Visualizing Higher Dimensions: Exploring the Concept of Seeing in 4D

[felipefas]

My conception of a two dimensional image is of an object with its sides, its front and its back. The only example I can think of is of a mirror's reflection (assuming that photons are not particles and therefore have no depth). We can now mimic anything we see with a mirror, a high definition screen TV, or a painting on a canvas (in theory though it is a 3D image). It follows that the only visual perception we have of any object is the refraction and reflection of photons on its surface and our only way to prove that what we see has depth (forming a 3rd dimension) is our examination through an extra sense (touch). Our brain then uses sight to perceive the world around us in two dimensions and uses the knowledge obtained from touch to come to the conclusion that what we are seeing has depth. Furthermore, if photons do exist only in 2 dimensions, then our perception of any object is a two dimensional image at different time intervals. If what I am saying is correct ( and I would appreciate anyone who would correct my view otherwise), then our problem understanding a fourth dimension is based on our state of consciousness. We still have appreciate the meaning of seeing in three dimensions.

 

[Eh]

The gist of it would seem correct. We cannot imagine a 4 dimensional object because we cannot even know what a 3 dimensional object looks like. We never see volumes - only the surfaces of objects. That doesn't prevent us from coming up with mathematical models to describe universes with more dimensions that we directly experience.

 

[felipefas]

At which height is an object three dimensional? is the photon the smallest before it can be considered to have depth? or do we need to refer to the Planck size to talk about two dimensions?

 

[felipefas]

So at what point is something considered three dimensional? Is a photon small enough to not have depth? or do we need to talk about the plank lenght? or is a two dimensional object a theory more than something we can describe?

 

[selfAdjoint]

A two dimensional object is really an abstraction - a theory if you like - in our world. Even a shadow falling on a surface is three dimensional because of the surface's irregularity.

 

[hypnagogue]

My conception of a two dimensional image is of an object with its sides, its front and its back. The only example I can think of is of a mirror's reflection (assuming that photons are not particles and therefore have no depth). We can now mimic anything we see with a mirror, a high definition screen TV, or a painting on a canvas (in theory though it is a 3D image). It follows that the only visual perception we have of any object is the refraction and reflection of photons on its surface and our only way to prove that what we see has depth (forming a 3rd dimension) is our examination through an extra sense (touch). Our brain then uses sight to perceive the world around us in two dimensions and uses the knowledge obtained from touch to come to the conclusion that what we are seeing has depth. Furthermore, if photons do exist only in 2 dimensions, then our perception of any object is a two dimensional image at different time intervals. If what I am saying is correct ( and I would appreciate anyone who would correct my view otherwise), then our problem understanding a fourth dimension is based on our state of consciousness. We still have appreciate the meaning of seeing in three dimensions.

The popular view is that we see in 2 1/2 D. The photonic images that strike our retinas are essentially 2D sheets of information, but the brain uses various heuristic tricks and tactics to convert information in those 2D images into some semblence of 3D information. For instance, binocular parralax (the relative displacement between retinal images in the left and right eye, as made apparent by alternately looking at an object with one eye closed and then the other) is used to infer some information about an object's distance. If one object in the visual field occludes another, the brain automatically deduces that the occluding object is closer than the occluded, thereby giving a clue about their relative distances. Objects appear farther in the distance the more they take on the bluish tint of the sky. The necker cube illusion demonstrates that the brain even constructs pseudo 3D models of objects at least partially on the basis of very basic aspects of their geometrical structure as encoded in their 2D projections onto the retina.

You are absolutely correct to say that our difficulties in understanding the 4th dimension arise from the nature of our consciousness. Our brains are basically perceptually hardwired to see and think in 2 1/2D. We can think abstractly of higher dimensional spaces, but it is just fundamentally beyond us to visualize such spaces in the same sense that we can visualize, say, a park as described in a book.

 

[felipefas]

A two dimensional object is really an abstraction - a theory if you like - in our world. Even a shadow falling on a surface is three dimensional because of the surface's irregularity.

