then we'll need to distinguish between different "types of touching".
Active touch is when a subject's finger moves over sa tationary surface which I believe is the motion that is being described.
The limit of discrimination with touch is about 0.8mm.
The limit of discrimination with active touch is about 20-40 microns (0.02 to 0.04 millimeters) (75% correct performance level)
The superior discrimination of active touch is thought to be due to more vigorous activation of mechanoreceptor populations and/or an ability to use neural code based on both temporal and spatial aspects of the mechanoreceptor response made possible by the relative tangential movements of the finger.
I don't know if 20-40 micron touch discrimination is enough to distinguish between different levels of finish but this limit is perhaps a better representation of the movement described.