What does VR reveal about the 4th dimension?

I recently played with a virtual reality app that gave me new insight into higher order dimensional thinking and by that I literally mean this application was designed to help three dimensional beings like ourselves think of and engage with a four dimensional object playing with this application confirmed one of my earlier suspicions which is when virtual reality is designed well it allows us and locks in the human race the ability to think in higher dimensional space and the reason this is is because virtual reality is a digitally mediated three-dimensional space so that digital mediation allows you to inflect other metadata on top of this three-dimensional composition today I'm going to talk about three different virtual reality demos all of which engage in higher dimensional thinking in their own right I'm only going to briefly cover the last two but the first one that I'm going to talk about I'm going to spend a lot of time on mostly because I learned a huge amount from it the demo is basically taking a four-dimensional hypercube and shoving it into three-dimensional space and allowing the user to rotate that hypercube and gain new insights on how hypercubes work okay so as I talk about this I'm realizing how ridiculous I sound and that's just sort of one of the things that happens when you talk about higher dimensional space but the reason I still want to forge past all this absurdity is the fact that virtual reality has really unlocked a totally new understanding for me like I've always wanted to get a good understanding of for whatever reason how four dimensional space works I've watched youtube videos and like read papers and read books or whatever and it just never really clicked it just didn't really fit into like my just understanding of the cosmos it didn't fit into my intuition but now with this virtual reality app I get it like it's in my bones right like I have it in a way that I didn't have it before and that's super exciting and that's that's that's the excitement that I want to share so before we do a deep dive into how multi-dimensional space works I want to do a quick shout out to the two brains behind this project when bolon and Ken Perlin they're also awesome enough to open source of projects so if you want to develop on it yourself or if you just want to download it and play with it because you happen to own a vive and want to learn how four-dimensional space works you can do that there's a link to the application in the description down below now before we jump into the VR experience I want to talk for a moment about it means to take a higher dimensional object and shove it into a lower dimensional space so here we have a three dimensional cube and it's being shoved into a two dimensional space which is the screen um now what's happening in this particular case right here if you were to ignore this shadow altogether is that you are seeing this cube as represented as nothing more than a square right not super descriptive when it comes to cube this so typically when it comes to representing higher dimensional objects of lower dimensional spaces we will rotate that object a bit so that we can get some offset so this is probably going to be more descriptive than the square we just saw right and as you'll notice here this line happens to be larger than this line and that's because this is a prospective projection in other words the camera location happens to exist in this three-dimensional space it's not off towards infinity and it's just how so happens that when you do that then objects that get close to the camera get larger and objects that get further away it gets smaller alternatively instead of prospective projections we do have orthographic projections so in this ortho projection let's say this is the yellow side and this is the red side this is usually used for more technical drawings to have an understanding of like schematics or maybe blueprints and this means that the camera is not existing in this three-dimensional space but it's off towards infinity and it has a projection of all the pixels just sort of flattened against the two-dimensional space here when it comes to cubes in two dimensional spaces we have a bunch of patterns that often look like this right so here is a very boring cube in two-dimensional space if you were to rotate at 90 degrees you get a cube that looks something more along the lines of this if you were to do this then you get something more along the lines of this this is called isomorphic projection another common technique for drawing cubes in three-dimensional spaces is to just have two squares that sort of overlap each other and then connect the vertices with all these lines and as you draw these lines you'll notice that you're creating new faces instead of just the bottom and top square you also have this square down here this one on the side this one on the side this on top the only reason I'm bringing up all these patterns is that they become sort of evident when you project a hypercube into three-dimensional space with an orthographic projection which is what this five app does so why don't we go ahead and just jump in and play with it great so here we are inside the VR experience and as you can see we are projecting a four-dimensional hypercube into three-dimensional space and as you can see this is also a very very boring projection that looks just like a cube this is very similar to when we took a cube a three-dimensional cube and projected it onto a two-dimensional surface and only drew a square not super descriptive but remember to make it more descriptive all we have to do is rotate it and in this app all you got to do to rotate is put your controller inside pull the trigger and move your hand around a bit so here we have a projection of a four dimensional cube onto a three dimensional space and as you can see very similar to how we create 3d cubes on 2d surfaces by drawing two squares and drawing a bunch of connective lines here we can draw two cubes and have a bunch of connective lines to fit those cubes together to create a projection of a hypercube now in a two dimensional projection of a 3d cube when you draw connective lines you're actually creating a bunch of other squares here when you're drawing connective lines you're creating a bunch of other cubes and this is one of the first revelations that I've had when I started playing with this was that Oh a hypercube is nothing more than a bunch of constituent lower-level cubes in the case of this hypercube right here we have the bottom left the top right and then the connective lines will create a bunch of other cubes as well 1 2 3 4 5 6 in total a hypercube is comprised of eight three-dimensional cubes as I kept playing around with it and actually the first half hours-- me just doing this but yeah as I started playing around of it I notice that there are a bunch of other projections that just made a bunch of really cool patterns so if I just offset it in this dimension you get some things that don't feel super descriptive but they are still cool nonetheless if you offset it in two dimensions you get me rotate what you get is this really weird interesting thing where you have you know the surface that is closest to us is actually the projection of a three-dimensional cube on to a two-dimensional plane right you have this square up here you have this square down here and you have all the connective lines that put them together and you get the sense of a cube that exists down here and in fact what I can do is I can rotate this hypercube to make this two-dimensional ish cube feel more like a three-dimensional cube see here's the volume inside that cube as I keep going right that cube now is is really big another interesting set of projections you can play with is by offsetting your cubes like this so you have this cube down here and then this cube up here and then playing with how much they're offset and getting a sense of what that looks like so here they're just barely offset there's a huge amount of overlap in between them and then here there's just a little bit of overlap in between them remember you know the bottom cube is here the top cube is here and so they're overlapping just a little bit here there is no overlap at all or there's only one point of overlap and there's something about this it just feels like a two-dimensional isomorphic projection of a three-dimensional cube right and last revelation that I had was playing with this application was I got a good sense of how cubes fit into the hypercube geometry in fact it's very similar to how squares fit into the 3-dimensional cube geometry so why don't we examine this for a moment and forget about its hypercube this what we have is a cube right and a cube is created from a bunch of constituent squares the top left right front back and bottom and each square so if I just take the front square it's connected to all the other squares except the one that's on the opposite side of the shape and the connection between one square and another square is always exactly one line now if you take this learning and you bring it into the hypercube space you'll notice that each cube is connected to all other cubes except the one that is on the opposite side of the hypercube so these two are not connected to each other these two are not connected to each other these two are not directly connected to each other and these two are not directly connected to each other and then any cubes that are connected to each other are connected through one lower dimensional object which in this case happens to be a square so this cube and this cube are connected through a square this cube and this cube are connected through a square and this cube in this cube etc etc now I'm not going to pretend to know everything about hyper cubes but I am going to say that this application for sure helped me gain a better understanding and appreciation of how hyper cubes work so that you know what I'm trying to understand how four-dimensional space works I'm not just sort of standing in a room imagining my body you know being projected in perpetuity and a non-euclidean dimension right I don't need to think about like multiple universes and like hyperspace or whatever all I have to do is like jump in and program an application to do this stuff for me and I get like a more granular intuitive understanding of how this stuff works so I have another application that I want to show here which basically depicts the fourth dimension in a different way instead of a fourth dimensional spatial Euclidean dimension it depicts the fourth dimension across the dimension of time which I'm hoping is very useful when it comes to dance education so let me just fire that up in a be right back so one cool example of where you can encode a bunch of additional information into your three dimensional spaces is this little app that I've created and all it does is it you know gives your hand your controller the ability to leave a trail when you pull the trigger button so you can leave a trail and then when you pull the grip button the trail will disappear now I sort of developed this because I'm really interested in human motion in three dimensional spaces I happen to also be a teacher of dance and the form of dance I do is called liquid which is Ray of style dancing and in this case you know this particular dance move is called the figure eight and it might not be evident why it's called the figure eight but if I were to leave a trail like this becomes pretty damn obvious why we call this the figure eight it is this nice repeatable motion that you get to do over and over and over again and I'm just all I'm really trying to point out here is that virtual reality is a phenomenal a 2-pack in extra information to encode it into three-dimensional spaces the last demo that I want to go over is this one right here it's very similar to the dance demo I was just leaving a trail behind before but here we have a chair it's going to be flung off into the distance and it's going to leave a trail and the the amount of the trail that we see is going to be controlled by this controller down here so now as you can see there's initial impact of the trail the chair it's sort of flung off into the distance and you know it has all these like awesome and cool protrusions so it leaves these really beautiful shapes in its path and then it hits the ground and then that's how it reacts right so now look at how cool this is right like I mean I would you know if I had all the resources in the world I definitely want to make this into a a sculpture and it's just so beautiful but you know I guess just to know like how meaningful it is and how much data there is in here I guess it just sort of goes to show that now that we have VR we can really start becoming four-dimensional thinkers so yeah thank you very much for watching if you want to download the 4d hypercube demo just go to my website thanks get to Cannon window for allowing me to not only feature the work but also to offer download if you want that stuff is completely open source so you can go to the github repo to download and play without yourself additionally oh no I guess I want to point out is that like to me VR is not just like pudding I mean it's pretty awesome to be able to have immersive experiences and to make first-person shooters that are super immersive or whatever but really what the power VR is to me is the ability to pack in additional information inside your 3d experiences to be able to embody a higher dimensional thinking so thanks again for watching and I'll see you next time

