
4D Toys: a box of four-dimensional toys - hcs
http://marctenbosch.com/news/2017/06/4d-toys-a-box-of-four-dimensional-toys/
======
yathern
This looks fantastic. If I had a VR device I would get this immediately. I've
always had a fascination with trying to grok higher dimensions. I think it's
just about impossible to have an intuitive understanding of it - 3D spacial
reasoning is in our wiring through both nature and experience.

You know the theory of how language shapes your thinking? For example, in
societies where there is no separate word for orange and red, they have
extreme trouble telling the difference between them. In some native tribe
where they use cardinal directions (North, South) - not relative (Left, Right)
- they have an almost supernatural ability to know which direction they are
without needing any other cues (sunlight, stars).

Point being - would being able to completely think in four dimensions have an
impact on how you understand the world?

~~~
indspenceable
Often when I see something about 4d it uses this same analogy: a 2d being
seeing a crosssection of a 3d world, in 2d. However, the video is in 2d, and
it's able to show 3d in a much better/more clear way, clearly, cause when it's
showing that example it's got a cutout of the "3d" view (which is still 2d!).

Why can't we do the same thing with 4d? Why does the object just disappear
when it bounces into the 4th dimension, can't we maybe see a projection of it
onto the 3rd dimension?

~~~
js8
Maybe they could do something like a fog? That is, if the object was farther
away in the 4th dimension, it would appear less distinct or more fuzzy/blurry,
like being in the fog.

~~~
hcs
Miegakure did something similar where it showed a shadow of the 3D space
immediately adjacent to the currently visible slice. I think he since removed
that, so I expect he must have experimented with something similar in 4D Toys
and decided against it.

------
chmod775
I'm curious how this would look if the 4D space was projected onto the 3D
space instead of taking a cross-section, much like we already project 3D space
onto 2D space (your display), to create "3d" graphics.

~~~
Rotten194
Isn't that what the traditional 3d visualization of a hypercube is? e.g.
[https://en.m.wikipedia.org/wiki/Hypercube#/media/File%3AHype...](https://en.m.wikipedia.org/wiki/Hypercube#/media/File%3AHypercube.svg)

~~~
BearGoesChirp
Isn't that a 2d projection of the 3d projection of 4d space?

It gets weird because our eyes see almost in 2d, and even with VR, there is a
2d feed to each eye that gets combined to add slight 3d depth perception. So
really we would be projecting a 4d world onto two 2d plains that our visual
cortex would try to merge to add slight depth perception.

------
js8
If you make a Kickstarter to 4D print them, I would support it for my kids. I
think for kids, it's more important to play with real-world physical objects
rather than their virtual computer representation.

~~~
placeybordeaux
Is this satire?

~~~
js8
It's a joke - I don't actually have kids. And I mean the 2nd sentence
seriously. Also, quick googling reveals that 4D printers haven't been invented
yet, so presumably one would need a KS for those first.

------
hcs
I considered linking to the game's site at
[http://4dtoys.com/](http://4dtoys.com/) , but this blog post introducing it
has more design details that I think will interest HN.

------
pmilla1606
This looks like fun, going to try this out over the weekend.

This is the same person who made this game (that also looks like good fun):
[http://miegakure.com/](http://miegakure.com/) that I remember reading about
some years ago but never got a chance to play with

~~~
sp332
The game isn't out yet.

~~~
i_cant_speel
Yes it is.

~~~
marctenbosch
Ah, miegakure is not out yet, sorry!

------
zitterbewegung
As a person who studied knot theory and sitting through other peoples
presentations about higher dimensional knots this looks like a neat treat!
After hearing about the concept I bought the game and tried it out. I like how
you replace actual physical actions to objects in 4 dimentions. Usually this
is projected on the time axis but with this interface it makes it much more
fun to play with it instead of having basically a generic slider.

~~~
thaumasiotes
Higher dimensional knots? I thought one of the first things you learned in
knot theory was that knots are only possible in three dimensions?

~~~
zitterbewegung
Yea so you consider a two dimentional sphere embedded in a four dimentional
ball. So it's a S^2 that is knotted in R^4.

