0721: "Flatland"

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vaneselk
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Re: "Flatland" Discussion

Postby vaneselk » Thu Apr 01, 2010 1:28 pm UTC

Some of you seem to be missing something that took a couple of hours for me to realise: The stick figure, to visit Flatland, must lie down! Once in the plane of Flatland, its arms, legs, and body are lines (women) and its head is a circle (a priest).

chanakrogue
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Re: "Flatland" Discussion

Postby chanakrogue » Thu Apr 01, 2010 1:59 pm UTC

All flatlanders appear as lines to other flatlanders. There would be no way for a flatlander to tell what kind of flatlander another one is without going all the way around the other one and calculating the length projections at every step. Either that or all flatlanders exude some kind of pheromones betraying their type.

EhloVader
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Re: "Flatland" Discussion

Postby EhloVader » Thu Apr 01, 2010 4:07 pm UTC

If you want to try thinking of other dimensions after the 4th once you get comfortable with the game mentioned in the hover text, you can try checking out the website http://www.tenthdimension.com/flash2.php it is for a book called imagining the tenth dimension, found it back when I found "What the bleep? Down the rabbit hole" a great movie which also mentions the flatlanders.

Berke
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Re: "Flatland" Discussion

Postby Berke » Thu Apr 01, 2010 6:00 pm UTC

I loved this one, but then when I read the alt-text

Also, I apologize for the time I climbed down into your world and everyone freaked out about the lesbian orgy overseen by a priest.


I DIED...


...laughing!!!


Randall, I love you man!
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Re: "Flatland" Discussion

Postby megmond » Thu Apr 01, 2010 6:15 pm UTC

TheKob wrote: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'.

Aww... I had hoped that I could contribute that one. I actually won a copy of that book years and years ago in a contest, and got hooked. The great part is that it explores all these wonderful ideas without resorting to mathematics (I think the whole book had only a single formula in it?). And has many funny pictures scattered throughout as well (in a way, it's like xkcd I suppose!)

By the way, I know the title as The Fourth Dimension: A Guided Tour of the Higher Universes. You can pick it up for a few dollars secondhand online.

P.S. The commandprompt actually caused me to find out that there is a forum associated with xkcd! What a wonderful idea to pick up on all the little jokes that I missed. On the other hand, now I have to go through over 600 threads to make sure I didn't miss anything :|

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rigwarl
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Re: "Flatland" Discussion

Postby rigwarl » Thu Apr 01, 2010 8:48 pm UTC

chanakrogue wrote:All flatlanders appear as lines to other flatlanders. There would be no way for a flatlander to tell what kind of flatlander another one is without going all the way around the other one and calculating the length projections at every step. Either that or all flatlanders exude some kind of pheromones betraying their type.

That's pretty clever, I never thought about that. Also you wouldn't be able to tell how far away others were!

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artifex
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Re: "Flatland" Discussion

Postby artifex » Thu Apr 01, 2010 9:38 pm UTC

rigwarl wrote:
chanakrogue wrote:All flatlanders appear as lines to other flatlanders. There would be no way for a flatlander to tell what kind of flatlander another one is without going all the way around the other one and calculating the length projections at every step. Either that or all flatlanders exude some kind of pheromones betraying their type.

That's pretty clever, I never thought about that. Also you wouldn't be able to tell how far away others were!


Well, not necessarily-- if the the lines had any detail or pattern to them, they could judge both distance and identity at a glance. After all, if you lined up all the pixels of a photograph over a single dimension, you wouldn't actually loose any information.

EDiT: No, wait, you would-- you'd reduce the total possible number of patterns, for the same reason you're more likely to find words in a random grid of letters then in a random string.

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Re: "Flatland" Discussion

Postby Twistar » Fri Apr 02, 2010 2:27 am UTC

artifex wrote:
rigwarl wrote:
chanakrogue wrote:All flatlanders appear as lines to other flatlanders. There would be no way for a flatlander to tell what kind of flatlander another one is without going all the way around the other one and calculating the length projections at every step. Either that or all flatlanders exude some kind of pheromones betraying their type.

