A number form, says Dudley in Chapter 18 of the book, is a shape inside some people's heads on which the natural numbers are represented. Here is an ASCII example of a (very) simple number form (based on an illustration from Dudley's book):
1 ----- 10
|
|
50 ------ 100 ---- 200 ---- 300
There are often different spacings between different numbers; the small numbers often have more space proportionally than the larger numbers do.
There has not been much research done recently into these objects; Sir Francis Galton, the famous British statistician and eugenicist, wrote some papers on them in the 1880s, and there seems to have been little written since. Only the eruditon of an Underwood Dudley has been able to rescue them from obscurity.
There are probably several reasons for this: it might be very difficult to prove to a sceptic that one actually has one of these things rather than just making it up, so it is hard to show that one is actually studying something real, and also there is no evidence that the possession of a number form is beneficial in any way. It's just something that you have or don't have, like a widow's peak or freckles or the ability to roll your tongue.
It's also an interesting example of a very minor subfield that has basically been left fallow for about a hundred years.
(**) The similarity, says Dudley, is that in both cases (most) people don't talk about them in casual conversation, or show them to other people.
