How is this POSSIBLE? - 4D Golf Devlog #8
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- Опубліковано 18 кві 2024
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To save CodeParade's sanity we should refrain from writing 6D in the comments.
To late‚ I want to see a 7D game
He did say that he tried 6D but that the movement mechanics would be too incomprehensible. I guess we don’t get to experience triple rotation 😢
@@Uni_974 try the 7D rubik's cube
XD
@@Uni_974 Tzeench in 9D castle main hall:
- Well-well-well. Wake up the Emperor!
I am 100% serious about this: You can absolutely get at least one academic paper published out of your 5D engine if you want to. And I predict that if you're so inclined, you can make an entire career out of offering consulting services for your engine once you release it (for which, by the way, you would be entirely justified in charging money for licenses).
as nice as this sound i very much doubt enough people would have a use for a 5D engine for this to be more than a neat novelty, and most if not all of the novelty comes with making it run in Unity.
You can already visualize 5d with more math oriented graphing tools, and none of the math done here is innovative. The main innovation comes from having to bridge the gap to 5d in code since Unity/C# doesnt support any sort of 5d math (for obvious reasons)
Yep, e.g. hyperrogue have scientific publications from their hyperbolic geometry engine
I've seen a lot of really cool and novel tech developed as a passion project never really get adopted anywhere. Or see some adoption but never really catches on, like Digital Molecular Matter destruction physics and the many attempts to develop fully procedural world generation techniques (ua-cam.com/video/Y5arfh0kJTo/v-deo.html)
I mean. Like. "a career out of offering consulting services for [a 4D and 5D] game engine"? you seriously can't be this out of touch. I'd be impressed if I saw a single new 5D game. simply put, 4D and beyond are simply... not... fun. they're cool as a tech demo/edutainment game but you can't use them to make a serious game, or a game about anything else other than it being 4D.
@@henrycgs You're just not thinking outside of the box. There are plenty of puzzle games you can make, exploration games, or even horror games.
At this point you are at the top of the list regarding people with most knowledge on higher dimensions
I'm pretty much convinced that CodeParade is himself a higher-dimensional being...
Serioulsy, I think *everybody* having *anything* to do with higher-dimensions knows you 🤗
Haha I love this take. Damn. It is absolutely correct.
i mean, we're all on the list, just not that high up🫠
@@PunmasterSTP he's trying to build a bridge back to his home dimension 😂
I was very confused when I got to the first beyond level and my fans kicked in to overdrive when there was like two track pieces lol
lmao
My potato laptop cannot go even one second on the default resolution without throwing a tantrum and turning the sound into static...
Same, I had no idea how my barely-gaming laptop was able to handle it
@@yeetrepublic9142golf is the sole reason I bought my new gaming pc
turning off antialiasing in those levels made my computer get like 10 degrees cooler
3:17 “I don’t really understand it, but that’s just how it works out” -most game devs and physicists
mathematicians too
@@thezipcreatorI mean mathematicians actually prove things and learn the proof to theorems they use so I think the understanding the thing is in the proofs. Sure they might not be able to visualize the 5th dimension, but they can work with the general principles and understand what they need to to say what they need to. The other fields often just use the results from mathematics without really understanding it so I’d agree there.
@@Happy_Abe I was more referencing that like mathematicians don't necessarily understand like _why_ shit is the way it is; for example, nobody knows why the pariah groups exist, they just do (under a logically bound system)
@@thezipcreator yeah that’s a good example. But why is a very philosophical question and many mathematicians won’t even deal too much in it. And I think the monster group is a unique case of this. The classification of the finite simple groups was proven in parts by so many different mathematicians that no one person probably has a full understanding of it, they just built off each other is my guess. But most things a mathematician will prove will be something they have a really good understanding of. I’m in a math PhD program now and I’m consistently blown away by how rich of an understanding my professors have of their field.
5 seconds into the video: "what could you even spoil about a golf game, i dont care about the story anyway, im here for the dimensions"
10 seconds later: "f*ck..."
Yeah... I was expecting it to be something like revealing a depiction of a 4D being...
