0721: "Flatland"

[Balesir]

Flatland is pretty good...it's a Victorian satire where those shapes with the most sides are higher up in society, and women are just lines.

Flatland is great - I happened upon an original copy in a country house I was staying in as a student more years ago than I will admit to.

I think this and other posts missed a key point, though. A shape's supposed intellect (and, thus position in society) is indicated not by the number of sides, but by the size of their smallest angle, IIRC. This makes women unusual/interesting in that their angle might be read as either zero or a complete 360 degrees, depending on how you look at it...

[marsman57]

I can't say with certainty, but I think this comic would be funny if I were familiar with Flatland.

As a result, it just came off to me as an ill-timed advertisement for Miegakure (since no beta is available). Either that or it is Randall bragging about being in a closed beta for it.

[rileyrulesu]

Dang it, they stole my idea. also i remember flatland that was cool. But im going to see if the demo is really availible now.

[masterwizard]

Flatland is pretty good...it's a Victorian satire where those shapes with the most sides are higher up in society, and women are just lines.

Flatland is great - I happened upon an original copy in a country house I was staying in as a student more years ago than I will admit to.

I think this and other posts missed a key point, though. A shape's supposed intellect (and, thus position in society) is indicated not by the number of sides, but by the size of their smallest angle, IIRC. This makes women unusual/interesting in that their angle might be read as either zero or a complete 360 degrees, depending on how you look at it...

No, I'm pretty sure that the book clarifies they aren't actual lines, they're just really really thin polygons. They can't technically be one-dimensional or they'd have no area/2-D-mass. So they'd have a really really small angle, slightly larger than zero.

[Mutex]

Flatland is pretty good...it's a Victorian satire where those shapes with the most sides are higher up in society, and women are just lines.

Flatland is great - I happened upon an original copy in a country house I was staying in as a student more years ago than I will admit to.

I think this and other posts missed a key point, though. A shape's supposed intellect (and, thus position in society) is indicated not by the number of sides, but by the size of their smallest angle, IIRC. This makes women unusual/interesting in that their angle might be read as either zero or a complete 360 degrees, depending on how you look at it...

No, I'm pretty sure that the book clarifies they aren't actual lines, they're just really really thin polygons. They can't technically be one-dimensional or they'd have no area/2-D-mass. So they'd have a really really small angle, slightly larger than zero.

Surely it depends on whether you're counting the inner angle or outer? If it's outer, then the women would have an angle of 180 degrees.

[cparker15]

BTW, here's some 2D porn: l l l l

I prefer my women taller: | | | |

Edit: Apparently this was my 111st post. I find that strangely appropriate.

Well, I prefer mine tall and thick: | | | |

BBWs rule.

[Mutex]

BTW, here's some 2D porn: l l l l

I prefer my women taller: | | | |

Edit: Apparently this was my 111st post. I find that strangely appropriate.

Well, I prefer mine tall and thick: | | | |

BBWs rule.

I like mine curvy: ~

[kaotik4266]

Oh, it's a book! I thought it was referring to this talk by Carl Sagan! http://www.youtube.com/watch?v=UnURElCzGc0

[Notch]

Well, this comic just ruined my april fools joke.. Get out of my head, Randall!
(I was going to announce minecraft 4d)

[TheKob]

Hi to all y'all.
i have come close to joining and posting a few times but finally felt i could add something [he says modestly]

The histroy of the fourth dimension is quite interesting having 'exlploded' into the human brain in the mid 19th centruy.
There are a couple of great books if you want to learn to think 4D; Charles Hinton 'the fourth demension' and Rudy Rucker 'the fourth dimension, and how to get there'.
Hinton moved in the same circles as Abbot and Carroll/Dodgson.

&
surely Portal is a 4-d game?

[dean.menezes]

For those who don't get the alt text:

circle = priest in Flatland and women = lines.

[Iraluq]

For those who don't get the alt text:

circle = priest in Flatland and women = lines.

You're not entirely right on that one.

It's actually kind of an inside joke, in reference to ConBust, which we attended this past weekend at Smith College. Speaking along the lines of how he didn't want to point out that it was, in fact, stick figures he was drawing (for that would be all people would think about then - and stick figures having sex is weird) he drew a comic idea he'd had for a while, but never posted, up on the board:


(I hope you don't mind me posting the image Randell. Feel free to remove it, or ask me to do so, if you wish!)

[Igelkuesser]

Hm... if you think about it... let's imagine a one-dimensional world with one-dimensional people in it. Let's also imagine they'd have sexual organs like us.


