
4D toys - wenderen
http://4dtoys.com/
======
rzwitserloot
Here's a thought I had watching the bit with 2D man:

Actually, the 3D view that 2D man does not understand but which we do
understand is... still 2D. My screen is flat.

You can use a 2D viewport to render a 3D scene in a way that is natural and
easy to understand for us humans: A human watching the 2D scene can very
quickly surmise from a glance at the viewport: Which objects are in the scene,
and where are they located, in _ALL_ 3 dimensions?

This raises the question:

Can you render a 4D scene onto a 3D viewport such that us humans are pretty
good at understanding where every object in the scene is, in all 4 dimensions?

I assume the answer is 'yeah, you can do that'. I wonder what that would look
like.

It's complicated of course; our eyeballs are involved and they kinda work in
2D and not 3D; where we humans can casually glance at a 2D viewport rendering
a 3D scene for a second and know what's happening, we'd have to walk around
the 3D screen rendering a 4D scene in order to even see everything.

~~~
simias
The problem is that while everything you see on your (2D) monitor is
effectively 2D our brain is good at taking 3D cues (shadows, perspective,
parallax etc...) to reconstitute 3D "data" from it. For instance look at 3D
rotating cube on your monitor:
[https://www.youtube.com/watch?v=5E10zYKln3g](https://www.youtube.com/watch?v=5E10zYKln3g)

Even though there's no shading, a bad resolution and zero context anchoring it
in a familiar setting you immediately see it as a 3D object when effectively
that's just 3 2D quadrilaterals changing colors and shape. We really need very
little to be able to extrapolate depth information from a very limited 2D-only
display.

If you did that with 4D cues in 3D space (say in VR or something) I think it
wouldn't work. It'd just look like a 3D object changing shape, not a
projection of a higher dimension (the same way an hypothetical 2D being would
see 3 quadrilaterals changing shape in the above video, not a solid 3D object
that would be an abstract concept to them, not a familiar reality).

Could we teach our brain to "think in 4D" and interpret these cues
differently? To a certain extent probably, maybe if you spent hours and hours
and hours in a VR simulation with 4D objects you'd start getting a feel for
it. I doubt you'd ever get as good as with 3D objects since we've been exposed
to these literally every waking moment since birth, but maybe I underestimate
the plasticity of our brain.

That actually leads me to an other question: is 3D somewhat hardcoded in our
brains or is it purely learned? If we were mad scientists and took a baby
brain into a 4D "plato's cave" style simulation, could it grow into being able
to perceive 4D as intuitively and effectively as we do with 3D space? Also
unrelated question: does anybody have a baby I could borrow?

~~~
scrollaway
> Could we teach our brain to "think in 4D" and interpret these cues
> differently? To a certain extent probably, maybe if you spent hours and
> hours and hours in a VR simulation with 4D objects you'd starting getting a
> feel for it. I doubt you'd ever get as good as with 3D objects since we've
> been exposed to these literally every waking moment since we're born.*

Good lord! Has anyone tried?

This reminds me of the backwards bicycle video on youtube
([https://www.youtube.com/watch?v=MFzDaBzBlL0](https://www.youtube.com/watch?v=MFzDaBzBlL0)).
I... really want to try what you're suggesting.

~~~
TheSpiceIsLife
In the YouTube video he says:

"So here's why I did. It was a personal challenge. I stayed out here in this
driveway and I practiced about 5 minutes every day. ... after 8 month it
happened ... in two weeks he (the son) did something that took me 8 months to
do".

Well, if you were serious about learning a skill you wouldn't just do one 5
minute session per day for eight months.

A more appropriate training regime would be way more intensive than one 5
minute session per day. Are we to believe he limited his son to one 5 minute
session a day?

Do children really learn languages quicker than adults? By age 3, children
will probably have words for almost everything. Babies might even say mama and
dada by 6 months of age.

Children have several language learning advantages over adults: complete
immersion; it is imperative they learn; effectively unlimited time; no
responsibilities.

But, it takes them _years_ to learn their native language to basic competency.

Compare: an English speaker can learn Afrikaans, Danish, Dutch, French,
Italian, Norwegian, Portuguese, Romanian, Spanish, or Swedish to _General
Professional Proficiency in Speaking and Reading_ in 600 hours carried out
over 24 weeks (25hrs per week). Cantonese, Mandarin, Japanese, Korean, or
Arabic will take 2200 hours over 88 weeks (25hrs per week).[1]

Is it _easier_ for a child? Yeah probably, they don't even have to look after
themselves.

If I could live as a child in a foreign language house in a foreign language
city, with only two tasks: learn to speak and read the language to basic
competency, and learn to ride a backwards bicycle, I'm firmly of the believe I
could out pace the 95th percentile of children at both tasks.

As an aside, he says his son is the closest person to him genetically, but
aren't his parents both equally as close to him genetically as his son?

1\. [http://www.effectivelanguagelearning.com/language-
guide/lang...](http://www.effectivelanguagelearning.com/language-
guide/language-difficulty)

