Could a Theoretical 2D Being See Anything?

[Hugh]

I'd like to hear any opinions about what a theoretical 2D (two dimensional) being could actually see.

The novel Flatland has a 2D being seeing lines, but in reality, those lines only have length, no height, there is no 3D "thickness" to them.

A 2D being could only look "along the plane" of its existence, and that plane has no thickness in the 3rd dimension.

If we think of ourselves looking at "a line", we can only see it because it has a thickness to it - it is in fact a very thin rectangle, but there is no thickness to a 1D line at all.

So if a 1D line cannot actually be seen, then a 2D being couldn't see anything, which is 0 dimensions, which is 2D less than what it is...

Thoughts anyone?

[Moonie2012]

I read Flatland and I had the same thought. Besides the "no thickness" aspect, would sight even be possible in 2D? How would light travel?

[Agent. Mulder]

I'd like to hear any opinions about what a theoretical 2D (two dimensional) being could actually see.

The novel Flatland has a 2D being seeing lines, but in reality, those lines only have length, no height, there is no 3D "thickness" to them.

A 2D being could only look "along the plane" of its existence, and that plane has no thickness in the 3rd dimension.

If we think of ourselves looking at "a line", we can only see it because it has a thickness to it - it is in fact a very thin rectangle, but there is no thickness to a 1D line at all.

So if a 1D line cannot actually be seen, then a 2D being couldn't see anything, which is 0 dimensions, which is 2D less than what it is...

Thoughts anyone?

yeah. it could see anything on a 2D plane.

[Hugh]

yeah. it could see anything on a 2D plane.

I don't see how it could though...

Take a piece of paper and look at it "on edge", now imagine that it has no thickness at all, it just vanishes from sight...

[Emma_Acid]

I'd like to hear any opinions about what a theoretical 2D (two dimensional) being could actually see.

The novel Flatland has a 2D being seeing lines, but in reality, those lines only have length, no height, there is no 3D "thickness" to them.

A 2D being could only look "along the plane" of its existence, and that plane has no thickness in the 3rd dimension.

If we think of ourselves looking at "a line", we can only see it because it has a thickness to it - it is in fact a very thin rectangle, but there is no thickness to a 1D line at all.

So if a 1D line cannot actually be seen, then a 2D being couldn't see anything, which is 0 dimensions, which is 2D less than what it is...

Thoughts anyone?

The problem here is that you've already made one vital assumption. A 2D being couldn't exist, so seeing as you've already jumped that bridge, why not make him see as well? Oh, and he can breakdance, recite the entire Birdseye Potato Waffles rap (backwards) and digest stone. I'm not being sarcastic here - I'm just pointing out that to answer an interesting question like this, it has to be based in some form of reality. A better start would have been "could a 2D lifeform exist?"

[Hugh]

The problem here is that you've already made one vital assumption. A 2D being couldn't exist, so seeing as you've already jumped that bridge, why not make him see as well? Oh, and he can breakdance, recite the entire Birdseye Potato Waffles rap (backwards) and digest stone. I'm not being sarcastic here - I'm just pointing out that to answer an interesting question like this, it has to be based in some form of reality. A better start would have been "could a 2D lifeform exist?"

It seems you've already made up your mind because you state earlier in your post that "A 2D being couldn't exist".

I'm not saying that they do, but I think that it may be possible somehow, somewhere in the universe or multiverse - if it exists.

Anyways, that's why I put in the title of the thread "a theoretical 2D being".

I'm just posing the question as a thought experiment...

[ShadowSot]

It would be able to view anything on a two dimensional plane.

You are approaching it froma three dimensional perspective. The ed being would be on the paper. Anything drawn on the paper would be an obstacle to it.

That is, of course, if it actually could see in anyway similar to the way we do.

Edited September 3, 2009 by ShadowSot

[Andami]

Actually, a 2D being would have all the same sight capabilities as us except for depth perception. They would see everything as flat. That;s my opinion anyway. Nobody can be for sure unless 2D beings actually existed.

[Sockmonster]

Never mind a seeing 2d being - can anything even be 2d?

[Andami]

Never mind a seeing 2d being - can anything even be 2d?

Yes, it can.

There is no known "First Dimension" but I believe it to be empty space.

2D is a flat shape. eg. square

3D is a shape with depth, eg. cube

4D is a 3-Dimensional world with time added as a variable. eg. Our Universe.

There are more dimensions, but science can not define them, or does not currently understand them.

Edited September 3, 2009 by Andami

[Hugh]

That is, of course, if it actually could see in anyway similar to the way we do.

That's the thing, what could it see of a 1D line?

What does a 1D line look like?

Any line that one can think normally think of has a thickness to it, but a 1D line has none.

[Hugh]

4D is a 3-Dimensional world with time added as a variable. eg. Our Universe.

There is also a possibility of a 4D spatial dimensional world with time added as a variable.

[Andami]

That's the thing, what could it see of a 1D line?

What does a 1D line look like?

Any line that one can think normally think of has a thickness to it, but a 1D line has none.

There is a difference between Spatial Dimensions and Mathematical Dimensions. While 1D in Mathematics is a Line, it may not be in Spatial terms. For example, the 4th Dimension is an object in Math, but in Spatial terms, the 4th Dimension is time.

