What is the 4th Dimension REALLY? - 4D Golf Devlog #2
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- Опубліковано 5 чер 2024
- A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend:
"Visualizing 4D Geometry" • Visualizing 4D Geometr...
"The things you'll find in higher dimensions" • The things you'll find...
"A Beginner's Guide to the Fourth Dimension" • A Beginner's Guide to ...
"4th Dimension Explained" • 4th Dimension Explained
0:00 Introduction
0:34 Flatness in 4D
2:29 Seeing Inside
3:15 Chirality
3:54 Klein Bottles
5:27 Double Rotations
Wishlist 4D Golf on Steam: store.steampowered.com/app/21...
#4dgolf
Devlog #1: • So I Guess I'm Making ...
Trailer: • 4D Golf | Release Date...
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Music (CC0 1.0)
Holizna - Autumn
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I think this video has finally convinced me beyond all reasonable doubt, I will never fully understand higher dimensions. But I can pretend to by playing this game when it comes out!
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.
3D people:
"2D people can never know how the 3rd dimension works."
Also 3D people:
"Here is how the 4th dimension works!"
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!)
honestly it's really impressive that you can even wrap your mind around a dimension beyond you let alone simulate it in a 3d space
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
"Congratulations on making it this far!"
Finally, the first sentence I can understand.
Thanks pal.
😭 send help
2:04 - "One of my goals for 4D Golf is that I don't want the navigation and movement to be the challenge of the game. That should be as easy as possible, which is the reason I have so many different visual and control options. The 4D stuff is there to give new golfing challenges that are fun to play."
Now that we've actually gotten our hands on the game, I really have to say you succeeded at this with flying colors, because this is the exact conclusion I drew on my own. The 4D stuff never felt like the biggest obstacle, because even when I couldn't fully wrap my head around what was happening, there are still enough different perspectives and ways to visualize things that I could often figure _something_ out anyway. You made a 4D game where the 4D stuff wasn't actually the hard part, and that is _seriously_ impressive.
Understanding the 4th dimension to this extent is already pretty tough, I can’t even begin to imagine how hard it’s gotta be to code it
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
I love how this is a video with PRACTICAL, LEARNED experience. Someone who went into the 4D trenches and came back older and wiser.
When I first learned about rotations in 4D it blew my mind. The way we're used to thinking about rotations (i.e. with an axis and an angle) only just so happens to work in 3D. In general rotations are actually defined by a plane rather than an axis. We just happen to think about things in terms of the one dimension that _isn't_ rotating, rather than in terms of the 2 dimensions that _are_.
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.
I describe 3D shapes in 4D as "flat but not" and you can go up the dimensional ladder and describe every layer below it as "more flat" than the current layer.
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.
I find the flatland analogy to be helpful in understanding the concept of 4d, but this seems to be the best way of visualizing it yet!
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
CP: "With me so far?"
Me: *still stuck trying to understand 4d flatness*
Dude, thank you for FINALLY getting out of the flatland explanation. I needed this.
Absolute respect for those who dare to traverse the comfort zone, and try to understand even merely one more dimension, one more rotation.
Not 1 more rotation, 3 more rotations.
I have always hated the concept of treating time as a 4th spatial dimension. It helps with the mathematics of Relativity, but time is not like a spatial dimension.
"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 UA-cam 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
The thing with swapping the axis for the 4th spacial dimensions with one of the first 3 to get an alternative view is something I have thought about for years, probably a decade at this point.
And this is the first time I got a visualization of that swap. Thank you so much.
I also have a suggestion:
How about having both views simultaneously side by side? One View Port in one angle, and the other rotated by 90° in the fourth dimension. I think it would make it very clear whats going on, especially with your ingenious 4d shadowing system.
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
omg yes PLEASE keep doing in-depth 4d videos. you're totally right that there's not much on YT beyond "let's imagine a flatlander", and there's so much more to learn-even if it does make my poor little 3d brain hurt
6:44
You can kinda see that "draw 2 cubes and connect the corners" type of projection!
yep!
honestly, i think the most satisfying explanation of higher dimensions comes about through math - linear algebra was when i felt like i finally understood how and why higher dimensions work the way they do. not that more intuitive explanations can’t work, but i just never really felt like it made sense through pure spatial intuition, since higher dimensions directly conflict with that intuition.
I've always thought I kind of "got" 4 dimensions from all the other kinds of explanations you mentioned at the start of this video. Then the next six minutes gave me a thousand more things to think about and made me realize that I've only barely scratched the surface (no pun intended) of 4D. I came away from this a lot more confused, and a lot more excited to keep learning about higher dimensions, so thanks for that! I'll probably come back to this a few more times to try to wrap my brain around it a little better.
