2d Perspective Viewing things in one dimension?

[jaychant 0]

I've read some articles and watched some online videos stating that since we 3-dimensional creatures view things in two dimensions, it can be inferred that 4-dimensional creatures view things in three dimensions. Does this mean that 2-dimensional creatures view things in one dimension?

 

First, we must imagine what it would look like if this is true. First, let's imagine that there are three creatures: a red circle, a blue square, and a green triangle. They are lined up like this. Now imagine a 2-dimensional purple eye comes up to the line from the side. From our perspective it would look like this:

 

That is what it looks like in two dimensions. Now we have to crop it down to one dimension. One dimension means that there is no width, only length. So from the purple eye's perspective the other creatures should look something like this:

 

But there's a problem: the purple eye's vision would only have one dimension: length. However, if you look closely at the image, it actually does have a small amount of width. The reason is blatantly obvious: When you have a length or width of 0, you can't see anything. Which means, perhaps it can be assumed that 2D creatures can't see at all, and can never see simply because they can't see in two dimensions.

 

On the other hand, if we delve deeper in, we can come up with a solution, and that solution is that 2d creatures' brains actually produce 2D images based on entry of light from one dimension. Using this analogy, one can assume that the three 2D creatures would look more like this to the purple 2D eye:

 

So as you can see, by using this analogy, we can assume that 2D creatures do in fact view their world in one dimension.

 

However, there's still one problem: How would this be at all useful? All that would be recognizable is length and color. It would be hopelessly confusing! But I can see a few solutions:

1. 2D creatures rely on color to guide them; instead of using shapes to guide them, 2D creatures would use color. They would live in a colorful world and learn to recognize where they are by looking at the colors.

2. 2D creatures rely more on other senses; this is a great explanation for how 2D creatures would navigate their world. Instead of relying on their limited vision, they could for example rely on echolocation.

3. 2D creatures have extremely powerful depth perception; With depth perception, in the same way we can look at things and tell that they're 3D, 2D creatures could use depth perception to sort of see in two dimensions. This is the one I think is most likely. With depth perception, more shapes could be identified.

 

Interestingly and paradoxically, 2D creatures, using this type of vision, would only see prisms and cylindrical shapes, and might be confused by seeing two dimensions and only being able to travel in one of them. This could lead to absolute understanding of the 3rd dimension very quickly because if a life form gained intelligence, they would notice how they can't go "up", and hypothesize a creature that has the ability to move along this unknown, third dimension.

Edited April 17, 2009 by jaychant (see edit history)

[Alex Cicala 0]

Dimensions are confusing.I don't see the point of dimensions. I'm thinking the when humans developed they drew pictures and shapes, by the time we get to 1000bc > then people start using the terms 2d and 3d. I'm saying that the term 2d and 3d was thought up by humans.As we know that 2d is Length and Width,3d is Length, Width, Depthand 4d is all three + time.What is 1d? there is no unit/value. I see what u mean.But by what we know everything that is living is in 3d. We dont know if 4d exists only theoretical, and 2d well that is something that is unknown

[Nabb 0]

jay -> The shape of an object can be realized from the shading. Read Flatland for a deeper comprehension.

cicala -> One dimension is merely length. Using time as a fourth dimension means that there is no reason why we can't have three dimensions as x, y, t - or two dimensions as x, t. Using another spatial dimension for the fourth dimension is probably more effective, also for the mathematics that may arise.

[Alex Cicala 0]

jay -> The shape of an object can be realized from the shading. Read Flatland for a deeper comprehension.
cicala -> One dimension is merely length. Using time as a fourth dimension means that there is no reason why we can't have three dimensions as x, y, t - or two dimensions as x, t. Using another spatial dimension for the fourth dimension is probably more effective, also for the mathematics that may arise.

It seems impossible to have another spacial dimension. My idea is still every thing is 3d and there is no such thing as 2d or 4d [4d is theoretical]

[rogerthecamel 1]

