Colourised+Equations

Yesterday, during a discussion about [|cognition], a colleague informed me that Physicist [|Richard Feynman] perceived colours when he saw equations. "When I see equations," he once said "I see the letters in colors - I don't know why." (Ref 1). This ability is a form of synesthesia by which there is cross-over from one sense to another. Daniel Tammet, an [|amazing savant], also has this gift. He "sees numbers as shapes, colors, and textures, and performs extraordinary calculations in his head", as he describes in his book, [|Born on a Blue Day]. This suggested to me that colourised equations would be a good aid to learning for some people. I took the well known roots of the [|quadratic equation]:

and used blue to identify irrational parts and red to identify negative terms. The mapping is not clear cut, because one term is plus-or-minus, and it is only the result of the square root that is irrational.

This image was created by entering the [|LaTeX] formula: \frac{\uc{red}{-b}\pm{\uc{blue}{\sqrt[]{(b^2 \uc{red}{- 4*a*c})}}}}{2a} into the equation renderer at: [|http://www.hamline.edu/~arundquist/equationeditor/] The LaTeX command **\uc{red}{-b}** defines that the term -b is to be coloured red.

The benefits of colouring may not be apparent for a single equation. I suggest that you try it the next time you need to present a long and tedious algebraic evaluation. The low-tech approach would be to use coloured highlighting pens to mark up a printed copy of the equations.

For the benefit anyone who is unable to view the images, the equation shown by the above images is: (-b +/- sqrt(b^2 - 4*a*c))/2a The negative terms -b and -4*a*c are coloured red and the sqrt function, which may be irrational is coloured blue. The square root may also be an imaginary number, if it is the square root of a negative number.

Ref 1: [|Sparks of Genius], By Robert Scott Root-Bernstein. The [|page containing Feynman's description] may be viewed in Google Books.