I debated it with myself but I was so curious as to wtf could be a "Huge spoiler" for a *golf game*
Same here. I've been clicking these videos, but never actually intended to get the game. It's a really cool concept, but since I'm already a little bit familiar with 4-d stuff, I felt I didn't have any really novel experience to look forward to. Now I know otherwise and I will be picking the game up when I've got some more free time.
IKR
@@Syrahl696 "It's a really cool concept, but since I'm already a little bit familiar with 4-d stuff, I felt I didn't have any really novel experience to look forward to."
That's extremely silly. You're doing yourself an extreme disservice here, any time you interact with a new 4D thing you gain soo much intuition that you didn't even know you were missing. If you don't care about 4D that's fine but if you do, never assume you know everything. Honestly, never assume you know everything in *any* subject.
the 5d reveal was amazing. It might be one of the best twists i've ever seen a puzzle game do.
it's gotta be tied with Hyperbolica, his ending there THREW ME WAY HARDER THAN EXPECTED
I wish I discovered it while playing (I only watched the devlogs)
who, what, where, when and why? How do you even have the sanity for this
He doesn’t, he just powers through it and hopes the code doesn’t explode
I got one better which direction did his sanity go
@@Shuck34 Cheers, I'll drink to that.
@@Uni_974 It disappeared into the secret 6th dimension
@@Uni_974 It doesn't go, it just experiences triple rotation
just imagining a 5D game built on a 4D world being rendered in a 3D world on a 2D screen sounds so tough a challenge
for your 1d brain to understand
Transmitted one dimensionally through a wire
as a 4th dimensional being myself, i can truly see the world you made in , however my 4th dimensional brain cannot process 5th dimensional courses are unimaginable and therefore a lot of trouble playing , but i made all of it by the end, this game is truly the best game
I think u mean trying to understand 5d golf in my 4d world through this 3d monitor which is perceived by my 2d eyes and finally my 1d brain
@@liam8370
👍
As a cybernetic fairy, I recommend you say goodbye to your organic brain. It’s so much easier to upgrade an artificial brain with photonic connections and quantum processors.
@@Wonders_of_Reality As a bionic creature, it's much more space efficient even than entanglement storage to just encode everything into DNA, and it's much faster too because I don't need everything to destructively interfere with itself to get what I want from memory. Robotics is the way, just organic robotics instead of artificial robotics.
If you're a higher dimensional being, it would be even more space efficient, as well.
This is literally "fine, I'll do it myself"-ing Miegakure.
Thats hilarious. The spoiler for your 4d golf game is that it's actually 5d.
This was the best part of 4D Golf. I came in looking for a game to grow my third eye with, and came out with a FOURTH eye (you can’t see it, it’s a few centimeters kata and deorsum)
Can we just take a moment to appreciate all the work codeparade has put into everything? Not only did he make 5 dimensional golf, but he also actively engages with his community. He reads nearly every message posted in his discord server. He listens to suggestions and bugs and actually *listens.* When the game first came out I reported a bug in the discord server, and in the same day, cp had fixed it and pushed a new version to steam. And on top of it all, he has been making this masterpiece of a video to explain it all.
We love you codeparade!!! 💚
He didn't help me move.
*-1 star.*
6 stars for the game & engagement, though;
so, 5 out of 5 in total
8:05 More triangles AND it even looks lower poly too, oucha...
Almost *no* bang for *all* the bucks 😆
He could've just got a 3d ball and superimposed it on top of the screen so it's looks like as it's part of the 4d/5d world.
@@MilkGlue-xg5vjI’m assuming it’s due to the engine he made. I’m imagining if the ball were 3D then it would not interact with 4D or 5D objects at all
@@SamRMoyer then it could maybe be an invisible 5d point instead of the 5d object, although it could not be able to roll probably.
@@MilkGlue-xg5vj Why would he cheat something like that? It would make no sense. 5d has low poly balls so you get a low poly ball 😅
I loved the reveal! The main I liked about it is that it was the first course where I really had to think in 4 dimensions. During the previous courses, I had gotten pretty good at reducing courses to 3 dimensions: making good use of the volume view and choosing my slice exactly so that the ball did not leave it and the course basically became 3 dimensional. Only during the 5d levels, there was no true volume view any more (this view was itself a slice). To get subpar on these levels I had to really wrap my mind around what was going on. I found myself doodling diagrams and 4d vectors on paper and actually paying very close attention to the compass.
