The spatial dimensions height, width, and depth as well as brightness are perceived by the visual sensory system, pitch by the auditory system, temperature by thermal sensors and weight, finally, by the kinaesthetic sensors.
... however, there is also a wealth of quality dimensions that are of an abstract non-sensory character. (Section 1.3.)
Somehow — probably because I believe innovation creates new domains and dimensions — my mind associates the phrase above with John Markoff's remark about Steve Jobs that he seemed to have a keen sense for big innovation opportunities. Maybe it was something like synesthesia, an ability to sense multiple dimensions where most of people perceive it as one.