language but this was assumed to mostly affect word problems. Now we know that is not the case, and the brain scans show there is more happening than meets the eye.

We found this fascinating and suggest more study is needed to further investigate this complex relationship – it may help our students and even one day help us communicate with beings not of this earth for the first time.

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