4d Visible To Human Eyes?

[ZacharyNardolillo]

Today I saw something about a tesseract, a 4D representation of a cube. http://www.cut-the-knot.org/ctk/Tesseract.shtml

 

It kind of just looks like a glorified hexagon to me however. But that's besides the point: something about it struck me. If we can make a 2D space LOOK 3D (movies) then could we possibly be able to make a 3D space look 4D? Tell me your thoughts on this.

[Boerseun]

'Course you can. But, like 2D representations of 3D objects where you have to include shadings to convey the fact that you're representing a 3D object, any representation of a 4D object must include motion. You can't look at a static representation of a tesseract and expect it to be representative. It'll be like an isometric drawing without the isometric extensions... kinda.

 

Any case, enjoy:

 

[Qfwfq]

Actually, our eyes can't even see 3D, each singly. Try playing ping pong with only one eye. Don't try driving your car, you would want to gradually get used to the lack of depth.

 

It is the visual cortex that is wired to give us depth, based both on perspective (look at a photograph of a fine Renaissance painting) and partly on parallax (having more than one eye). The visual cortex is not wired to so automatically sort out 4D.

 

It kind of just looks like a glorified hexagon to me however.

It is a 2D figure and you have neither paralax nor perspective to aid you, as well as limited assistance of the visual cortex. It is very confusing to sort out but if you follow the step by step concept you can figure it.

 

If we can make a 2D space LOOK 3D (movies) then could we possibly be able to make a 3D space look 4D? Tell me your thoughts on this.

Of course, Use toothpicks or something. You could possibly taylor their lengths in order to have perspective, though it would be hard to get it right; at the most it could be calculated exactly for one viewer position and I don't know how much it would help.

 

Boerseun's video is, in the end, still a 2D figure. I think the best bet would be a computerized stereoscopic image, the kind you wear special specs to view, with calculations of perspecitve as the bugger turns around.

[Moontanman]

Actually when you think about it a 3D movie is a representation of a 4D object...

[ZacharyNardolillo]

Actually when you think about it a 3D movie is a representation of a 4D object...

 

Lol how do you figure that? I'm not counting time as a 4th dimension btw

[CraigD]

If we can make a 2D space LOOK 3D (movies) then could we possibly be able to make a 3D space look 4D?

This is an interesting question.

 

Decades ago, I amused myself and others by putting a simple program on a computer (a Timex-Sinclair Color Computer– I said this was decades ago :)) in a semi-public place (our just-off-campus living room – we had a lot of traffic) that showed the shadow of a wire frame cube of (practically) any number of dimensions (20 was a popular number of dimensions). The only input was an Atarii 2600 joystick – essentially a d-pad and a single button. With the button unpressed, the joystick rotated the n-cube in the current horizontal (x-z) of vertical plane (y-z) plane. With the button pressed, the joystick changed the current plane – exchanged the x-z or y-z plane with some of the other dimensions. It was played as a game – someone randomly played with the joystick until a complicated n-hyper-cube shadow appeared, then he or someone else would try to restore the shadow to its original 4-line square. We suggested that getting good at this meant you were “learning to live in hyperspace”.

 

This view holds that if you can effectively and intuitively manipulate a many-dimensional object, you can be said to “see it” in many dimensions. Of course, you’re really just seeing a 2-dimensional image on the computer screen, representing the shadow that the many-dimensional wire frame cube would cast on the screen, if it were physically real.

 

Really, we perceive 3 spatial dimensions, because our brains are physically arranged – “wired” – to do so. Playing a computer game in 20 dimensions doesn’t dramatically rearrange our brains – by “seeing”, we mean we’re using our reasoning ability to imagine a 20-d cube (you could also sensibly call it a 20-d line or a square).

