4D Toys: a box of four-dimensional toys

June 2, 2017 12:42 PM

What if you received a box filled with mysterious toys from a fourth spatial dimension? [Direct YouTube Link]

Miegakure is a game (currently under development) that takes place in 4 dimensions. The developer, Marc ten Bosch, released 4D Toys for iOS and Vive as a way to further explore a fourth spatial dimension.

[via HN]

posted by Nonsteroidal Anti-Inflammatory Drug (42 comments total)

Side note, the YouTube video was uploaded in 1080p at 60fps. I had to lower the video quality to get parts of it to smoothly play on my computer.
posted by Nonsteroidal Anti-Inflammatory Drug at 12:43 PM on June 2, 2017

I haven't tried the software yet, but I love the illustrations (scroll to the bottom).
posted by phooky at 12:50 PM on June 2, 2017

Is there any chance this guy worked on BeamNG.drive?
posted by theodolite at 12:53 PM on June 2, 2017 [3 favorites]

I can see these objects, and I can see them disappear, but I can't visualize a fourth dimension, so it looks random to me.
posted by clockzero at 12:55 PM on June 2, 2017

"Mimsy Were the Borogroves", Lewis Padgett
posted by Quindar Beep at 12:55 PM on June 2, 2017 [28 favorites]

I was literally coming into the thread to post the Padgett story.
posted by LizardBreath at 1:00 PM on June 2, 2017 [4 favorites]

I like the explanation except for when he talks about "moving into the Nth dimension" as it if were a place to which objects could travel. More accurate would be to say that the objects move outside of your frame of reference along the axis of the Nth dimension.
posted by grumpybear69 at 1:05 PM on June 2, 2017 [8 favorites]

Also see: —And He Built a Crooked House—
posted by Confess, Fletch at 1:28 PM on June 2, 2017 [4 favorites]

Here's what the solar system looks like in 4D. It's a bright wormy thing shooting through the void.

That's just the solar system in 3D if you no longer assume the sun is static but if you are viewing it moving, the lines are the paths traced by the planets in orbit.

Also I used to have a bunch of 4D toys but they all rolled under, uh, beside, well, sort of... beyond... the couch.
posted by GuyZero at 1:32 PM on June 2, 2017 [19 favorites]

I was never able to find mine once I opened the box.
posted by Samizdata at 1:41 PM on June 2, 2017 [1 favorite]

GuyZero, except that the 4th dimension is time, so seeing something in 3D moving along the axis of time is a legitimate way to visualize it.
posted by MythMaker at 1:46 PM on June 2, 2017

GuyZero, except that the 4th dimension is time

ok fine be like that I guess, sure.
posted by GuyZero at 1:54 PM on June 2, 2017 [1 favorite]

*rubs temples*

look, i know this "time is the 4th dimension" thing is cute and all, but time is not a spatial dimension, like, at all. you can illustrate the passage of time along a 4th spatial dimension if you want, that's cool and all, but just let's be a little careful with our verbiage here because this line of reasoning does not end well
posted by phooky at 2:00 PM on June 2, 2017 [13 favorites]

let's be a little careful with our verbiage here because this line of reasoning does not end well

You say this as though you've had to clean up a lot of 4th dimensional time spills in your day.
posted by saturday_morning at 2:09 PM on June 2, 2017 [22 favorites]

My D goes to 11.
posted by It's Raining Florence Henderson at 2:12 PM on June 2, 2017 [2 favorites]

look, i know this "time is the 4th dimension" thing is cute and all, but time is not a spatial dimension, like, at all. you can illustrate the passage of time along a 4th spatial dimension if you want, that's cool and all, but just let's be a little careful with our verbiage here because this line of reasoning does not end well

Eh, "forward in time" and "backward in time" are just as legit directions as "ana" and "kata."
posted by straight at 2:30 PM on June 2, 2017 [5 favorites]

What if you received a box filled with mysterious toys from a fourth spatial dimension?

