

How to walk through walls using the 4th dimension [video] - numo16
http://marctenbosch.com/news/2014/08/new-trailer-how-to-walk-through-walls-using-the-fourth-dimension/

======
panarky

      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-
dimensional head around what "A Sphere" can do.

[https://en.wikipedia.org/wiki/Flatland](https://en.wikipedia.org/wiki/Flatland)

~~~
gdubs
Wonderfully illustrated by Carl Sagan in the original Cosmos:

[http://www.youtube.com/watch?v=UnURElCzGc0](http://www.youtube.com/watch?v=UnURElCzGc0)

~~~
shangxiao
So that's what a tesseract is!

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metadept
I was really hoping for a continuous (rather than discrete) fourth dimension.
The concept is cool and looks to be well executed, but it's not very different
from other alternate reality implementations such as the Dark World in Legend
of Zelda.

~~~
DougWebb
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 models, rather than just putting 3D models
into 4D space, would be hard to wrap your head around. And the tools, both for
world creation and for rendering, are almost certainly limited to 3D so you'd
have to write your own tools for everything. No more GPU acceleration, unless
your 4D to 3D transformation creates models and textures on-the-fly to pass to
the GPU.

~~~
gliese1337
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 building by just auto-generating 4D mazes
with hypercubical cells, because maze-generation algorithms work in arbitrary
dimensions.

For simplicity, my rendering engine is a dead-simple raytracer which doesn't
even bother with reflections- just cast rays and record the first surface they
run into. Handling rotations and projections is really easy, but there are two
problems I have found:

1\. It's just really frickin' slow. Raytracing just ain't fast enough, though
I may be able to find some additional optimizations to make it better.

2\. In terms of gameplay, navigating the space is _really_ , _really_ hard. It
is so easy to get completely lost regarding which direction you're facing and
what hyperplane you're on when you can make arbitrary rotations in all four
dimensions. It might be something I could get used to, but so far I feel like
it's practically necessary to have some mechanism that will snap you back into
alignment with some set of gridlines.

~~~
Retric
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. <Set bomb off> Walls gone but cave collapses. <walk
though wall> <go back in time> <keep walking>.

Or simply let you flip times direction. Going vary slow or backward prevents
changing things, but you get to move. So, you might be able to for example
walk on water when moving backward in time etc.

~~~
lt
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.

------
ericHosick
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.

~~~
HeyTyson
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 area is
either in the past or in the future (when the wall fell or was being built).

Then he goes through the wall and hits the button again and walks back to his
original 3rd dimension.

That's what I took from it anyway. Seems really neat.

~~~
coldtea
> _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)._

No, time is actually a 5th dimension in this 4D game projection.

The developer has actually done the proper 4 to 3D projections, like he has
done for the 2/3D that he shows in the beginning.

In the 2D to 3D you can definitely see that he's not moving through "time",
because you can see the 3rd dimension.

The problem is just that we can't intuitively visualize a 4th spatial
dimension that makes this difficult.

But he's definitely not moving through "time" or in some "past" when the "wall
wasn't there". And of course moving through time has different properties than
moving through a 4th spatial dimension, so it's not really comparable.

E.g if we had a gradual rise in temperature from 0oF to 100oF in the time-
dimension, then if you could move through the time-axis you'd experienced
different temperature at will, whereas moving through any spatial axis would
you'd only feel a partial rise in temperature.

------
biot
This is a very interesting way of explaining the 4th dimension by relating it
to the difference between the 2nd and 3rd dimensions. However, I think what
would really solidify my understanding is to see the 4D level editor.

I'm not sure how truly 4D this world is, but it appears to let you switch
between a fixed set of different 4 dimensional positions, each of which has a
different 3D representation. Just as a plane in a 3D environment is a 2D
slice, a plane in a 4D environment is a 3D slice. You could effectively fake
this by imagining a triangular prism (like a cylinder, but triangular instead
of round). Each face of the prism contains a fully defined 3D world. Switching
to the alternate face of the prism is effectively doing the swap to the other
4th dimension, where you can walk along the alternate 3D environment to avoid
the obstacle, then switch back to the original 3D environment.

~~~
sp332
That's not quite what a 4th dimension is like. In your example, the faces are
completely separate from one another. But really they would be connected, in a
continuous line. You'd be able to push something a little bit along the
dimension, or run a long distance. You could rotate an object in 4D so that
parts of it ware poking a little bit into each dimension at the same time.

~~~
biot

      > That's not quite what a 4th dimension is like.
    

Of course not. You'll notice that I questioned how truly 4D the game was and
said the game appears to have fixed sets of 4D positions (ie: not a continuous
range). I also said that my example was fake 4D. If the developer were to show
the level editor, I suspect that we'd see it's not really 4D at all, but my
fake approximation of 4D via a fixed number of 3D environments that the player
can transition between.

