I wish I had a proper write-up of this project, but I tried to make something like this in college once. I wanted to make a thing where you could type a word and then letters would move to spell that word. I didn't accomplish that fully, but managed to just get the "moving" functionality sort of working. Let's see what I remember about it...
For the board: I just used a large magnetic whiteboard in a classroom.
For the pieces: I made alphabet letters, kinda like scrabble tiles but ~3x3 inches each, with magnets so that they could stick to the whiteboard.
For moving the pieces: I followed various online tutorials (I forgot which) to make an XY plotter, kinda like this:
I used two stepper motors that were somehow attached to the whiteboard using suction cups.
However, instead of moving around a pen that would draw stuff, my XY plotter moved around an electromagnet. This was all controlled by an Arduino and keyboard. So the user could move the electromagnet, turn on the electromagnet to pick up a letter tile, move the letter, and turn off the electromagnet to disengage.
Of course, none of this worked perfectly, but I still learned a ton, and maybe gives you some inspiration!
genuine question because I've never heard this phrase, and search engines did not yield useful results: what do you mean by "east coast school of thought"? and then is there a corresponding "west coast school of thought"?
I will admit I was briefly even more confused reading that the "west coast" model includes New Jersey (an east coast state) and the "east coast" model includes Stanford (a west coast university)... but whatever lol.
I recommend The Manga Guide to Linear Algebra! I read it the summer before college and their visuals and analogies really helped me grasp basic concepts.
I disagree. I personally found that one to be a poorly written "Manga Guide". (Manga Guide to SQL was a good one, but there really weren't as many good analogies for Linear Algebra).
A lot of the "examples" were "This is complicated and abstract, so we'll just say it is and go to textbook form".
I am indeed here posting my original question after first trying the Manga Guide to Linear Algebra and finding it was not what I was looking for. Where I wanted visual explanation they went to textbook definitions, not helpful. A few illustrations in the book I did think were valuable so it wasn't a total loss.
LA is about vectors and rotations and stretches of vectors, which is what happens when you multiply a vector by a matrix. That’s what you will be visualizing.
Try the Kahn videos, then watch the 3B1B videos, which are very visual, but somewhat advanced. Or, watch both of them several times in parallel.
This is why I asked "what field are you learning Linear Algebra?".
Elsewhere, I've discovered that this poster is going into image processing, which is likely "signals and systems" linear algebra.
In signals and systems, your vectors can have infinite dimension, and these infinite-dimension vectors Fourier-transform into other infinite dimension vectors under a new basis.
Any field with more than "3 dimension" vectors / matricies is very difficult to visualize geometrically. Trying to do so is counter-productive to the understanding of the field. This geometric interpretation is really useful in graphics programming / 3d animation however.
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Or perhaps a more concrete example... your "visualize the matrix in X dimensions" advice just doesn't cut it if you're dealing with an 8x8 matrix JPEG DCT coefficient matrix (https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform), unless you can imagine 8-diemsional space in your brain.
On the other hand, imagining the 8x8 matrix as 64 linearly-independent "Basis" to your 64-dimension discrete signal is... easier. (Well... for a definition of easier at least). And the transform from time domain into Fourier domain is a transformation in basis that contains the same information.
Are you trying to learn to use Figma specifically? I think you can just pick it up and start using it pretty easily. Good design principles are ultimately tool-agnostic though.
- The Design of Everyday Things by Don Norman is the classic for learning design.
- Don't Make Me Think by Steve Krug is another classic, and very digestible.
Ultimately, good design is informed by research - what is the problem you're trying to solve? What is the user's goal and how can you make that easy for them to achieve? What are you trying to communicate? Start with interviewing 5+ potential users, distilling that data into actionable opportunities, and sketching wireframes on paper before jumping into Figma.
Don't Make Me Think is a great book. Even though the example screenshots are from the early 2000s, the principles still apply. I recommend that book to all of my engineers.
However, I recently read The Design of Everyday Things and was really disappointed. The sections about door handles, stoves, and elevator buttons are interesting but that's only 1/3 of the book. The rest is about iterative design and system failure, for which there are better books like The Lean Startup and Drift Into Failure.
For the board: I just used a large magnetic whiteboard in a classroom.
For the pieces: I made alphabet letters, kinda like scrabble tiles but ~3x3 inches each, with magnets so that they could stick to the whiteboard.
For moving the pieces: I followed various online tutorials (I forgot which) to make an XY plotter, kinda like this:
https://www.instructables.com/XY-Plotter-Drawing-Robot-Ardui...
I used two stepper motors that were somehow attached to the whiteboard using suction cups.
However, instead of moving around a pen that would draw stuff, my XY plotter moved around an electromagnet. This was all controlled by an Arduino and keyboard. So the user could move the electromagnet, turn on the electromagnet to pick up a letter tile, move the letter, and turn off the electromagnet to disengage.
Of course, none of this worked perfectly, but I still learned a ton, and maybe gives you some inspiration!