Fascinating. Not what I would have expected. I was, however, thinking
of an exhaustive set of all possible words rather than a small sample.
But since all lexicons represent only a very small sample from the
universe of possible words, that was a bad assumption on my part.

In addition, a particular morphology/orthography could very easily
break up the uniformity of the distribution. For example, having only
a limited number of consonant clusters, or perhaps even single
consonants only, between vowels would immediately result in a
non-uniform distribution.

I guess my common sense, and unexamined assumptions mislead me. :)

--gary

On Mon, Jan 10, 2011 at 10:59 AM, Alex Fink <[log in to unmask]> wrote:
> On Mon, 10 Jan 2011 10:21:02 -0800, Gary Shannon <[log in to unmask]> wrote:
>
>>If the points are distributed
>>across the plane (or in the N-space) with uniform randomness then it
>>seems to me as if most of the cases will result in only one cluster.
>>(This is a strictly intuitive guess and I may be way off base.)
>
> Well, mind also that a uniform independent random selection of not hugely
> many points in a region in the plane doesn't look well-spaced.  Even so,
> this immediately appears to me as the sort of problem where human intuition
> is often wildly wrong, in two dimensions, much less in many.
>
> So I took ten minutes and hacked together a little thing in NetLogo to test
> this in the plane (actually, I used the default torus).  And the number of
> groups was never one, in a thousand runs of various numbers of points.
> Instead it looks basically linear in the number of points, about 0.3 groups
> per point on average.
>
> Alex
>