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).

To save CodeParade's sanity we should refrain from writing 6D in the comments.

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..."

At this point you are at the top of the list regarding people with most knowledge on higher dimensions

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

3:17 “I don’t really understand it, but that’s just how it works out” -most game devs and physicists

who, what, where, when and why? How do you even have the sanity for this

This is literally "fine, I'll do it myself"-ing Miegakure.

the 5d reveal was amazing. It might be one of the best twists i've ever seen a puzzle game do.

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

Thats hilarious. The spoiler for your 4d golf game is that it's actually 5d.

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

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)

8:05 More triangles AND it even looks lower poly too, oucha...

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!!! 💚

comments: make 5d golf codeparade that already made 5d golf: haha very funny

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

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"

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.

5d golf? I thought my brain was already broken but now I have a splitting headache too

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.

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.

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.

I can't even understand 4D and this guy is programming in 5D.

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.

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.

Top 10 video game plot twists.

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.

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

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

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.

I've been waiting for this devlog ever since I reached Beyond. What a twist it was.

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..."

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.

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.

I never thought about how higher dimensions require so much more compute but it makes sense of course

There are spoilers for golf?! Huh, I guess I do have to play the game now.

I am now convinced that you are a multi-dimentional creature tring to make us humans understand higher dimensions

Your perseverance is crazy. I would love to see a game you'd make if you teamed up with talented environmental artists/animators!

I was wondering why there wasn't a 5d option in the level editor. Now it makes sense.

The mathematics and scientific visualization communities may well have other applications for some of the code in the game.

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.

Somebody get matt parker and his book in here

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

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.

4D: Nah this is easy 5D:

Imagine the sheer size of the jaws of the people who jokingly asked for a 5D game. This is nuts.

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

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#”

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 😂

8:28 people joke about absolute beginners building sh!t like that but here we are

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.

(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

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!

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.

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.

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?

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!

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.

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?

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!

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.

Obviously the next step is to make golf embedded in a Calabi-Yau manifold with 11 extra compactified dimensions. M-theory golf, Molf!

This is the video that convinced me to get 4D golf! It's great!

Thank you for making something so forward thinking, and sacrificing your sanity...

Somewhere currently in the future a person watched this and is dreaming of how to optimize a 5D graphics card.

This is incredible, thank you for sharing!

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!

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

Wow. Amazing to see what it takes to go beyond 4D!

Polymorphism at its best indeed

This was the best devlog I've ever watched, Thank you for your hard work

WAIT A SECOND 10:07 THATS ME my celeb debut

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.

I was REALLY amazed, impressed and confused when reaching beyond, thinking I'd missed a gian announcement, this is so cool!

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.

The 5 d surprise was great. I found it surprisingly not to difficult compared to 4d

I love the tripy, low-poly visuals

Is the object in "Blocked Chakra" a duoprism prism? because that's wild!

"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

Omg, you are incredible. A true mad lad. Cheers mate.🎉

1 dimensional binary runs 2 dimensional graphics that represent 3 dimensional versions of 4 dimensional versions of 5 dimensional things. very cool

needing spoiler alert for a GOLF game is something insane I think most devs wish they could say they did you've made it

crazy stuff. and im struggling with rotating a sword in my game

your 4d game devlogs broke my brain... to find out that theres a 5th dimension involved.... I can't even fathom

i spent the whole last section absolutely losing my MIIIIIND. I was screaming when the big reveal happened.

Oh man, mad props dude.

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.

3:08 ain't no wayyyy, bro using pentagrams to render the graphics 💀

You really push this game to its new level because of your genius intelligent brain.

Love it, such a cool thing.

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

Oh my god yes I was waiting for this one!

So impressive!