Another fantastic video, CP! I like how adamant you are about the exact nature of 4D space; you opt for explanations that are difficult to fully grasp, but are as accurate as possible, in contrast to explanations that are very easy to grasp, but are also inaccurate. I feel like I have a much better understanding of 4D space after watching your videos.
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
It takes imagination to understand 4D, and it takes massive effort and intelligence to get out the flatland explanation, especially when it's interactive and comprehensible. And I think you're the first one I ever seen. Love the gravity analogy and it lightens me up. Bravo brother.
This is the perfect example of UA-cam teaching me more than school.
With every new devlog I become increasingly convinced that you're actually some next-level genius us mere mortals will never quite reach
This is great, I've always been fascinated by 4D and the topics you've covered here are really unique!
As a math major, I found your intuitive explanation of the fourth dimension really interesting and useful!
I, too, long for more 4D content on UA-cam that goes beyond the basic analogies, and I'll be here for it if you make more :)
That double rotation rendering at the end really was helpful, it let me just barely brush against the possibility of understanding the rest
I would love to watch an almost uncut video or live stream of you creating and testing a level.
I feel just being able to see the level design kind of gradually come together would really help me and others to get their head around the weird behaviour of the geometry in this world. Would that be something you might be interested in sharing with us CodeParade?
Also, in the next devlog, I think it would be helpful to give a quick refresher on what the orientation indicators in the top right are actually showing.
Thanks for the very interesting video as always!
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.
You probably have one of the best videos/games I've seen that shows really good control of rotations and views across all 4 dimensions, you even use wireframe mode when flipping "height" for "kata depth", and show the trees and objects in their "perspective shadow" shape, which is awesome.
Finally, a good Klein bottle explanation!
Yeah I am a 4/5, 4.5/5 on a good day on the "inner vision" scale and I think anything less than a 5/5 makes it impossible to do anything besides understand the math behind 4d space/objects. (And even if you have perfect 5/5 inner vision, perfect phantasia, it's still impossible for you to actually fully understand, it'll just be easier for you to see a series of 3d projections in your head, making it way easier to avoid comprehension errors when learning the math.) I might be able to learn the math if I spend a lot of time in lectures and classes, but I don't have time for that. All I've got is videos like these. This layman's understanding from youtube videos isn't enough to actually say I understand 4d space, but maybe I'll be able to play this game with some success thanks to the layman's understanding. Thanks for making these devlogs. They're interesting and entertaining.
I remember in middle and high school, my math and physics teachers were always like “What? No. It’s impossible to think spatially in 4D” when I would share my wacky ideas. Thank you for not only having wackier ideas, but truly implementing them! It’s all about going back and building better wings, rather than giving up when your first pair melted.
Thank god you shot down the 'time' aspect of 4d immediately in the beginning, one of my pet peeves when people use time to describe 4D space.
Multiplayer for this would be amazing. Even if it's nothing more than being able to see a friend's ball with no collision. Just because I feel like the confusion of trying to see how 2 points in 4d space relate would make for a really interesting way for players to talk about the game with each other.
Excellent! A breath of fresh air in 4D programming and thinking; on another level. I'll have to ponder.
I remember when you announced this. I love to see the updates. One thing I really like is that this explanation evolved naturally after working in the space. It shows that you have made progress on the project. Or to me at least. Keep up the fantastic work
The extra visualisation options look really cool, looking forward to see how you made them!
RE: Klein bottles, I had it explained to me that the familiar 3D Klein bottle was only a "shadow" of a true 4D Klein bottle. This was somewhat intuitive to me as I could see the shadow of a cube unfolding into a net and back again, and still see it as a cube, and that to the proverbial flatlander it would look really weird because parts of the shape would appear to warp and deform to them, but in reality its just going sideways into the third dimension. I believe this was Matt Parker's lecture at the RI which I'm remembering.
Really excited for this! Are there any plans for a VR mode? I enjoyed that in Hyperbolica a lot.
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
all the videos I've watched about the 4D have prepared me for this video.
the more info one gets the harder it becomes to find new information. it all becomes repetitive.
that's why i loved your explanation of how 3D objects are flat in 4d and have a 4D top and bottom. that concept WAS new to me
This is fantastic. A fundamental step in elevating human perception, awareness, and consciousness...
Your amount of knowledge about these things is unbelievable! I love your videos and explanatory videos and how you try to simplify them for my dumb brain.
Love ya
(My brain is still like a boiling kettle after watching this video)
Code Parade is the official authority of 4D explanations
Thank you so much for this. When you explained the double rotation at the end, I finally managed to visualize the 3D flattened result of rotating a 4D object. The closest I've ever gotten to having an intuition about the next dimension.
4D space has always fascinated me and was the single biggest thing that got me to love math in the first place. Thank you so much for the visualizations, can't wait for the final game ❤
this video gave me that mystical feeling again. I used to really have a firm grasp on 4D objects and 4D space, but this really shook everything up. Thanks!
