Any visualization is also language, and ultimately convention[1]. The privileging of the visual, or even the division of the senses, is a construct.
“I have had an experience of this kind, similar to that reported from many parts of the world by those who have had occasion to show photographs to persons who had never seen a photograph before. To those of us accustomed to the idiom of the realism of the photographic lens, the degree of conventionalization that inheres in even the clearest, most accurate photograph, is something of a shock. For, in truth, even the clearest photograph is a convention; a translation of a three-dimensional subject into two dimensions, with color transmuted into shades of black and white. In the instance to which I refer, a Bush Negro woman turned a photograph of her own son this way and that, in attempting to make sense out of the shadings of greys on the piece of paper she held. It was only when the details of the photograph were pointed out to her that she was able to perceive the subject.” Herskovits, Art and value, from Aspects of Primitive Art, New York, 1959
Maybe thinking without obvious support is what we call intuition ?