Detail #310: Topologies of Morphologies

Often when making agglutinating morphologies, it's easy to end up making a fairly Cartesian-product like morphology. One way of avoiding the "excessive regularity" of this could be not to introduce irregularities in the formation - to in fact keep it exactly that way, but introduce oddities in how parts of the thing stick together.

Consider the number of features your morphology marks for - also include zero marking for any feature as a distinction. Make a table where you project all the dimensions of the morphology space, in the following way:

		I			II			III
		א	ב	ג	א	ב	ג	א	ב	ג
1	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.
2	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.

If a combination of markers of features - say 2bIIIג - really just combines the meanings of features 2, b, ג and III - we're dealing with a topology that corresponds to an entirely flat surface.

We can, however, make this surface more interesting; we can add a twist to it:

		I			II			III
		א	ב	ג	א	ב	ג	א	ב	ג
1	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.
2	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.

I like throwing ugly colour combinations your way; yep, that's pretty much the only conceivable explanation.

Now, one could imagine a similar twist happening both in 1 and 2, and of course it could just as well appear in some way for the hebrew-letters or for I/II/III. Basically, this 'twist' could appear in any dimension, e.g:

		I			II			III
		א	ב	ג	א	ב	ג	א	ב	ג
1	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.
2	a	.	.	.	.	.	.	.	.	.
	b	.	.	.	.	.	.	.	.	.

This twist is also sort of 'tube-like' - each highlighted element in 2a is offset by one in the {I,II,III}-dimension, if we assume the entire structure "turns around" so the right edge of III is glued on to the left edge of I. This isn't necessary, though - the offset might be more like a braid-shaped twist.

I am not going to try and impose the little topology I've learned from youtube here, but I think this kind of thing might give a sufficient idea about possible ways of turning cartesian products into interesting and creative things whose structure is less trivial.