I’m not sure what my brain is doing when it thinks about analysis but I’m not convinced it’s visuospatial.
More concretely, let’s suppose I’m trying to analyze the asymptotic behavior of some function which is a sum of terms that have different growth rates, say f(x)=1x+ex. What I could be doing, if I were doing this visually, is visualizing the the asymptotic behavior of ex (“grows fast as x gets big”) as a curve that curves up really fast, and similarly for 1x (“grows fast as x gets small, goes to zero as x gets big”) as a curve that starts big and gets small.
But I think that’s not what I’m actually doing first, although that is a mode of thought I can use and find helpful. I think I am actually working with something like a primitive felt sense of bigness and smallness, which is not about visual tallness (to triangulate, another metaphor for bigness that isn’t visual is weight: ex gets “heavy” and 1x gets “light”). Not sure though, because the visual thought also happens pretty quickly after this and everything is correlated (heavy things are large in my visual field, etc.).
I’m not sure what my brain is doing when it thinks about analysis but I’m not convinced it’s visuospatial.
More concretely, let’s suppose I’m trying to analyze the asymptotic behavior of some function which is a sum of terms that have different growth rates, say f(x)=1x+ex. What I could be doing, if I were doing this visually, is visualizing the the asymptotic behavior of ex (“grows fast as x gets big”) as a curve that curves up really fast, and similarly for 1x (“grows fast as x gets small, goes to zero as x gets big”) as a curve that starts big and gets small.
But I think that’s not what I’m actually doing first, although that is a mode of thought I can use and find helpful. I think I am actually working with something like a primitive felt sense of bigness and smallness, which is not about visual tallness (to triangulate, another metaphor for bigness that isn’t visual is weight: ex gets “heavy” and 1x gets “light”). Not sure though, because the visual thought also happens pretty quickly after this and everything is correlated (heavy things are large in my visual field, etc.).