What a 2d room might look like

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

What a 2d room might look like

Postby anderscolingustafson » Wed Mar 12, 2014 6:07 pm

I designed a 2d room

2d Room.png
2d Room
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I designed the room to be underground to prevent it from getting in the way of dionians who are passing by.

I made the room with thick walls in order to prevent it from caving in as in 2d without the extra walls in 2d the room would be more likely to cave in without having thicker walls.

Since the door helps support the roof I thought that if the door is opened or closed it might cause the roof to cave in so I designed it so that instead of opening and closing it spins around so that the hole that a dionian would get into moves. It has teeth that interlock with the teeth of the wall to help hold it in place.

I placed some handles on the right wall and on the ceiling near the door to allow a dionian in the room to climb up the wall to get to the door. I also put some handles in the door to give anyone getting into the door something to grab onto when climbing into the door.

I put some plants on the floor to prevent anyone in the room from suffocating from the fact that the air in the room is cut off from the air outside.

The thing at the far left of the room is to help spin the door by sliding between the teeth of the door and then pushing against a tooth to help move the door along.

I made a window at the top of the room to allow light into the room for the plants and to light up the room.

I made a bridge over the door to prevent dionians passing by from falling on the door and getting hurt by the teeth of the door.

So what do you think of my 2d room?
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Re: What a 2d room might look like

Postby ICN5D » Thu Mar 13, 2014 3:08 am

Have you thought about 2D planes that are not vertically oriented? Surely, there would be no gravity, but it would help alleviate the issues with structural failure and/or falling into someone's house, or suffocating to death. Just a little morsel of food for thought :)
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Re: What a 2d room might look like

Postby anderscolingustafson » Thu Mar 13, 2014 3:50 am

The problem with having a building above ground in 2d is that it would create a boundary so that passers-by would have to cut through it, climb over it or fly over it.
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Re: What a 2d room might look like

Postby ICN5D » Thu Mar 13, 2014 4:33 am

Correct, which is why I mentioned a 2D world much in the way of Flatland.

Like this, as I described:

http://www.youtube.com/watch?v=UnURElCzGc0
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Re: What a 2d room might look like

Postby wendy » Thu Mar 13, 2014 8:11 am

A very good book on how two dimensions work is William Poundstone's 'Planiverse'. It gets down to things like terrifying flying snakes and rivers. A "river" is an overland flood, when you think about it. I mean if you go from A to B, you cover every point between A and B.

A 2D room is pretty much held up by its doors. You can't open both doors, otherwise the roof would fall down.
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Re: What a 2d room might look like

Postby anderscolingustafson » Thu Mar 13, 2014 3:43 pm

I have heard of the idea of flatland but I haven't given much thought to it. The issue I have with flatland is how do you get matter to condense to form life without gravity?
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Re: What a 2d room might look like

Postby ICN5D » Fri Mar 14, 2014 12:14 am

Well, it's quite possible that a minimum of 3D is required for life to emerge. 2D is too restrictive, and has all sorts of issues just as you point out. The best way for the vertical 2D houses to function, in my entertaining idea, is with maglev roofs, with drapes for walls. Of course, this pretty much omits the entire neanderthal-era of evolution, where advanced tech isn't available.
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Re: What a 2d room might look like

Postby Polyhedron Dude » Fri Mar 14, 2014 2:23 am

wendy wrote:A very good book on how two dimensions work is William Poundstone's 'Planiverse'. It gets down to things like terrifying flying snakes and rivers. A "river" is an overland flood, when you think about it. I mean if you go from A to B, you cover every point between A and B.

A 2D room is pretty much held up by its doors. You can't open both doors, otherwise the roof would fall down.


Correction - Planiverse was written by A.K. Dewdney - great book!
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Re: What a 2d room might look like

Postby wendy » Fri Mar 14, 2014 7:24 am

That's right - poundstone wrote a very good book about conway's game of life and its theological implications.
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Re: What a 2d room might look like

Postby Eric B » Sun Mar 16, 2014 12:41 pm

I still can't imagine what 2D vision would be like. The field of view would like in a 1D line, but it wouldn't be a line, because you're totally unaware of the missing dimension.
It seems about as hard to imagine as 4D vision!
(I bet if we could could imagine 2D vision, then it would be that much easier to know how to add the missing dimension and then be able to visualize 4D)
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Re: What a 2d room might look like

Postby ICN5D » Sun Mar 16, 2014 3:41 pm

Well, each time you "see" something, no mater how many dimensions you have, the missing one is depth. One cannot see behind an object of the same dimension.