That's pretty clever, I never thought about that. Also you wouldn't be able to tell how far away others were!


Well, not necessarily-- if the the lines had any detail or pattern to them, they could judge both distance and identity at a glance. After all, if you lined up all the pixels of a photograph over a single dimension, you wouldn't actually loose any information.

EDiT: No, wait, you would-- you'd reduce the total possible number of patterns, for the same reason you're more likely to find words in a random grid of letters then in a random string.


In the actual Flatland book (or essay or whatever) flatland is covered in fog, objects farther away look dimmer than objects closer up. Now imagine looking at a triangle and one of the triangles vertices is pointed directly at you. The vertex would be very clear and dark, black as it were. The two other vertices which are to the left and right in your vision, but also farther away in the 2 dimensional world would appear much dimmer, or gray. The 2 lines connecting the respective vertices to the near vertex would be slanted with respect to you, and as a result the parts closest to you (the parts of the line by the near vertex) would be black and the parts further away, towards the far vertices would be dim. so it would be dim-lessdim-dark-darkest-dark-lessdim-dim if that string represents the line. Now, a square would look the exact same, except the steepness of the dimming would be less since we are dealing with a 90 degree angle as opposed to some angle less than 90 degrees. Flatlanders live in flatland so they can tell in an instant what shape the person approaching them is by the gradient on their sides. However, in flatland no fog is actually bad weather because then there's no gradient and all shapes look the same.

Now, this is such a long explanation because flatlanders only have one eye for some reason. If they had two eyes then they could judge distance with parallax just like we do, because after all, we, with our 2 dimensional vision can judge 3 dimensional distances. Granted, we can be tricked in optical illusions. I'm curious to see how shading could be used to help us comprehend more near 4d objects and more far 4d objects.

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kryton
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Re: "Flatland" Discussion

Postby kryton » Fri Apr 02, 2010 11:32 pm UTC

Ok I admit it, I overthought the alt-text. I had projected Randal's character into the "real world" analogs (people type body) and then imagined trying to see how a 2d cross section of a human could look like intersecting/overlapping line segments with a circle nearby. Then the Oh me yarm moment hit and I realiaed the character is a 2D stick figure made of intersecting line segments with a circle nearby.
D'OH.

BTW for thoes interested in reading flatland, I found this

http://www.geom.uiuc.edu/~banchoff/Flatland/
1298 and counting

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theta4
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Re: "Flatland" Discussion

Postby theta4 » Fri Apr 02, 2010 11:57 pm UTC

The problem with any projection of a 4D object is that it's usually a 2D projection of a 3D projection of a 4D object. Too much data gets lost by looking at a 4D object that way. That's like A. Square trying to understand a 3D object by looking at its 2D projection from the sides with his 1D retina.

A 4D creature would have some sort of 3D retina, like we have a 2D retina. This means that the information is reaching their eyes as a space, not a plane. So to think like a 4D creature, you've got to imagine several 3D space slices of the 4D object, just like a 3D object can be cut into several 2D slices, like a doctor uses several 2D slices of the brain to compose a 3D object.

What I'm trying to say is that our brains don't naturally have the capability to imagine 4 dimensions. Too many people try to approach 4 dimensions with 2 dimensional projections. You've got to *think* of space. You've got to think of the space, not its projection. Only then will you be able to imagine 4D's 3D projection.

That's why every time I see any misunderstanding of 4 dimensions like this Miegakure game, it annoys me. Too many people are still trying to approach this with 2 dimensional projections. A truly 4D game would allow you to stand on one layer, and be in another, just like in a 3D platformer you can stand on an object in one plane while being higher up in several other parallel planes. In Miegakure, you're still interacting with objects in your own 3D space, not objects in the other parallel spaces.

Admittedly, Miegakure is a step in the right direction, but it's far from being truly 4D. Hopefully nobody misunderstands this. In fact, any truly 4D game would be impossible, because in order for the 4D info to get to our brain, it has to be projected down to 2D to be displayed on the screen, and received by our 2D retinas, then unprojected back up to 4D.