I already knew that 3d objects would feel flat, but the way you showed the 3d ground, and then went "inside" of it was so cool. I forgot what its like to not fully get the fourth dimension, thank you for filling that niche on youtube like you were saying.
Before this video, my understanding of 4D golf was that it was essentially 3d space and a slider between a number of level layouts, but with rotations and things making everything so much more complicated. Knowing about volume mode has finally confirmed for me that I will buy and enjoy this game. Even with height complicating things, that has suddenly made 4D space so much more intuitive for me!
This was a fantastic demonstration of a 4th spacial dimension. Amazing. Best I've ever seen.
FINALLY someone on UA-cam says something other than “flatland” when talking about higher dimensions. The big problem with infotainment is that once you’ve seen all the big subjects, the only way to find out more is to either go back to college or dive headfirst into scientific papers and hope you understand it. A little variety now and then is very nice.
You did a great job explaining this. You disprove many misconceptions about 4D
Wow I didn’t understand a single thing, but the explanations were great, I just can’t comprehend this. Great video!
can't wait for the release!
22nd of March, 2024!
You gave us a taste of what double rotations look like projected into 3d but I wonder what would the visual difference of the 3d projection look like between two hypercubes double-rotating around one plane in the same direction but in opposite directions for the other plane? I assume it wouldn’t be just a mirror image/time reversed copy since that would probably be what happens if you rotate both planes opposite to the other hypercube. I feel like understanding that would probably allow me to conceptualize double rotations better
Yeah, for me comprehension of the double rotation could have been helped by more examples like this
So many things I didnt think of about 4D, this is really interestjng
Nice to see a poster who understands these additional things. It was good to finally hear somebody mention solid Klein bottles (which I refer to as Klein Strips in recognition of their higher dimensional equivalence to the lower dimensional Möbius Strip). I will certainly be interested to buy and play your 4D game to observe your 4D implementation.👏
Holy cow dude. i kinda want you create a course that explains 4D more - this kinda blew me away. Look, i'm not much a golf person. But damn i'd pay you whatever the golf game costs if you can explain more of this 4D stuff to me.
I'm generally interested in exotic physics and have seen quite some videos about the "flat lands" explanation of 4D and always had trouble really grasping it.
Your video material really is awesome and you at least seem to know the fourth D deeper.
That was amazing!
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)
its AMAZING how you're really pushing unity to do something I never thought it could handle.. seriously, awesome work on this project so far and THANK YOU for these awesome explanation videos that really help get a better understanding/idea of something as complex as 4D
I just found your channel, and I love the way you explain things and now I can't stop watching you.
Seen so many videos struggling to understand em, you managed to explain it in a way i could understand, cheers for that.
Love the volume view mode, cant wait for the game!
Wait only until the 22nd of March
Damn I was very surprised to see that wireframe view at the beginning.
I thought this stuff was rendered with SDF's again, like those 4d demos on shadertoy
Nope, everything uses a traditional render pipeline. You'll see in the next Devlog ;)
You're really bright and this is fascinating. Keep going.
Seeing the 3d mirroring is when it finally clicked for me. I understood it conceptually, but not viscerally.
This game better have an AMAZING tutorial 🤣
Very excited for it
Great video. It's definitely a struggle to understand this stuff as we can't perceive the 4th dimension but you did a cracking job explaining!
YES!!! 4D!!! Your video explained so well some new concepts of higher dimensions that were just so fascinating. Something I would really like to see is how to model 4D objects… It’s just something I really would appreciate to see!
There is a desire for this kind of information. I love it.
I watched this twice, listened intently, and still have no clue how this all functions. Can't wait to play!
Then wait to play on the 22nd of March
I got a C- in further understanding but at least I'm still levelling up my knowledge.
I think this is the first video that actually gave me some new insight into 4D beyond the flatland stuff. When he said all 3D shapes have a 4D top and bottom it just clicked for me lol.
I'm jealous of how you get to work directly on 4D and train your brain on it
Even understanding this is tricky. But you went ahead and made a game 🤯. This is some god tier stuff.
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
5:24 actually now I am not able to think anymore
tysm for this video! idk if its just how my brain is wired but this makes so much more sense to me than the flatland explanation 😅
Kids are going to grow up on this and grow up being familiar with visualizing 4D space. The next generation is definitely going to solve FTL speed.