 

Our brains pretty reliably (they’re occasionally tricked by optical illusions) construct 3-d images from 2-d patterns projected on the linings (retinas) of our eyes. This is enhanced by our having 2 eyes (binocular vision), but 2 eyes are not essential to perceiving 3 spatial dimensions – contrary to some popular opinion, a one-eyed person can perceive 3-d in most situations about as well as someone with 2 eyes. Binocular vision is just one of several senses that our visual system uses to create depth perception – a good thing, as otherwise most of us wouldn’t have much depth perception beyond 10 meters or so, and 1st-person perspective video games wouldn’t be very popular. Other sense include brightness and relative motion of seen objects.

 

If you consider only binocular 3-d perception to be “real” 3-d perception, then to really see 4 or more spatial dimensions, you would need to have 3 or more eyes, “wired” to brain centers suited to the task of using them. If, however, all of the sense systems involved in depth perception are considered, you’d need only the rewired brain vision system, and clues such as brightness and relative motion in more than 3 spatial dimensions. You’d also, however, have to experience a universe that actually had 4 or more macroscopically perceivable spatial dimensions, which all theory and evidence of which I’m aware concludes in not true of our universe.

 

If you’re even more liberal with your definition of “really seeing”, to include learned skill like that show by players of my old computer game, you need only practice with some 1st-person perspective computer system coded for objects in more than 3 dimensions – assuming it’s actually possible, with any amount of practice, for a given person to learn such a skill. I’d have to do a lot more scientific testing than the informally watching people play with a computer I did all those years ago before I’d be confident concluding yes or no to that.

[Qfwfq]

Actually when you think about it a 3D movie is a representation of a 4D object...

This would go for all our perception of motion except that it isn't how we are wired to interpret it.

 

If you see a cube appear instantly and then instantly disappear, do you perceive it as a motionless hypercube? If you see a sphere inflating from a point, its radius sinusoidally increasing to a maximum and then back down to the point, do you perceive it as a motionless hypersphere?

 

This view holds that if you can effectively and intuitively manipulate a many-dimensional object, you can be said to “see it” in many dimensions.

Which remains distinct from having a physiological, automatic perception as opposed to the ability to conciously figure it by deductive reasoning. Getting the hang of it can make it come easier but I doubt getting an actual internal image; over the decades I often meditated on visual perception in more than 4D, I always conclude that I can understand but can't quite see it.

 

Binocular vision is just one of several senses that our visual system uses to create depth perception – a good thing, as otherwise most of us wouldn’t have much depth perception beyond 10 meters or so, and 1st-person perspective video games wouldn’t be very popular. Other sense include brightness and relative motion of seen objects.

Much as perspective is important and people who've lost an eye can adapt, I think you are underestimating what parallax counts and even the distance up to which it does, if one has good acuity with or without the help of corrective lenses. Admittedly, I've always had great vision and I'm only having trouble at distances well under a metre, maybe I'm not the best witness but I tried just now making comparisons at several times the distance of 10 m and I find a noticeable difference when I uncover the other eye. For objects of furniture in the 40-50 m range I found the difference very noticeable. Looking out a window, the twin wings of a nearby building at 80 m looked pretty flat. I kinda figured there being a continuous sequence of three walls, with two corners, until I began to notice achitectural cues but with both eyes they were more clearly two wings with the separation between. I caught it on Google maps, see attachment, I was looking from the building upper left, out a window where the cursor arrow indicates and I put a red dot between the twin wings near the bottom, just right of centre. Even the building to the right has more depth with both eyes.

 

If you consider only binocular 3-d perception to be “real” 3-d perception, then to really see 4 or more spatial dimensions, you would need to have 3 or more eyes, “wired” to brain centers suited to the task of using them.

I disagree about the number of eyes in related to number of dimensions.

 

More than one gives parallax. With only two, the only direction for which they won't give distance is that of their displacement, no matter how many dimensions the geometry has. A third eye that isn't on the same line as the other two can cater for that direction. This goes for two and any greater number of dimensions.