This post is very scattered and disorganized, but you're all smart people; I know you'll know what I mean.
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Jackpot
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Re: "Flatland" Discussion

Postby Jackpot » Sat Apr 03, 2010 10:15 am UTC

since that game isn't avalible, I'm playing time fcuk again.

http://www.newgrounds.com/portal/view/511754
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tastelikecoke
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Re: "Flatland" Discussion

Postby tastelikecoke » Sat Apr 03, 2010 11:49 am UTC

^ the best game crafted in flash.

theta4-ene wrote:Admittedly, Miegakure is a step in the right direction, but it's far from being truly 4D. Hopefully nobody misunderstands this. In fact, any truly 4D game would be impossible, because in order for the 4D info to get to our brain, it has to be projected down to 2D to be displayed on the screen, and received by our 2D retinas, then unprojected back up to 4D.

This post is very scattered and disorganized, but you're all smart people; I know you'll know what I mean.


If flatland universe doesn't exist, what's beyond the 4th dimesion exactly?

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Re: "Flatland" Discussion

Postby hcs » Sat Apr 03, 2010 10:17 pm UTC

theta4 wrote:A 4D creature would have some sort of 3D retina, like we have a 2D retina. This means that the information is reaching their eyes as a space, not a plane. So to think like a 4D creature, you've got to imagine several 3D space slices of the 4D object, just like a 3D object can be cut into several 2D slices, like a doctor uses several 2D slices of the brain to compose a 3D object.

As Marc points out on his blog, the 3D world that you maneuver at any one time (which is perceived directly as a 2D projection) is a slice of the 4D world, not a projection. There are "shadows" of adjacent slices (or was it "nearer" slices?), but that's as close as it gets. It's sort of presented as a set of 3D worlds sitting independently, then when you rotate it changes to a new 3D world made from a slice (exactly which slice depending on where you're standing) out of each of those worlds. When you collect the maps, this is shown in the little world representations in the lower left.

I don't think Miegakure is the misunderstanding you think it is. I could have quoted a lot more of your post, but the author seems to have come to the same conclusions you do.

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tastelikecoke
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Re: "Flatland" Discussion

Postby tastelikecoke » Sun Apr 04, 2010 4:36 am UTC

and I come up with another question. How do flatlanders see the world?

horizontally or vertically?

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Re: "Flatland" Discussion

Postby nahkaimurrao » Mon Apr 05, 2010 10:54 pm UTC

http://www.youtube.com/watch?v=87PbQv-H_4U&feature=related
Seeing it in action, I have to give this game a bit more credit. The transitions are what really get me. I kept rewatching them, trying to comprehend them.

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Re: "Flatland" Discussion

Postby sje46 » Tue Apr 06, 2010 12:39 pm UTC

tastelikecoke wrote:and I come up with another question. How do flatlanders see the world?

horizontally or vertically?

I don't think I can answer that question meaningfully. I don't even understand what you're asking. I will say this though: Flatlanders see everything as points and lines. if they see a woman facing away from them, that will appear as a dot. Everything else will see lines of varying lengths. IIRC they're much more dependent on touch.
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Re: "Flatland" Discussion

Postby Strillz » Fri Apr 16, 2010 8:20 pm UTC

jspenguin wrote:
Ethliel wrote:I'm assuming the "lesbian orgy" thing is some reference to what different types of people look like in flatland and the shape of a stick person's body?
I really need to read that book...


Basically, social rank is based on how many lines a polygon has. Women are line segments, low-class males are isosceles triangles, then equlateral triangles, and so on. The priests have so many sides that they are considered circles.

So a lesbian orgy overseen by a priest would be a bunch of lines topped by a circle.

Women aren't actually line segments, they're really just really thin quadrilaterals.

nahkaimurrao
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Re: "Flatland" Discussion

Postby nahkaimurrao » Fri May 07, 2010 12:41 am UTC

here is an interesting take on a multi dimensional maze
I have successfully completed a 4D 4x4x4x4 maze!

