Matrices can be your friends (2002)

"In Experiment 2 we have shown that people with aphantasia report higher AQ scores (more traits associated with autism than controls), and fall more often within the range suggestive of autism (≥32)."

https://www.sciencedirect.com/science/article/abs/pii/S10538...

> Anyone who has taken linear algebra should know that [...]

My university level linear algebra class didn't touch practical applications at all, which was frustrating to me because I knew that it could be very useful to some background doing hobbyist game dev. I still wish I had a better understanding of the use cases for things like eigenvectors/values.

I took a linear algebra class, as well as many others. It didn't work.

Most math classes I've taken granted me some kind of intuition for the subject material. Like I could understand the concept independent from the name of the thing.

In linear algebra, it was all a series of arbitrary facts without reason for existing. I memorized them for the final exam, and probably forgot them all the next day, as they weren't attached to anything in my mind.

"The inverse of the eigen-something is the determinant of the abelian".

It was just a list of facts like this to memorize by rote.

I passed the class with a decent grade I think. But I really understood nothing. At this point, I can't remember how to multiply matrices. Specifically do the rows go with the columns or do the columns go with the rows?

I don't know if there's something about linear algebra or I just didn't connect with the instructor. But I've taken a lot of other math classes, and usually been able to understand the subject material readily. Maybe linear algebra is different. It was completely impenetrable for me.

For my fellow visual thinkers who might be looking for a linear algebra book that focuses more on developing the geometric intuition for stuff like this, rather than just pure numeric linear system solving, let me recommend:

"Practical Linear Algebra: A Geometry Toolbox" by Farin and Hansford.

> Is your "wandering" of this sort of pseudo-visual nature, or do you see actual visual images that could be drawn?

They're like if the abstract machines you talk about in CS theory classes were physical objects.

For example, thinking about a data processing pipeline, I might see the different components performing transformations on messages flowing through it. I can focus on one component and think about how it take apart the message to extract the structure it's trying to manipulate, interacts with its local state, etc. If something is active and stateful it feels different than if it's just a plain piece of data. I run the machine through its motions to understand where the complexity is and where things could break, comparing different designs against each other.

I'm thinking about a data format, I think about the relationships between containers, headers, offsets between structures, etc, like pieces that I can move around to see how their relationships change and understand how it would work in practice.

It's more than an image that can be drawn because the pieces are in motion as they operate. It's the same kind of "material" that mathematical objects are made out of when I'm thinking about abstract math. It's immensely useful skill for doing my job, in designing systems.

I actually struggle a lot with translating the systems in my head into prose. To me, certain design decisions are completely obvious and wouldn't need to be stated, so when we all understand the product goals I often to neglect to explain why a certain thing works the way it does, because to me it's completely obvious how it's useful towards achieving the product goals. So that's something I have to actively put more effort into.

I also really struggled when I took a real linear algebra class, since it was taught in a very blackboardy "tabular" style which was harder for me to visualize. I was unfamiliar with it due to being used to thinking about matrices in the context of computer graphics and game engines.