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Synesthesia – Do Your Numbers Have Colour?

Synesthesia is another topic which provides insights into how people perceive numbers – and how a synesthetic’s perception of the mathematical world is distinctly different to everyone else’s.

Those with synesthesia have a cross-wiring of brain activity between 2 of their senses – so for example they may hear sounds when they see images,  sounds may invoke taste sensations, or numbers may be perceived as colours.

Daniel Tammet, an autistic savant with remarkable memory abilities (he can remember pi to 22 thousand places and learn a new language to fluency in one week).   He also has number synesthesia which means that he “sees” numbers as each having their own distinct colour.  This also allows him to multiply two numbers in his head almost instantaneously by “seeing” the two colours merge into a third one.

Dr Ramachandran (of phantom limb fame) has written a fascinating academic article looking at synesthesia – and estimates that as many as 1 in 200 people may have some form of it.  A simple test of grapheme colour synesthesia (where people perceive numbers with colours) is the graphic below:


For people without synesthesia, locating the 2s from graphic on the left is a slow process, but for people with synesthesia, they can immediately see the 2s as standing out – like the graphic on the right.  This test is easily able to distinguish that this type of synesthesia is real.

Those with grapheme synesthesia also report that the image below changes colour – depending on whether they look at the whole image (ie. a five) or concentrate on how it is made of smaller constituent parts (of threes):


What is truly remarkable about synesthesia is what it reveals about our brain’s innate capacity for mathematical calculations far beyond what average people can achieve.  Francois Galton, the 19th Century polymath who first documented the condition (which he himself had) described how synesthetics often also experienced a tangible number line in their mind – that was not straight but curved and bent and in which some numbers were closer that others (an example is at the top of  the page).  This allowed him, and others like Temmet, to perform lightening fast mental calculations of unimaginable complexity.  In the above video Daniel is able to divide 13 by 97 in a matter of seconds to over 30 decimal places.

Numberphile have also made a short video in which they interview a lady with synesthesia:

Could one day we all unlock this potential?  And what does this condition tell us about whether numbers exist in any tangible sense?  Do they exist in a more real sense for a grapheme synesthic than someone else?

If you enjoyed this topic you may also like:

Even Pigeons Can Do Maths – a discussion about the ability of both chimps and pigeons to count

Does finger ratio predict maths ability? – a post which discusses the correlation between the two.

Essential resources for IB students:

1) Revision Village

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Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams.  I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.

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There is a comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank of graded questions.  What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

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The Practice Exams section takes you to a large number of ready made quizzes, exams and predicted papers.   These all have worked solutions and allow you to focus on specific topics or start general revision.  This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides and Paper 3 Resources

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I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.

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All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

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Free HL Paper 3 Questions

P3 investigation questions and fully typed mark scheme.  Packs for both Applications students and Analysis students.

Available to download here

IB Maths Super Exploration Guide

A Super Exploration Guide with 168 pages of essential advice from a current IB examiner to ensure you get great marks on your coursework.

Available to download here.

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