Channel: Albert Hwang

Views: 1,147,141

Rating: 4.8211088 out of 5

Keywords: VR, Virtual Reality, Vive, HTC Vive, Steam VR, 4d, forth dimension, 4th dimension, ixd, interaction design, hypercube, tesseract

Id: S-yRYmdsnGs

Length: 13min 0sec (780 seconds)

Published: Thu Jun 23 2016

Reddit Comments

[u/iwiggums]

Pretty cool app. It would be interesting to get some other 4D objects in it as well.

[u/2EyeGuy]

The demo should colour the "faces" (3D cubes) so you can see what's going on better.

Also, it would be good to see a 3D cross-section rather than the entire orthographic projection.

[u/Sir-Viver]

I don't understand how a hypercube represents a fourth dimension in a 3D space. Would a hypersphere provide the same representation? A hyperoctahedron? A hyperhuman?

[u/brzzzzzzzzzzzzzzzzzz]

https://www.youtube.com/watch?v=HgPSUer1ujM

[u/Killit_Witfya]

cool! gonna try this. always looking to expand my mind

[u/Ananas4]

Cool, I've been waiting for some hypercube apps for Vive

[u/wargarrrblll]

This is awesome, but I'm still going to be frustrated by only being able to watch a 3D projection of the object instead of the real thing. Stupid biological limitations!

[u/BASH_SCRIPTS_FOR_YOU]

They're talking 4 physical dimensions. (euclidean dimensions), time is special and not generally thought of when mathematicians talk dimensions

[u/nrgapple]

This demo is going to be huge in convincing further research at my job towards the Vive!