There is no way you actually used diagrams for the beyond. It’s just 5d.
God yeah this level set wrinkled my brain when I streamed it. It was so crazy trying to wrap my head around it I was basically forced to play it by ear and just keep pointing myself at the hole and hope for the best lol
Yeah, that was basically my strategy. Trial and error...
That's how I've had to handle the 4D levels! I'd have no chance!
Me at 0:06 "This is fine, I know it'll take me forever to get through my backlog anyway"
Me at 0:12 "Oh, I guess 4D Golf is at the top of my backlog now"
comments: make 5d golf
codeparade that already made 5d golf: haha very funny
if i had to guess why 5D has such little symmetry, i would say it has to do with the insolvability of the quintic, which has to do with the simple group A5, and why it’s simple.
But the same is true for degree 6+ polynomials, and those dimensions can have more symmetry
I think that it relates to Mathieu 11 group instead of A5. Maybe tracking the sporadic group can help us know more about special dimensions like 5 dim
We should ask Mxyzptlk
When i got to the reveal i think that was the quickest ive ever drawn myself choking out a game character, regardless of the “being of light”ness or not
As a mathematician and a programmer, this is fantastic and fascinating! However as a player I felt like the 5D courses were a chore where you spend way too much time just figuring out where to look. Certainly a novel experience to feel that lost in all of those extra dimensions, though.
Would it be better, or worse, with a ball-stealing jump-scare creature lurking in the out-of-alignment dimensions?
@@prophetzarquon1922 That might be a fun addition to the marble mode. The pacing doesn't fit golf mode IMO.
It is definitely a novel experience. I do think I found a more methodical way for moving through 5D. Enter volume view and align the horizontal slice as normal. Then, whirl by 90 degrees, and align *that* horizontal slice. Now, exit volume view, and you should see the path forward.
From what I’ve gathered, inside Volume View mode, whirl swaps the vertical axis between the 4th and 5th dimensions.
You need to be careful to make 5D rotations as close to 90 degree increments as possible to avoid a confusing situation. If you get knocked into the fifth dimension, you might need to take a minute to align your rotation again.
I loved this whole game, but especially Beyond. The vibe you get when you open the course, and it looks super easy but clearly is not, fills you with foreboding. And then that's confirmed when you don't make it to the hole, and a cutscene plays -- you're in 5D!!
Crazy fun.
The 5D reveal in the game was crazy, quite the twist. I did power through them - but I don't think I'll revisit the bonus material for them. 4D twisted my mind enough as-is. I can only imagine trying to code such a monstrosity; it looks like you pushed engines and compilers and shaders to their limits.
This is absolutely insane how you managed to get not just 4D but 5D to work AT ALL, not even talking about it being as smooth as it is. I can't read any of the code you showcase in this video, which I find ever so fascinating! I really liked the finale, even though I barely understand 5D compared to me more or less understanding 4D.
I wish there were more options and objects for levels, so you could possibly make some non-golf levels in 4D/5D, that would be really sick.
I don't think that he has time to develop something like this, but CodeParade promised that he will open source the engine of 4D Golf just like he open sourced the engine for Hyperbolica
I can't even understand 4D and this guy is programming in 5D.
I think your over reacting‚ all he did was buy himself a 5D PC
@@Uni_974 A big flat multi-layered 4D chip that uses 5th dimension for cooling actually sounds like a computer with superpowers
@@akeem29834D pcs would be soooooo space efficient. I mean, it’s quadratically better
Man, the second you mentioned needing to make a Vector5 since Unity only has Vector4, I felt a pain in my soul as a Unreal dev.
I have to make a matrix math library this weekend and I'm not excited.
On the upside, at least you're not dealing with Unity...