If we were talking about space, I'd say the first dimension is empty space, as I stated above. Essentially nothingness, therefore a 1D being cannot exist.

I am probably wrong though, as most 14 year olds have no knowledge of physics lol.

Edited September 3, 2009 by Andami

[Hugh]

Here's a link to the Wikipedia article of the fourth spatial dimension which has some good reference definitions:

http://en.wikipedia.org/wiki/Fourth_dimension

Time is a different sort of dimension than the spatial ones we know.

http://en.wikipedia.org/wiki/Spacetime

Getting back to an earlier comment Andami you said that 2D beings "would see everything as flat".

It's interesting when you think about it, that if something is perfectly flat, and you're looking at it "edge on", like a 2D being would see its surroundings, you can't see it...

[Andami]

Sorry, but this thread has exceeded my knowledge. I no can no longer tell if you're agreeing with me, slightly agreeing with me, or telling me I'm crazy. lol if was fun while it lasted though

[Hugh]

Sorry, but this thread has exceeded my knowledge. I no can no longer tell if you're agreeing with me, slightly agreeing with me, or telling me I'm crazy. lol if was fun while it lasted though

lol sorry about that Andami...

[Andami]

lol sorry about that Andami...

It's okay. I'll just move to another thread where I can start another argument

[TheSearcher]

It's okay. I'll just move to another thread where I can start another argument

Isaac Asimov, in his foreword to the Signet Classics 1984 edition, described Flatland as "The best introduction one can find into the manner of perceiving dimensions." Maybe a good time to read it and learn something more

[Hugh]

Isaac Asimov, in his foreword to the Signet Classics 1984 edition, described Flatland as "The best introduction one can find into the manner of perceiving dimensions." Maybe a good time to read it and learn something more

Here's a quote from Flatland near the beginning, explaining what Flatlanders see:

_________________________

Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a Triangle, or a Square, or any other figure cut out from pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you as a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle -- who represents with us a Tradesman of the respectable class. Figure 1 represents the Tradesman as you would see him while you were bending over him from above; figures 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.

_________________________

The problem is that the analogy is incorrect.

A penny has a height, so if you look at it "edge on", it does appear as a straight line, but 2D triangles and squares have no height, so there is no line visible to see "edge on".

[TheSearcher]

Here's a quote from Flatland near the beginning, explaining what Flatlanders see:

_________________________

Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view, and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a Triangle, or a Square, or any other figure cut out from pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you as a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle -- who represents with us a Tradesman of the respectable class. Figure 1 represents the Tradesman as you would see him while you were bending over him from above; figures 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.

_________________________

The problem is that the analogy is incorrect.

A penny has a height, so if you look at it "edge on", it does appear as a straight line, but 2D triangles and squares have no height, so there is no line visible to see "edge on".

You have to consider when the book was written too, in 1884, this was still a rather novell idea to start with, so it's likely to contain a few errors.

Besides, it was written as a satirical novella, offering pointed observations on the social hierarchy of Victorian culture. The examination of dimensions was not the main goal, in my opinion. It was rather the means to an end.

Edited September 4, 2009 by TheSearcher

[Andami]

Just popped into my head! 2D beings could not see as depth is required for our eyes to see.

Light enters through the pupil and crosses at the back of the eye, forming sight. 2D beings are flat, and as such, cannot perform this process.

[allen_iverson]

this dude explains everything

[lookingfortruth]

maybe just an awareness would be possible.

[Hugh]

You have to consider when the book was written too, in 1884, this was still a rather novell idea to start with, so it's likely to contain a few errors.

Besides, it was written as a satirical novella, offering pointed observations on the social hierarchy of Victorian culture. The examination of dimensions was not the main goal, in my opinion. It was rather the means to an end.

I agree, but one of the points of this thread is to discuss if one of the errors is what 2D beings would actually be able to see... is it a line of some sort or nothing at all.

Just popped into my head! 2D beings could not see as depth is required for our eyes to see.

Light enters through the pupil and crosses at the back of the eye, forming sight. 2D beings are flat, and as such, cannot perform this process.

The flatness does pose a big problem for the 2D eye, because it is trying to see something that hasn't got a thickness to it at all...

this dude explains everything

That dude has it wrong I think...

At 0.44 he puts his finger into the 2D plane, and from an edge on view, there is a thickness to the plane, which is not accurate, and the 2D beings are shown as cubes, which is not accurate, then at 1.04 he says that the flatlanders "have no understanding of cubes"... but they were just shown as cubes!

If one views a 2D plane from the side, it completely vanishes from sight. The 2D beings can't see his finger as a cylinder (as shown), or a line at all.

maybe just an awareness would be possible.

This is an interesting point lookingfortruth, there may be some sort of awareness that other 2D objects are around them, also if two 2D beings meet on the plane there may be some sort of awareness that they are "touching" or "intermingling" in the same 2D space...

[tuogex]

if you think about it, a 2d object has no depth, witch means you cant see anything on the side, yet u can see the front, even paper has a depth of atleast 0.01 mm, so even paper has depth. if 2d objects have no depth, they cant exist.