------
mihaifm
The video explaining it is really well made, but for some reason I still can't
grasp the 4th dimension. Perhaps it's one of those things that you only need
to know they exist at the theoretical level.

~~~
eriknstr
Same here. I understand perfectly everything that was said in the video but I
still don't understand how the fourth dimension quite works.

However, having only heard of hypercubes and not hyperspheres before I decided
to see if there was anything useful about them online and I found this video
that I just started watching and already 1 min 50 sec into the video something
very interesting was said;

> Everybody knows what the sphere is. I'm thinking of a hollow sphere so like
> a basketball right. That's a two-dimensional surface living in a three-
> dimensional space. The hypersphere is generalized one dimension up, so in
> four dimensions you have this three-dimensional space called the 3-sphere or
> the hypersphere.

[https://www.youtube.com/watch?v=krmV1hDybuU](https://www.youtube.com/watch?v=krmV1hDybuU)

Already this is telling me something that I have not heard before, and which I
find much more helpful than talking about what a shape looks like from the
perspective of someone living one dimension further down. That being said it
was still useful having that explained as well, which is what Flatland: The
Movie (2007) was about as well. Just this fact I quoted above was even more
useful IMO.

~~~
eriknstr
Another quote from the video I linked in parent comment.

6:19

> As complex numbers are to real numbers, quaternions are to complex numbers.
> It's like a way to build up even further. [...] Real numbers are one-
> dimensional. Complex numbers are two-dimensional. [...] For three dimensions
> there is no natural number system, but for four dimensions there is and it
> looks like this.

~~~
jacobolus
That’s really misleading. The complex numbers are not a two-dimensional
Euclidean space directly, but are a space of transformations (scaling &
rotation) on two-dimensional Euclidean vectors, where 1 represents the
identity transformation, and _i_ represents a quarter turn anticlockwise.

In a similar way, the quaternions are the space of transformations (scaling &
rotation) of three-dimensional vectors. (It’s a little more complicated
because 3-dimensional rotations are not commutative, and must be combined by
sandwiching, so there are 2 choices of quaternion corresponding to every scale
and orientation in 3-dimensional space. For an introduction see
[http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf](http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf))

~~~
eriknstr
>The complex numbers are not a two-dimensional Euclidean space directly, but
are a space of transformations (scaling & rotation) on two-dimensional
Euclidean vectors, where 1 represents the identity transformation, and i
represents a quarter turn anticlockwise.

You might be right, I don't know. Could you explain a bit more how you mean?

~~~
jacobolus
Complex numbers have multiplication defined on them. If you multiply two
complex numbers, you get another complex number. (They compose via
multiplication in exactly the same way as scaling & rotation operators on
2-dimensional vectors.)

If you just have 2-dimensional vectors, there’s no obviously well-defined way
to multiply two vectors and get out another vector.

In other words, both 2-dimensional vectors and complex numbers are made up of
2 coordinates, but they don’t have the same mathematical structure.

------
tyingq
Reminded of this Carl Sagan video that I watched as a kid.
[https://www.youtube.com/watch?v=xTL02N9EHzU](https://www.youtube.com/watch?v=xTL02N9EHzU)

~~~
comboy
These videos are such a treasure. All these years and nobody came even close
(new Cosmos is ok, but not that profound).

This is how you make a nation great. You can do whatever you want with the
economy, but without proper education you still have a nation of.. people..
who choose their president.. based on their beliefs and understanding of the
world.

~~~
tyingq
Shows the relative importance of a great presenter too. The props he uses are
laughably cheap, yet he does a better job getting the point across than vastly
more expensive productions.

------
gmuslera
Now is a good moment to reread Lewis Padgett's Mimsy were the Borogoves,
specially if your children start playing with those toys.

~~~
jerf
[http://jabberwockland.blogspot.com/2007/03/mimsy-were-
borogo...](http://jabberwockland.blogspot.com/2007/03/mimsy-were-borogoves-by-
lewis-padgett.html)

My favorite short story of that era. Still have not watched the movie out of
sheer fear they didn't get it and I don't want it wrecked. (Still have no idea
how that even made it out...)

------
rjeli
Love the idea! Unfortunately it's not compatible with iOS plus-sized screens
:(

~~~
Twisol
I'm hitting the same problem -- the app only renders to a smaller rectangle of
the whole screen rooted at the bottom-left (when held sideways), but touch
events _are_ scaled to the whole screen. I could probably live with the
smaller view, but it's very hard to accurately manipulate the objects when it
thinks I'm touching further left than I actually am.

~~~
octalmage
Same issue here. Has anyone reached out to the developer?

~~~
marctenbosch
I am aware of the issue and fixing right now!