Top 10 video game plot twists.
before watching and after playing the game. when i got there i felt it was a bit flat, and given the title beyond i felt some pull was gonna happen, especially since i saw this thumbnail when it was published. got the game yesterday and blasted through the courses last night and today. when he said we're not 4D my brain sank and exploded with excitement "you're 5D?" i guessed. he said we've actually 5D and i nearly ell out of my seat. it struck me as odd the entire game how in 4D and even in volume mode the ball would nearly ceaselessly warble its shape and surface. because it was a 5D ball the entire time, and i just stayed perfectly still in that 5th axis the rest of the game. so congratulations. i felt the entire process of watching this devlog and seeing the complete pipeline of creating a 4D game from scratch was massively impressive enough. 5D, you got me man, now to watch this video explaining the math and code...
watching video
YOU ADDED INTEGER TEMPLATES TO C#‽‽‽‽‽‽‽
of course you did, you've reimplemented so much and generalized for higher dimensions. that ladder for 3D to 5D meshes was terrifying, and i know each step of that path.
also dear CHRIST, i remember the VR and multiplayer for this, but i ENTEIRLY FORGOT you were gonna publish this engine OPENLY for more higher dimensional games to be created with it. the future of this is going to be incredibly insane. but in the end, i'm interested to see what you're gonna get up to after being stuck with golf for so long? can't wait to see. and i didn't even THINK of seeing for videos of people playing the game. but what i'm most needing to get used to is Anna and Katta, as when i learned about 4D stuff when iw as a kid i always found people saying "in" and "out" as the directions, and only about a year ago did i first here whispers of anna and kata. feels like the AD and BC to CE and BCE switch all over again.
anyways, enough rambling. thank you from the bottom of my overly mathematical nerdy heart for this, and developing a soon to be open 5D/4D engine that works and works WELL.
Actually, no, the 4D parts of the game aren't 5D, at least on the level of the game engine. Ball seemingly morphs and changes shape even in volume mode because volume mode is also just a slice of the full 4D world, but in the different direction. In volume mode, the ball is actually more likely to have weird-looking rotation because it's unlikely for the ball to have one of its rotation planes parallel to the ground
My man has been playing 5d chess with us the whole time 💀
in 3D, a line can intersect a 2D plane at only one point, but in 2D, that same line cannot intersect the 2D plane at one point except for in specific edge cases. So there is a lower dimension analogue for a 3D mesh intersecting a 2D plane at only one point.
Can't wait for 6 dimensional golf where the ball Coles out of the screen and kills me on the beyond² levels
I've been waiting for this devlog ever since I reached Beyond. What a twist it was.
Ditto
I never thought about how higher dimensions require so much more compute but it makes sense of course
I was wondering why there wasn't a 5d option in the level editor. Now it makes sense.
Interestingly you can already create 5D levels in a text editor if you know the syntax, or can guess-check the syntax, and import them. The syntax is similar to 4D level creator exports except the integers select from an increased list of 5D direction options. Examples of 5D elements in this syntax are: "Straight4" and "Turn4,1" More details on the steam forum for this game, and CodeParade said there that he hopes to add a guide for that soon. Someone also posted the complete textfile for Beyond level 2 and it works!
I can't imagine how hard it would be to debug the renderer. "Oh, the whole screen is just visual nonsense again? I wonder what went wrong this time. Better review all my code..."
I am now convinced that you are a multi-dimentional creature tring to make us humans understand higher dimensions
Section 31: Agents en route
The way the reveal played out gave me the same vibe as the reveal in My First Quantum Translocator.
At least this time, nobody was trying to kill me.
The mathematics and scientific visualization communities may well have other applications for some of the code in the game.
Yes, this is really worth publishing a paper
There are spoilers for golf?! Huh, I guess I do have to play the game now.
When I'd gotten to The Big Reveal I've gotten absolutely flabbergasted beyond belief. Knowing how hard it'd been so far, I've gotten absolutely PETRIFIED after it'd started to sink in just HOW MUCH the possible complexity might grow.
And then I just said no. No. Nope. Nu-huh. Nope. I'm not going there. This forbidden knowledge should stay forbidden. I'm sorry, the multidimensional entity, I failed you. And I didn't launch the game since.
