Say you have two distinct points x and y. Consider all points whose distance to x is the same as to y. What can you say about the location of these points in terms of the line connecting x and y?
Try to solve any geometry puzzle with only your mind and you will be forced to do visual thinking.
I’ve never seen any image of any kind in my mind, nor have I experienced any other imagined sense. Visual thinking is merely activity within a region of the brain associated with a visual experience. If you were to shoot a charged particle through your occipital lobe, you may experience it as a flash of light. Those with aphantasia process thought in a different region of the brain that is not associated with the experience of visualization.
Where that thought takes place will determine the structure and connections within the neural network that processes that information. Most complex neural networks can solve any basic problem, but some structures are more efficient, more accurate, or faster than others. When thought occurs in an atypical structure it can give rise to deficits or strengths. Synesthesia is a common example, but there are also examples of people with “human calculator” like abilities and more.
When you say visual thinking, visualization is merely an experience and is not necessary to solve multidimensional problems. It is however a very fast and efficient method to do so. Studies which have compared the problem solving abilities of those with aphanatasia and visual thinkers found that those who relied on visualization were faster, but less accurate problem solvers. I’m not a fast problem solver, but I virtually always get the right answer because I solve problems with logic rather than visual intuition.
This is not visual thinking when you can not use your visual brain. From my perspective, it’s just “thinking”.
So I find I can force myself to visualise that but it would be consistently born of the concept thought first, like “oh that’s a line perpendicular to the line between X and y” and then I can paint the graph in my mind. But I don’t need to—I can think the concept and then apply it to paper without visualisation and I tend to find that easier.
What intrigues me precisely is visual thinking for problem solving—ie a student who can easily perform arithmetic between graphs by visualising the transformations in their mind rather than doing calculations on paper.
First of all, if you can solve it without visualization, I think that this is preferable, precisely because it is faster. There is no need to force oneself to visualize everything.
To visualize something, you need to create a map from the formal domain you are studying to visual transformations. In other words, you need to understand “what the formula” mean (or at least one way of looking at them). Do you know what it means visually to multiply one complex number to another? If you don’t, you will be stuck doing calculations. If you do, then you can visualize it and quickly come up with the solution.
From my experience, some people naturally tend towards visual thinking, while others don’t. But if you consistently try to apply it, it will become natural at some point (it may take some time, don’t give up prematurely).
One area where a lot of visual thinking is necessary, but that is relatively easy to visualize, is graph theory. Try to prove that a (connected undirected) graph has an Eulerian cycle (i.e. a cycle that contains every edge exactly once) if and only if all of its vertices have even degree.
Say you have two distinct points x and y. Consider all points whose distance to x is the same as to y. What can you say about the location of these points in terms of the line connecting x and y?
Try to solve any geometry puzzle with only your mind and you will be forced to do visual thinking.
I’ve never seen any image of any kind in my mind, nor have I experienced any other imagined sense. Visual thinking is merely activity within a region of the brain associated with a visual experience. If you were to shoot a charged particle through your occipital lobe, you may experience it as a flash of light. Those with aphantasia process thought in a different region of the brain that is not associated with the experience of visualization.
Where that thought takes place will determine the structure and connections within the neural network that processes that information. Most complex neural networks can solve any basic problem, but some structures are more efficient, more accurate, or faster than others. When thought occurs in an atypical structure it can give rise to deficits or strengths. Synesthesia is a common example, but there are also examples of people with “human calculator” like abilities and more.
When you say visual thinking, visualization is merely an experience and is not necessary to solve multidimensional problems. It is however a very fast and efficient method to do so. Studies which have compared the problem solving abilities of those with aphanatasia and visual thinkers found that those who relied on visualization were faster, but less accurate problem solvers. I’m not a fast problem solver, but I virtually always get the right answer because I solve problems with logic rather than visual intuition.
This is not visual thinking when you can not use your visual brain. From my perspective, it’s just “thinking”.
So I find I can force myself to visualise that but it would be consistently born of the concept thought first, like “oh that’s a line perpendicular to the line between X and y” and then I can paint the graph in my mind. But I don’t need to—I can think the concept and then apply it to paper without visualisation and I tend to find that easier.
What intrigues me precisely is visual thinking for problem solving—ie a student who can easily perform arithmetic between graphs by visualising the transformations in their mind rather than doing calculations on paper.
First of all, if you can solve it without visualization, I think that this is preferable, precisely because it is faster. There is no need to force oneself to visualize everything.
To visualize something, you need to create a map from the formal domain you are studying to visual transformations. In other words, you need to understand “what the formula” mean (or at least one way of looking at them). Do you know what it means visually to multiply one complex number to another? If you don’t, you will be stuck doing calculations. If you do, then you can visualize it and quickly come up with the solution.
From my experience, some people naturally tend towards visual thinking, while others don’t. But if you consistently try to apply it, it will become natural at some point (it may take some time, don’t give up prematurely).
One area where a lot of visual thinking is necessary, but that is relatively easy to visualize, is graph theory. Try to prove that a (connected undirected) graph has an Eulerian cycle (i.e. a cycle that contains every edge exactly once) if and only if all of its vertices have even degree.