Whew, so I am not the only one who keep getting these? That four-dimensional bobcat was a handful.
posted by ricochet biscuit at 2:34 PM on June 2, 2017 [4 favorites]

I know that the 5th Dimension aka Dimentia 5... is ILLUSION!
posted by Zack_Replica at 2:38 PM on June 2, 2017 [1 favorite]

metafilter: this line of reasoning does not end well
posted by Bringer Tom at 3:26 PM on June 2, 2017 [1 favorite]

look, i know this "time is the 4th dimension" thing is cute and all, but time is not a spatial dimension, like, at all. you can illustrate the passage of time along a 4th spatial dimension if you want, that's cool and all, but just let's be a little careful with our verbiage here because this line of reasoning does not end well

Can you expand on this then? Genuinely curious. I always thought a visual representation of the 4th dimension was three dimensions moving through time. Would love to know the reality if this is actually off base.
posted by Aya Hirano on the Astral Plane at 3:32 PM on June 2, 2017

In the 4th dimension, we think the expression "off base" is silly.
posted by Obscure Reference at 3:44 PM on June 2, 2017 [1 favorite]

In 4th dimension, time moves through you.
posted by Cookiebastard at 4:12 PM on June 2, 2017 [1 favorite]

The 4th dimension sounds like a pretty dry place.
posted by Aya Hirano on the Astral Plane at 4:20 PM on June 2, 2017

The problem with visualizing a fourth spatial dimension as time is that it doesn't help you imagine rotations. What does a rotation involving the time axis look like?
posted by panic at 4:53 PM on June 2, 2017 [3 favorites]

Hrm.

So they're showing a 3d cross-section of a 4d space. And to illustrate what that's like, they show a similar UI where it's a 2d cross-section of a 3d space. There, everything's all weird and stupid and doesn't make any sense, but listen, it's because stuff's happening outside of the planar cross-section. Look there's a projection in the corner, and if you watch that, and things do make sense.

I think they're intending that I'll, by analogy, understand how 4D shapes interact. But I think what they really show me is that cross-sections are just hard to understand. I have decades of practice thinking about 3D objects, and I still really can't look at the animated 2D cross-sections and visualize how things are moving in 3D. Instead I had to look at the projection to really figure it out.

So I wonder if this would be a bit more helpful if they projected the 4D down to 3D, then gave you regular 3D camera controls, and projecting the 3D down to 2D for display. Maybe add a little "fog" to show 4D 'depth'.
posted by aubilenon at 4:55 PM on June 2, 2017 [2 favorites]

What if the fun toy was a Buick 8?
posted by lagomorphius at 5:38 PM on June 2, 2017

Eh, "forward in time" and "backward in time" are just as legit directions as "ana" and "kata."

Sort of... The biggest problem with just thinking of time as "the" fourth dimension is that what physicists call "timelike" and "spacelike" dimensions genuinely behave differently, and our world has three spacelike dimensions and one timelike dimensions (at least as far as we can tell, string theory suggests things may be much wierder).

The most obvious difference is with pythagoras theorem. In two dimensions it has the familiar form a^2 + b^2 = h^2. When we add a third spacelike dimension we can generalise it to a^2 + b^2 + c^2 = h^2. This toybox adds a fourth spacelike dimension which obeys the formula you might expect a^2 + b^2 + c^2 + d^2 = h^2. However in our world with time as the fourth dimension, because it's not a spacelike dimension, you instead have to use the formula a^2 + b^2 + c^2 - d^2 = h^2. This has all sorts of consequences like the existence of a universal speed limit in the speed of light.
posted by Proofs and Refutations at 5:56 PM on June 2, 2017 [5 favorites]

Guys, imagination is the fifth dimension. A little mite-sized Batman said so.
(Warning: Tripthoughts on comics ahoy. If that not be yer desired destination, abandon ship now.)

As for the sixth dimension, well. Some of the songs are fine, but there's a reason why the basement oughtta be kept locked.
posted by byanyothername at 6:13 PM on June 2, 2017

No, the Fifth Dimension is the one that lets the sun shine in.

But I love this "toybox". I'd love to find something similar to "play" around in hyperbolic space.
posted by Zonker at 6:56 PM on June 2, 2017 [3 favorites]

I've been interested in Miegakure since I heard about it several years back, but it seems like it's one of those games that's perpetually "in development". Maybe someday...
posted by traveler_ at 6:58 PM on June 2, 2017 [2 favorites]

However in our world with time as the fourth dimension, because it's not a spacelike dimension, you instead have to use the formula a^2 + b^2 + c^2 - d^2 = h^2

This seems to imply that every space-time coordinate has an infinite number of other different space-time coordinates that are 0 distance away? What does that mean?
posted by aubilenon at 8:41 PM on June 2, 2017