...so if you had sex with both "line-persons" to each side of you and you're unlucky and your children would be born on your side... you'll have to have sex with your children (or none at all)


Oh shit I've got a headache.

[Geekoid]

"Not much, What's up?"

That is funny as hell. Well done.

[Wolfkeeper]

Technically no computer game could be truly 4D given the third dimension is always simulated.

Ah... but technically no computer game can ever be truly be 2D, given that computer memory is only one dimensional, and the second dimension is always simulated.

[karlzt]

really good one

[Istaro]

Well done, but about the original panel from ConBust, wouldn't an xkcd stick figure descending through Flatland look not like women, but rather a bunch of points? (Followed by a size-changing priest, if the stick figure's head is actually a sphere; otherwise, the "priest" would just be two more points, I guess.)

This problem is because none of Stick Figure's lines are parallel to the ground . . . but I suppose if e descended through Flatland at the right angle, a woman-like apparition would briefly appear.

[phillipsjk]

Technically no computer game could be truly 4D given the third dimension is always simulated.

Ah... but technically no computer game can ever be truly be 2D, given that computer memory is only one dimensional, and the second dimension is always simulated.

If you open the case, you will find that the memory is in fact 3/(4 if you count time) dimensional. The unidimensional memory map is just a convenient abstraction. An abstraction that may not be as convenient in a world where multiple processors are the norm. From the OS point of view, memory has been 2 dimensional since the i386 with its virtual memory extensions: Each program gets its own virtual (1D) address space.

</Tangent>

[VapidFrobie]

So...

People in flatland see in one dimension, because all they can make out is a line. We see in two dimensions, but we analyze the differences in the two images our eyes give us to judge depth, right? So do four-dimensional beings see in three dimensions? They could probably see all sides of a three dimensional object at once. Is that correct? I've read A Wrinkle in Time, an excerpt of Flatland, and seen dozens of youtube videos, but that's the extent of my experience with this (I'm not going to count the movie Hypercube). It's pretty trippy to think about.

Forgive me if I sound stupid.

Also, tentacles. &

[Wolfkeeper]

Technically no computer game could be truly 4D given the third dimension is always simulated.

Ah... but technically no computer game can ever be truly be 2D, given that computer memory is only one dimensional, and the second dimension is always simulated.

If you open the case, you will find that the memory is in fact 3/(4 if you count time) dimensional. The unidimensional memory map is just a convenient abstraction. An abstraction that may not be as convenient in a world where multiple processors are the norm. From the OS point of view, memory has been 2 dimensional since the i386 with its virtual memory extensions: Each program gets its own virtual (1D) address space.

</Tangent>

In case you missed the very subtle joke, a game can be any dimension you want, because you can fold any dimension down to 1 (although you typically have to process and consider the n-dimensional space in some sort of discrete way.)

I think that the contributor meant the display is only two dimensional, but then so is your retina, a truly 3D game is always folded back down to 2D by the user.

[fleshBasedProcessor]

Ok, the comic was absolutely terrible, but the title text was brilliant.

[MarkSmash]

For those interested in reading said missive:

http://books.google.ca/books?id=R6E0AAA ... q=&f=false

[nahkaimurrao]

To call these kind of games fourth dimensional is misleading and disappointing. The 4th dimension should be a 4th spatial dimension that is equivalent to and indistinguishable from the other 3. This game would be more like 3.000....00001 dimensions as you only get a finite amount of points in the 4th direction. This really doesn't make sense as the other 3 dimensions are infinite continuums with no discrete points (at least at the macroscopic level).

I would say Portal is more of a 4-d game than this as Portal is a 3d game that gives you the ability to fold 3 space through the 4th dimension.

I would love to see a true 4space game utilize the 4th dimension as a true 4th spatial dimension that you can translate and rotate through just like any other spatial dimension. I realize designing a game such as this is virtually inconceivable at the moment but I believe it can be done and in such a way that any person can pick up the game and gain an intuition to play in this new and unfamiliar world.

Mathematically one can invent a law of physics that functions similarly to ours in the 4th dimension and the rules only need be tweaked slightly. The challenge lies in trying to wrap our brain around this new and unexplored idea. Our mind's eye has no way of visualizing in any but the 3rd dimension+ time. We can't even visualize in the 2nd or 1st dimension let alone the 4th. In fact I bet that trying to visualize the 1st and 2nd dimension from the view point of a 1-lander or a 2-lander may give us what we need to visualize 4-space.