I guess, It couldn't be that bad after all knowing now that you didn't go all the way with the 5th dimension. Maybe I should try again?..
But yeah, that Big Reveal hit me hard.
The Beyond levels incorporate mechanics from all the previous zones, but I didn't find them much harder to birdie than Dunes or Mezzanine, at least once I figured out what way things went.
The main Beyond course is honestly easier than the stuff before it because the actual golfing is a lot easier to compensate for the extra complexity.
Beyond Challenge, though... oof.
@@SSM24_ tbh I found beyond challenge easier than dunes challenge. Dunes challenge was by far the hardest map for me, all the hills destroyed me...mainly because hills destroy me in regular minigolf and then you add 4D slopes to your hills and forget it
@@SSM24_ Birdie-ing Spirit Bridge was kinda hell, though. Only time I had to use a near 180° bank shot to birdie a hole
i finally understand what my friends hear when I talk about programming struggles. I can only really tell what you're talking about by tone lmao
Imagine the sheer size of the jaws of the people who jokingly asked for a 5D game. This is nuts.
Your perseverance is crazy.
I would love to see a game you'd make if you teamed up with talented environmental artists/animators!
I remember completing 4D golf, i swear that caught me off guard, also i enjoy how the first level that uses 4D and 5D are the "same" (same layout, expect one has the wall and hole in 5D)
GPUs are most definitely good at 5x5 matrix multiplications and vector5 dot products, it is just HLSL that is not set up for it. These kinds of operations are common place in ML workloads, with matrices often being above 1000x1000 in size. So if it is possible to make some custom CUDA, Metal or Vulkan kernels, which are called from HLSL, then a lot of the problems you had would be solved.
Of course, but for rendering output and working within a game engine, there's not the level of flexibility I would need for that, at least not that I could figure out.
@@CodeParade That makes sense, even if you could import CUDA code into the shader, you would still have had to write the same kernel Metal, Vulkan and all other shader languages you wanted to support. It is a shame though that you can't just use compute shader functions from within a vertex shader, since the compute shader language is a abstraction of native CUDA, Metal and Vulkan, code. In that way you could have had both the performance benefits of custom kernels, and the native support for all platforms.
@@CodeParade It can be done - for example one of the first CUDA books, 'CUDA in examples' has an entire chapter on CUDA/OpenGL interoperability.
Obviously the next step is to make golf embedded in a Calabi-Yau manifold with 11 extra compactified dimensions. M-theory golf, Molf!
Coming Soon:
_Dimensionless Group Golf_
4D: Nah this is easy
5D:
Somebody get matt parker and his book in here
You should've said "you should finish the game before watching"! I played the game but didn't finish it yet. I thought you were going to talk about the volume view or something so I got spoiled.
Ookayy... Yoou did say "How did I do that finale?" Maybe I couldn't wait then... Oh well, at least now I really wanna finish it.
The fact you went out of the way not only to make a 4D game engine, already complicated as hell on its own, but also making a 5D game engine...
I have to use a low quality 4:3 screen just to get rid of 80% of the lag in Beyond...
I'd think this video would give the game even more marketing, even if it's spoilers
8:00 there is a maximum of volume of hyperspheres at exactly 5 dimensions. Every number of dimensions above or bellow have lower volume for the same radius.
This isn't quite true, because an N-dimensional volume can't be properly compared to an N+1-dimensional volume - they have different units. It's like saying "which is bigger, 100 metres or a metre squared". There's no canonical, consistent way to compare the two values.
The calculation you're referring to ignores the dimensionality by declaring that the radius is 1, which is arguably an arbitrary choice. This does return the result that a 5D hypersphere has "the largest volume". But other choices return different results; for example, setting the diameter equal to 1 (meaning the hypersphere is the largest hypersphere which fits in a hypercube of side length 1) results in the volume of the hypersphere monotonically decreasing as dimension increases, and the 1D hypersphere is the one with maximal volume. Setting the radius to a number greater than 1 makes the peak occur at higher than 5 dimensions.