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archagon
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?

~~~
Glench
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.

~~~
archagon
That's great news!

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smtddr
I've been watching this vid on repeat trying to fully comprehend what's
happening.

This is another vid trying to explain the same thing -
[https://www.youtube.com/watch?v=UnURElCzGc0](https://www.youtube.com/watch?v=UnURElCzGc0)

I really want to believe this is possible and this is how we'll be able to
travel far into space. Like how we have to spend time walking around a very
long wall when a bird can just fly over it in a fraction of the time, we
wouldn't have to think about traveling light-years because there would
something else we can do that's faster than a straight line.

~~~
sp332
That's not very likely, because you don't have to walk around some kind of
obstacle to get to a star. Even as a bird, you still have to travel the full
distance to your destination.

You could make a shortcut in space, which is called a wormhole. You can either
make one using extra dimensions, or in 3 dimensions with negative energy to
stabilize it, but neither of those seem to exist. Edit: link
[https://en.wikipedia.org/wiki/Wormhole#Traversable_wormholes](https://en.wikipedia.org/wiki/Wormhole#Traversable_wormholes)

~~~
JoeAltmaier
Unless 3d space is 'wrinkled'; in 4D you could travel straight there. Imagine
a crumpled sheet - the 2D traveler would have to trace a route through all the
convolutions to reach the other end of the sheet. The 3D traveler may only
have inches to go. 'A Wrinkle in Time' was a story about this.

~~~
sp332
You'd just have to hope that the place you want to go to is wrinkled up so
that it's next to you, and not still far away.

~~~
mordocai
From my vague recollections they were somehow causing the wrinkles to be close
together. It has been years since i've read the series though.

------
dschiptsov
Why not consider the idea that any "dimensions" are nothing but "[useful]
concepts of the mind", like "universal time" and even "limited space", the way
some ancient mystics (?) of various cultures believed?

The simplest example is about time - we (humans) have notion of time
"entirely" due to the certain properties of our environment in which we have
evolved - that there is day/night, Moon phases, seasons, periodical changes
(due to rotation of the planet and its motion around the Sun, of course, but
this is a very recent discovery).

Now imagine that you are somehow "suspended" in the outer space without any
motion relatively to the Sun. What would be your notion of time?

The time of a certain process (a mass in motion) has nothing to do with time
of another, completely different process (like radioactive decay) and the
notion of some "common, universal time" is just a "creation of the mind" which
is very handy and useful but "does not exist in reality".

Ancient Buddhist notions of "emptiness" or "void", and pre-Buddhist
(Upanishadic) notions of "everything is mind" (which is wrong, but very close
and accurate) are insights to the same "truths".

Your "dimensions" are "primitive concepts" of the same kind. Any coordinate
system imposed on so-called "reality" is nothing but a "concept of the mind".)

~~~
bottled_poe
> we (humans) have notion of time "entirely" due to the certain properties of
> our environment

That sounds very philosophical and all, but it seems to me that we have an
internal perception of time based on the rate that electrical impulses
propagate throughout our brains. Perhaps it would be distorted based on the
lack of external stimulus, but I believe we would feel the passage of time all
the same.

------
anoother
The game looks fascinating. I'm still trying to get my had around the
analogies, but get the feeling that playing the game for real will bring a
level of intuition to the experience.

In the meanwhile, can anyone help me out?

In the 2D->3D example, you have one shared axis (Z -- vertical), and an
alternating pair for the second axis (X and Y -- horizontal). In effect, from
the 2D character's point of view, 'jumping' into the third dimension is just
swapping your horizontal axis. Your previous horizontal axis is a vertical
section through your current one, and vice versa. As such, when swapping axes,
you would expect one 1D line (ie. a 1-pixel-wide vertical band) to be the same
before and after the swap.

When going 3D-> 4D, you have _2_ shared axes. Your third axis alternates, as
before. When switching between your 'third' axes, then, you would expect one
entire _2D plane_ of your perceived world-view to remain the same[1]. This
doesn't seem to be the case.

What am I missing?

[1] EDIT: This plane is likely to be a section through some concrete objects,
so you won't necessarily have 'seen' it before, though it will have been
there.

~~~
tomerico
The plane exists - it is passing through the character body (perpendicular to
the ground) and parallel to the desert, grass border in the example video.

You can see when the 4D rotation occurs there, that in that plane, everything
stays constant (e.g. rocks stay there, trees, etc.) You just look at the
objects from different angles as it rotates.

