Exploring the 3rd Dimension: A Deeper Understanding

[JamesU]

While we're in a 3-D world, we can only see two dimensions at a time. By seeing all three dimensions, we would be able to see every face of every object in our world. But a lot of people, when I explain that to them, don't accept it and say it's false. Can anyone come up with a good explenation for this? :grumpy:

 

[<<<GUILLE>>>]

If they tell you that this is false, it is because it is false.

Go diagonal to your computer, you can now verify that it is 3-dimensional, that you can see 3-dimensions and that everything is 3-dimensional.

This is because you can see it's nearly and aparently 2-dimensional face, and it's depth.

 

[nightcleaner]

Hi.

A humble opinion:

The retina is basically flat, a layer of light sensitive cells arranged on the inner back surface of your eyeball...two dimensional. You look at a landscape, or at a photo of a landscape, and it is two dimensional. Only when you can move and record many images from many angles do you get a sense of three dimensional reality. Of course you can't do that with a photograph, or with a single glimpse of landscape. But if you see the table from all angles over a short period of time, you remember,and build within your mind a relational database containing what you see in a glimpse, two dimensions, and what you remember, a third dimension which provides the information you need about depth.

be well,

nc

 

[marlon]

If they tell you that this is false, it is because it is false.

Go diagonal to your computer, you can now verify that it is 3-dimensional, that you can see 3-dimensions and that everything is 3-dimensional.

This is because you can see it's nearly and aparently 2-dimensional face, and it's depth.

Correct, the image that you see really depends on your position towards to object you are looking at

marlon

 

[Spin_Network]

While we're in a 3-D world, we can only see two dimensions at a time. By seeing all three dimensions, we would be able to see every face of every object in our world. But a lot of people, when I explain that to them, don't accept it and say it's false. Can anyone come up with a good explenation for this? :grumpy:

Its a fundamental fact of observation, that any 3-D object in relation with another 3-D object forms part of a 3-Dimensional Spacetime. Take an object such as a tennis ball, if you remain in a fixed location, and OBSERVE the tennis ball, there is a limit of what you can observe, at most your observation can amount to 50% of the ball.

For other Geometric shapes, the % would differ, the shape defines the limit of observation. Now if you were rotating about the tennis ball , this would not alter your ability to view it WHOLE, unless your motion about it increases by a huge factor, then the warping of spacetime can induce a FALSE perspective in relation to observation!

 

[arivero]

Stereoscopy

Ask your friends to cover one eye, then try some coordination such as touching fingers or putting a cap on a pen.

 

[arivero]

For a related, more on topic, theme: How does WMAP get to draw a 3D map of galaxy distribution?. They use two coordinates... and redshift. And I supposse, they hope no two galaxies are exactly in a straight line with our planet.

 

[nightcleaner]

If they tell you that this is false, it is because it is false.

Go diagonal to your computer, you can now verify that it is 3-dimensional, that you can see 3-dimensions and that everything is 3-dimensional.

This is because you can see it's nearly and aparently 2-dimensional face, and it's depth.

I cannot agree with Marlon and Guille on this. Guille, notice that you have instructed the observer to "Go" to a diagonal view...so I presume you intend to invoke memory of the straight on view. In support of this assumption, you then say "you can now verify," which seems to imply that you are making a comparison with the previous view. You are using a pair of two dimensional views to create the perception of depth. In addition, as Arivero points out, humans have two eyes, which we use in tandem to produce a three-D mental construct.

Three dimensional vision is a personal favorite of mine. This is because I had the experience as a child of undergoing a surgery to correct for "lazy eye", a condition in which the eyes don't track together. One moves, then the other follows a short instant or two later. This results in double vision when tracking moving objects like tossed balls and so on. Mostly they don't do surgery to correct for this any more, since it usually resolves on its own.

In my case the surgery only made the problem worse. My eyes don't track exactly to this day, but I can compensate for it and have learned to catch thrown balls well enough for anyone who is not athletically inclined.

The point of this personal history is that one day, and I can remember the circumstances very clearly, I discovered three dimensional vision. I was seventeen years old and walking in a park among ancient oak trees, when suddenly the perception of depth exploded upon me. It was quite astonishing.

I was already aware of depth as an idea, and knew quite well that one can walk around objects. I just was never aware of the fact that my eyes, like anyone elses, can work together to form the illusion of depth as a perception.

If you study optical illusions you will discover that people have many ways to trick the part of the brain which has the function of assembling information about depth from two or more views. Perspective drawing is one example. Those hidden image three-D pictures you see in the Sunday comics are another example.