Just as Einsteins theory of the bent of space and time in a third dimension, would a shadow on a surface still be two dimensional on a bent dimension? Because the surface is three dimensional does not mean that the shadow does not occupy a two dimensional plane

 

[felipefas]

The popular view is that we see in 2 1/2 D. The photonic images that strike our retinas are essentially 2D sheets of information, but the brain uses various heuristic tricks and tactics to convert information in those 2D images into some semblence of 3D information. For instance, binocular parralax (the relative displacement between retinal images in the left and right eye, as made apparent by alternately looking at an object with one eye closed and then the other) is used to infer some information about an object's distance. If one object in the visual field occludes another, the brain automatically deduces that the occluding object is closer than the occluded, thereby giving a clue about their relative distances. Objects appear farther in the distance the more they take on the bluish tint of the sky. The necker cube illusion demonstrates that the brain even constructs pseudo 3D models of objects at least partially on the basis of very basic aspects of their geometrical structure as encoded in their 2D projections onto the retina.

You are absolutely correct to say that our difficulties in understanding the 4th dimension arise from the nature of our consciousness. Our brains are basically perceptually hardwired to see and think in 2 1/2D. We can think abstractly of higher dimensional spaces, but it is just fundamentally beyond us to visualize such spaces in the same sense that we can visualize, say, a park as described in a book.

At this point then let me ask a question many may think as inane as lacking of any possibility of experimentation.

Ancient books and modern books have described a sixth sense as a metaphysical sense existing within us that allow us to "feel" things we may not "see" coming (to over-simplify). I watched a Discovery special on the sense of a shark (or may be a dolphin) where they send sonar waves which have the effect of an MRI. They receive a full three dimensional image of an object in front of them. Almost like the integration of a three dimensional object in many two dimensional slices from the head to the tail. This seems to me like a three dimensional perception. Couldn't we have an extra sense that allow us to feel different frequencies with more information than just a surface representation? I ask of this because I don't know if is a subject that has been taken seriously or if is still a hoax.

 

[Eh]

So at what point is something considered three dimensional? Is a photon small enough to not have depth? or do we need to talk about the plank lenght? or is a two dimensional object a theory more than something we can describe?

I'm not sure I understand the question, but an object is 3 dimensional when it requires an X,Y,Z axis to locate all it's points.

 

[felipefas]

I'm not sure I understand the question, but an object is 3 dimensional when it requires an X,Y,Z axis to locate all it's points.

Yes... but we understand a two dimensional object to require an X,Y axis to locate it. Can we find any example of a two dimensional object within this dimension? If we can...then what is the size of the Z axis that makes a two dimensional object a three dimensional one. For example: If a photon is considered not a particle but a wave, then is considered to have no depth. In which case, a reflection in a mirror can be described to have an X,Y axis but no Z axis. So it is a two dimensional object. Unless you think of the photon as a particle having depth and therefore a reflection is a three dimensional occurence.

 

[Olias]

Yes... but we understand a two dimensional object to require an X,Y axis to locate it. Can we find any example of a two dimensional object within this dimension? If we can...then what is the size of the Z axis that makes a two dimensional object a three dimensional one. For example: If a photon is considered not a particle but a wave, then is considered to have no depth. In which case, a reflection in a mirror can be described to have an X,Y axis but no Z axis. So it is a two dimensional object. Unless you think of the photon as a particle having depth and therefore a reflection is a three dimensional occurence.

The best way for this is to understand Electro-Magnetism, for they are the 2-D field left in the wake of a traveling Photon. In a sense Electricity and Magnetism are 2-Dimensional, we cannot see these, because we are made from 3-D matter and cannot reduce our field of Vision to below 3+1 reference frames, we only "RECIEVE" ie see Light Energy, not Magnetic resonances.

There was an experiment I placed on the old Physic Forum, where one can delight in some Quantum Relativistic insights .

PS I do believe that marine animals "feel" light not as we see it, they are sensitive to field variations, namely vibrations of E-M energy through the medium, salt water.

 

[felipefas]

The best way for this is to understand Electro-Magnetism, for they are the 2-D field left in the wake of a traveling Photon. In a sense Electricity and Magnetism are 2-Dimensional, we cannot see these, because we are made from 3-D matter and cannot reduce our field of Vision to below 3+1 reference frames, we only "RECIEVE" ie see Light Energy, not Magnetic resonances.

