CorsairMac is right on the technical stuff: spinning can be done very, very slowly. Still, as I see it, in general conversation, "spinning" is associated with high cadence in easy gears and "mashing" with low cadence in high gears.

Regarding using the computer: when I'm riding flats and I see 70-75 on the cadence monitor, it means it's time to hit an easier gear. So I downshift. On the opposite side, I don't need to see 110 to know that I'm spinning.