In the red – 赤字 – Números rojos

I was thinking that “in the red” (English), “赤字 – red characters” (Chinese and Japanese) and “números rojos – red numbers” (Spanish); are all similar expressions which have “red” in common and they are all referred to the same concept: budget deficit. It’s interesting ¿Why most of the cultures associate the red color with negative numbers and black with positive? ¿Why red and not another color? Ockham would say that we humans associate red with danger and deficit is a dangerous, but let’s explore other ways to think about the red-deficit relationship.

At the beginning of the first millennium some Chinese mathematicians wrote a book called “The Nine Chapter on the Mathematical Art”. It was the first book in the history with a consistent explanation on how to calculate using negative numbers.

The begining of the first book ever that explained the idea and use of negative numbers

In this book they explained a system to operate using negative numbers in which the representation of the positive numbers was made using red ink and negative numbers using black ink. Nowadays is the “same” but swapped, red for negative and black for positive.

Negative numbers in black and positive numbers en red. Image from Maths.org.

Why black changed from from negative to positive? No idea, do you know why? I’ve been thinking and sometimes, at least in Japan, red is still used for “positive” things like for instance when representing candlestick charts in Japanese websites where the red bars indicate gains! What I see pretty obvious is that the colors red and black where chosen because those where the two easiest ink colors to acquire in the old times.

Chinese emblem using red ink.

In Asia they’ve been using negative numbers since 2000 years ago, in the western world we had to wait until Descartes arrived with his coordinate system in the XVII century. It was hard for us to accept the number 0, even harder was to consider negative numbers as acceptable.

If you want to learn how to add and subtract using red and black rods here and here you can find more information.

This article is an hypothesis, any comments or ideas?