It makes me think how much we rely on things we dont even think about. Its only when in extremely unusual circumstances that our assumption are shown to be just that. It kinda reminds me of when you see people wearing upsidedown glasses
Btw this is such a fantastic thing you are doing. I wish you luck with it and am looking forward to your next video
👍😊
3:10 Please tell me more about these 4D tops and bottoms 🤔
give 4-dimensional lovers some privacy, geez
Wow. This was the first time watching a video about the fourth dimension that I actually started to grasp the idea. Reminds me of my closed eye visuals during trips when I see the grids here
There was once a Minecraft custom map that was meant to be "4D", where the space was actually made of multiple 3D "W-axis slices", and you had an item that could swap Z and W, so depending where you were when you swapped, you'd see a series of one-block-wide strips of all of the W slices, and whichever strip you were in when you swapped again is which slice of the W axis you'd end up back in. I suppose the 3D equivalent would be LittleBigPlanet, analog movement on a 2D plane (X and Y) with 3D movement constrained to switching between discrete layers of the Z-axis, only briefly passing through the points in between (so inter-plane movement could be prevented by masses in between the two planes in 3D, but you had no interaction with those blocking layers except when actively trying to change planes).
That Minecraft map was essentially 4D if you constrained it to integer voxel coordinates, and to this day, it is the only analogy of 4D that I have ever even remotely had a chance of understanding. Having the W axis be as fractional-movement as XYZ is? *brainsplode*
A 3D cube resting on a 4D table might "fall over" seeing as it is resting on a super thin side in the 4th dimension.
Ironically, the "double rotations" part is actually what made 3D slices and such 'click' for me. Wow !!!
Code Parade: "I am gonna skip explaining 4D"
Also Code Parade: Explains 4D perfectly so I could understand it for the first time, also Quaternions make sense now
I'm not sure how quaternions would make sense from this since they're fundamentally 3D objects despite having 4 components. A 4D equivalent (sometimes called a rotor _not an octonion_ ) would need 8 components in order to have complete rotational freedom in 4D.
@@angeldude101 well, I assumed that because you can form 2 planes with the 4 components of a quaternion and rotate them individually, that you can prevent gimbal lock from happening. But maybe I still didnt really understand
@@SmoinsLP Not really, the planes represented by the 3 imaginary quaternions will always share an edge and so can instead be interpreted as a single plane. 4D rotations have planes that don't share _any_ edges in common, and so can't be collapsed in such a manner.
The scalar part also doesn't represent a plane, only how much to rotate through the plane specified by the other components.
Speedruns of this game are going to be insane
Thanks for making this! I agree that there is not much out there in terms of more in depth 4D education. I think things like double rotation could probably afford more screen time, even getting explained in multiple ways. It’s such a difficult concept to understand that I don’t think it would hurt to spend more time on this kind of video. But thanks again! I really love trying to wrap my head around 4D and it’s really great to see you unpacking things that unique to higher dimensional space.
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.
Have you heard about geometric algebra before? I find it to be a super interesting rabbit hole
A while ago I thought about the logistics of making a 4 dimensional golf game but I didn't really go anywhere with it, so it is really cool to see this project so far ahead. Can't wait to hit a hypersphere with a 4 dimensional club!
Very cool, especially the rotational things such as reel, tumble, and twirl
Awesome video!
Here's a youtube video title I will share to you all.
The title is:
"Is there a dimension between third and fourth?"
Feel free to share it with other.
:-)
This looks amazing, I played a few 4D “games” without really grasping what was happening but this really helps to understand this concept better.. BTW I just played hyperbolica and It was really inspiring. I’m a game developer as well, I made a game called Broken Reality and I found a few parallelisms between them, I think you might enjoy it, keep up the great work.
I think your switching of the y and w axis actually got me just that little bit closer to understanding the fourth dimension. I still can't fully visualize it, but I hope that getting to actually interact with it in this game will change that because I think your system for people to see and view the fourth dimension is very smart and way better than any other visualization I've seen, at least when it comes to actually being in a 4D space.
You will be able to actually interact with it onwards from the 22nd of March, 2024.
my god. Your brain. This is absolutely crazy to imagine conceptually
Considering how you can switch between the two views, a miniature of the other view would be helpful. Just so that you can always see how your shot will behave horizontally and vertically.
This is extremely impressive from a technical standpoint, but I can't imagine myself enjoying the gameplay because I'm unable to build an intuition for how any of this works.
Don't worry, there's a tutorial :)
@@CodeParade I'll give it a proper chance when the game's finished, it's a little unfair of me to criticise the complexity of this game from a mathy devlog
@@BrandNewByxorIt will release on March 22nd
That's really cool. Mathematician William Thurston claimed he could visualize 4D space, and he made a convincing case of it by publishing profound results on the topic.
Your work shows that it's actually possible, and that you don't have to be a Fields medalist to do it
Awesome way to hype up your game. I'll def be wishlisting it!
I wonder if playing a game like this in VR would make it somehow easier to grasp? Would be interesting to see.
Don,t wait much for next video man! Very done well, ha
Well, it is good to see an explanation that make us realize we are ignorant in some topics. Good job
If you are a 4D creator in a 4D world everything looks normal
(Puts on horrors-beyond-comprehension glasses)
"This looks fine."
imagine what speedrunning this game would be like