 

If, however, all of the sense systems involved in depth perception are considered, you’d need only the rewired brain vision system, and clues such as brightness and relative motion in more than 3 spatial dimensions. You’d also, however, have to experience a universe that actually had 4 or more macroscopically perceivable spatial dimensions, which all theory and evidence of which I’m aware concludes in not true of our universe.

It would be a matter of experiencing the perception that you would have, with the sensory system altered to give it, even if it's just an appearance (which would require reality to be contrived to make it work).

 

A being in 4D reality with eyes that are 4D optical systems projecting onto a 3D retina could have a visual cortex using perspective and parallax to give 4D perception, just like we have 3D from eyes with a 2D retina. For practical reasons, positions on each retina are translated into direction and the processing adds distance. An extra eye doesn't add an extra angular parameter to the polar coordinates.

[HydrogenBond]

We can already see 4-D since the four dimensions are X,Y,Z,t. If someone threw a ball at you we see the 3-D ball as a function of time.

 

As far as seeing a 4-D object apart from time, this would be an illusion that is mathematically possible.

 

As an analogous example, the image below is a 3-D representation draw in 2-D. In reality, it is only 2-D (touch the screen to verify 2-D), yet based on shadowing and highlighting we can create the illusion of 3-D. We can also make 4-D illusions using a 2-D computer screen.

 

What is interesting is this spatial illusion (3-D illusion using 2-D) can also apply to integrated systems of ideas for example political parties. The 2-D aspect is based on logic (cause and effect). What we do is highlight our good points and shadow or dump on the other's good points, to create the 3-d illusion. If you don't do the touch test, one can be fooled.

[granpa]

we see in 2.5D.

we see a 2D picture but with an extra value at each pixel for how far away it is from us.

we cannot see in 3.5D.

Its impossible

 

4D has an up and a down just like 3D

4D has a forward and back just like 3D

But 4D has, as it were, 2 rights and 2 lefts.

 

the most accurate way to imagine 4D is to use time to represent the extra dimension

[Kharakov]

Hi all,

 

Interesting subject matter, at least to my mind, as I've been working on various higher dimensional fractals recently (will provide a few links below). Had a bunch of thoughts, edited them out before posting however. If you can view my 4 dimensional post you can read them, if you care to do so.

 

If I threw a ball in 4 dimensional space, it has 4 axes of velocity: up/down, left/right, front/back, mu/tau. To see it in 4d, you'd need 4 eyes, as you'd need to combine 2 3d images into one 4d image. So if you meet a being with 4 equally spaced eyes, chances are it's a 4d-space being. I'd think that 4d objects may be quite beautiful, and 4d sex... hrmm. To create structures in 4d.. would be interesting. You'd need 4d bricks to build a 4d wall....

 

Anyways, here are few fractals I made with a few of my formulas:

 

 

There are others on my channel, although only the latest have my improved coloring formula (for greater varieties of interesting colors).

[Boerseun]

Qfwfq quite rightly points out that we can't see 3D, because the 3D image we think we see is actually the final result of our brains combining the 2D images we get from our two eyes conveniently located a few centimeters apart to give sufficient parallax for the purpose. But then, using the same argument, we can't see 2D-images, either. Because the 2D image you think you see is merely the final result of your retina combining the input it receives from all the cones and rods on its surface, being struck by individual photon streams. The only real "seeing" you can do, then, is the mere on-and-off flashing as a cone or a rod reacts to light. Which will result in a 1-dimensional flash. Any higher-dimensional image you see, or think you see, is the result of finely-tuned biological machinery working together to compile a bunch of 1-dimensional nerve inputs first into a single 2D image, and then combine the two 2D images from both eyes into a final 3D image.

 

I agree with the proposition that in order to see in more dimensions we'd need more eyes. Think about it. To see in 3D, you need two eyes. Two images overlain to create the image. Now take three eyes, spaced at the tips of a triangle. Combine the images from the first two tips of the triangle, and you have normal 3D vision. But now overlay the image from the third tip, and it will not look at all like a 3D image. You'd then be able to properly image tesseracts.

