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How to walk through walls using the 4th dimension [video]

marctenbosch.com

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Re: How to walk through walls using the 4th dimension [video]

#81

Post by richmarr »

tejon wrote: post #72
DougWebb wrote: post #20

Earlier quoted context omitted.

That would be really cool. The mathematics involved don't seem too difficult; you have to add another axis to your vectors, points, and transform matrices, and you can place and orient your models in 4D space, set up lights and a camera in 4D space, and project the camera's view into 3D space first then onto the 2D display. I think the hard part is creating the models and writing the rendering engine. Creating 4D mod…

We already have 4-dimensional models; we just keep the 4th dimension separate and call it an animation path. In fact, Skyrim has 5-dimensional models: there are two versions of each walking animation, roughly "feminine" and "masculine," but each character actually uses a specific blend-point between the two. Similar analogies with facegen textures. All the pieces are there, they just need to be glued together right.

Can you clarify why having two animation paths makes 5 dimensions? Surely the dimension is time, you're just deforming the 3 spatial dimensions along two different paths as you progress uniformly along the 4th?

Re: How to walk through walls using the 4th dimension [video]

#82

Post by clwk »

panarky wrote: post #24

Flatland: A Romance of Many Dimensions is an 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. Writing pseudonymously as "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture; but the novella's more enduring contribution is its examination of dimensions. "A Square" feels sorry for poor, limited "A Line", but can't wrap his two-…

For a visceral and entertaining exploration of what a literal fourth spatial dimension might be like from our perspective, try Rudy Rucker's hilarious 'Spaceland'.

'In a tribute to Edwin Abbott's Flatland, a classic mathematical fantasy about a 2-dimensional being (A. Square) who receives a surprise visit from a higher-dimensional sphere, Rudy Rucker's Spaceland describes the life of Joe Cube, an average, modern-day Silicon Valley hotshot who one day discovers the fourth dimension from an unexpected visitation. Spaceland contains scenes that are violent and sexual in nature as well as suggestive illustrations.'

https://en.wikipedia.org/wiki/Spaceland_(novel)

Re: How to walk through walls using the 4th dimension [video]

#83

Post by lmm »

ars wrote: post #80
gtremper wrote: post #79

Earlier quoted context omitted.

There are no shortcuts. The straight line connecting 2 points in 3d space is shorter than any path connecting the points that goes through a higher dimension. The same applies to 2d compared to 3d. If you have 2 points on a sheet of paper, the shortest path is on the paper. Any path that went "off" the paper into the 3rd dimension would be longer, so no "shortcuts".

Imagine a strip of paper bent into a U. You can travel from one end of the strip to the other through 3D space with a much shorter distance than along the entire paper.

Sure, but that's not what we're talking about here. We're talking about Euclidean 4D space projected orthogonally onto Euclidean 3D slices, not some nonstandard projection onto some weird 3D surface embedded in 4D space.

Re: How to walk through walls using the 4th dimension [video]

#84

Post by mtbcoder »

HeyTyson wrote: post #19
ericHosick wrote: post #4

As a game, this is really cool. But when he got to the 4th dimension it didn't make much sense as an explanation (rubble from 3rd dimension showing up in the 4th). However, if the 4th dimension was time, then you would walk back (or forward) in time to when the wall wasn't there (isn't there anymore cause it is now rubble), move "past the wall", and then walk forward/backward to the original time.

I thought the same until I watched it a second time. 4th dimension is still time. 'The button' takes you to your character's view of moving across a 3rd dimensional plane. I'm assuming the two different textures on the ground represent the change in the 4th dimension (time). So when you cross to that other side and hit the button again, you're back in the 3rd dimension across a different plane (time). So the desert a…

That's how I saw it as well. When you rotate to the "side" (pivot) in the 4th dimension, you see the wall and its change over time as one entity. So then you can either pick going around the start (when construction of the wall began) or at the end (when the wall falls). Naturally the landscape would also experience change, hence the desert. When you pivot back, you are at the same location in time and space of the 3rd dimension, just in front of the wall now.