~~~
jesusth1
Yeap, [https://youtu.be/oI2aMKwXXnE](https://youtu.be/oI2aMKwXXnE) this guy
took a more serious attempt at learning to ride the backwards and it seems it
didn't take him that much time.

~~~
TheSpiceIsLife
Thanks for finding that.

So it only took him about an hour, over three days, to get it worked out well
enough to not immediately fall off, and an hour and a half over four days to
get to 50 meters.

There's a comment in on the YT video from Destin saying _" the RC helicopter
pilot was able to learn it in about an hour but I don't think his brain is
normal"_ \- good point, the RC helicopter pilot has more experience
understanding reversed input while the helicopter is flying toward him, also
he had the opportunity to watch Mike learn first.

I reckon the learning process could be sped up even more by taking the pedals
of, turning it in to a balance bike, learning how to ride it down slight
inclines, get that sorted then putting the pedals back on.

------
throwawaymath
This is an old video [1], but it remains the clearest visual explanation of
multiple dimensions that I've ever seen. I really can't recommend it highly
enough. I think anyone trying to visualize a 4D object will get something out
of watching it.

I played with the 4D toys app after it showed up on /r/math a while ago. I
like it and I think it's useful. My only complaint would be that it's a little
too open ended. While it's nice to provide a simulated tactile experience of
four dimensions, I think the app should provide a bit more visual intuition.
That's one of the things I like about this video. ________________

1\.
[https://www.youtube.com/watch?v=90olwwLdEYg](https://www.youtube.com/watch?v=90olwwLdEYg)

~~~
shawn
Reminds me of
[https://youtu.be/K4JhruinbWc?t=110](https://youtu.be/K4JhruinbWc?t=110)

~~~
throwawaymath
That was really great, thanks for sharing!

------
chubot
Wow, cool to see this here. I've been working on reproducing some of it in
numpy/matplotlib for the past 2 weeks! I liked their 3D-sliced 120-cell
(equivalent of the dodecahedron), and it wasn't too difficult to reproduce.

Step 1: Use Schlafli generator from here [1]. Schlafli numbers are a compact
description of regular polytopes, and there is a recursive algorithm to
generate vertices, edges, faces, etc. from them. The base case of the
recursion is dimension 1, so you make 4 calls to get to dimension 4.

Step 2: Intersect the edges of the polytope with a hyperplane (a 3D subset of
4D).

Step 3: You get a set of 3D points out of step 2. Draw the convex hull of
them, which gives you triangles.

Step 4: Render the triangles somehow. I used matplotlib's 3d facilities
(mplot3d), and we are working on raytracing them.

Step 5: Animate over different hyperplanes. Take the min and max in the w
plane and that will give you non-empty slices. Now you can "see" the 4D
polytope using time as the 4th dimension.

I sure he is doing something more advanced (4D collision detection), but this
is all we needed to reproduce something that looks kinda cool.

[1] [https://github.com/aruth2/schlafli](https://github.com/aruth2/schlafli)

------
anotheryou
Can someone help me out here?:

I can represent 3D quite comfortably on 2D monitors, can there be an intuitive
mapping of 4D to a 3D VR view?

I know 3D mapped to 2D suffers from occlusions and heavily relies on clues
like perspective, shadow etc. But given enough time even a less intuitive 4D
view could become intuitive with time, too.

edit: found this:
[https://youtu.be/S-yRYmdsnGs?t=252](https://youtu.be/S-yRYmdsnGs?t=252)

even better: [https://youtu.be/dy_MUfBuq2I](https://youtu.be/dy_MUfBuq2I)
(turn on subtitles)

~~~
arketyp
What would be the benefits of the 3D VR? There will always be a 2D bottleneck
on your eyes' retina. The most important perspective clue I would say is
temporal sampling. For dynamical systems, Takens theorem says that a high
dimensional topology can be restituted by the sequential sampling of a single
variable alone. It seems likely to me that our perception generally works by
this principle. That being said, I think we are quite heavily hardwired to 3D
perception. I suspect these circuits cannot be wholly overridden.

~~~
matte_black
What would a 3D eye even be like? Is it something like having independent
depth perception per eye?

