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As an architect I often think spatially without symbols (words or numbers). I think conceptually in terms of form, volume and voids. (I'm sure there are other fields where this is common). To express my ideas I have to build a 3D model or draw a 2D drawing to express a 3D concept.

I've often wondered if there were a way to think about other non-spatial concepts without language or symbols but I don't think I have been able to do this. Some musical composers were said to have been able to compose music conceptually and then play it withough having to trascribe it to musical notation. I'm sure mathematicians are able to think like this too, very theoretical without actual numbers.

There is also a condition known as synethesia in which people can smell a form or taste a number or letter or hear a note in place of an image (say of a tree) or see a color in place of a symbol. In this condition people mix up their senses. It's a facinating condition.

I do think you're on to something.

BTW, I don't think I've often tended to mix up my sensations, but I grew up with distinct impressions of some letters and may be even more, numbers; even a tendency to feel what they would be like if they were personified. I think that may be due to being quite "right-brained" (intuitive and so on) while having to deal with very "left-brained" (logical, linear) tasks, but... there is more to such things, it seems to me.

One tends to naturally (humbly) ascertain that there is much more there, than what our human concepts reach, eh? More there than the stolidness of our words relate, especially.

a way to think about other non-spatial concepts without language or symbols

Eventually there will be symbols in the results. As a relatively recent development, database analysis and the Geographical Information System, GIS, is coming along to be a powerful tool where words still fail.