We might start by understanding how our minds view the world we live in. We see the world by viewing 2D images and inferring the 3rd spatial dimension and time dimension by how these 2d images warp and change. We see distance by an object appearing to get smaller and fuzzier as it moves away, or larger and clearer as it moves closer. When a cube rotates in 3-space its angles are skewed and its lines are warped.

Can we imagine what we would see if an object moved (translated) purely in the 4th dimension?

what would it look like if an object distant in the 4th dimension started moving closer to you? Well first how does this work in 3D? Imagine you are on a space station awaiting a space cruiser to arrive(lets call it the 3ship). You look out the window in the direction it is coming from. At first you strain your eyes but see nothing. Then you make out a spec far in the distance. As the ship gets closer this spec will get larger and larger until arrives at the station. So we can infer that an object moving closer in the 4th dimension will start as a speck and slowly get larger as it gets closer. Now say this spec suddenly appears in the air in front of your desk and say that it is actually a space ship currently distant in the 4th dimension (lets call it the 4ship) which is moving closer to your current position. The speck will currently remain motionless as the ship is moving only in the 4th dimension. You can get up and walk around the 4ship, you can even walk up to and through the 4ship. Wait, through it?! Actually you are not walking through it but it may appear so to a 3Dlander. You are truly walking in front of it but in the 4th dimension. It is just like if you were to see that 3ship in the distance out the window on the space station and moved your hand in front of the 3ship, blocking your view of the 3ship. It looks like your hand just enveloped the 3ship but really it is simply collinear with the 3ship in the direction from your eye to the 3ship. Your hand can not actually touch the 3ship until it actually gets within a couple feet of you. From this it follows that while you may pass your hand "through" what appears to be the location of the 4ship in our office really the 4ship still only exist elsewhere in 4space. You will not be able to touch the ship until it arrives within a certain distance to you, close enough to touch. This also requires that both you and the 4ship have a finite size in the 4th dimension. Up until now I have neglected to visualize how one would appear along this 4th dimension. For our example we can imagine that our objects and characters exist as 4prisms in the 4th dimension. that is to say you appear as your current 3self but exist over a finite 4D distance, much like a 3prism is a 2d shape like a triangle or square that has a finite 3space dimension. If a true 4D world were to exist it is unlikely that this would be the case as this results in asymmetry between the normal 3 dimensions and the new 4th dimension. Imagine you are looking at the face of a triangular prism, you will see a triangle, but if you suddenly rotate it along another axis suddenly the shape will no longer be a triangle but a vastly different shape as the 3prism is not rotational symmetrical in all 3 dimensions. In a true 4D world the symmetry of an object would extend between all 4 dimensions. However this complicates matters and is at the moment not necessary to incorporate 4d rotational symmetry in a game. I believe most future games that will use 4space will likely involve a normal 3space person that somehow gained ability to move (only translational movement no rotational) through 4space. For simplicity sake they will likely be their usual selves with a finite 4th dimension size.

From this visualization experiment we can see that it is not impossible to create a 4d virtual world, but it does take a little thought and ingenuity. If I were a game programmer I would get right on this as I am sure it would be a sensational even revolutionary game! So someone please make it!

[Funaho]

Dewdney's planiverse is a good follow-up to Flatland. His 2D world has gravity (so the directions are forward, backward, up and down), and he actually considers some 2D physics issues.

I don't think it's treated in the planiverse book, but in a 2D world, I suppose gravity would be inversely proportional to distance rather than distance squared (as the radius of a circle is proportional to its circumference, whereas the radius of a sphere is proportional to the square of its surface). Now I'm not a physicist, and I'm too lazy to make a simulation, but I think I've heard somewhere that you can't get stable orbits with gravity inversely proportional to distance. So you couldn't have a planet orbiting a sun... anyone got an idea what a 2D universe might look like?

Wow that takes me back...I read that book while I was in high school, over 20 years ago. Now I think I need to buy a new copy so I can read it again...

And yes they did talk about the gravity problem, at least a little...it was in the back of the book where the author discussed some technical issues of a real 2-D universe.

[Kethis256]

@nahkaimurrao

Not sure if I am responding to a troll or not but...



Its a computer simulation. All axes are discrete collections of finite points. Just because one dimension has a small number of points doesnt make it less of an axis than the others. It certainly does not make it 3.0001 dimensions. For stuff about that, look up fractional dimensions - a property expressed by fractals.