~~~
wruza
This app is very cool. Do you have a plan to add projection mode in addition
to crosssection?

~~~
marctenbosch
Something like that, yes.

------
drewolbrich
Related: (iOS only)
[http://www.fourthdimensionapp.com](http://www.fourthdimensionapp.com) If you
email me at temp6 at traipse.com I will send you a promo code for a free copy.

------
prbuckley
This is very cool. It reminds me of the classic geometry novel Flatland. If
you like thinking about dimensionality I highly recommend it...

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

~~~
wyager
The game this engine is for, Miegakure, is inspired by flatland.

------
gene-h
Now it's a cool toy, but there might be more practical applications for a 4D
rigid body physics engine. Some materials design approaches[0] involve
iterating through shape space to determine what shape a particle should be to
get it to assemble into a desired structure. A 4D physics engine might be
useful for this shape space iteration, as movement through shape space could
be accomplished by moving a 4d rigid body along the 4th axis.

[0][http://pubs.acs.org/doi/full/10.1021/acsnano.5b04181](http://pubs.acs.org/doi/full/10.1021/acsnano.5b04181)

------
Qantourisc
What annoys me most: "thing disappear" I don't recall 3D -> 2D mapping making
things disappear, just surfaces hiding other surfaces. But this might not work
in 4D?

With the 2D->3D they are taking cross-section, I really don't like these. Just
throw it all on there ! This would also mean you project your 4D world on a 3D
camera, you project on a 2D surface to display.

[https://www.youtube.com/watch?v=BVo2igbFSPE](https://www.youtube.com/watch?v=BVo2igbFSPE)
<= this method is "saner" imo.

~~~
sp332
That's if you do a "projection", like light rays from a 3D object focused onto
a screen. This is more like taking a 3D slice of a 4D object. If you think of
taking a 2D slice of a 3D object, you can see how objects disappear when they
move out of the plane that you're drawing.

~~~
pbhjpbhj
If you sliced a tesseract then presumably you'd encase it in the knife and a
square, with no depth (the depth is in the 4th dimension that we're not
experiencing), would appear?

Hypercubes have always been a difficult one for me to intuit, basically I have
no 4th dimensional intuition. When I think of a 4D hypersphere all I can get
is a simple sphere. I don't have any intuition as to whether that's wrong, it
seems in a way it should be a sphere with infinite spheres on it's surface -
from analogy with the tesseract - but from analogy of constructing a sphere
from a circle it should be a case of rotating the sphere around itself
perpendicular to the extra dimension?

~~~
Crespyl
It might help if you consider spheres as a _surface_.

3D spheres are a 2D surface wrapped into a 3D space, likewise, hyperspheres
would be a 3D surface wrapped into a 4D space. There's no "infinite spheres on
its surface", I think the "rotation" is a better analogy.

Take a line rotated around an orthogonal axis and you have a circle, a circle
rotated around an axis orthogonal to the other two is a sphere, a sphere
rotated around another orthogonal axis is a hypersphere.

