I'm surprised the author depends on a single visual model for numbers. To provide another data point, my ordinal numbers are brightly colored (maybe an associat

I'm surprised the author depends on a single visual model for numbers. To provide another data point, my ordinal numbers are brightly colored (maybe an association with award ribbons I'd get in elementary school); cardinals with no extra structure are specific clusters of bluish cubes (8 is 2x2x2); when ring structure shows up, they're malleable grids (maybe because the distributive law's self similarity made learning the times table easier); for just multiplication, colored lights in a poset (so L-function identities "look like" intricate lattices of Christmas lights). For general groups, not much: I just feel like I'm playing a board game. It's hard to imagine having only one instinctive visualization for integers.