And also, you seem to misunderstand the difference between perspective and the number of dimensions. The games you deride have 4 simulated dimensions, but lack the type of stereo perspective your eyes are used to seeing. They instead use orthographic projection, a perfectly legitimate presentation of the same data. I agree stereo perspective in 4d is interesting. An example can be found here: http://www.urticator.net/maze/download.html

(also, lrn2paragraph)

[bowserevilking]

Get out of my head Randall! I've been trying to comprehend hypercubes for a while now.
In Flatland, would they see 1D like we see 2d? Would there be 1D art? I don't think a single point counts as art, does it?
Yes, I did register just to post this.

[diotimajsh]

In Flatland, would they see 1D like we see 2d? Would there be 1D art? I don't think a single point counts as art, does it?

Vaguely relevant link courtesy of Abstruse Goose.

Yeah, they're supposed to be able to see one dimension, but they see a section of it it all at once the way that we see 2D images all at once. (The Abstruse Goose comic linked above isn't quite an accurate depiction, I believe, since the line of colors still has a small vertical length... but I don't think there's any way for us to visually represent (or mentally visualize) a truly one-dimensional field of experience anyway). Flatlanders, according to Abbott, get an impression of other objects thanks to something like an "atmospheric haze" that reveals depth: objects farther away become fuzzier--or lighter, blurrier, I forget exactly. This is analogous to the effect created by atmospheric haze for us here on Earth in 3D.

Flatlanders can also move around, which, coupled with their "depth perception", allows them to get reasonably good ideas of object shapes. If necessary, they can make little tangential movements (literally tangential, in the mathematical circular sense) to reveal more detail about an object from other angles. Naturally, they'd have to circle around completely to see the other side and get a full picture--just as we have to circle around a 3D object to get a full picture of it. However, we're pretty good at inferring the rest of an object from a 2D representation that only shows about half (or less) of it, and presumably a Flatlander could do the same.

So anyway, if they have some method of creating and distinguishing "colors" or something analogous, yeah, I think they could have art. Confusingly, they could probably create optical depth illusions by coloring a flat object to appear as though it had angles that protruded and receded, just as we do with 2D optical illusions. Color and a means of depth perception other than size probably aren't strictly necessary for some kind of art, but they make things so much easier; it's a lot harder for me, at least, to understand how a Flatlander would see "art" (or other objects at all) without similar perceptual aids.



P.S. Didn't anyone notice the pun in the last bit of dialogue? "That was out of line".... the stick-figure really is drawing "out of line" by adding new ones to a Flatlander.

[LewieP]

I just interviewed Marc Ten Bosch, creator of Miegakure, along with the makers of the other 5 of the games that made up the PAX East Indie Showcase. You can hear it and the others here:

Boston Indie Showcase: Where everybody knows your game

[Fieari]

Color definitely exists in Flatland, but in the days of A. Square, it was outlawed due to fears of impersonating a higher class using just the art trickses of imitating angles that you described. I seem to remember the example given was that a woman wearing two colors was mistaken for priest, which was absolutely scandelous... and honestly dangerous, if you remember that to touch a woman's endpoint is nigh-instant death.

[LTK]

Wait a second...

A flatlander lives on a flat plane, so it sees other flat objects on the plane as lines. But the legs of the xkcdian are made out of one-dimensional lines that stand on the plane, extending into the third dimension. So this means the xkcdian is invisible to the flatlander.

What that implies? I don't know, it just occured to me.

[artifex]

Here's another game with 4D perspective

Hmm, all of the 4D games I can find that project 4D down to 3D instead of using a 3D crosssection just use hypercubes. Someone really needs to try to make a game with solid objects in 4D perspective-- if they added visual cues like haze to show distance, and maybe some sort of mouseover effect to see overlapping objects, it might even be easier to comprehend then a wireframe hypercube. Or, at least, simple translations would be comprehensible.

EDIT: Although, come to think of it, I suppose what you get when you project 4D down to 3D is a solid volume of color, like a 3D photograph-- with no transparency (like, the sky in a photo is blue, not transparent). So, I guess to make a game with real 4D perspective, you'd have to heavily fake transparency and surfaces somehow.

[JustDoug]

Ok, this one is just mean! I want to play in four dimensions too! But the game is not yet released... sadness exists.

It was supposed to be released, but the original plan of sliding a copy of the code back along the time axis after it had been finalized and de-bugged didn't work, as it's not the same as a spacial axis in our spacetime.

The good part is that some guy named Abbott just[1] discovered some mysterious, mostly incomprehensible manuscript and is drawing inspiration from some portions of it.


[1] Standard english temporal tenses really don't work right in this situation.