It may seem impossible to us to have another spatial dimension but to a 4 dimensional creature it would be totally natural. This is because we exist completely in 3 dimensions. Our brains don't really have the ability to comprehend what a 4 dimensional world would even look like.Nabb has some good points that I have to agree with. Time is a poor forth dimension as it doesn't work the same as any of the others, so a 4th or 5th dimension, if they exist would likely be spatial. And a 2 dimensional creature can still view shading, and it can use this shading of the light reflected off the objects to build a model in its 2D brain about how these fit together in a 2D way. Just as we build a model in our brains of the world in a 3D way even though our sight works in only 2 dimensions.jaychant:"1. 2D creatures rely on color to guide them; instead of using shapes to guide them, 2D creatures would use color. They would live in a colorful world and learn to recognize where they are by looking at the colors."The world doesn't conform to a creatures vision/senses, the creatures vision/senses evolve to fit the environment they are within. Bats in dark caves don't even use vision because of lack of light, they developed other senses to sense the world. The same is true of any environment lacking in some detail, even if its the third dimension.The real questions come from when you think about how this 2D world would really work, physically. I mean for starters their planet would be a circle which they walk on the surface of, but the problem with this, unlike most platform games the 2D creatures would not be able to walk past each other without climbing on top of them, because they cannot occupy the same space. For this reason it is likely 2D creatures would be swimming or flying (which are technically the same thing).

[jaychant 0]

jay -> The shape of an object can be realized from the shading. Read Flatland for a deeper comprehension.

I was considering that when I said "depth perception"; My thought, though, is that 2D creatures would evolved with incredible depth perception, boosting their vision even further.

 

The real questions come from when you think about how this 2D world would really work, physically. I mean for starters their planet would be a circle which they walk on the surface of, but the problem with this, unlike most platform games the 2D creatures would not be able to walk past each other without climbing on top of them, because they cannot occupy the same space. For this reason it is likely 2D creatures would be swimming or flying (which are technically the same thing).

In the 2D world, there would be no such thing as the ground and it would be impossible to move up or down. So yes, they could not go over each other. It's kind of like us not being able to jump over people in a line. Don't think of the 2D world like a platform game. Instead, think of it as being like a top-down game. The only difference is that there is no floor. Since the third dimension doesn't even exist, 2D creatures would never see "below" them because there is no such thing as "below", in the same way that in our universe there is no such thing as a fourth dimension and whatever directions that dimension goes in.

 

Another important thing to note is as 3D creatures, we would be able to see the insides of 2D creatures just by looking at them, while 2D creatures would have to dissect the other creatures to look inside them. For example, take a look at this picture:

 

To us, this looks really ugly. But you need to keep in mind that 2D creatures can only see in one dimension. So to a 2D creature, it would look like this:

 

Which means that what we were looking at was the insides of the 2D creature (heart, lungs, intestines, brain, etc), which is why it looked so ugly. The reason is because not having another spatial dimension, the creature could only cover it's outsides as they are in the 2D world. I expect that in the same way, 4D creatures would look at us and see our insides surrounded by our outsides, or skin.

[rogerthecamel 1]

I was considering that when I said "depth perception"; My thought, though, is that 2D creatures would evolved with incredible depth perception, boosting their vision even further.

2D creatures may not need to evolve better depth perception as they can rely on the same cues that we use every day to judge depth. That includes size of objects, occlusion, even paralax.

In the 2D world, there would be no such thing as the ground and it would be impossible to move up or down. So yes, they could not go over each other. It's kind of like us not being able to jump over people in a line. Don't think of the 2D world like a platform game. Instead, think of it as being like a top-down game. The only difference is that there is no floor. Since the third dimension doesn't even exist, 2D creatures would never see "below" them because there is no such thing as "below", in the same way that in our universe there is no such thing as a fourth dimension and whatever directions that dimension goes in.

This isn't necessarily correct. While a top down view works, at least for the creatures, the 2D universe would mean some interesting things. Firstly there would likely still be stars and planets and black holes and atoms, as all these things work perfectly fine in 2D. Living things could not exist without water or air just as they can't in the 3D world. So they would have to exist on a planet. So I think the easiest way a 2D creature could exist is kind of like a fish in the sea. There is the sea floor and the waters surface and the fish can swim everywhere in between. Birds would also be possible in a 2D world although their mechanism for flying would have to be different, but land walkers would be a lot less likely as they are restricted in their motion.

Another important thing to note is as 3D creatures, we would be able to see the insides of 2D creatures just by looking at them, while 2D creatures would have to dissect the other creatures to look inside them.
To us, this looks really ugly. But you need to keep in mind that 2D creatures can only see in one dimension. So to a 2D creature, it would look like this:

Which means that what we were looking at was the insides of the 2D creature (heart, lungs, intestines, brain, etc), which is why it looked so ugly. The reason is because not having another spatial dimension, the creature could only cover it's outsides as they are in the 2D world. I expect that in the same way, 4D creatures would look at us and see our insides surrounded by our outsides, or skin.