Looking in your own dimension:

A 2D being scans its 2D world with 1D snapshots, where it cannot see behind a 2D object

A 3D being scans its 3D world with 2D snapshots, where it cannot see behind a 3D object

A 4D being scans its 4D world with 3D snapshots, where it cannot see behind a 4D object

A 5D being scans its 5D world with 4D snapshots, where it cannot see behind a 5D object



Now, if you're a HIGHER dimensional being, looking " down " on lower-D, you CAN actually see the entire lower shape, all at once. Not only the entire outside, but the entire inside as well.

Looking into a lower dimension:

A 2D being can look down on a 1D being and see its entire insides and outsides in a single glance

A 3D being can look down on a 2D being and see its entire insides and outsides in a single glance

A 4D being can look down on a 3D being and see its entire insides and outsides in a single glance

A 5D being can look down on a 4D being and see its entire insides and outsides in a single glance


It's a fairly simple number pattern analogy, which holds true for any dimensional world. Analogies are where it's at, when comparing high-D / low-D abilities.
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Re: What a 2d room might look like

Postby Eric B » Sun Mar 16, 2014 10:55 pm

Thing is, higher dimensional beings see inside and around lower dimensional objects by looking at a perpendicular angle (the extra dimension they have) to the lower space.

Depth is the primary dimension; we could call it the "first" dimension, because it is the view out into one's own dimension. Height then is the dimension of gravitational attraction. Width then becomes the "extra" dimension of 3D existence. (So 4D is described as like "a new kind of left and right").

Still can't envision what it would be like not to have it, though
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Re: What a 2d room might look like

Postby ICN5D » Sun Mar 16, 2014 11:18 pm

Still can't envision what it would be like not to have it, though


That's the thing: there is always depth. In 1D, you see only depth, it's the only extension of space. In 2D, you would see width and depth, where a 2D shape can obscure another, by being further away in 2D. In 3D, shapes have width, length and depth, where width x length is the 2D image, or side you see of a 3D shape. Things that are behind a 3D shape are further away in 3D, according to the perspective of the 2D scan our eyes make.

So, in 4D, the depth would then be through 4D, where a 4D shape can obscure another 4D shape. The surface scan 4D eyes would make is a 3D image, of length, width, and height, where 4D is the new depth.
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Re: What a 2d room might look like

Postby Eric B » Sun Mar 16, 2014 11:26 pm

In 1D also; what does it mean to see only depth? That's even harder to imagine!
Your whole field of vision is just a single point, and not even a point like period, but a point having no height or width at all; and even if you could see it, it wouldn't look like a point, because you're not even aware of the existence of height or width!
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Re: What a 2d room might look like

Postby quickfur » Mon Mar 17, 2014 12:24 am

Eric B wrote:In 1D also; what does it mean to see only depth? That's even harder to imagine!
Your whole field of vision is just a single point, and not even a point like period, but a point having no height or width at all; and even if you could see it, it wouldn't look like a point, because you're not even aware of the existence of height or width!

You can't see depth in 1D, because it's impossible to have stereoscopic vision. :lol: So sight becomes pretty meaningless in 1D. Fortunately, you don't need sight in 1D anyway, since you can only ever have two neighbours, and they will be your neighbours your whole life (unless they die first). You can't swap places with them unless they die, so they are basically your lifelong companions. If they're not walls, that is. :o In which case you're just in a lifelong prison cell, and you might as well not live, since there's nothing to do anyway. 1D is a pretty boring place.

Also, from the day you're born, you're stuck with the same companion (with your mother on the other side) your whole life. Until your mother gives birth to another child, then that will be your lifelong sibling, since none of you can swap places. So all in all, a pretty dreary existence.
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Re: What a 2d room might look like

Postby anderscolingustafson » Mon Mar 17, 2014 12:41 am

In 1d light wouldn't have any space to dilute so something that was far away would be just as bright as something close by as the light wouldn't dilute with distance. In 1d an object 1 meter away would look the same as an object 1 light year away.
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Re: What a 2d room might look like

Postby quickfur » Mon Mar 17, 2014 12:50 am

anderscolingustafson wrote:In 1d light wouldn't have any space to dilute so something that was far away would be just as bright as something close by as the light wouldn't dilute with distance. In 1d an object 1 meter away would look the same as an object 1 light year away.

