One question I like to ask in conversations about aphantasia: when you do relatively complex arithmetic in your head (for instance, compute 47 * 68 real quick), do you visually perform the gradeschool multiplication algorithm? Or something else?
I've surveyed a lot of people on this - probably forty or so in person, plus another 100 or so in a poll on reddit once - and there's a pretty clear trend: people who perform the visual algorithm tend to be 'not math people', and are less accurate and less confident in their answer, or not even willing to try.
I'm aphantasiac and I can do a calculation like that fairly quickly and accurately, without any special practice. I basically use my verbal memory to store and recall cached computations instead of any visualization. My theory is that the visual brain is not really designed for storing precise information so much as the gestalt of an image, so it does less well on precise numeric details.
That's an interesting question! I don't have aphantasia, and can visualize things pretty vividly - but I also resorted to "verbal memory" to do that calculation.
I foiled it like the other comment says (maybe somewhat of a visualization, since I "visualized" it as 40x60 + 40x8 + ...), and I remember the running sum by "saying" it to myself inside my head.
I performed each multiplication (grade-school multiplication memory lookup table, not actually doing the visual algorithm) and added the right number of 10's place zeros, then added it to the running sum. For this addition step actually, I do visualize as stacking the two numbers and carrying if needed. Then I "say" the result to myself and remember it for the next multiplication.
I will say that my first reaction to seeing "calculate 47x68 real quick" was reluctance and it was not an easy task to do mentally, but it was mechanically straightforward.
I'm also aphantasia and never considered that people would do blackboard math visibly in their head. I, like you, use verbal memory to store numbers. But I've never been particularly good at doing math in my head. At the same time, I can map 47*68 into a rectangle and either add and subtract slivers to get the right answer, all without seeing it.
Something else which blew my mind, people who use image search preferentially to everything. Ironically the only time I use image search (unless I'm trying to find an image) is when I want a graph or tabular data.
My mental method is not quite FOIL, for what it's worth. I distribute over one of the numbers -- so 47 * 68 = 47 * 60 + 47 * 8, and then compute the compute those (2400 + 420 = 2820). Then I grab additional terms: 2820 + 40 * 8 = 3140. 3140 + 7 * 8 = 3196
Among other things this scales better to larger numbers. I use it because it's more 'linear' -- I only need to remember one accumulated number at a time.
I've surveyed a lot of people on this - probably forty or so in person, plus another 100 or so in a poll on reddit once - and there's a pretty clear trend: people who perform the visual algorithm tend to be 'not math people', and are less accurate and less confident in their answer, or not even willing to try.
I'm aphantasiac and I can do a calculation like that fairly quickly and accurately, without any special practice. I basically use my verbal memory to store and recall cached computations instead of any visualization. My theory is that the visual brain is not really designed for storing precise information so much as the gestalt of an image, so it does less well on precise numeric details.