So I must insist that the perception of depth is a mental construct, made from two or more two dimensional views. We rely on separation, movement, memory, and hence, time, to give us our idea of a three-dimensional reality.

This gives me the hope that the human mind is flexible enough to develop a sense of higher dimensional realities. If we can build up a three dimensional construct from several two dimensional views, why not a four dimensional construct from several three dimensional views? I have devoted a considerable amount of meditation time to this attempt and I feel I have had some success.

By the way, if you want a less personal presentation of this argument, look for topics under information theory, holographic theory, and black hole theory. There is an idea around that the universe is "really" a two dimensional surface like the event horizon of a black hole.

Be well,

nc

 

[JamesU]

But if we could'nt touch or rotate anything, over time you'll realize that what we see is only 2-D. (because with only the vision sense, the picture in our brain IS 2-d.)

 

[nightcleaner]

But if we could'nt touch or rotate anything, over time you'll realize that what we see is only 2-D. (because with only the vision sense, the picture in our brain IS 2-d.)

In most quantum theories I have seen there is a problem deciding where, exactly, the observer ends and the object under observation begins. I myself find it useful to imagine a third condition existing between the observer and the object, which I think of as the view screen. This view screen is selected arbitrarily depending on the nature of the object we wish to look at.

Then I can think of the observer as existing in some dimensionality, say a 3 space one time system like {-t,x,y,z}, and the observed object existing in another dimensionality, maybe in two dimensions like a photograph, or in four dimensions like a ballistic event, and the screen between them existing in a third dimensionality, say a two dimensional graph or a sequenced group of two dimensional photographs.

By adding the screen, admittedly an artificial altho sometimes physical insertion, I am able to ignore the question about how many dimensions the observer has or how many the object has, and instead focus on the mapping of events between them.

Perhaps this construct will help you get past the existencial questions and on into the more interesting questions that come up when we try to count and measure things.

be well,

nc

 

[jtox]

Um, not that it matters at this point, but don't the terms "parallax" and "basis" come to mind ?

 

[Huckleberry]

While we're in a 3-D world, we can only see two dimensions at a time. By seeing all three dimensions, we would be able to see every face of every object in our world. But a lot of people, when I explain that to them, don't accept it and say it's false. Can anyone come up with a good explenation for this? :grumpy:

The eye cannot see all sides of an object in 3 dimensions. It can see all sides of a 2 dimensional object. Having 2 eyes gives us a sense of depth perception that facilitates our spatial 3 dimensional perception. (Even a person with one eye still realizes the world is 3 dimensional even though they may have some difficulties with spatial references.) In order to see all sides of a 3 dimensional object one would need to view the object from a 4th dimensional perspective.

 

[jtox]

Close. It will always be possible to have unknown variables no matter how many dimensions you work with, four or four thousand.

(Yes, I'm a lurker, yes, this *was* a dead topic - my bad, and yes, I discovered this by accident while browsing google)

All I'm saying is that you don't need high-level physics to explain this phenomenon (because I can tell you right now I'm no physicist -but that'd be nice- I'm just a simple enthusiast in college): this is a problem that can be explained by classical physics and algebra - so why is this with strings and LQG?
You're simply getting incomplete information from all four dimensions:

1: all but blind spot
2: all but circles of confusion
3: 2D depth cues and parallax (intersection of two viewing frustums)
4: movement (would that be continuous parallax?)

It's not all-or-nothing; it's some of everything.

And depending on what you're viewing, what angle you view it at, what light you're viewing it with, and with what reference frame, much of this information changes.

Will somebody please give me a sanity check on myself?

 

[DaveC426913]

The statement that we see only 2 dimensions from any single point of view is arguable. In fact, I think it is the crux of the discussion.

I am not convinced that the statement is true. It may require a definition of terms: What is 3 dimensional? What is two dimensional?

 

[arivero]

Um, not that it matters at this point, but don't the terms "parallax" and "basis" come to mind ?

parallax is the trick, of course, to see 3D from combining different 2D captures. It works for us (eyes), but it fails for deep space (no enough resolution).

 

[arivero]

The statement that we see only 2 dimensions from any single point of view is arguable. In fact, I think it is the crux of the discussion.

I am not convinced that the statement is true. It may require a definition of terms: What is 3 dimensional? What is two dimensional?

For a discrete distribution of points, consider N(p,r) to be the number of points at a distance r of a given point p. We can say that the distribution is tridimensional if N(p,r) is approximately a cubic function of r; it is bidimensional if N(p,r) is approximately a cuadratic function of r.