Cool! If the author is reading, have you looked at synaesthesia, and do you think it applies here? The idea of addition having both a visual appearance and a kinetic feel is alien to me (perhaps partly because I avoid mental arithmetic like the current plague). But it's apparently reasonably common to have colour and spatial associations with numbers.

I'm also curious if you are an unusually quick calculator compared to others you know. Synaesthetes can sometimes turn their condition into a talent, like the famous Shereshevsky who had a photographic memory; every experience was utter sensory overwhelm, making mundane information very memorable.