It also feels like you’re asking something like, “what’s the most important problem you are trying to solve by having visual perception?” It’s kind of just how I navigate the world at all (atoms or math).
But let me take your question at face value and try to answer it.
I think the main answer is something like “semantics”. So much of my experiential knowledge is encoded in this physical, 3D physics manner, and when I can match up a symbolic expression with a physical scenario, I get a whole bunch of understanding for free. So it at least makes many of the “computations” far faster.
I also use it as a working memory scratchpad. If I’m trying to multiply two numbers, I often come up with a way to FOIL them, and then I hold all four of those terms in a visual space in my mind. As I calculate, I replace terms with their new values.
(There’s probably more, but that’s what I got from the first attempt at introspection.)
The first math problem I created was spawned from a visualization on a rare occasion smoking marijuana. I started imagining cubes falling from the sky, and just observing this process. I got curious about the chance of one cube landing on top of another. This led to the problem:
Given a square boundary of size B, place squares of side length S one at a time completely inside of the boundary at random locations. How many squares on average will you place before a pair of squares overlaps?
What’s the most important problem you are trying to solve by visualizing?
Heh, well, see the aforementioned
It also feels like you’re asking something like, “what’s the most important problem you are trying to solve by having visual perception?” It’s kind of just how I navigate the world at all (atoms or math).
But let me take your question at face value and try to answer it.
I think the main answer is something like “semantics”. So much of my experiential knowledge is encoded in this physical, 3D physics manner, and when I can match up a symbolic expression with a physical scenario, I get a whole bunch of understanding for free. So it at least makes many of the “computations” far faster.
I also use it as a working memory scratchpad. If I’m trying to multiply two numbers, I often come up with a way to FOIL them, and then I hold all four of those terms in a visual space in my mind. As I calculate, I replace terms with their new values.
(There’s probably more, but that’s what I got from the first attempt at introspection.)
The first math problem I created was spawned from a visualization on a rare occasion smoking marijuana. I started imagining cubes falling from the sky, and just observing this process. I got curious about the chance of one cube landing on top of another. This led to the problem:
Given a square boundary of size B, place squares of side length S one at a time completely inside of the boundary at random locations. How many squares on average will you place before a pair of squares overlaps?