Number Forms

Do numbers make a pattern in your head?  They do in mine.

This diagram shows how I picture numbers. Drawing the diagram gave me a surprise, as I do not usually picture the whole diagram at once. Instead, I "look" at the diagram from local viewpoints and in directions indicated by the arrows.

The dotted lines indicate how I might magnify my view in some cases, but they do not really exist on the small scale of the diagram. For example, my more global view turns right at 100, but when I consider numbers between 100 and 200, they follow the dotted line which takes the shape of the number line from 0 to 100. This would also be true, though to a lesser extent, with other ranges of numbers, for example between 300 and 400. Thus, the diagram has a "fractal" nature. This can also be seen in the way the pattern repeats when counting in thousands and millions. However, for the thousands I have a strong sense of both the location and orientation as shown on the diagram, but when I get to more than about 20 million I really think in millions and go back to the start of the diagram, which is vaguely shifted (but not rotated) into the "millions" area.

The diagram is frighteningly powerful when I think of myself or of other people. Then, I consider myself to be standing on the line at the point of my age in years, and I sometimes observe other people among my family and friends from that point to where they would be standing. There is a subtle distinction between how I observe people in relation to myself (I look from my standpoint) and how I might think of someone in their own right (my viewpoint reverts to the red arrows on the diagram).

Does anyone out there have a pattern of this sort?  I have heard that some people see numbers as colours, but I've hardly ever heard of anything quite like this.  The nearest was a smaller pattern (going up to about 100) and, if I remember rightly, heavily based on 3s.  That was in a book in Guildford public library in about 1975.  I would be interested to find out more about this.  E-mail me: mike@trikeshed.com

Since writing the above, I have had a short discussion with Professor Ramachandran of San Diego University, and have discovered that my number form is a kind of synesthesia.