Cool—that makes sense! Thanks.

I've been thinking a little more about how the space of software engineering knowledge might be structured though, and one thing I'm betting is that it wouldn't be an N-ball, but instead some complex sponge looking thing (because the extent of software engineering knowledge isn't equidistant in all directions/aspects). Ordinarily I'd think the N-ball would be fine to use as an idealization, but since the hypercube behaves so differently, I bet the idealization would end up changing the character of the situation.

I'm also trying to consider what the analogy of a plane would be in software engineering knowledge. Let's say it's on two dimensions: X and Y; and let's say X is knowledge relating to text editor usage, and Y is knowledge about unit testing. It seems like the XY plane is mostly full of empty space, since most facts (single points) from either field are unrelated to the other. So, if we have a pure text editor fact X=5,Y=0 —what legitimate fact might exist at X=5,Y=1? It would have to be some single, constant piece of text editor knowledge which meaningfully combines with a unit testing fact. There may be some points in this plane on the line X=5 which are valid, but since all unit testing facts don't have a meaningful connection to text editing, there will be gaps.

Additionally, it seems like the way you'd navigate the space would be different than walking a single contiguous path. Some of our knowledge is map-like and can help give at least sketchy knowledge of the boundaries of the field without walking to them step by step. And some facts are dependent on knowing other first so that you have 'pass through' in a particular order, but a lot of the facts about a single subject are still unordered, so you would be doing a lot of teleporting.

Just for amusement, here's another idea for an alternate way of spatially structuring knowledge: each general principle is some high dimensional object of its own; each axis corresponds to a parameter to the general principle. So you have a general structures like: ProgrammingLanguage(syntax, semantics, runtime, standard_library) —each of the parameters is a different axis, and you always get a meaningful ProgrammingLanguage back if you change to a different position on some axis (seems like this structure is recursive though since each of the parameters could be a general principle itself, so I guess these objects are nested?).

When you learn things you are jumping around between these non-intersecting objects (which are even in differently structured spaces) without realizing, until you inductively discover these general principles/categories. Additionally, the speed with which you move around inside an object increases dramatically once you acquire knowledge of its general structure (since learning new facts which are just different instantiations of already known general facts is easier for us).

I wonder if there is some kind of 'meta-space' that would be useful for describing the relationships between all these objects which exist in spaces of different dimensions. Also not sure about the geometric significance of the 'general principle objects' being recursive...

Edit: seems like the recursive/nested 'sub-objects' would just be lower dimensional slices of the whole higher dimensional 'general principle object'...