[arkain101]

Imagine a person enters a room walks around a few places then exists the room on the other side. All the while, you are sitting quietly in a corner watching the entire event. Imagine that for some reason the person leaves a perfect 3 dimensional representation of himself behind 60 times per second. Therefore, it would look like the person is actually leaving a very long streak of matter behind them.

 

After the person has exited the room you stand up and observe this long human shaped streak of the persons form.

 

The streak is the time dimension brought to a standstill within the 3dimensional realm. Imagine for some reason you can interact with the person at any point along this streak. You can punch them. High five them. Or whatever you want at any point along the streak. And lets say that when you do this, the person reacts.

 

If you punch them, then lets say we observe the 3dimensional streak come alive and react to your action and change its shape, form, and path of direction.

 

I think this would be in some sense an interaction with another dimension of space and or time, which is of course always intwined, when dealing with reasoning.

 

You however, as the observe are outside of the space-time continuum and can interact and change past and future.

 

 

Well enjoy the exercise... quite an odd one to think about.

[Ken]

This is an interesting question.

 

...snip...

 

 

Really, we perceive 3 spatial dimensions, because our brains are physically arranged – “wired” – to do so. Playing a computer game in 20 dimensions doesn’t dramatically rearrange our brains – by “seeing”, we mean we’re using our reasoning ability to imagine a 20-d cube (you could also sensibly call it a 20-d line or a square).

 

Our brains pretty reliably (they’re occasionally tricked by optical illusions) construct 3-d images from 2-d patterns projected on the linings (retinas) of our eyes. This is enhanced by our having 2 eyes (binocular vision), but 2 eyes are not essential to perceiving 3 spatial dimensions – contrary to some popular opinion, a one-eyed person can perceive 3-d in most situations about as well as someone with 2 eyes. Binocular vision is just one of several senses that our visual system uses to create depth perception – a good thing, as otherwise most of us wouldn’t have much depth perception beyond 10 meters or so, and 1st-person perspective video games wouldn’t be very popular. Other sense include brightness and relative motion of seen objects.

 

If you consider only binocular 3-d perception to be “real” 3-d perception, then to really see 4 or more spatial dimensions, you would need to have 3 or more eyes, “wired” to brain centers suited to the task of using them. If, however, all of the sense systems involved in depth perception are considered, you’d need only the rewired brain vision system, and clues such as brightness and relative motion in more than 3 spatial dimensions. You’d also, however, have to experience a universe that actually had 4 or more macroscopically perceivable spatial dimensions, which all theory and evidence of which I’m aware concludes in not true of our universe.

 

...snip...

 

 

Were you once a student of mine? :D

 

Let's take it from the top. There are two types of cues that give rise to the perception of depth.

 

The first, and simplest, and least accurate, are monocular cues. Cues such as gradient of texture, height in a (geometric) plane, relative size, superposition (which object blocks part of the view of another) and so on. Most common optical illusions make use of the "artful" arrangement of one or more of these cues to form a false interpretation.

 

The more important, and more accurate, cues are binocular cues. They operate on the basis of retinal disparity. The simple lecture device that I used was to have students place one of their hands perpendicular to, and touching, their face. I would have them close one eye, then the other, viewing their hand with only one eye at a time. Obviously each eye saw an entirely different view; one eye seeing the palm and the other eye seeing the back of the hand. Extending the hand about a foot from the face the images seen by each eye were only slightly different, or disparate. At full arm's length the disparity between views was even smaller.

 

Simple geometry puts a limit on the extent of this cue, in humans it works out to perhaps 15 or 20 feet. At this point I always showed a slide of a WWI artillery spotter's binocular, almost two periscopes angling out. This gave a wider spacing between the two objective lenses, much like making the head wider. B)

 

The information about apparent depth is decoded in the visual cortex in the occipital lobes of the cerebral cortex.