Hmm. You're right! And if there was gravity in 1D, it wouldn't dilute either, so over time, all the mass in the 1D universe will compress together into a giant line, and gravity would be so strong nothing could stand upright on either end. So nothing interesting could exist other than the universal line segment that contains all of the mass in the universe.
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Re: What a 2d room might look like

Postby anderscolingustafson » Mon Mar 17, 2014 2:17 am

quickfur wrote:
anderscolingustafson wrote:In 1d light wouldn't have any space to dilute so something that was far away would be just as bright as something close by as the light wouldn't dilute with distance. In 1d an object 1 meter away would look the same as an object 1 light year away.
<br abp="650">Hmm. You're right! And if there was gravity in 1D, it wouldn't dilute either, so over time, all the mass in the 1D universe will compress together into a giant line, and gravity would be so strong nothing could stand upright on either end. So nothing interesting could exist other than the universal line segment that contains all of the mass in the universe.


If Gravity doesn't dilute would it still act as an attractive force between two objects? If gravity was the same everywhere then how would an object even "Know" to go in the direction of the other object when the gravity would be the same on either side of it?
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Re: What a 2d room might look like

Postby quickfur » Mon Mar 17, 2014 3:13 pm

anderscolingustafson wrote:
quickfur wrote:
anderscolingustafson wrote:In 1d light wouldn't have any space to dilute so something that was far away would be just as bright as something close by as the light wouldn't dilute with distance. In 1d an object 1 meter away would look the same as an object 1 light year away.
<br abp="650">Hmm. You're right! And if there was gravity in 1D, it wouldn't dilute either, so over time, all the mass in the 1D universe will compress together into a giant line, and gravity would be so strong nothing could stand upright on either end. So nothing interesting could exist other than the universal line segment that contains all of the mass in the universe.


If Gravity doesn't dilute would it still act as an attractive force between two objects? If gravity was the same everywhere then how would an object even "Know" to go in the direction of the other object when the gravity would be the same on either side of it?

Everything will just gravitate towards the direction of more objects. Gravity does not stop as soon as it encounters the first object in its path! It is not the same on either side unless 1D space is filled with an infinite number of objects. As long as there are a finite number of objects, there will be one direction in which there are more objects, and that's where things will fall towards.
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Re: What a 2d room might look like

Postby ICN5D » Tue Mar 18, 2014 1:15 am

quickfur wrote:You can't see depth in 1D, because it's impossible to have stereoscopic vision. :lol: So sight becomes pretty meaningless in 1D. Fortunately, you don't need sight in 1D anyway, since you can only ever have two neighbours, and they will be your neighbours your whole life (unless they die first)


Yeah, I guess you're right about that. Monoscopic vision isn't that great. Plus, life in 1D would be pretty crappy as you described! I suppose that the most basic analogy of vision and depth would be the direction required for occlusion. The extra dimension in you field of view that makes things be further away, or behind something, is depth. Just as you pointed out: If we assume that, hypothetically speaking, in 1D there is ONLY depth, according the the 0-D eyeball scan of a mononian, then they cannot see past each other. In 2D, dionians have 1-D eyeballs ( eyelines ). Objects they see are 1D scans of their 2D world. The other dimension is the 2D depth, according to their 1D scan. The depth allows 1D scans to be behind others. Now, in 3D, we have 2D scans. The third direction, according to our 2D scan, is the 3rd dimension of depth. Things displaced further in 3D will be further away or behind another 2D scan.
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Re: What a 2d room might look like

Postby quickfur » Tue Mar 18, 2014 1:49 am

It's not just about what mononians can/cannot see; it's also about the constrictions that 1D space imposes upon objects that exist within it. Even if a mononian were to somehow acquire "magic" vision that allows it to see the entire 1D line, it would still be pretty useless, because it can't physically move past its neighbours or otherwise interact with the world beyond its own confined little line segment. Since its life is confined to that tiny space between two neighbours anyway, it's pretty pointless to see anything beyond that.
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Re: What a 2d room might look like