The point is that while what you're saying is true in a particular scenario, it's not a particularly enlightening one because it relies on a somewhat-arbitrary choice to be a well-posed question at all. The actual reason why 5D has so few symmetries (which is related to why the 5D ball needs so many triangles) is some pretty deep group theory which I admit I'm not fully familiar with.
8:28 people joke about absolute beginners building sh!t like that but here we are
With 24 possible rotations, no wonder you haven't yet released an editor for Beyond style levels.
At least gravity is only aligned to one dimension at a time 😂
Nebula Beyond Challenges 👁️
Is the object in "Blocked Chakra" a duoprism prism? because that's wild!
Yup! Or you can think about it as a product of a disk and a cylinder.
5 dimensions in a 4D game where dimensions are projected on a 3D space rendered on a 2D screen. It makes my head hurt (in a good way) just to think about it. Amazing game!
Most devs: “our final boss will have an extra health bar”
This guy: “my final boss will require me to write a 5-dimensional engine in C#”
I couldn't understand most of the video but it was still very interesting.
Now I'll put my tiny brain back so sleep. It's been a hard day.
Thank you oh so much for all your hard work on this. I figured it would involve taking a 4D slice of a 5D space and then a 3D slice of that, and both steps would be pretty similar to what you already did.
What I was curious about is how you *textured* this mess; 4D textures were already a pain as you mentioned, but how did you figure out 5D that looked like anything reasonable? The floors seem like a logical extension of a 4D cube tiling, but how did you sort out the backdrop and things like the eyes to look like what you wanted? Not to mention how you modeled the 5D chess pieces in the one course to look reasonable?
The curse of dimensionality. Always fun. :) You can fit a lot of sh*t in high dimension space.
I would seriously love to look at your code. As a comp sci major who has taken a visual graphics course, I find this all extremely fascinating. I can of course understand why you wouldn't want to make that public, though.
The engine will be open-sourced soon.
I have a degree in mathematics so I wasn't expecting to get mindblown, but those levels absolutely broke me! Thank you so much for that experience! I finally figured out how to use the whirl and it's just insane!
Somewhere currently in the future a person watched this and is dreaming of how to optimize a 5D graphics card.
With 5D lithographic chipsets, I hope.
The 5 d surprise was great. I found it surprisingly not to difficult compared to 4d
When I finished this game on stream, I said this was the best game ever made from a technical standpoint. And after watching this video, I am even more convinced of that. No one would have minded if the game was "just" 4D, but you went the extra mile ... or extra dimension in this case. CodeParade, you are a mad lad.
"at a reasonable framerate"
I know my computer is old, and it shows because I gave up on the beyond challenges since my framerate was like 4 or 5 and it was just such a pain to try to control anything at that speed
In the settings there's a toggle graphics toggle to disable ghost shadows and only allow wireframes. It should at least quadruple the framerate or better.
If my brain was melted and reconstituted by this game just by playing it, I can only imagine how you managed to wrap your head around it enough to make it!
You are a madman and I love everything you do.
crazy stuff. and im struggling with rotating a sword in my game
That final world was crazy, and I have nothing but awe for what you've been able to code!
Out of curiosity, would you ever consider doing some kind of crossover between 4D Golf and Hyperbolica, like making a level where you golf in a world with spherical geometry, or where just one of four dimensions was hyperbolic?
I can't even imagine a computer powerful enough to render it in "realtime" 😂
@@YandiBanyu Yeah I think it'd be tough. But maybe since he already has levels with either spherical or hyperbolic geometry, he could port a minigolf game into that...
You can't have "just one hyperbolic dimension". You need at least 2 dimensions to have curvature.
I'm not sure that "where just one of four dimensions was hyperbolic" exactly makes sense. Like, for a 1D space, there's not much of a notion of intrinsic curvature, I think.
One could definitely take a product of e.g. the 2D euclidean plane and a 2D hyperbolic plane, and it would seem to make sense to me to describe that as being "hyperbolic in only 2 dimensions"?
Perhaps closer to what you want might be, if there is a foliation of the 4D space by some 3D slices, where each 3D slice is euclidean, but the way they relate to each-other is so that the overall 4D space has some hyperbolic stuff to it?