Edit: Link to the relevant point in the video -
[https://www.youtube.com/watch?v=9yW--
eQaA2I#t=148](https://www.youtube.com/watch?v=9yW--eQaA2I#t=148)

------
alpeb
If this topic interests you, you should definitely check "Imagining the Tenth
Dimension"
[https://www.youtube.com/watch?v=zqeqW3g8N2Q](https://www.youtube.com/watch?v=zqeqW3g8N2Q)

~~~
tfgg
That video is incoherent nonsense, especially from the '5th dimension' and
onwards, and in no way resembles the modern understanding of dimensions in
physics or mathematics. I wouldn't bother watching it except for
entertainment.

~~~
gabriel34
Care to expand? I'm not sure if it is possible to imagine these dimensions
with the "modern understanding of dimensions in physics or mathematics", but
it would be nice to at least know why this way is incorrect

~~~
tfgg
One could waste one's entire life trying to correct rubbish attempts at
physics on the internet, especially when it's full of non-sequiturs like the
video. But as a start, the description of quantum mechanics is nonsense and
I'm guessing the narrator got their understanding of it by reading popsci
books (I'm trying to avoid a personal attack on the author, but it's hard when
they've said a lot of wrong things so very confidently). The dimensionality of
a typical QM Hilbert space is infinite, not five. People get wound up
wondering what the N^th dimension is, when all dimensionality is, somewhat
simplified, is how many numbers you need to describe the position of
something.

The top comment on this stack exchange thread has more:
[http://physics.stackexchange.com/questions/55824/is-
imaginin...](http://physics.stackexchange.com/questions/55824/is-
imagining-10-dimension-video-by-rob-bryanton-has-any-invalid-wrong-informatio)

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laxatives
I remember being really excited about this game a few months ago. Part of me
is a little concerned whether there is enough to gain some sort of intuition
on where you are and what is exactly transforming with each input. I'm a
little concerned it will just become a game where you try things and hope for
the best and have a very incomplete mapping of whats really going on. But
anyways, its neat to see such a well produced game attempt to take on these
challenges.

------
jader201
This is exactly what Guacamelee does:

[https://www.youtube.com/watch?v=FQDwqrqAvwk](https://www.youtube.com/watch?v=FQDwqrqAvwk)

~~~
readerrrr
Yep, except it is in 3d. I was hoping for some continuous movement, but it
looks like it only switches between two worlds.

Maybe they will implement some more levels to make it look seamless. But there
is simply too much work to design the world in 4d as a single piece of land
holds a lot more information.

------
aoldoni
I saw something similar on the demos of what was supposed to be the Sonic
X-treme game. This was supposed to be the debut of the Sonic franchise in the
32-bit world.

[https://www.youtube.com/watch?v=wzvS_beXtXk](https://www.youtube.com/watch?v=wzvS_beXtXk)
[http://en.wikipedia.org/wiki/Sonic_X-
treme](http://en.wikipedia.org/wiki/Sonic_X-treme)

------
nanoleoo
That made me think a lot at this really nice open source game :
[http://stabyourself.net/orthorobot/](http://stabyourself.net/orthorobot/)

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yutah
Can you travel faster then the speed of light if you use the fourth dimension?
(my Internet ping is too high)

~~~
aruss
No, mathematically speaking the 4th dimension is no different than the 3 that
we are used to dealing with, and is held to the same physical constraints.

~~~
ars
It would certainly looks like you traveled faster than light. But you didn't
actually, you just took a "shortcut" as it were.

~~~
gtremper
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".

~~~
ars
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.

~~~
lmm
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.

~~~
ars
We don't really know that. Let's suppose the universe was really 4D. We don't
currently know if the universe is flat or not. A curved universe can be both
unbounded and finite which would be very elegant.

Einstein proposed a test to find out. I'm hoping this test will eventually be
Gravity Probe D (Probe C will be a repeat of the failed Probe B).

~~~
lmm
We're talking about a game. We know exactly what geometry the game world has.

~~~
ars
No we are not. He asked about the speed of light.

And the game world has some super weird discrete geometry anyway.

------
kazinator
People use 4D to go through walls all the time, when those walls take the form
of sliding doors. They stand in one place in space, in front of the door,
while naturally moving forward in the fourth dimension (time) to arrive to a
slice of space-time in which the door isn't there. In this range of space-time
they traverse space by a small distance (a meter or two), and also slip
forward in time by a several seconds (which is not long enough to leave this
special range of space-time). By so doing, they reach a point in space on the
other side of where the door was. Then they slip forward in time again, to a
time when the door is there again, at which time they smugly find themselves
on the other side of the door.

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mattwad
Looks like a neat game, but I'm skeptical how it would work in reality. For
example, it looks like the 4th dimension (time) gets frozen (for the observer)
when you want to traverse it. That means, the second you 'travel in time,' the
Earth, at its current velocity, would already be 30km away.

~~~
0x0
... or did the rest of the universe move 30km the other way? :)