Yes, I agree with this completely, otherwise there would be no way for the creature to have any internal organs as what you see in 2D is all that is there, nothing is hidden. But I never considered what you said about 4D creatures seeing the insides of us, which is completely true. I always just thought of it as them seeing the 3D world much like we do but all at once, so no objects are hidden behind others. But it makes complete sense that they would also see the insides of everything too. Interesting to think about how that would look.

[jaychant 0]

This isn't necessarily correct. While a top down view works, at least for the creatures, the 2D universe would mean some interesting things. Firstly there would likely still be stars and planets and black holes and atoms, as all these things work perfectly fine in 2D. Living things could not exist without water or air just as they can't in the 3D world. So they would have to exist on a planet. So I think the easiest way a 2D creature could exist is kind of like a fish in the sea. There is the sea floor and the waters surface and the fish can swim everywhere in between. Birds would also be possible in a 2D world although their mechanism for flying would have to be different, but land walkers would be a lot less likely as they are restricted in their motion.

If the 2-dimensional world was like a platformer game, all creatures would have very strange movements. I also can't think of a way that flying or swimming could be possible. Also, you have to consider that creatures wouldn't be able to turn, which means that for example birds would have to either only go in one direction their entire lives, or to go in the other direction they would have to turn upside-down, complicating movement even more.

I don't think flight or swimming with a platform-like reality would be possible simply because of the way creatures do these in the 3-dimensional world. For example, fish have a tail that moves back and forth and fins attached to either side, but 2D creatures couldn't have either of these. Assuming the particular view, flight or swimming would be impossible. However, I think you're right about planets, stars, etc. Therefore, to solve this problem, creatures would have to move like a slug, snake, or worm and have two sets of eyes (one on each side). It could also be possible for creatures to adapt to rolling in order to get where they need to go. However, I fail to see how they would be able to successfully swim or fly.
Edited April 20, 2009 by jaychant (see edit history)

[rogerthecamel 1]

Here is an example of how a 2D fish might look:Basically as you suggested we can see the insides of it, complete with bones and its breathing/eating system. Obviously the picture doesn't include complete detail but it gives you an idea of what a fish might look like. Its tail works a lot like a 3D fish but a top down view, it can wave side to side to give propulsion. And its fins could "flap" to give extra propulsion or direction, which may or may not work but this model could potentially work for a flying animal. Flying and swimming are two similar mechanisms in many ways, one is just in a much thinner substance. Basically in a 2D world animals would have to turn right over to change direction unless they can just move in reverse, that is less of a problem for swimming and flying creatures.

[jaychant 0]

Regardless of propulsion mechanisms, the change in gravity could easily cause problems. Because of this, I think that 2D creatures would have another set of eyes and be able to move backwards. It would solve that problem.I guess we can establish that bird-like creatures would have to be upright, and flap towards the ground to stay up, then use something else to move them. For this, they would have to have eyes on either side so it could see where it was going.

[rogerthecamel 1]

I don't think there is any problem with 2D fish swimming up, down left or right. Gravity has much less effect under water. As for air, flapping downwards is probably not a very effective flight mechanism, 3D birds only do this went they take off because it requires too much energy to keep in the air like this. Air travel often involves speed so that gliding is possible, and as such turning around isn't much of a problem, it would just use its momentum and whatever it uses to turn to flip itself the other way and keep flying. And reversing would likely be out of the question in that case, but if they did just downward flap then it could possibly be more likely.

[iGuest 3]

