What I think we're doing is, you know, forming concepts which are not constrained to spaces. I dont even really think our concepts, which are mostly just bundles-of-techniques, live within the space of the target object, nor its measurment space (ie., that of experience).
Eg., my "pen" includes being able to grasp a pen (indeed, the relevant motor skills are prior-to and necessary-for the abstract concept formation).
What you're talking about is a pixel-space projection of "pen" being able to function like the (animal, body-first) concept "pen". It doesnt.
Rather "pen" in pixel space is, sure, an "internal langauge" of a sampling of AllPixelPatterns concerned with pixel-space projections of "pen". This i'd call a "template", and I dont think it has almost anything to do with concepts/representations/etc.
What we are doing when we acquire motor techniques which produce "ways of sensing and moving" that eventually could become reified as the abstract "Pixel Pen" is really nothing at all like sampling PixelPenSpace and deriving a tempalte.
To see the difference, consider that our concept allows us to resolve ambiguities -- eg., if I think something might be a pen, I can go beyond one space of measurement (eg., sight) -- eg., move the pen, write with it etc. -- and thus return to the target space "Is Pen?" with sufficient confidence.
Once such "mere templates" exist, everything we do, isnt required. Indeed, a calculator can take over at that point; put it in a cupboard forever to repeat whatever thin inferences pixel templates admit.