Shout-out to the authors for releasing their code

I speak on behalf of all the people out there that would indeed have trouble reading it, as they didn’t even reference the simple concept of a map, where such studies originated in the first place.

Because it’s a research paper, not a textbook on graph theory.

They exclusively use complicated terms like ‘planar graph’

A planar graph is (loosely) a graph that can be drawn on a single sheet of paper without intersecting the branches. Not very complicated. More importantly, you can find these definitions in any graph theory textbook.

If you would like to read a textbook on graph theory, I highly recommend A First Course on Graph Theory by Gary Chartrand and Ping Zhang. It’s a Dover book (cheap), and it’s available on LibGen. You will notice that their textbook is printed in black and white, yet their explanation of the Coloring Problem is quite crisp regardless.

Sometimes simple minded people like to learn as well, so why no reference to a simple map?

Because people who have no background in graph theory are simply not the audience for this paper.

Are you stupid or something?

Nah you Dunning-Kruger ass buffoon, I was trying to be helpful, in particular to show people who don’t know shit about graph theory that it is no longer inaccessible knowledge. You clearly need to reread whatever graph theory book you have if you seriously think that planar graphs need to be explained in a research paper or that the Coloring Problem needs to be illustrated with literal colors.

Also, you said you’re familiar with topology. Topology and graph theory are related but distinct subjects! In topological graph theory, the topology is an additional structure imposed upon a graph. So knowledge about topology is mostly irrelevant for graph theory, except for topological graph theory results.

A dimension is a measurement, by basic definition.

Nope. It’s a historical accident (and mistake IMO) that (mathematical) dimension and physical dimension have the same word “dimension”.

For example, in dynamical systems, we often work with so-called non-dimensionalized systems, i.e. we multiply the equations by the reciprocal of the physical dimension and end up with a system of unitless equations. This system may then be a N-dimensional system of unitless equations, i.e. you have N scalar equations.

Edit: Fuckit, I just realized that Fahrenheit and Celsius are both the same dimension, just with a different scalar and constant offset. Not much different with Kelvin…

Basically correct. Fahrenheit, Celsius, and Kelvin are all different units of the same dimensioned quantity, namely temperature.

Because it’s a completely different algorithm. Intuitively: graph theory algorithms can get very complicated because you work with very large but finite objects, so combinational algorithms enter the party.

Because sometimes there is no intuitive visualization, or the visualization may even be deceptive. E.g. … the Coloring Problem is not literally about colors. It’s not even about maps. It’s about the abstraction itself. It’s about the math.

except for the people that don’t understand multiple dimensions…

…which is most people, actually. So you’re kinda making the case against having a figure, because you would have to project your 5D object onto a 2D space, where both topology and graph theory simplify dramatically. Topological graph theory can tell us that there exist graphs with topologies that cannot be embedded into 2D or even 3D space without intersections, meaning you would have to make some sacrifices to draw these graphs within your framework.

But that’s not even how it works. If you allow for intersections, you can always draw a graph on a piece of paper. Which they do.

Every gamer in the world is already processing in 6 dimensional visual memory space.

Nah, by your logic, they’re processing in much higher dimensions, one for each cone cell. But your brain processes these sensors into a two-dimensional spatial image that varies with time. (When a signal processing system performs this, we call it sensor fusion. And in fact, machine learning is a huge part of sensor fusion.) But even then, gamers aren’t just responding to the visual stimuli, but they’re tracking the abstractions of the game, such as players, enemies, terrain, etc. And then the physics engine inside a modern game typically implements either 2D or 3D space, plus time. And then the configuration space of all the objects a gamer needs to track adds dimensions.

But these high-dimensional objects…they really have structure that enables us to split them into groups of 1, 2, or 3. That’s not necessarily a helpful move for high-dimensional spaces in general.

Like I’m not saying that you literally never can or should visualize high-dimensional objects, e.g. in Hilbert spaces a lot of plane and 3D geometry intuition survives, but some situations are just not amenable to visual learning. (Conversely, of course, some situations require visual learning. But it’s important to be able to use all learning styles to some extent.)

Unironically yes.

So when I did my undergraduate math courses…yeah, those books and assignments were locked behind digital subscriptions, so I cannot access them anymore. I think the reason is that these systems do automatic grading of homework, so they don’t have to hire as many graders. And then for the books, they probably (correctly) assume they’re on LibGen or at the library. where they won’t need to use the ma

But advanced undergraduate and graduate level books can usually be bought like ordinary books…or borrowed from a shadow library (make sure you’re running uBlock Origin).

In fact, some authors even give out their books for free, and most authors are willing to send you an electronic copy if you ask. Authors make exactly $0 per sale.

Also the fuck you mean AI slop? The book I recommended (Chartrand and Zhang) predates AI.

I am literally an electrical engineering PhD student. I literally took a course on sensors last year. I know how compasses work. I did not mean to imply that compass sensors are AI sensors (whatever that means).

I’m acknowledging that your experience of people being mean to you for being right, while frustrating, is irrelevant to draw any conclusions about the book I recommended.

but they treat me like shit, as if I don’t know what a fucking compass sensor is…

I’m sorry that’s happening to you, but that’s completely irrelevant. The book I recommended predates AI, so it cannot be AI slop.