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snowyowl
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Re: "Flatland" Discussion

Postby snowyowl » Sun May 09, 2010 1:35 pm UTC

theta4 wrote:That's why every time I see any misunderstanding of 4 dimensions like this Miegakure game, it annoys me. Too many people are still trying to approach this with 2 dimensional projections. A truly 4D game would allow you to stand on one layer, and be in another, just like in a 3D platformer you can stand on an object in one plane while being higher up in several other parallel planes. In Miegakure, you're still interacting with objects in your own 3D space, not objects in the other parallel spaces.

Watch the demo video. The reason you can't stand on one layer while being in another is (I'm fairly certain) simply an oddity of gravity: gravity pulls along the w-axis, but the game forbids you from trying to rotate the view so that you can only see the x,y and z-axes (which would be required for what you are describing). The reason it does this is primarily to simplify the controls, and to avoid having an entirely different gameplay mechanic in the views where gravity is "inwards". I suppose you could modify it to solve this, but Miegakure chooses not to.
As for interacting with objects in parallel spaces, that is quite simple in Miegakure. Notice the ring in the demo video. Fro a certain perspective (which is not shown in the video), it would appear as a pair of points with a line through the fourth dimension (in reality the rest of the ring) connecting them. Pushing against the points causes the entire ring to move, including the parts not in the current 3-dimensional layer.

theta4 wrote:Admittedly, Miegakure is a step in the right direction, but it's far from being truly 4D. Hopefully nobody misunderstands this. In fact, any truly 4D game would be impossible, because in order for the 4D info to get to our brain, it has to be projected down to 2D to be displayed on the screen, and received by our 2D retinas, then unprojected back up to 4D.


By the same logic, you could argue that 3D is impossible to display, because although humans have stereoscopic vision, we only perceive a two-dimensional view of the world at any time.
In fact, even 2D is impossible for a computer to display, since the data sent to the screen is a 1D stream of bits.

My point here is: A 4D game is simply one that can be taken to represent a universe with 4 spatial dimensions (I'll leave the discussion of temporal dimensions for someone else). In this respect, Miegakure is 4D, and so are all the other games linked to here with "4D" in their titles. It doesn't matter how we perceive them or how they are programmed, what counts is what they are supposed to represent.
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Re: "Flatland" Discussion

Postby Assasinof6 » Fri May 14, 2010 3:56 pm UTC

sje46 wrote:
tastelikecoke wrote:and I come up with another question. How do flatlanders see the world?

horizontally or vertically?

I don't think I can answer that question meaningfully. I don't even understand what you're asking. I will say this though: Flatlanders see everything as points and lines. if they see a woman facing away from them, that will appear as a dot. Everything else will see lines of varying lengths. IIRC they're much more dependent on touch.



I understand what he's asking- he's asking, if we were able to the see the two dimensional plane they live on, would it be horizontally flat, like a piece of paper lying on the ground, or vertically flat, like a paper stuck to a bulletin board.

When I was reading flatland, I assumed it was horizontally flat most of the time, but when the square says that it rains from "the North", and they have "Roofs to keep out the rain", I assume it is a vertically flat surface.
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Xerox_Cat
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Re: "Flatland" Discussion

Postby Xerox_Cat » Mon May 24, 2010 4:29 am UTC

RANDAL GET OUT OF MY HEAD
we just had to read flatland for geometry. I had not heard of it until then

MattTheTubaGuy
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Re: "Flatland" Discussion

Postby MattTheTubaGuy » Tue Jun 08, 2010 1:42 am UTC

trying to think in 4 dimensions is difficult but kind of fun!
I have a 3D net of a 4-cube beside me made out of plasticine at the moment :D

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Re: "Flatland" Discussion

Postby enderverse » Wed Jun 16, 2010 3:39 am UTC

I initially found this book in high school because it was the first book in the whole library. It was pretty good. Read one of the sequels but Haven't seen any of the movies yet. Are any of them any good?