For that, I think the 4D analogy to the Poincaré half-plane model, would probably do the trick?
so, for ds^2 = (dx^2 + dy^2 + dz^2 + dw^2)/w^2
so, if w was held constant, this would just be the metric for normal 3D space (but, like, scaled by a factor)
I think maybe this would give what you are wanting?
I don't know whether or not different simply connected hyperbolic spaces with constant curvature in 3D or 4D are all equivalent...
So, idk if this would pick out one particular hyperbolic 4D space, or whether this just picks out one way of representing the(?) 4D hyperbolic space of a particular curvature .
Idk, it feels like it should be different from others? but idk.
EDIT: turns out that there is a unique simply connected n-dimensional manifold with constant "sectional curvature" -1 (for all n > 1)
So, I guess the half-space model is in a sense, no more "only hyperbolic in one dimension" then is any other (because they are all isometric)
hm.
Still, it seems like the half-space model would at least make it clear one way to make the slices so that some things look euclidean.
But I guess, that means that in any model, there would be a way to take a slice that looks Euclidean? That seems weird.
How do you define how to take a slice?
I guess if you take a point, and like, take 3 orthogonal directions, and consider the subgroup of translations generated by those 3 directions, and consider all the points that that point would get translated to under that subgroup?
seems very weird.
Would *every* slice look euclidean?
Surely not, right?
Like, if you made it from the product of hyperbolic plane with Euclidean plane...
though, maybe that wouldn't be hyperbolic in the same way?
well, at least in that case, if you took 2 directions from the hyperbolic plane, and one from the euclidean plane, would look non-euclidean...
@@galoomba5559 That's a really good point; thanks for correcting me! So maybe there could three or four total dimensions with curvature between two of the specific dimensions.
This was a lot of effort you went through. I totally didn't give up trying to understand the 5d stuff and just trial and errored it.
Looking forward to more 4D games!
as a 2d being, i played this game on a 1d screen and i had to think in 3 dimensions higher, that took so much brain power that i randomly fell asleep mid game
When I realized the layout of 5D chess wasn't even in 5D, I couldn't stop laughing! That's probably something only a handful of people would even notice, but is the perfect joke knowing this game's audience!
Edit: The knights aren't even moving in 5D either, this is too perfect!
(In advance: sorry for my English, it's not my native language)
CodeParade, I have an idea that I think would make the volume view better. Instead of showing the slice of the world at the current height, I think it would be better to show the projection of the world on the xyz hyperplane (if the w coordinate represents the height), and instead of representing slopes with just walls, you would represent them with arrows. And with that, you should add a height scale that shows your ball's height and the track's height at your xyz position (relative to a fixed point).
3d example with area view:
A level has a starting platform, a slope up, and a finishing platform, so the projection would be this:
0⬱1 (numbers represent the height of the flat parts of the track)
The area view is a 3x1 rectangle, at the second square there are arrows pointing to the starting square.
At the start, the height meter would show 0 for both ball's and track's heights. After putting, the heights would gradually increase, and then they'll stay at 1.
Another 3d example: a level has a starting platform, a ramp, a gap and a finishing platform:
0⬱ 1
Area view: a 4x1 rectangle with a missing part before the finishing platform; at the second square there are arrows pointing to the starting square.
After putting:
1. both heights increase, then
2. track's height disappears
3. ball height changes quadratically (because it's a second integral of a constant (g))
4. as you become in the same vertical "column" as the ending platform, the track's height appears on the scale, then, one of three things happen:
a) you fly over; on height scales, your ball's height stays higher than the track's height, then track's height disappears; in area view, you fly through the hole and through the back end of the ending platform
b) your ball's height goes down to the track's height, you land on the platform; in area view, you get in the hole or bump into the back end of the finishing platform;
c) your ball's height is lower than the track's height and stays lower; then track's height disappears; in area view, you fly through the hole and through the back end of the ending platform.
You could also make every object in area (volume) view go shadowy if you are not on the track, since when it happens, you can't interact with anything.
