Don't give up!!! It's definitely hard and takes time, but it's still possible!

what's really annoying to me is that I fully understand it conceptually, it's just impossible for me to visualize. it feels like I'm so close and yet I just can't do it.

@@thezipcreator Yeah that's pretty much my situation, too. I probably can't say I fully understand everything about it right now, but I can tell that even if/when I do I will still never be able to visualize what's "actually going on." It sounds kind of obvious, but it's that impossibility to visualize it that makes it really seem like I'll never _truly_ be able to understand it, which don't get me wrong is perfectly fine, but it is a little irritating...

@@thezipcreator and this is precisely why mathematics is useful, when you can't just tell what's going on, but you can calculate it.

Yeah I’m with you. I’ve tried to grasp just non-Euclidean geometry for a good while and.. water off a duck. But it’s great to have stuff like this keeping me humble, at least. Lots of reminders that I don’t know shit, and not everything is within my grasp.

Simulating it is much easier than understanding it. The math is simple.

It's not the math or simulation that's difficult, it's trying to force a graphics system that was designed for triangles to work with 4D structures and have it be efficient and fast enough for most hardware. There's a lot of crazy tricks for that, you'll see in the next Devlog.

@@CodeParade Really excited to see how you construct the meshes!

@@kinoko384 My guess is that instead of triangles it is tetrahedrons of varying shapes that then form the surface of 4d polygons

@@CodeParade that’s what I’m worried about. Adding volume is killer on any CPU

I mean, idk how 2D people can represent or visualize 3D, all they see is lines 💀

@Пётр Бойков it would look similar to us. Weird morphing 3d shapes, and for them it would be weird morphing 2d shapes

@@why_oh_elle they can take snapshots of the 3d project passing through and then compile them to get a loose understanding of what the 3d object looks like in 2d

If we could see all of 3d space at once and inside things then we might have a shot

You can't intuitively understand it, but you can understand the mathematical theory behind it and then apply that theory meticulously to an idealized graphical simulation. You can never manifest or interact with a 4d object in 4 dimensions, you can never ever see it or picture it in your head in its entirety, but you can maybe memorize what a sequence of projections along a 3d plane of some 4d object looked like, so you can know the object again when you see a very similar set of projections. This would enable you to, with a lot of training, play simple games like 4d golf. But you will never be able to "rotate a 4d cow in your head." And the flatlanders would never be able to rotate a 3d cow in their head like we can, either. (Sorry to the aphantasia folks out there, but hey the good news is that you have a bunch of comrades in the mental cow rotation problem among all the flatlanders now!)

Key is analogy ,reverse engineering and emergence . I'm trying to solve the exhaustive enumeration of order 3 magic hypercubes and find a general formula for the dth case. Problem scales up exponentially past 4d and it becomes a great CS problem. At that level I often have absolutely no idea about the visualization part but while proceeding logically along abstract routes ,all the emergent mathematics gets to be pretty interesting and i even get the pseudo feeling that I am conquering higher dimensions. Discover ur particular higher dimensional niche and who knows, u might end up in awe of ur own creations ,even while ur completely baffled. At one level its like how so many Ai developments are blackbox for Ai researchers themselves. But that doesnt prevent them from doing all the back end coding.

Actually i'm pretty sure its easier to code, since its just math, what would really be harder would be to debug or even notice bugs

​@@elnico5623How would you know it's being represented correctly if you don't have a good grasp on 4d?

@@mgord9518 that's what i said

😭 send help

Totally agree. Helped me see 4D in a new context. Including solid Klein bottles and double rotations.

It's the exact same thing, he just elaborated on further details

i find the flatland one confusing and it doesn't really help me understand it, but this explanation was really helpful and now i actually understand 4d. Especially the view mode where you can swap y with w, it made me actually understand it a lot

It's so great because after making that realization, you go back and think about rotations in 2D and realize that it was so obvious all along because it's not like you pick an axis in 2D to rotate around, you pick a plane which just so happens to be the only plane.

There is actually a sense in which an axis is more helpful, and it's with regards to parallel rotations. Rotations don't just need a plane to be fully defined, but also a point on that plane to be rotated around. In normal linear algebra, everything has to pass through the origin, so there's an implied center, but the moment you want to move off the origin, things break. Axes not only have a direction perpendicular to the plane of rotation, but more crucially specify the center of rotation. The trade-off is accepting that "axis" doesn't mean "line." An axis could just as easily be a point in 2D, or, mind-bendingly, a plane in 4D. In 3D projective geometry, axes technically _are_ planes that are just rendered as lines where they cut the projective plane. This is related to why it only takes 4 numbers to define a plane in 3D, but 6 to define a line.

Hmm, does that generalize to 5D+? Or is it rather that you're always rotating about an axis, but what "axis" means depends on the dimension? So in 2D you rotate about a point, in 3D you rotate about a line, in 4D about a plane, etc.?

@@fatcerberus Correct! Technically they don't need to be straight lines/etc, but the axes of rotation in ND are always N-2 D surfaces.

​@@angeldude101 It works because the 'point' that becomes the origin of that plane is the intersection point of the (N-2)-space and the complement plane, but you might as well just specify that point instead of increasing the 'complexity' of the model. But in 3D & 4D a line/plane happens to be 'less complicated' than a plane-point pair (although a plane-point in 3D has the same number of parameters as a line in 3D) and in 3D lets you identify a basis of (eulerian) rotations with a basis of the space, in 2D the plane can always be implied so we still end up specifying just a point in either method. So I'd say for more than 4 dimensions it's more natural to use a plane-point pair, and it's really a choice in lower than 4 dimensions, but to be the most 'general' and consistent to higher dimensions when dealing with lower dimensions I'd still argue for plane-point pairs. Especially since this way we have a natural correspondence between rotations and 2D affine subspaces which promotes a decomposition into things we have a better shot at visualising even in more general settings. But I do see the advantage specifically for 4D that complement planes can describe rotations better than plane-point pairs.