~~~
pbhjpbhj
Are all spheres hyperspheres? When you rotate in the 4th, or higher ordinal,
dimensions don't you get the same shape?

~~~
Crespyl
I guess it would depend on whether you consider all circles to be spheres (or
all spheres circles)?

------
dmix
Easily the hardest part of learning about string theory for me (via reading
"The Elegant Universe" [1]) was grasping the idea of multiple other
dimensions.

The book tried it's best to explain it by exploring a world starting with 1D
and evolving to 3D, but it's still quite difficult to visualize, especially
ones shaped like a "Calabi–Yau manifold" [2].

The one good thing I got out of learning about Calabi-Yau manifolds (and
randomly reading another layman story involving Yau's clash with the guy who
solved Poincaré conjecture) was a new interest in learning more about math and
a getting a laymans grasp of topology. Although I later learned manifolds are
quite an advanced subset of topology.

I enjoyed the linked video, I was looking for a way to better understand 4+D
in a way I could wrap my head around and an interactive game makes a lot of
sense.

[1] [https://www.amazon.com/Elegant-Universe-Superstrings-
Dimensi...](https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-
Ultimate/dp/039333810X/)

[2]
[https://www.wikiwand.com/en/Calabi%E2%80%93Yau_manifold](https://www.wikiwand.com/en/Calabi%E2%80%93Yau_manifold)

------
nautilus12
This is so cool, but its driving me crazy. I was wondering if someone could
provide me with more resources that help intuit about 4d space. For example,
in Miegekure, he walks through the 4th dimension to get to the other side of
the wall, but thats assuming that no part of the wall extends into the forth
dimension (aside from rubble). What would happen if he switched back to the
normal 3 dimensions in the middle of the wall. In miegekure everything is kind
of discretized (grassy area to desert area), but in reality that would be
continuous. What would that actually look like, for example, the area right
next to the wall? How would this work at a subatomic level, would electrons be
traveling in and out of the 4th dimension? Could this explain things like
action at a distance or black holes? How does the explain shared surfaces in
the 4th dimension? I can't even answer a basic question like, if I were
sitting in an easy chair and started looking down the 4th dimension what would
happen. Since it has to share one cross section of the easy chair would it
have to be simply a fatter or skinnier easy chair? But that is true for any
cross section of the chair correct? The easy chair is the 3d cross section of
the 4d object then what (would/could) the 3d cross section exchanging one of
our spatial dimensions for the hidden one look like? How does gravity work in
those 3 dimensions (2 of our spatial dimensions + 1 of the hidden dimension).
Supposing the world was like this, wouldn't it be obvious if any object was
extending into the 4th dimension thus we can stand to reason our world must be
strictly 3 dimensional? If there were 4 dimensions since we can't see or
interact with it, does it stand to reason that the spatial extent of any
object doesn't extend into the 4th dimension? For example, since the three
dimensional projection of a hypersphere changes diameter, does that mean the
4d dimensional analogues of earth are just different size earths? I also
notice that in one of the miegekure videos the windmill in the new 3d space is
like a cross section of the windmill but extending for a distance, Im guessing
this is a product of the way the 4th dimension is discretized but Im
wondering, what would that really look like if the game weren't made that way?

~~~
jameshart
I found this Matt Parker lecture provided some good tools for getting your
head around the fact that extra dimensions really do let you go around things,
not through:
[https://youtu.be/1wAaI_6b9JE?t=2299](https://youtu.be/1wAaI_6b9JE?t=2299)

(the whole thing is worth watching, but the bit about higher dimensional
visualization starts there)

~~~
ghusbands
I'll save people the effort and point out that the only relevant things (to
the given questions) the entertaining video shows are a proper klein bottle
and the nature of projection into 3D. In 4D, klein bottles don't self-
intersect, just as mobius strips don't self-intersect.

It does not cover the question of putting oneself inside a wall or how to go
around 4d objects, and the projections show detail that a 4d person would not
see.

------
KeyboardFire
It's a shame it's only for iOS and Vive. I wonder how difficult it would be to
make an open source desktop/browser version? Even if it's a lot simpler, it
would be neat to feel what it'd be like to play around in 4 dimensions.

~~~
hcs
4D Toys is now available for non-VR PC, I just noticed this tweet from the
author:
[https://twitter.com/marctenbosch/status/871073480573202432](https://twitter.com/marctenbosch/status/871073480573202432)

------
drewrv
One of the first things I thought of when I got a vive is building an app to
let one intuitively navigate and understand four dimensional space. I never
had the time or talent to hack something together though so I'm glad this
exists.

Something similar but less polished can be found here: [http://www.albert-
hwang.com/blog/2016/6/what-does-vr-reveal-...](http://www.albert-
hwang.com/blog/2016/6/what-does-vr-reveal-about-the-4th-dimension)

------
ghusbands
This and Miegekure show cross-sections or projections of a 4d space that are
common but that show details that could not possibly be seen by functional 4D
eyes. Are there any attempts out there at showing a 3D representation of what
4D eyes could see? (For example, if you have a solid 4D cube, you can only see
the outside of it, but the cross-section shows parts of the inside, as happens
you take 2D cross-sections of a 3D cube)

------
JoeDaDude
There are several 4D games, but the one I found gave me the best grasp of the
4D world is this one [1], a puzzle in which you manipulate a hypercube. You
first play in 2D and 3D before going to 4D. You end up with an intuitive
understanding of 4D.

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

------
Benjamin_Dobell
Odd. I just bought this on my wife's iPad. It opens, drops some shapes and
then repeats. If you touch the screen it instantly crashes

~~~
Benjamin_Dobell
I'm guessing there's a missing/incorrect OS/functionality check somewhere
cause she's on iOS 8.2. Upgrading now and will report back. Also grabbed the
crash-logs and will email them through.