 

All of this is a long way around to suggest that the human eye doesn't see three dimensions but rather that it detects differences in retinal disparity and several monocular cues and interprets those cues to allow judgements about depth (distance). If you could fabricate a true 4-Dimensional object the human eye would detect some aspects of it. Those aspects would include retinal disparity, height in a plane, variations in optical sharpness (aerial perspective), etc. Many aspects of such an object would be distorted by the attempt to interpret them in the manner that the individual has learned to use those cues to interact with his/her normal environment.

 

So, the best that Physiological Optics can offer is that some parts of a 4 dimensional object could be detected but would not provide any useful information. :rolleyes:

[Ken]

We can already see 4-D since the four dimensions are X,Y,Z,t. If someone threw a ball at you we see the 3-D ball as a function of time.

 

No. What you see is a set of successive images each one increasing in size. The "frame rate" is a function of the speed of neural transmission of discrete impulses.

 

As far as seeing a 4-D object apart from time, this would be an illusion that is mathematically possible.

 

As an analogous example, the image below is a 3-D representation draw in 2-D. In reality, it is only 2-D (touch the screen to verify 2-D), yet based on shadowing and highlighting we can create the illusion of 3-D. We can also make 4-D illusions using a 2-D computer screen.

 

What is interesting is this spatial illusion (3-D illusion using 2-D) can also apply to integrated systems of ideas for example political parties. The 2-D aspect is based on logic (cause and effect). What we do is highlight our good points and shadow or dump on the other's good points, to create the 3-d illusion. If you don't do the touch test, one can be fooled.

 

 

What about a comparison test? Could you tell the difference between your blue "sphere" 2-dimensional figure and a real sphere of the same size? :P

[Ken]

we see in 2.5D.

we see a 2D picture but with an extra value at each pixel for how far away it is from us.

...snip...

 

 

Reminds me of the joke about the thermos. "It keeps hot things hot and cold things cold." "O. K. Mr. Smarty, how does it know?"

 

 

How does your "pixel" know the distance?

 

Sorry, but you can't just ignore the physiology of the visual system.

[granpa]

Reminds me of the joke about the thermos. "It keeps hot things hot and cold things cold." "O. K. Mr. Smarty, how does it know?"

 

 

How does your "pixel" know the distance?

 

Sorry, but you can't just ignore the physiology of the visual system.

 

Huh? the 2 images are combined and the distance to each point is calculated in the brain producing a 2.5D image.

[Ken]

Hi all,

 

Interesting subject matter, at least to my mind, as I've been working on various higher dimensional fractals recently (will provide a few links below). Had a bunch of thoughts, edited them out before posting however. If you can view my 4 dimensional post you can read them, if you care to do so.

 

If I threw a ball in 4 dimensional space, it has 4 axes of velocity: up/down, left/right, front/back, mu/tau. To see it in 4d, you'd need 4 eyes, as you'd need to combine 2 3d images into one 4d image. So if you meet a being with 4 equally spaced eyes, chances are it's a 4d-space being.

 

Does Anableps anableps (the four-eyed fish) exist in, or see in 4 dimensions? Do spiders live and see in 8 dimensions?

 

Seriously, what is your mu/tau dimension? Is it anything more than a mathematical derivation? If my simplistic notion that it is time is close to correct then you need to know that time plays a part in the interpretation of visual data. Two quick examples - the marquee effect (do the lights really move on the marquee?) or the Pulfrich Phenomenon (a pendulum moving in a plane parallel to the plane of the eyes and viewed through different density filters appears to move in an ellipse, not in a flat plane). Both are related to temporal issues).

 

 

I'd think that 4d objects may be quite beautiful, and 4d sex... hrmm. To create structures in 4d.. would be interesting. You'd need 4d bricks to build a 4d wall....

 

Anyways, here are few fractals I made with a few of my formulas:

 

 

There are others on my channel, although only the latest have my improved coloring formula (for greater varieties of interesting colors).

 

Those images are exquiste. Bravo!!