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Re: "Flatland" Discussion

Postby lsdigit » Thu Jul 15, 2010 2:01 am UTC

thanks to the power of the internet i found this

http://librivox.org/flatland-a-romance- ... tt-abbott/

I know, it is almost like the internet has supernatural powers or sumfing.
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Re: 0721: "Flatland"

Postby j6m8 » Tue Feb 19, 2013 3:36 am UTC

Reminds me of the concept video game that was floating around a while ago where you play a stick figure on a black and white 3d 'jungle-gym' style field. It's laid out isometrically so that, if you line up two 'floors', even though one of them is further away (it doesn't appear so because it's isometric), you can step from one to the other. Anyone know what I'm talking about? Ring any bells? ...Bueller?

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Re: 0721: "Flatland"

Postby jasonkoller » Wed Feb 19, 2014 3:58 pm UTC

Has anyone heard anything about this game's "development"?
I't's been nearly 4 years and I really want to try it.

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Re: "Flatland" Discussion

Postby PayasYouDraw » Tue Feb 25, 2014 11:32 am UTC

pgn674 wrote:"What's up?" ... Hah, I laughed pretty hard at that.


Just clicked. :oops: Brilliant. :D

Just trying to get my head around 4D and this is the only case I can actually get my head round.

If we consider a sphere as a "hypercircle" and we have it traverse through Flatland, then what the Flatlander would see would be a point appearing, becoming an ever larger circle, and then getting smaller again before disappearing.

So a 4D hypersphere passing through our world would appear as if from nowhere as a growing ball, and then shrinking before disappearing again.

I can just about extend this idea to other shapes, but it get really complicated. A cube being pushed through flatland normal to one face would be a square, suddenly appearing and then just as suddenly disappearing. But if it travels through at any other angle it will go through a variety of cross-sections. At this point I begin to lose it. So a hypercube passing though our world could appear as a shape I can't imagine unless one of it's solid's ("faces") is "normal" to our world, whatever that means, and then it would be a cube, suddenly appearing and then disappearing.

Anything else and my brain breaks down.
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Re: 0721: "Flatland"

Postby Pfhorrest » Tue Feb 25, 2014 11:18 pm UTC

A hypercube's cross-section in 3D space would still always be an ordinary 3D shape, not something imaginable. My intuition tells me that if it intersected by a corner, we in 3D space would see a tetrahedron (three-sided pyramid) appear, similar to how a corner of a cube's intersection with a plane is a triangle. Then as further corners of the hypercube passed through our 3D space, in turn, corners of the tetrahedron would flatten out through a variety of irregular polyhedra, culminating in an octahedron, then other sides of that octahedron would shrink back down to points until you had a tetrahedron again, which would then shrink until it vanished; much like as a cube's other corners pass through a plane, the corners of the triangle flatten out into into additional sides until you have a hexagon, then the original sides shrink down to points until you have a triangle again, which then shrinks until it vanishes. But I'm too lazy to work out the actual geometry right now.
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PayasYouDraw
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Re: 0721: "Flatland"

Postby PayasYouDraw » Thu Feb 27, 2014 4:48 pm UTC

Trying to imagine that makes my head hurt. I wonder if anyone round here would be able to animate that?
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Re: 0721: "Flatland"

Postby Klear » Thu Feb 27, 2014 7:04 pm UTC

PayasYouDraw wrote:Trying to imagine that makes my head hurt. I wonder if anyone round here would be able to animate that?


He's a 5D Rubic's Cube: http://www.gravitation3d.com/magiccube5d/index.html Each colour sticker on it is a tesseract.

You're welcome.

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Re: 0721: "Flatland"

Postby Pfhorrest » Fri Feb 28, 2014 6:28 am UTC

PayasYouDraw wrote:Trying to imagine that makes my head hurt. I wonder if anyone round here would be able to animate that?

I can't help with the the animating, but I can maybe paint a clearer picture in words.

Picture one of the pyramids of Giza. Big stone thing, square bottom, four triangular sides that come up to a point, you know it.