~~~
arketyp
Photons travel in 3D space and may only be occluded by 2D surfaces. There is
no getting around that fundamental aspect of reality. In this universe.

~~~
jonbarker
This is why as an armchair physicist I'm excited about the new neutrino
observations and research going on, mainly because neutrinos aren't affected
by gravitational lensing and other effects other particles encounter as they
'roll around' on space-time. Would it be possible to understand conceptually
how other dimensions extend out of space time? I'm imagining a Y-axis
perpendicular to the space-time fabric....

~~~
scentoni
Gravitational lensing is a distortion of spacetime. It affects all particles,
including neutrinos.

------
netgusto
There's also Miegakure, another beautiful game based on 4D puzzles.

[http://miegakure.com/](http://miegakure.com/)

~~~
shinryuu
I've been waiting for that game for more than 5 years now I think.. It'll
probably stay in development for another 2 years or so.

~~~
MrEldritch
It's getting _really_ close, though. Puzzles, mechanics, dialogue, effects,
all finished. At this point, according to the dev, all that's really left for
him to do is "small things like fix collision bugs, and I will keep placing
props in levels and program the occasional cool 4D thing. We still need a
bunch of 3D modelling done."

I'd give a 50% shot it lands on Steam before the end of 2019. (35% it doesn't
make 2019 but lands before the end of 2020, remainder that it lands later or
never releases.)

~~~
GuB-42
90% done. It means we are halfway there :p

My gut feeling is that we are not there yet, and that 4D toys is an attempt by
the author to monetize his development tools in order to be able to complete
the main project. I hope it turns out well, Miegakure is definitely in my
watch list.

------
gertgoeman
Kinda reminds me of "Flatland":
[https://en.wikipedia.org/wiki/Flatland](https://en.wikipedia.org/wiki/Flatland)

~~~
albertgoeswoof
This book is incredible, it’s hard to believe it’s 134 years old.

------
MAXPOOL
"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space
and say 'fourteen' to yourself very loudly. Everyone does it." – Geoffrey
Hinton, A geometrical view of perceptrons,
[https://www.coursera.org/lecture/neural-
networks/a-geometric...](https://www.coursera.org/lecture/neural-
networks/a-geometrical-view-of-perceptrons-6-min-sPEhK)

* but remember that going from 13D to 14-D creates as much extra complexity as going from 2-D to 3-D

~~~
forgotpwd16
There is a joke that goes like this: A mathematician and an engineer attend a
lecture on the 11-dimensional M-theory. At the end of the lecture the
mathematician delighted says how much he enjoyed it. The engineer puzzled asks
him how anything even makes sense. The mathematician replies "It's easy.
Visualize an N-dimensional space, then let N go to 11."

------
yuvalr1
This is amazing and looks really fun! I remember reading a short science
fiction story once, "Mimsy Were the Borogoves"[1], where small children were
playing with such 4D toys, which were found to be educative in unpredictable
ways.

It really makes me want to try it out. I wonder if it's really the same
without VR.

[1]
[https://en.wikipedia.org/wiki/Mimsy_Were_the_Borogoves](https://en.wikipedia.org/wiki/Mimsy_Were_the_Borogoves)
(watch out, there are spoilers here!)

~~~
undershirt
the bottom of the website includes an illustrated frame and excerpt from that
very story

~~~
yuvalr1
Wow, you're right! Didn't see that, Thanks! :)

------
dang
Discussed last year:
[https://news.ycombinator.com/item?id=14471931](https://news.ycombinator.com/item?id=14471931)

------
tehsauce
If anyone wants to play with a 4D toy right now in their web browser, here is
an interactive tesseract (4d cube) that I built.
[http://transdimensional.xyz](http://transdimensional.xyz) It doesn't have
physics but features a novel interface that I designed to help build an
intuition about different rotations. (There are six axes of rotation in 4
dimensions)

------
DC-3
Using the 4th Dimension, the two interlocking rings can be separated. However,
what would be the equivalent puzzle for the 3rd dimension? What 2D system
requires the 3rd dimension to be separable? Is there even an equivalent?
Clearly a circle within a circle is one such system, but it corresponds to a
ball wholly contained by another ball in 3D, not a pair of interlocking rings.