Postby anderscolingustafson » Tue Mar 18, 2014 1:55 am

Part of the reason you can't see depth in 1d is that depth perception requires the ability to triangulate using two eyes. We detect depth because there is a slight difference between the position we see things in using both our eyes. In 1d you couldn't have two eyes next to each other and so you wouldn't be able to use triangulation to tell how far something is.
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Re: What a 2d room might look like

Postby quickfur » Tue Mar 18, 2014 2:06 am

anderscolingustafson wrote:Part of the reason you can't see depth in 1d is that depth perception requires the ability to triangulate using two eyes. We detect depth because there is a slight difference between the position we see things in using both our eyes. In 1d you couldn't have two eyes next to each other and so you wouldn't be able to use triangulation to tell how far something is.

Light and shade also break down in 1D, because there's no room for a light source to be present to illuminate something from the side, so either you're looking directly at the light, which will be blinding, or the light is behind you or the object, so you won't see a thing (you block the light from reaching the object in front of you), or you're the light source itself, which is still useless because (1) the light always strikes the object's surface at a 90° angle so there can be no difference in light and shade, and (2) light doesn't attenuate with distance so the object appears the same at all distance.

All in all, 1D vision is pretty useless. :)
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Re: What a 2d room might look like

Postby wendy » Tue Mar 18, 2014 7:49 am

If Stephen Jay Gould "The Burgess Shales" is to be believed, the pre-cambrian life forms did not see, but were eventually wiped out by the new pentadactyl-forms with the power of sight. We belong to this form.
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Re: What a 2d room might look like

Postby ICN5D » Tue Mar 18, 2014 8:17 pm

All right, fair enough. Without getting too lost in the particulars of 1D dynamics, I think y'all see my point of view :)


As for the precambrian evolution, I can agree with this. I like to reflect on the horseshoe crab, and the super primordial eyes it has. This was one of the original designs nature was experimenting with at that time. It has two main spots on its actual shell that have an array of about a hundred light sensitive receptors, in addition to several lines and arrays around its front and sides. That's why horseshoe crabs rock, they're so primitive and ancient, but still alive and well.
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Re: What a 2d room might look like

Postby Eric B » Tue Mar 25, 2014 2:01 am

Back to reality now; all this seems to make clear that 1D existence (let alone vision) is probably impossible. Doesn't look much better for 2D.

What I'm hoping is that this doesn't mean 3D is the only reality, and there's not such thing as "higher" dimensions. Perhaps the concept of "dimensions" is illusory, and we surmise higher dimensions cause we're able to conceive of a flat surface, a line and a point. But these are just surfaces in our universe, not really kinds of universes in themselves. We have only generalized them as such.

Of course, string theory would fall if this were so. (Even with the notion of "curved" space, I've read that for 3D space to be curved, it doesn't have to be embedded in any higher space, as we would assume).

Really hope there are higher dimensions, and perhaps whatever existence after this one to just see what that's like, and to finally see a tesseract, hypersphere and duocylinder. I would love to see time laid out as the fourth dimension, so you could see any given place's entire history at once.
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Re: What a 2d room might look like

Postby ICN5D » Tue Mar 25, 2014 3:38 am

Oh, no, higher spatial dimensions are definitely real. We have to understand them through analogies and comparisons. The part that makes them real is their surface equations. These mathematical curiosities describe a shape that requires more than 3D to exist. Or, rather these are the shapes that are allowed to exist, when given extra 90 degree directions to build things with. A sphere, cube, cone, tetrahedron all have elegant and simple equations that detail their structure and surface. Higher dimensional shapes also use these equations, but they're more complex, naturally.

Take the surface equation for a torus:

Image

simplified into its toratope notation, it gets reduced to this: ((II)I)



Now, take a six dimensional hypertorus:


Image



Which when reduced to its toratope notation looks like: (((II)I)((II)I))


So as you can see, these shapes are not a figment of the imagination. They just require a special thought process to imagine. Most of us come to create our own methods of visualizing, but there are some good universal tricks to learn.
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Re: What a 2d room might look like

Postby Eric B » Tue Mar 25, 2014 3:49 am

But isn't that what we would call a "generalization" (That's not absolutely verified?
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Re: What a 2d room might look like

Postby quickfur » Tue Mar 25, 2014 5:24 am

Let's not confuse the mathematical existence of higher-dimensional spaces with physical existence. We postulate hypothetical 2D beings and 4D beings as a means of developing an intuitive understanding of spaces of different dimensions, but that in itself is no proof of the actual, physical existence of such spaces. Indeed, we use these dimensional analogies to learn to visualize spaces of different dimensions -- it's possible to learn to do this regardless of whether such spaces have physical existence.

