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Gerald Koenig wrote:

[snipped]

> >Is there any natural language that uses only 2 core cases?
> >Something seems to make 3 the right number,
> >and I often wonder why.

> I ask how
> they are found grouped in nature, ie how they can be packed. It takes a
> minimum of 4 spheres to form a stable three dimensional structure in
> gravity or held by attractive forces. I just tried it on the table
> with some of my favorite organic grapefruit. That structure is a
> tetrahedron. The tetrahedron is a very fundamental structure of carbon
> based life. It is the minimal three dimensional structure and it
> requires 4 elements.

There's also map-coloring on a flat surface, thinking of Michael
Arbib of USC, and neural maps. The verb would be Switzerland ...
But the cerebral cortex could easily bypass that "limit" of 4
by using a more complex topology; donuts take 7.

> The verb and its 3 arguments total 4 elements forming the basic
> grammatical structure of a full sentence. Just as we have 2 dimensional
> structures, such as writing, we can have 2 dimensional languages, as
> attested by Nick, but they are not fully formed.

Language "branches" fractally to turn 1-dimensional speech
into N-dimensions, but there is still something about 3.
It appears elsewhere: 3 areas of the brain, one each dedicated
to processing verbs, nouns, and attributes (this is somewhat iffy).
Normally, deictics and persons tend toward 3. Many other examples,
but not without controversy. I have a theory, too.

Then there's the "7 plus or minus 2" thing.