In 3d, in area view, cone on the track would become 2d circle made of arrows pointing away from the center; in 4d, in volume view, 4d cone (or how it is called) on the track would become a ball made of arrows pointing away from the center.
I think making it like that would make it more intuitive
An interesting addition to the game would be to add a "retina" mode. Instead of slicing the 4D scene and rendering the contents of the slice to the screen, project the 4D scene onto a 3D screen (a "retina" or "camera sensor") that shows up as a transparent cube in front of the player. It would have to only be available as a ghost/wireframe view and even then may only be useful for simple scenes (too much clutter otherwise), but it's a strategy I've seen used in at least one other 4D engine.
Less immersive, but an intriguing potential visualization scheme that I've never seen used is an "intersecting planes" scheme. Slice or project the scene onto the forward-back-left-right plane and separately to the up-down-ana-kata plane (our some variation on that), and then just plop the two planes down onto the left and right halves of the screen. This is more of a " top down third person" view than a first person view, so might not be entirely appropriate for 4D golf, but might at least be interesting to have access to in the mezzanine tour.
This was the best devlog I've ever watched, Thank you for your hard work
3:08 ain't no wayyyy, bro using pentagrams to render the graphics 💀
This is incredible, thank you for sharing!
Omg, you are incredible.
A true mad lad.
Cheers mate.🎉
I remember getting to that area... I knew the calculations must be legit, cuz my machine started WIZZING on these 5d levels hah! I do have too admit that the reduced frame rate and my brain not quite catching up meant I brute forced trialed and errored my way through the 5D sections, I'm sure I did not get the full appreciation you hoped out of players trying to experience 5D but I love that you pulled it off all the same
Polymorphism at its best indeed
I wonder if 4D Animal Crossing could function.
I wonder if it'd add anything.
Those primitive beings have only 3D stuff. Stealing Will be a piece of cake.
ig you'd get like way more space for your space
that's pretty much all I could think it would add
@@thezipcreator Imagine what a 4th dimension would add to Your Real Life even.
I was REALLY amazed, impressed and confused when reaching beyond, thinking I'd missed a gian announcement, this is so cool!
I can't pretend to having gotten any closer to understanding 4d, but my brain has gotten shockingly comfortable creating a '4d intuition' that helps me navigate.
I imagine it's a lot like being an ant - you don't have to understand 3d, 2d is enough if you combine it with the right methods and shortcuts.
Maybe someday 4d will start to click, but I imagine it will take a lot of practice, and is likely completely impossible depending on a persons exact brain structure and life experience.
Thank you for making something so forward thinking, and sacrificing your sanity...
This is the video that convinced me to get 4D golf! It's great!
your 4d game devlogs broke my brain... to find out that theres a 5th dimension involved.... I can't even fathom
I am so glad I paused the video and went and finished the game. What a great surprise, and what a tragedy if you let yourself get spoiled.
Wow. Amazing to see what it takes to go beyond 4D!
"Yes, a 3D space intersects a 2D plane in a single point in 5D" hmm yes indeed I understand how that follows from the previous statement
I loved the 5D section and I'm looking forward to more levels in 5D, and maybe the ability to edit and create 5D holes
That is already kind of possible to do through text files
1 dimensional binary runs 2 dimensional graphics that represent 3 dimensional versions of 4 dimensional versions of 5 dimensional things. very cool
A lot of people tried to string the 1, 2, 3, 4, 5 together, but you nailed it.
Well done
i spent the whole last section absolutely losing my MIIIIIND. I was screaming when the big reveal happened.
Now make a 4D golf but with time as the extra dimension
that's just 3d golf
A game without time is basically just the level editor.
There's a game like that already, an RTS called Achron.
You really push this game to its new level because of your genius intelligent brain.
I love the tripy, low-poly visuals
Surely adding extra dimensions leads to factorial growth, not exponential… and factorials are much worse
I literally beat the game a few seconds ago. I was simply astounded. I knew had no idea the twist was this ambitious. CodeParade, I'm not exaggerating when I say you've done something historic both for gaming, mathematics, and programming.
This is so incredibly inspiring, especially regarding the 5D engine!, You are definitely a pioneer in higher dimensional engines and games!