The way I like to think about it is that there are different types of "volume". 2d shapes have area, which is just what volume is but in 2d, but they don't have 3d volume. similarly 3d shapes have volume, but they do not have the 4d equivalent to volume, and so on and so forth.

3D volume sort of becomes “hyperarea” when you are in 4D

2:52 so this means your could draw 3D objects on 4D paper? ….This is wild to think about 🤯

…now thinking about 3D “flip flap” books, changing various parts of a 3D shape on a page by flipping part of a 4D page😵‍💫🤯 please let me know if this is how this works…

@@CaptainWizard3000 yes, thats definitely something you could do, although you would need 4d eyes to truly appreciate it.

"But Marty, you're not thinking forth dimensionally!" The real reason the masses think time is the 4th dimension.

Time looks like a fourth dimension as long as it only has one direction, like if "up" didnt exist and there was only "down"

yeah, it doesn't make sense since time does exist in lower dimensions

Actually, is a misunderstanding to think that time is the fourth dimension. What we consider the fourth dimension is the product of time times the speed of light: tc, and it has the correct units.

I think it's fine, but it depends on what you're going for. You can very much so visualize time as a fourth spatial dimension, you just have to keep in mind certain oddities. And also acknowledge that 4D doesn't inherently mean time, just as 3D doesn't inherently mean space. Most videos on KZfaq are 3D if you are including the time dimension and even can play around with the video in an odd way as a result. I think it's a neat way to visualize things and is technically accurate, but is overgeneralized

Not 1 more rotation, 3 more rotations.

One view could be up in the corner like a minimap, being able to swap between them at will Though that'd probably mean you'd need twice the processing power to display both at the same time

I wonder if you could get used to processing each image in each eye? You can kind of do that for sound - you can play a different sound in each ear to compare them - but I don't see many people doing that for visuals besides just normal depth perception. Maybe it could be possible to develop a secondary way to process visual data?

@@circuitgamer7759 not too relevant, but this just reminded me of this color experiment i've seen before, where an object is displayed with different colors to each eye (ex. Red in the left, blue in the right). Intuitively, you expect your brain to merge the two images together and make the object one color (purple) but no, the object is instead seen as both red and blue at the same time. Kinda trippy!

@@preferablygeneric yeah i got this nonfiction book with 3d glasses and i also got that effect with the red and blue side, it looks kind of like when two textures overlap in a video game

It may also be possible to overlay the two views so the vertical direction is both Z *and* W

yep!

you seriously abbreviate codeparade to that?

@@kakyoindonut3213 That's the obvious abbreviation. It's the words code & parade & C & P are the first letters.

@@Mo_Mauve do you know what else called cp?

@@kakyoindonut3213 Club Penguin :)

@@doplop my god don't remind me of the time I would search cp online to get to club penguin

The game comes with a level editor, so you'll be able to do it yourself too!

@@CodeParade wish we could get an in-game hyperbolica editor, best we could get was a 4d editor

@@CodeParade A 4D level editor? Now this is something I never seen before.

How to explode your brain

probably idk im not codeparade

How could you look around in 4d?

There appear to be plans from the dev to add VR support some time later after the release

Yeah, for me comprehension of the double rotation could have been helped by more examples like this

Well, for biology-related stuff the # of dimensions matters a whole lot, especially in regards to the scaling laws they follow. 3D life uses powers of 4 because it runs in 4D. Yes, that isn’t a contradiction. Fractals are weird. (The book Scale explains)

Nope, everything uses a traditional render pipeline. You'll see in the next Devlog ;)

give 4-dimensional lovers some privacy, geez

Agree man is insane, but i will say at lest you can have the computer do the math 😄thats whats great about games. But that said, even knowing the right formals for 4D is pretty wild

Then wait to play on the 22nd of March

Allow me to try. Rotation is a phenomena which occurs in a plane, not around an axis. This is why things can rotate in 2D space, despite there being no z-axis to rotate about. You can think of rotation vectors in 3D as pseudo-vectors, AKA not actually vectors at all but can be described with 3 numbers in 3D space. A more mathematical description would involve an anti-symmetric matrix which describes rotation. So the yx component of the matrix describes the same rotation as the xy component, but reversed. In 3D, the planes of rotation are xy, yz, and zx, which all share at least one axis with each other. In 4D, you can have wx and yz planes of rotation, which share no axes. Hence the double rotation.

I don't think so? especially since _we don't actually see in 3d._ We see in *2D,* and then use time, our other senses and our experience of being 3D creatures as interpreting what objects are 2D and what are 3D. For example, I sometimes get thrown off by what 'seems' like a pillar in the distance, only to come closer and realize it was just a 2D cutout. Optical illusions that make street art look 3D is another example. We're just living a movie where the screen our brain shows us looks 2D, it's just that we _know_ it's 3D and can tell it apart from 'fake' 2D (like animations.) to see in 4D, we'd need to have a brain that can just look at an object and immediately see all sides of it. I don't think 4D creatures can see inside 3D things. It's not like we look at squares and see every 1D line in it- it'll take an infinitesimal number of slices and our brains skip computing all that and just go to the shape. To 'see' every object of a 3D object at once and truly achieve 4D vision, we'd need something like a black hole's ability to bend light around it such that the light from the _back_ of a black hole comes back round to the front to be visible- and this is where our brains melt, lol

You will be able to actually interact with it onwards from the 22nd of March, 2024.

22nd of March, 2024!

Wait only until the 22nd of March

That's right! 3D objects can't really exist in a real 4D world because they'd always have some thickness.

@@CodeParade thanks fren very good video