Now picture it with a triangle on the bottom instead, and three triangular sides coming to a point instead. Same general idea. You could imagine the point maybe being off center, or the triangle on the bottom being an irregular triangle, or any other irregularities, but you've still got roughly the same shape: a tetrahedron. Note how this shape has four points, and also four sides altogether, including the bottom. That's important.

Imagine a microscopic version of that pyramid appears floating in mid air all of a sudden, and begins growing to visible size. Easy enough so far, right?

Now imagine that there's a big invisible force field of that same shape surrounding the pyramid, except it's upside-down and backwards, so that every point on the stone pyramid faces a side of the force field. If anything crosses the force field, it gets vaporized completely; so if you stuck one corner of the pyramid through the force field, it would be like you cut that corner off, and there'd be a stump ending in an extra triangle. If you did that to every corner, instead of a four-sided shape, you would have four extra sides, one for each cut-off corner: an octohedron.

So imagine that as the pyramid grows, the force field surrounding it shrinks, and eventually the corners of the pyramid start to get vaporized off. At first this will leave you with the original triangular sides now being hexagons, and the new corner-stump sides being triangles, but as the stumps get stumpier and stumpier, three sides of each hexagon shrink with them until they disappear entirely, the hexagons become triangles, and eventually you have an octohedron made of eight triangles.

This is the mid-point of the process. So far the pyramid has been growing, even as its points got cut off. But from here on, the shrinking force field will cut off more of the pyramid's volume than the pyramid creates from its own growth, and the overall shape will shrink.

As the force field continues to shrink, the stumps butt up against each other and their once-triangular faces grow extra sides where they meet, until you now have growing hexagonal stumps, and the dwindling original sides of the pyramid are now shrinking triangles.

As the pyramid grows and the force-field shrinks, those triangular original sides shrink down into nothingness, as eventually the whole volume of the force-field is filled with pyramid-rock, and the pyramid is once again a tetrahedron -- just upside-down and backward, the shape and orientation of the force field.

As the force field continues to shrink, that tetrahedron shape shrinks down with it, until eventually it vanishes into nothingness.


That's what a hypercube passing through out three-dimensional space would look like, if it passed through at an irregular angle, one corner first.

If it passed through with one edge (a line segment, not a square or cube) parallel to our space, the initial pyramid would just appear with one corner cut off already, and all its walls parallel -- a triangular prism, two parallel triangles joined by four squares. As the next parallel line passed through, two "corners of the pyramid" would get cut off by the force field at once, meaning one corner of each of the two triangles, and the line that connects them, creating a quadrilateral prism -- two quadrilaterals joined by four squares. That new side to the prism would grow, as the other one shrinks, and for a brief moment both quadrilaterals would be squares, and the prism would be a cube. Until one face of the cube shrinks back down to a line, and you're back to your triangular prism again, which then shrinks down to the nothing it came from.

If it passed through with one face (square) parallel to our space, you'd just start with that quadrilaterial prism, which would grow and shift into a cube, then back again, quite predictably.

And if it passed through with one whole cube parallel to our space, well, you'd just start with a tiny cube that grew and then shrank and vanished again.

Each case is just a more special case of the previous one, so the irregular example we started with is the best way to understand it thoroughly.
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Re: 0721: "Flatland"

Postby PayasYouDraw » Fri Feb 28, 2014 10:48 am UTC

You have an excellent way with words Pfhorrest.

I do have to pick you up on a couple of points. A triangular prism would be two triangles connected by 3 squares.

