How can I improve my ability to visualize mathematics?

[Mulz]

Hello everyone!

I am having difficulties interpreting mathematical phenomenons visually speaking. I am trying to create an image in my head to explain how the mathematics works, for example, I have tried explaining the term brightness with close results but still flaws.

So how do you become better at "seeing" mathematics? I really want to, do I just draw pictures of it? Where do I even begin in that case? Also, I have severe spatial problems (being very low compared to the average, I can not manipulate objects in my head, only to a certain degree with lots of difficulties), is that maybe why it is harder for me to work on it?

I prefer people that are good at this to explain, or who has been in a similar situation as I am in.

 

[PeroK]

I usually grip the top of my head with both hands, lean forward, put my elbows on the desk, screw my eyes shut and think until my brain hurts!

 

[symbolipoint]

Hello everyone!

I am having difficulties interpreting mathematical phenomenons visually speaking. I am trying to create an image in my head to explain how the mathematics works, for example, I have tried explaining the term brightness with close results but still flaws.

So how do you become better at "seeing" mathematics? I really want to, do I just draw pictures of it? Where do I even begin in that case? Also, I have severe spatial problems (being very low compared to the average, I can not manipulate objects in my head, only to a certain degree with lots of difficulties), is that maybe why it is harder for me to work on it?

I prefer people that are good at this to explain, or who has been in a similar situation as I am in.

Using different wording, the same question has recently been discussed:
https://www.physicsforums.com/posts/4893975/

Being able to manipulate 3-d images all in ones head is an unusual ability, which is why most people construct, form, build models.

 

[homeomorphic]

Practice visualizing whatever you can. It's like lifting weights. You do what you can and progressively give yourself more difficult challenges. You might start out by just visualizing a dot moving around in 2-d, then maybe make it a line. You can get pretty far with just 2-d pictures.

I used to keep trying to visualize things over and over again and eventually I got to the point where I didn't need to practice that much to understand new results, although in certain cases, finding a visual interpretation of some particular things might be a pretty challenging problem that could take a lot of thought. Part of it is carefully choosing exactly what to visualize, so that you don't strain your imagination beyond its limits, so part of the skill is actually learning to work within your limitations and still be able to comprehend things. I was naturally fairly good at visual thinking, but I can say it still took a lot of practice. Studying electromagnetism and reading Visual Complex Analysis and trying to visualize all the arguments in it played a big part. Sometimes, you can even bring in other things besides the visual. For example, in differential geometry, one of my tricks to boost my intuition is to make a certain configuration (a frame of vectors) with my hand and move it around, so I add a kinesthetic sense of how it works. External aids like props, drawings, the diagrams found in textbooks, and computer visualizations can also help. I intend for my next big hobby which I haven't really started on to be using a computer to make mathematical visualizations.

I'm also an artist and used to fold a lot of origami, and it's conceivable that there was some transfer from that. I'm also an amateur pianist (started at age 12), which could have some effect, but I'm only aware of data to this effect for younger children:

http://faculty.washington.edu/demorest/rauscher.pdf

http://www.ncbi.nlm.nih.gov/pubmed/10100200

In general, a thing to watch out for is practicing a certain skill tends not to generalize that much, but there are some striking exceptions to that, such as that study. I'm not sure this means adults should all go and take piano lessons, but it appears to be a good idea for younger children, at least. If you did it with 1st graders, rather than preschoolers, I'm sure there wouldn't be too much difference, but I don't know at what age it will start to be less beneficial.

 

[CellCoree]

I can understand your struggle with visualizing mathematical concepts. It is important to remember that not everyone learns in the same way, and some people may have a harder time visualizing abstract concepts. However, there are some techniques that can help you improve your ability to "see" mathematics.

One approach is to use diagrams and visual aids to represent mathematical concepts. This can help you to better understand and remember the relationships between different elements in a mathematical problem. You can also try drawing pictures or diagrams to represent the problem and its solution. This can help you to visualize the steps and logic involved in solving the problem.

Another helpful technique is to practice visualizing mathematical concepts in your mind. This may take some time and effort, but with practice, you can improve your ability to manipulate objects and visualize them in your mind. You can start with simple problems and gradually work your way up to more complex ones.

It is also important to remember that mathematical visualization is a skill that can be developed and improved over time. So don't get discouraged if you don't see immediate results. Keep practicing and seeking out resources and techniques that work best for you.

Lastly, it is possible that your spatial difficulties may make it harder for you to visualize mathematical concepts. In this case, it may be helpful to work with a tutor or seek out additional resources that cater to your specific needs. Don't be afraid to ask for help and find support from others who have been in a similar situation.

In conclusion, while some people may have a natural ability to visualize mathematics, it is a skill that can be learned and improved upon with practice and the right techniques. Don't give up and keep exploring different methods until you find what works best for you.