[one-more-minute]

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.

[igpay]

I'm now pretty convinced that this could be classified as some form of synesthesia, though I'd never thought of it that way before. When I'm actually doing math I tend to _feel_ the shapes of the numbers and their interactions, rather than it being a highly visual sensation like some others experience. The visualizations of the shapes only really happen when I slow down and focus.

I'm not an exceptionally quick calculator as far as I'm aware, though I've never tried to measure. I don't have strong associations with numbers greater than ten (though certain classes of numbers like multiples of five tend to have forms in some contexts), so I do arithmetic on larger numbers digit-by-digit, which is inherently kind of slow.

[jimmux]

I have synaesthesia and your description of numbers just feels right to me. I have the fairly common association of letters and numbers with colours, which (at least with people I've shared this with) often is stronger up to 10, with further numbers typically blending the properties of their digits.