This is an old thread, but I hope those in the this forum won't mind if I share my insights. First, any amount of dimensions are possible, believe it or not. As rogerthecamel said, it would seem impossible for creatures like us living in three dimensions to imagine living in more or less dimensions, but that is because our brains are rarely, if ever, are called upon to do so. Dimensions up to three are  experienced by us on a regular basis, such as distance, which is a 1D measurement, GPS coordinates, which track one's position on the 2D sphere that is Earth (which is a whole other topic), or the three coordinates that determine a character's position in a video game. Each of these may not be "real", that is exist in the world we do, but they do exist just as the dimensions they exist in do (they are virtual, which, again, is an entirely different topic). Whether a human brain would be capable of processing more than three dimensions, though, is a topic with which I am very interested and still debating. In case you were wondering, there is also something that has no dimension at all: a point. As to vision in 2D, I agree with all above except that a 2D creature would "see" the world in 2D. It is true that a line would have no 2D surface area and therefore would seem to be invisible to us, you have to remember that brains don't think in dimensions. The creature's brain wouldn't have to think of the data it was collecting as 1D or 2D, it would only need to process the data as it was. Of course, we can't imagine how that would look, just as we can't imagine what the colors other animals see look like. Oh also, rogerthecamel, parallax is the main way humans create depth perception. Locomotion in 2D would be very interesting. All of the ideas would stated could be possible ways a creature would locomote. There isn't just one way to do something, which is why there so many novel creatures in our world. Whether there would be planets or not would be a matter of how similar there world is to ours, but I could imagine some crazy rollers, climbers, and diggers if there are. Of course, one thing I am surprised no one has touched on yet is the fact no 2D living thing could live in one piece because whatever would move through them would also have to split them. Steven Hawking, in his book The Universe in a Nutshell (another mind twisting read and the first to truly make me think outside the box), actually states this as a reason why 2D beings could not exist, but it really isn't too hard to thing of a living thing that doesn't need to constantly be in one piece. I couldn't imagine how something could live in 1D though, because nothing could move around anything else, but I would love to be surprised.

-reply by EtherianKeywords: 2d living thing

[iGuest 3]

4d geometry2d Perspective

I am recently going throung a book called, flatland, and sincerely woried about the how the creatures perceive time? It may be the same way as we do. Its like shaping a graph paper (2 dimensional paper) to give a 3d existance and a 3rd dimension as time.

Is it really so that due to presence of matter, the space -time or the structure(viz, the geometry ) is shaped. Why only matter? Which property of matter is responsible of our future shaping. I am sure there is something unknown about the characteristic of the matter. I wornder it may be a link to existing pillars, general theory of relativity and quantum mechanics.

Please answer.

-question by Abhishek Parida

[iGuest 3]

I wonder where is the Center of Gravity in 2D and how do the 2D beings visualize it? According to Flatland and other 2D analogies, the 2D beings seem to float along their plane (and not grounded over the line at the bottom of the plane - in fact flatland analogy doesn't have any line as the starting boundary of emergence to the 2D beings. The plane is infinitely expanded in all four directions). Where as in our 3D world, we are grounded on a surface (in contrast to what I thought the 2D beings should have grounded over a line as a second version of flatland analogy) and our center of gravity is below our feet.So where is the center of gravity in the 2D world? And how the 2D beings visualize it? Are they unaware of the concept of center of gravity itself? Is Center of Gravity insignificant in flatland? According to flatland analogy, if at all there is any center of gravity (as I see) it seems like it is in a direction perpendicular to the body of 2D beings (and not below their feet), but strangely the flatlanders cannot visualize that direction!And also I'm surprised at one more thing. A flatlander is always in a threat of attack from all 4 directions around him (Another being can easily stamp over his head by moving around him) whereas in our 3D world, the direction of attack is limited to left-right, front-back. The top-bottom attacks are possible only if we use airways, missiles and explosions. (In brief, all flatlanders can literally fly in their world, where as in our world we have both living forms. OR is there a possibility that even the 2D World has both living forms?)One more thing... How do a flatlander greet and shake hand with a friend in his land? It is only by touching each others hand through a linear contact, and they can't cross over the hands (because it needs a third dimension to do so)Also they tell the view of 2D beings is 1D. So even a square will look like a vertical line (or horizontal line). But I'm not clear how it will appear to them (Vertical or Horizontal). But in any case, the line will have a thickness (and that thickness should exist in the third dimension - I mean 3D). But then the 2D beings will not remain 2D in this analogy! So we have probably not understood the 2D concept (at least me) let alone 4D.A 2D being would understand a square by moving around it and seeing 4 nodes (and 4 edges) and will visualize a circle again by moving around & not finding any sharp node. But a 2D being would not be aware of the full picture (face on) of a 2D Shape (if I am not wrong). Likewise shall we say we have not actually seen a sphere's shape properly. To do that we may have to get into the 4D world?I also feel that if a flatlander is rooted to ground (line) in their plane (center of gravity over a line), then their movement will be limited to only one direction (front & back). The other movement will be flying above and digging the ground. Life becomes really difficult/tedious then! Overtaking someone becomes impossible (unless you jump or fly over him). So I think the floating flatland analogy is better served.I have several other doubts regarding 2D analogy (Probably I'm failing to understand the 2D analogy fully just like 4D. Do others also feel the same OR can I be clarified?)