~~~
panic
I'm seeing the same thing. It looks like the app is calling
-[UITraitCollection forceTouchCapability], which isn't available on iOS 8.

~~~
marctenbosch
A new build is being reviewed by Apple!

~~~
panic
Awesome, thank you for the super fast response!

------
wyager
Does anyone have any resources on orthographically projecting 4D objects to 3D
or 2D spaces? I'm curious if it looks better than taking a cross-section.

It seems like it should work similarly; deform a 4-frustum into a 4-cube and
drop one or two of the axes. I guess the number of axes you can drop depends
on the symmetry of the frustum...

~~~
coldpie
I tried googling "orthographically projecting 4D objects to 3D" to see if I'd
strike gold and, boom:
[http://eusebeia.dyndns.org/4d/vis/vis](http://eusebeia.dyndns.org/4d/vis/vis)

Edit: In particular, this page shows a good summary of how the "slices" shown
in the game relate to the hypercube projection you're familiar with.
[http://eusebeia.dyndns.org/4d/vis/09-interp-1#Interpreting_4...](http://eusebeia.dyndns.org/4d/vis/09-interp-1#Interpreting_4D_Projections_1)

------
based2
[https://translate.google.fr/translate?sl=fr&tl=en&js=y&prev=...](https://translate.google.fr/translate?sl=fr&tl=en&js=y&prev=_t&hl=fr&ie=UTF-8&u=http%3A%2F%2Festhetopies.ihp.fr%2Findex.html&edit-
text=&act=url)

------
amelius
I wonder if, after playing many hours with this game, the brain will suddenly
"grasp" the concept of 4d.

~~~
wruza
I think it will. I'm aware of two somewhat related experiments: upside-down
vision and magnetic field vision. In first experiment, participant wore
vertical flipping glasses for a week. He was walking, eating, cycling and so
on, never taking glasses off. At the end of experiment he was pretty good at
it and it seemed natural. When glasses were finally off, he felt very
discomfortable for some time.
[https://en.wikipedia.org/wiki/Neural_adaptation#History](https://en.wikipedia.org/wiki/Neural_adaptation#History)
\-- one of these experiments.

In the second experiment participant wore belt (iirc) that signaled north pole
location to his skin. After wearing it for a long time, that feeling turned
completely into new sense of magnetic field. You simply know where "north" is,
anytime. After taking it off, he responded that it was pretty stressful, like
you lose one of your senses or limbs. Experiment group was concerned to that
they stopped these experiments. (no link found, but seen on HN)

All this shows that our brain is probably not specific to available
senses/setting and can "grasp" any concept, if exposed to it for a long time,
but both in and out may take a hard time.

~~~
_Microft
Check the following links for information on such a belt. It's a spin-off from
research on "sensory substitution" at a german university (in Osnabrück).

[http://www.feelspace.de/navibelt/](http://www.feelspace.de/navibelt/)
[http://www.feelspace.de/research/](http://www.feelspace.de/research/)

------
aboodman
I can't get this to run on iOS. Is it supposed to work? It just sits at the
splash page playing a slightly interactive animation over and over. There's an
arrow that I tried tapping and dragging and nothing happens.

~~~
thsowers
Same thing happened to me, I think I fixed by swiping left

~~~
aboodman
I'm seriously swiping as hard as I can in every direction.

~~~
marctenbosch
Are you on an iPhone 6+ or 7+? If so, a new build is being reviewed by Apple.

~~~
aboodman
Yep. For a minute there I was worried this was some Myst-like intelligence
test that I was failing.

Looking forward to the be build.

------
throwaway135634
I'm surprised that Flatland[0] wasn't mentioned in this

[0][http://www.gutenberg.org/ebooks/201](http://www.gutenberg.org/ebooks/201)

~~~
js8
They actually do mention Flatland at 4dtoys.com.

------
moopling
it would be interesting to see multiple views at the same time, like how when
we try to represent 3d shapes in 2d (think mechanical design drawing,
archetictural drawings, etc)

------
gyrgtyn
Might be useful for figuring out how to battle cthulu

------
Razengan
I'm immensely interested in the prospect of higher spatial dimensions. Is it
even possible to prove/disprove their existence from our 3D existence, and
have there been any notable attempts to do so?

------
microcolonel
Why a box and not a hyperbox?

------
yev
Damn, it's so cool!

------
bbcbasic
He's going to make some coin from this.