There was an experiment I placed on the old Physic Forum, where one can delight in some Quantum Relativistic insights .

PS I do believe that marine animals "feel" light not as we see it, they are sensitive to field variations, namely vibrations of E-M energy through the medium, salt water.

I have to come back to my original question that some people have agreed upon. We see in two dimensions. Someone said 2 1/2. So we do reduce our field of vision below 3 + 1 frames. I also don't know if we can't see electricity and magnetism because they are in a different dimension or because the components are so small we only see their actions. If we had a powerful enough microscope...could we see a photon? can a microscope observe a two dimensional figure?.

Furthermore, when i mentioned marine animals, i am suggesting the idea of perceiving, not seeing. I agree that to perceive something we have four other senses besides sight.

 

[shrumeo]

Furthermore, if photons do exist only in 2 dimensions, then our perception of any object is a two dimensional image at different time intervals.

I thought EM radiation was perceived as oscillations in an electric field orthogonal to oscillations in a magnetic field. Since each oscillation is "2D" and are orthogonal to each other, wouldn't an EM wave be 3D?

Yes... but we understand a two dimensional object to require an X,Y axis to locate it. Can we find any example of a two dimensional object within this dimension?

How can there be any "object" in this (perceived) 3D universe that is really 2D? We can also conceive things like plane waves that ACT in 2 dimensions, but is this a 2D object?

As to how we see and what we are seeing: What we are seeing is a projection (onto our retina), which is 2D, but only in concept. But since your vision is simply info processed into a concept then I guess it could bethought of as 2D.

 

[sarephina]

Just as Einsteins theory of the bent of space and time in a third dimension, would a shadow on a surface still be two dimensional on a bent dimension? Because the surface is three dimensional does not mean that the shadow does not occupy a two dimensional plane

What is a shadow? It's more the absence of light than a presence in itself. If you have a hole in a piece of cheese, is that hole 2D or 3D? Projected onto a surface (like if you smear paint on it and smush it onto a piece of paper), it seems to be 2D. But once the paper is bent, it ceases to be a 2D object. So what about the painted hole?

I've heard someone say once that a shadow will propagate instantaneously, but I don't get the logic to that; if a shadow is the absence of light, and light energy does not propagate instantaneously, how could the absence of light propagate instantaneously??

 

[shrumeo]

a shadow, of course, is a place where there is less light reflecting compared to a place right next to it with more light reflecting. Since our vision can detect differences in light intensity, then we see these differences as a shadow.

Is the shadow "something" ? well, maybe only in our heads do we want to make it an object. is it 2D? Well, since it is some kind of projection, then conceptually it is 2D, just as the projection on your retina is conceptually 2D. but the rod/cone cells that absorbed the light, the neurons that fired to register a difference in light intensity, and the other ones that interpreted it as an shadow were all 3D. The rocks on the ground, the sand, the grass that the shadow covers as a projection are all 3D.

and a shadow would not propagate instantaneously, would it? for example as the moon eclipses the sun, the moon starts blocking some light rays, but the moon would move between the Earth and the light rays that "made it" through before being reflected away from the earth. I think it takes a little over a second for light to reach the Earth from the moon, so the shadow of the moon you see passing over the sun is one second old.

someone clear me up on this if I am wrong.

 

[Olias]

a shadow, of course, is a place where there is less light reflecting compared to a place right next to it with more light reflecting. Since our vision can detect differences in light intensity, then we see these differences as a shadow.

Is the shadow "something" ? well, maybe only in our heads do we want to make it an object. is it 2D? Well, since it is some kind of projection, then conceptually it is 2D, just as the projection on your retina is conceptually 2D. but the rod/cone cells that absorbed the light, the neurons that fired to register a difference in light intensity, and the other ones that interpreted it as an shadow were all 3D. The rocks on the ground, the sand, the grass that the shadow covers as a projection are all 3D.

and a shadow would not propagate instantaneously, would it? for example as the moon eclipses the sun, the moon starts blocking some light rays, but the moon would move between the Earth and the light rays that "made it" through before being reflected away from the earth. I think it takes a little over a second for light to reach the Earth from the moon, so the shadow of the moon you see passing over the sun is one second old.

someone clear me up on this if I am wrong.