~~~
lifeformed
It would be a ring with a stick through it. In a 2D slice down the middle, it
would look like a donut with a circle (the slice of the stick) in the hole.
The circle appears to be stuck inside it, with no way out in 2D. In 3D, you
just pull the stick out of the ring.

------
xtiansimon
How curious. What would a haptic VR experience be like? Does a 4D object still
exert mass in the other 3Ds? Could you _intuit_ the other 3Ds even if they
were not visible?

~~~
marctenbosch
The VR version has haptics. It's kinda interesting. I think there is a little
bit of intuition to be gained.

------
bhouston
I would have through the he would have done a projection from 4d space to 2d
space similar to how 3d graphics does a projection from 3d to 2d. Similar to
[http://christopheremoore.net/4d-renderer/](http://christopheremoore.net/4d-renderer/)
It I guess in that case it would be difficult to interact with it in VR.

I guess this slicing technique works but it would be a bit weird.

------
JoeDaDude
Some might remember this excellent treatment of higher dimensions [1] in which
you first manipulate shapes to solve a puzzle in 2D, then 3D, and finally 4D.
YYou develop a keen sense of 4D objects:

[1]
[http://harmen.vanderwal.eu/hypercube/](http://harmen.vanderwal.eu/hypercube/)

------
beefield
Agreeably playing with 4d objects is mindboggling enough, but still I would
like to somehow visualize myself moving around in 4d space. I am not quite
sure how a 4d room would look like and what kind of doors to other 4d rooms
would be like, bit for sure navigating around a 4d house could be fun...

------
rekshaw
The video ends saying that trying to fit a 4D cube in a 4D hole is like a
child playing with toy blocks. Hypothetically, if a child was raised with
regular VR simulations that allowed the child to manipulate 4D objects, would
their brain "learn" it and in a way unlock the 4th dimension?