The other is that in the final special case, of the cube being parallel to our space, then it surely wouldn't grow and shrink, but simply appear and disappear. If we compare to the 2D/3D case of pushing a cube through a plane, you would have a square appearing and remaining a constant size until it disappears all at once. What you've described would be the 3D/4D equivalent of pushing an octohedron (of the two pyramids connected at the base type) through a plane with the middle square being parallel to the plane.
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Re: 0721: "Flatland"

Postby orthogon » Fri Feb 28, 2014 11:51 am UTC

Thanks, Pfhorrest, for your description, which inspired me to try to draw it.
hypercube1.jpg
hypercube1.jpg (22.78 KiB) Viewed 5151 times

This is work in progress. I should be able to animate it, but I want to improve the accuracy first. (Mathematica is supposed to be better at this stuff so I'm a bit disappointed, but hopefully there are some options I can fine-tune. Suggestions from other Wolframites welcome!)
If I'm not mistaken, there are six rotational degrees of freedom in 4D, but three of those correspond to rotations within our 3D hyperplane, so I have only provided the other three (which correspond to rotations in the w-x, w-y and w-z planes where we are plotting the intersection of the hypercube with the hyperplane w=constant). I also have a single translational degree of freedom, defined by the value of w.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0721: "Flatland"

Postby orthogon » Fri Feb 28, 2014 2:15 pm UTC

Here's a better version using ContourPlot3D instead of RegionPlot3D:
hypercube2.jpg

[Sorry to doublepost but something strange happened with the attachments when I tried to add a new picture]
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0721: "Flatland"

Postby Whizbang » Fri Feb 28, 2014 3:50 pm UTC

Pfhorrest wrote:
PayasYouDraw wrote:Words.



Ok, now try that in Up-Goer 5 style.

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Re: 0721: "Flatland"

Postby Pfhorrest » Fri Feb 28, 2014 7:02 pm UTC

PayasYouDraw wrote:You have an excellent way with words Pfhorrest.

I do have to pick you up on a couple of points. A triangular prism would be two triangles connected by 3 squares.

The other is that in the final special case, of the cube being parallel to our space, then it surely wouldn't grow and shrink, but simply appear and disappear. If we compare to the 2D/3D case of pushing a cube through a plane, you would have a square appearing and remaining a constant size until it disappears all at once. What you've described would be the 3D/4D equivalent of pushing an octohedron (of the two pyramids connected at the base type) through a plane with the middle square being parallel to the plane.

Yes, you are correct of course. Thank you for catching that!
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Re: 0721: "Flatland"

Postby orthogon » Sat Mar 01, 2014 11:24 am UTC

I left it going overnight in the end. No idea how long it took:
hyperCube.gif

I got the range a bit wrong so it made about 25 frames in which there was no intersection at all! I might do a smoother one now I know it works.
Note that this one is at a more general angle than the case Pfhorrest was talking about. I guess that case was at 45 degrees in the w-x, w-y and w-z directions? I might have a go at that case.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0721: "Flatland"

Postby jameslovecraft » Sat Mar 01, 2014 12:18 pm UTC

This remains one of my favorite xkcds since I first saw it. I tried reading Flatland first when I was 7, then again at 13, and I never managed to get through it... maybe I'll try again in a couple of years.

Someone's earlier explanation about a 4D-er being able to see all faces of a 3D object at once (like we can see all sides of a 2D object at once) helped me understand 4D more viscerally. I wonder how a 4D person would do drawing lines on a 3D graph represented 2-dimensionally... (I suck at 3D graphing, and 2D graphing is one of the few math things I do well).

Coincidentally "--And He Built a Crooked House--" is my favorite Heinlein short story. (Hm. Maybe I should build said house in Minecraft.)

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Re: 0721: "Flatland"

Postby Klear » Sat Mar 01, 2014 2:18 pm UTC

jameslovecraft wrote:Coincidentally "--And He Built a Crooked House--" is my favorite Heinlein short story. (Hm. Maybe I should build said house in Minecraft.)


I always build that house in every game which allows building something like that. It hasn't collapsed so far though.

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Re: "Flatland" Discussion

Postby addams » Sun Mar 02, 2014 3:44 am UTC

kryton wrote:
BTW for thoes interested in reading flatland, I found this

http://www.geom.uiuc.edu/~banchoff/Flatland/

And:
lsdigit wrote:thanks to the power of the internet i found this

http://librivox.org/flatland-a-romance- ... tt-abbott/

I know, it is almost like the internet has supernatural powers or sumfing.


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