I may be wrong here?..but are not shadows Scale/Size dependant?..if you take a luminous source of certain size, for instance the Sun, if the Earth was exactly the same Size, and the Moon again the same Size, then there would not be any eclipse's if the three bodies were at identical distance's.

Question, what would the Lunar/Solar Eclipse effects be if the Moon Was the only Luminous source in our Solar System?

 

[sarephina]

I may be wrong here?..but are not shadows Scale/Size dependant?..if you take a luminous source of certain size, for instance the Sun, if the Earth was exactly the same Size, and the Moon again the same Size, then there would not be any eclipse's if the three bodies were at identical distance's.

Question, what would the Lunar/Solar Eclipse effects be if the Moon Was the only Luminous source in our Solar System?

shrumeo, I agree; I think the "leftover" light should still be there even after the rest of the light is blocked off.

Olias, I don't understand what you're trying to say about the lack of eclipses.
But I think the point-ray nature of solar radiation would lead to an increase in shadow size as you move the shadow recipient farther away from the sun, or as you move the sun farther away, or as you move the shadow caster closer to the shadow recipient. Kind of like how a hawk's wing can "block out the sun" when it's flying low enough.

If the Moon were the only Luminous source in our Solar System? I think it'd take on the role of the Sun. And we wouldn't be alive to observe the effects. But if everything kept their configuration and if we were still alive, then we wouldn't have eclipses like the ones we have today. We'd have a very close source of light, and unless we get another moon that's closer to us than this Luminous source is, we won't have any eclipses of this Luminous source. If we do get a closer satellite, we'd just have our old sun-moon system back, except the sun would really be revolving around the earth, and Galileo might have lived to a ripe old age. hehehe

Since shadows are intangible, can we really assign them a 2 or 3D?

 

[reilly]

While reasonably intuitive, the notion of dimension is techncally exceedingly complex and difficult, and belongs to the study of topology. At the practical level of physics and engineering, a space has dimension N if the description of a point requires N numbers for its description. And over the centuries, we've found that our space is well described by three numbers -- this description was crucial for getting us to the moon, for designing airplanes, for climbing mountains, and on and on. Naturally, this description is consistent with our perceptions -- except for fractal systems and fractal dynamics, which do not play a strong role in our perceptions.

Then, in addition, there are numerous supporting examples in scientific theory. Mathematically, for example, the electric potential of a charge in two dimensions is very different from the potential in three dimensions. Standard Quantum theory, Electrodynamics, both quantum and classical, and classical mechanics are formulated in three dimensions (+ time) and would not describe actual phenomena otherwise. Photons, for example, are usually described by their momentum, a three dimensional vector.

It's basically simple, and highly abstract, that our math and science describe what we perceive, and, so far, the description in three dimensions works very well, except for the very small and very large. So dimension, mass, distance and other key concepts are both fundamental and based on practical experience -- and hard to explain.

Regards,
Reilly Atkinson

 

[Allah]

If you are having trouble imaging the 4th dimension, then imagine N-dimensional space and let N go to 4.

 

[catch.yossarian]

If you are having trouble imaging the 4th dimension, then imagine N-dimensional space and let N go to 4.

...not working.

 

[selfAdjoint]

You can't really imagine the fourth dimension. Mathematicians have spent generations working out the properties of three dimensional manifolds without boundary (i.e. shapes that can exist on four dimensions), and only bit by bit are they accomplishing anything, because they can't "see" the shapes and have to work from theory. Google "Thurston's Geometrization Conjecture".

 

[juju]

HI All,

One four dimensional object that can be partially visualized is the hypercube, a four dimensional cube. The hypercube has eight 3D cubic volumes as its 3D boundary, and these eight volumes can be drawn in perspective on a flat sheet of paper.

Another form that can be seen in the same manner is a hypertetrahedron.

Other forms such as the hypersphere are more difficult to visualize.

In all cases the visualiztion needs to be accompanied by the understanding that the 4D space exists within the boundaries of the bounding 3D volumes.

juju