Re: How to walk through walls using the 4th dimension [video]

#85

Post by NickPollard »

raimondious wrote: post #56
sp332 wrote: post #28

Earlier quoted context omitted.

Mathematically, they're identical to any other dimension. You can move a little bit into a fourth dimension just like moving a little bit left-to-right. Or you can rotate things around the fourth axis just like turning something clockwise. In the case of this game, he only shows a 2D projection of a 3D cross-section of a 4D world, so that might be adding to the confusion. What you see in the video is only 3D "slices"…

One of the axes introduced by the fourth dimension. There are 3 in 3D, 6 in 4D. XYZ space has axes perpenicular to the planes xy, xz, yz. WXYZ space has axes perpendicular to the planes xy, xz, xw, yz, yw, zw.

No. There are only 4 axes in 4-dimensional space - every point is described as a 4d vector, i.e scalar positions along each axis: (x,y,z,w).

xy, xz, etc. are not planes in 4d space - they are 3d-hyperplanes, and perpendicular to them are planes, not axes. Imagine this: you have a 4d vector and you hold x and y constant. You still have 2 degrees of freedom: a plane, not a line.

Re: How to walk through walls using the 4th dimension [video]

#86

Post by archagon »

Glench wrote: post #78
archagon wrote: post #35

I've been getting progressively more excited about Miegakure over the past year, but I haven't heard anyone who's played the game talk about how easy it is to "grok". Does moving between dimensions become intuitive over time? Or do you always have to consciously think about what you're doing?

I've also played it semi-recently, and it's really, really intuitive – just like playing another game where you don't quite understand the rules. Things slowly start making sense. Marc (the creator) is an extremely talented designer for building a progression of levels that teaches you the concepts just through level design. You definitely don't get a formal understanding of the 4th dimension, though.

That's great news!

Re: How to walk through walls using the 4th dimension [video]

#87

Post by archagon »

marctenbosch wrote: post #61
archagon wrote: post #35

I've been getting progressively more excited about Miegakure over the past year, but I haven't heard anyone who's played the game talk about how easy it is to "grok". Does moving between dimensions become intuitive over time? Or do you always have to consciously think about what you're doing?

Jim Rossignol from Rock Paper Shotgun played a recent build: http://www.rockpapershotgun.com/2014/03/18/miegakure-preview... He said: "Flipping through dimensions is remarkably intuitive- [...] I shifted dimensions, messing about with this strange toy until I quickly understood most of the problems that I faced."

Really glad to hear that. Now I'm even more excited!

Re: How to walk through walls using the 4th dimension [video]

#89

Post by lt »

Retric wrote: post #60
gliese1337 wrote: post #30

Earlier quoted context omitted.

This is something I've been working on as a side-project on and off for a while. It's complicated by the fact that every existing engine is built around the assumption that you only want to use 3 dimensions, not four, and not arbitrarily many, so I've been pretty much writing everything from scratch (and very limited GPU acceleration, as you said, because GPUs also assume 2 or 3D). So far, I'm punting on model buildi…

I would just avoid the rotation issue. Time works as a 4th dimension so if you have a charter that can flow backward or forward in time you can 'solve' 4d mazes without major issues. From a game-play perspective plenty of games have you vary limited control over time but you could make some vary interesting puzzles with full control. EX: walls in the way. Walls gone but cave collapses. . Or simply let you flip times…

That's pretty much the idea of Braid, an awesome indie game. It uses time manipulation in different ways to create mechanics in that vein. Recommended.

It's a different concept than true 4D though.

Re: How to walk through walls using the 4th dimension [video]

#90

Post by TophWells »

ericHosick wrote: post #4

As a game, this is really cool. But when he got to the 4th dimension it didn't make much sense as an explanation (rubble from 3rd dimension showing up in the 4th). However, if the 4th dimension was time, then you would walk back (or forward) in time to when the wall wasn't there (isn't there anymore cause it is now rubble), move "past the wall", and then walk forward/backward to the original time.

In the 2D/3D world, the rubble just fell off the wall and landed next to it. It's only strange because it fell in the direction that the player character doesn't normally perceive.

In the 3D/4D world, the rubble fell off the wall and landed next to it.

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