Sep 15

Why is negative left of zero & positive right?

Why do negative numbers appear to the left of zero on the number line and positive numbers to the right of zero?

This question was asked recently and few people realise the convention began in 1685.

The English fought three naval wars with the Dutch in the 1600s, so if a line was to be drawn with England on the left and Holland (The Netherlands) on the right, then advancing towards the Dutch enemy would mean moving to the right (East), which is positive for the English admirals. Retreating from the Dutch enemy would mean moving to the left (West) which would be negative for the English admirals.

So if a starting point in the 'battle line' was depicted, then advancing 5 to the right could be seen as 5 in a positive direction. If after advancing to the right 5, the English had to retreat 7 to the left, then they would have advanced less than nothing, as they were 2 further away from the Dutch enemy.

Had the English been at war with the Irish to the West in the 1600s, rather than the Dutch to the East, negative numbers might today appear to the right of zero on a number line!


John Wallis, A Treatise of Algebra, 1685.


The first number line image from John Wallis (1685) that led to negative numbers appearing to the left of zero.

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