I think it means that light pulses emitted from all of those space-time coordinates are reaching your space-time coordinate right now -- i.e., from where/when you are standing, all the points in space one light-second away (a^2 + b^2 + c^2 = 1) are showing you what was happening one second earlier (-d^2 = -1). And/or one second from now those points in space will all have access to your present moment.
posted by nobody at 9:12 PM on June 2, 2017

Aw, it's like Flatland for the digital age!
posted by lollusc at 9:26 PM on June 2, 2017 [1 favorite]

Speaking of dimensions, getting ready to watch Buckaroo Banzai with a buddy in a sec.
posted by Samizdata at 9:44 PM on June 2, 2017 [2 favorites]

The problem with visualizing a fourth spatial dimension as time is that it doesn't help you imagine rotations. What does a rotation involving the time axis look like?

Rotate an object through the fourth dimension and its length in one of the spacial directions will be proportional to the amount of time it has existed and will exist. I would guess the length would be about 300,000 kilometers for each second of existence. If so, it would be pretty awkward rotating anything that isn't extremely short-lived. Except anything smaller than a large planet will disappear almost instantly when one of its spatial dimensions is rotated into the time dimension (Jupiter would disappear in about half of a second; our sun would last about 4.5 seconds).
posted by straight at 9:52 PM on June 2, 2017 [1 favorite]

That's why, when rotating, one must give oneself a little push along the time-axis to keep from fading out. Also it's better to make quick 180 degree turns, with the rotation centered a bit further along the time-axis.

And here's the full text (with typos) of the Mimsy story people mentioned upthread.
posted by nobody at 3:57 AM on June 3, 2017

Came to ensure the Padgett story had already been posted, was not disappointed. I am among my people.

(I have written before about how x logic scared me half to death when I first read the story.)
posted by adamgreenfield at 4:26 AM on June 3, 2017

one way to help think about and visualize 4d is imbuing 3d objects with a greyscale, spectrum or 'temperature' -- corresponding with its (orthogonal to 3d space) fourth dimension. so for example while two intersecting planes with the same shade will always intersect in a line, if the plane is shaded with consistent gradation then the two planes can be 'twisted' into 4d space to intersect at just a point! (where their shades match ;) to analogize a bit further, 3d objects with the same shade can be thought of as on the same 'hyperplane' while ones with other shades -- not gradated -- exist on parallel hyperplanes.
posted by kliuless at 10:55 AM on June 3, 2017

Can you expand on this then? Genuinely curious. I always thought a visual representation of the 4th dimension was three dimensions moving through time. Would love to know the reality if this is actually off base.
posted by Aya Hirano on the Astral Plane at 15:32 on June 2 [+] [!]

I'm surprised there's been no response to this except snark.

It's not unreasonable to consider time as a fourth dimension, but it's a very strange and unique dimension compared to space, at least in the universe most people inhabit. In particular, you can only travel along it in one directions at a fixed rate, which is very different from space. I can go left and right at any (sub-light) speed, but in time I can only go forward at one second per second.

In the case of the video in this post, they're representing four spatial dimensions and one time dimensions (or 4+1 dimensions, in a slightly less-confusing short-hand notation), whereas you and I seem to live in a 3+1 D world, and the Super Mario Brothers live in a 2+1 D world. The solar system video is overlapping images from a 3+1 representation, projected into 2D with lines to show paths in time and various visual effects to represent the third spatial dimension. It's very cool (and not something I'd seen before - thanks!) but quite a bit different from representing physical objects in a 4+1 world mapped into a 3+1 representation, as the original post attempts to do.

(I've never been able to make much sense of 2D visualization of 4D space. The math works, but the intuitive version seems terribly confusing and not helpful.)
posted by eotvos at 11:20 AM on June 3, 2017 [3 favorites]

I can go left and right at any (sub-light) speed, but in time I can only go forward at one second per second.

Well you only go left or right at one meter per meter, though.
posted by aubilenon at 11:36 AM on June 3, 2017 [2 favorites]

We talk about dimensions as properties of space but I have often wondered - and perhaps someone can enlighten me - if the dimensionality we associate with space is really a conceptual tool for describing space rather than a property of space. In other words, does space "have" three dimensions or are the dimensions an aspect of the way we describe space and specify location?
posted by Jode at 12:21 PM on June 3, 2017

What, no truncated hypercones? I guess it's good that I don't have any of the necessary devices, 'cause I would want my money back.
posted by XMLicious at 9:19 PM on June 3, 2017