[msutherl]

This was fascinating to read. I think in much the same way, but less vividly. For instance, when reading a formula, I do not immediately form a picture in my mind. I can do this if I've taken the time to establish the association, but with algebra I'm prone to rely on my visual understanding of the rules. Instead of switching to a visual representation, I've learned to visually move the symbols around on the page according to visual analogs of the rules of algebra.

I do, however, do exactly the same thing when derivating the sine function since it is so closely associated with the graph of sin(x) by default.

I found your example of building system diagrams interesting. I think I may do the same thing, but often it is unconscious. I do not see the image as I'm constructing it, but if I look, it's probably there.

I'm also tempted to suggest that I have a secondary mode of thinking that involves constructing arbitrarily complex logical trees (i.e. if this is the case, then this must be the case) since I seem to detect logical inconsistencies intuitively and without delay. I do not see them, they just occur to me with no representation at all. Perhaps this is a bit like the "just know it" type of thinking expressed in the parent post.