[unus vox]

There are times when I miss the finer points of an XKCD comic, but I have to admit this one went completely over my head. I couldn't even the "whoosh" it was so far away...

[clanders]

I'm not convinced Randy is even trying to be funny anymore.

[tastethesun]

For those who don't get the alt text:

circle = priest in Flatland and women = lines.

You're not entirely right on that one.

It's actually kind of an inside joke, in reference to ConBust, which we attended this past weekend at Smith College. Speaking along the lines of how he didn't want to point out that it was, in fact, stick figures he was drawing (for that would be all people would think about then - and stick figures having sex is weird) he drew a comic idea he'd had for a while, but never posted, up on the board:

I think that confirms that dean WAS correct. Just because the joke was used twice doesn't change the interpretation.

[hcs]

I would love to see a true 4space game utilize the 4th dimension as a true 4th spatial dimension that you can translate and rotate through just like any other spatial dimension.

It may entertain you to know that this is exactly what Miegakure is. You can only move about in three dimensions (2D walk and jump) at any one time, but the extra rotation (exchanging a dimension of the projected 3 space with the mostly-hidden 4th one) works almost exactly like the normal left and right camera rotation in the 3D platformer.

I was just thinking today that there's sort of a 5th dimension, but movement is even more restricted (and no rotation): the line along which the levels are strung. I wonder if that ever comes into play? There is a dedicated button (go through gate) to move along it, when unobstructed...

[JustMe]

I'm not convinced Randy is even trying to be funny anymore.

It's always interesting how differently people see things. My response to the last 3 or 4 has been "Hurray! Randall's back!"

[Twistar]

Here's another game with 4D perspective

Hmm, all of the 4D games I can find that project 4D down to 3D instead of using a 3D crosssection just use hypercubes. Someone really needs to try to make a game with solid objects in 4D perspective-- if they added visual cues like haze to show distance, and maybe some sort of mouseover effect to see overlapping objects, it might even be easier to comprehend then a wireframe hypercube. Or, at least, simple translations would be comprehensible.

EDIT: Although, come to think of it, I suppose what you get when you project 4D down to 3D is a solid volume of color, like a 3D photograph-- with no transparency (like, the sky in a photo is blue, not transparent). So, I guess to make a game with real 4D perspective, you'd have to heavily fake transparency and surfaces somehow.

Ah I was just about to post this one. This is the best 4d game I've seen and you can really walk yourself through from 2 to 3 to 4 dimesions to really help yourself out. The other important thing is about this game is that you play it with stereoscopic vision so you are essentially playing with a 3d shadow of a 4d object. This is important because SO much information is lost if you take an N-2 dimensional shadow of some N dimensional object. In other words, It will be almost impossible to figure out what's going on if you're trying to play a 4d game on a computer screen. I suppose shading and such can help with perception but I think the stereoscopic vision bringing you up another level is just a smart way to give you an edge on visualizing that fourth dimension.

The thing that helped with this game that I thought was interesting was:
Think about those .gifs of rotating tesseracts, where the inside cube passes out the top of the whole structure, and the lower cube passes and becomes the central cube, basically the cubes rotate through themselves within the larger cube, which is also passing through the other cubes. It's hard to explain but if you've seen what I'm talking about it makes sense. Now, when you're playing the 3d version of this game rotate the 3d cube. This is a very familiar motion to you since you're a 3d person. But now imagine you're a flatlander perceiving the cube, and note how the FACES of the cube pass through eachother just like the CUBES of the hypercube. if you rotate the cube counterclockwise from the top then the front FACE which from a 2d perspective looks like it is enclosing the other faces, will pass and become the right face, while the old right face will shift from being a trapezoidal thing on the right to being a square thing in the center of the object. The same can be said for the sides of the 2d game.

Sorry if I'm rambling, I just find this all really interesting. The thing about that game is it is very easy in 2 and 3 dimensions because your used to it. But you have to make it hard on yourself and perceive your 3 dimensions in a new way so you can figure out the fourth.

Also, is it conceivable that one could perceive four dimensional space and or objects within their minds? I've heard that some people can do this through meditation. I don't see why not. These type of games show that one can become functional in four dimensions with enough thought and visualization and the fourth dimension is perfectly well defined mathematically.

[tastelikecoke]

Transplanting it in our world, We will see objects appearing ramdomly in thin air.

What's miegakure? Ooh thats cool!
*baited to play*

[atarianXCD]

When I read "What's up", I got goosebumps. And then my goosebumps got goosebumps. Such a brilliant yet succinct joke.

I joined the Fora just to make this comment.