However, just because something exists in the mathematical sense doesn't necessarily mean it exists in the physical sense. So far, I don't know of any evidence that might suggest that spaces of higher dimensions have physical existence. Note that I'm talking about Euclidean spaces, which are where these dimensional analogies apply; the kind of higher-dimensional spaces postulated in string theory are a different kind of space, where not all dimensions are spatial, and they are not all equivalent. The two kinds of spaces are mathematically related, but they are not to be confused with each other, because they are treated differently. It is a grave mistake to confuse Euclidean 4D space with Minkowskian 4D space-time, as some popular fiction authors have done. The mathematics, while related, are not the same, and making false associations of 4D objects with time travel only serves to confuse, rather than to clarify.

Actual, physical spaces of higher dimensions, if they do exist, must be so utterly foreign to us that we would probably find it very difficult to comprehend them -- so far we already know that 4D atoms cannot exist because the Schrödinger equation for the 4D hydrogen atom doesn't have any non-trivial minima, so electron orbitals do not exist. We also know that planetary orbits are inherently unstable in 4D, so there will be no such thing as solar systems and galaxies the way we know them. And recently, we also learned that 4D waves have certain counterintuitive properties that implies that the 4D equivalent of electromagnetism will exhibit strange behaviour, such as light "echoing" back on itself, so that vision will be inherently blurry; thus communication via radio waves will probably be unworkable. So if there are such things as 4D lifeforms, they will have to be so utterly alien that we will probably be unable to comprehend them, and we may not even recognize them as lifeforms as such!

Nevertheless, we still freely use dimensional analogies like "4D cities" and "4D vehicles" because they allow us to learn the geometry of 4D space using objects and concepts that are familiar to us.
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Re: What a 2d room might look like

Postby ICN5D » Tue Mar 25, 2014 5:26 am

Hmm, well, I suppose it's a matter of " trust but verify". A key word around my workplace :) , so I hear it a lot. My recent renderings of a six dimensional shape show what the object would look like in a 3D line of sight. When we cut down the shape, we lose information about it, each time. We can still move the cut around and trace out its hidden structure, but it's hidden from view. The shapes that show up in the cross sections are part of the actual structure itself, but we're only seeing a cut of a cut of a cut from its entirety. The rest of it ties all of the different shapes and strange structures together, that are connected into one surface.

The best way to visualize and understand the toratopes, or hyperdonuts, is by their cuts and cross sections. They are very predictable shapes, and we can also tell what's going to happen when we move the cut plane away from the center. So, as mentioned, it's a matter of trusting that the shapes are mathematically sound and possible, but verifying this supposed fact with an investigation. This is exactly what I have done with my new renderings. The cut algorithm I learned from Marek does actual math in a condensed form. It basically tells you what the axial mid-section cuts will be in 3D or what ever dimension. It can also tell you what the merge sequence will be when we move our reduced viewing plane away from the center.

I trusted that this system was correct, and that this shape did indeed have the two special arrangements of the 8 fully separated torii. I recently have verified this to be true, including many others. You can see in the pictures the exact arrangement as predicted. The rest are oblique, or rotated viewplane slices. These show us diagonal cross sections, some of which can connect all separate torii into one structure. These are my favorite, because they are perfect crosses between the two different arrangements of 8 torii. These cross sections are the real proof that these crazy wild shapes are real.

I basically shined an ultra thin 3D flashlight around, and the light reflected off of all the different parts of its 6D structure. Since this shape is much further reaching, being six dimensional, the reflections we see are very complex. And of course, maintaining in your mind, the concept that all of these cross section shapes you see are all part of one and the same shape. It just extends into this mysterious " higher dimensional " space that you cannot see, or touch, and is both everywhere and nowhere. It's in directions that are completely outside of our thin 3D sheet of existence.
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