~~~
freehunter
I was wondering this too as I watched the video. As an adult I know how
physics works and I know that what I'm seeing is not normal based on decades
of experience. If you showed this to a 1 year old and let them play with 4D
virtual toys for a few years, would they more intuitively understand 4D
objects? Or would it still remain foreign due to the fact that they can't see
things moving around the fourth dimension?

~~~
vhold
As I played around with 4D toys, I did start to gain a sense of things that
were "Behind" or "In Front" of me in 4D space, that is I could start to feel
their presence after they had been pushed out of sight, if I knew in what
direction they were moving in the 4th dimension. If I didn't know that I could
only feel that they were near.

It helps that there is a little visualization that is just a line-per-object
showing where you are, and where all the objects are intersecting the 4th
dimension, that you also use to move "back and forth."

One thing I found myself doing was grabbing objects at one of their edges in
the 4th dimension, by moving myself to near their boundary, and then using
them like brooms. It's really easy to understand with the case of a
hypersphere, since at its edge it's just a smaller sphere than at the middle.
So you grab that small sphere at the edge, and push in the direction towards
its middle in the 4th dimension, and it will act like a bowling ball. You
won't see the stuff you are pushing around because the sphere is "ahead" of
you, unless they roll around the sphere, then you'll pass them. Once you reach
the edge of the 4th dimension, all the stuff you kept pushing will be there.

Predicting how 3D intersections change as objects rotate about in the 4th
dimension still seems like chaos to me though, except in the case of
hyperspheres, which basically don't change as they rotate, but I only played
around for about an hour or so. The only way I found to rotate objects in the
4th dimension was to have them collide with each other, or the walls and
floor, which makes it kind of hard to carefully experiment with their
rotations.

------
_Codemonkeyism
"Goundbreaking 4D+Time Physics Engine that uses new mathematics created for
this project."

New mathematics no less!

------
kranner
This passage from Death's End by Cixin Liu really gave me pause to stop and
wonder about what the experience of seeing extra dimensions might be like
(here translated to English by Ken Liu): \--

A person looking back upon the three-dimensional world from four-dimensional
space for the first time realized this right away: He had never seen the world
while he was in it. If the three-dimensional world were likened to a picture,
all he had seen before was just a narrow view from the side: a line. Only from
four-dimensional space could he see the picture as a whole. He would describe
it this way: Nothing blocked whatever was placed behind it. Even the interiors
of sealed spaces were laid open. This seemed a simple change, but when the
world was displayed this way, the visual effect was utterly stunning. When all
barriers and concealments were stripped away, and everything was exposed, the
amount of information entering the viewer’s eyes was hundreds of millions
times greater than when he was in three-dimensional space. The brain could not
even process so much information right away.

In Morovich and Guan’s eyes, Blue Space was a magnificent, immense painting
that had just been unrolled. They could see all the way to the stern, and all
the way to the bow; they could see the inside of every cabin and every sealed
container in the ship; they could see the liquid flowing through the maze of
tubes, and the fiery ball of fusion in the reactor at the stern.... Of course,
the rules of perspective remained in operation, and objects far away appeared
indistinct, but everything was visible.

Given this description, those who had never experienced four-dimensional space
might get the wrong impression that they were seeing everything “through” the
hull. But no, they were not seeing “through” anything. Everything was laid out
in the open, just like when we look at a circle drawn on a piece of paper, we
can see the inside of the circle without looking “through” anything. This kind
of openness extended to every level, and the hardest part was describing how
it applied to solid objects. One could see the interior of solids, such as the
bulkheads or a piece of metal or a rock—one could see all the cross sections
at once! Morovich and Guan were drowning in a sea of information—all the
details of the universe were gathered around them and fighting for their
attention in vivid colors.

Morovich and Guan had to learn to deal with an entirely novel visual
phenomenon: unlimited details. In three-dimensional space, the human visual
system dealt with limited details. No matter how complicated the environment
or the object, the visible elements were limited. Given enough time, it was
always possible to take in most of the details one by one. But when one viewed
the three-dimensional world from four-dimensional space, all concealed and
hidden details were revealed simultaneously, since three-dimensional objects
were laid open at every level. Take a sealed container as an example: One
could see not only what was inside, but also the interiors of the objects
inside. This boundless disclosure and exposure led to the unlimited details on
display.

Everything in the ship lay exposed before Morovich and Guan, but even when
observing some specific object, such as a cup or a pen, they saw infinite
details, and the information received by their visual systems was
incalculable. Even a lifetime would not be enough to take in the shape of any
one of these objects in four-dimensional space. When an object was revealed at
all levels in four-dimensional space, it created in the viewer a vertigo-
inducing sensation of depth, like a set of Russian nesting dolls that went on
without end. Bounded in a nutshell but counting oneself a king of infinite
space was no longer merely a metaphor.

~~~
matte_black
Wow, if this is how it’s like to see three dimensions then where would one be
able to hide information to the viewer? Probably another dimension. By moving
an object from one location to another the information about the position in
the previous states are lost. And information about the future states remains
hidden. Alas, present states conceal everything hidden behind them, or ahead
of them.

------
abhiminator
This is incredibly cool. I feel this would be super useful for teaching
children (like my nephew who's 11-years-old) to think about the fourth
dimension as a component of the fabric of space instead of time as it's
usually understood.

------
beaumayns
I'd love to know the math behind the physics engine, particularly angular
momentum. Planar rotations are weird in 4d.

------
eerikkivistik
What tools were used to build this I wonder?

~~~
MrEldritch
Part of it is that the developer's spent the last decade building a game
engine and toolchain for 4D content while developing his 4D puzzle game
Miegakure ([http://miegakure.com/](http://miegakure.com/))

~~~
eerikkivistik
That looks incredible. Do you know if the developer has published any papers
or code on the subject?

------
anxtyinmgmt
This is the best visualization of 4 dimensions I have ever seen.

------
thelastidiot
Can't wait to see the 5D version. But seriously, what's the use of that? I
don't get it.

~~~
netgusto
It's meant to give an intuition about what a 4th space dimension might feel
like, thru self experimentation.

------
csomar
Can this explain some of the quantum weirdness? Like some of the things
quantum entanglement have is due to a forth dimension we are not aware of.
Might have to do with general relativity and it is the 4th dimension in
smaller scales.

Now where is my noble price?

