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Look into 4D Space – a Stereographic Simulation

by howtolivehappily on June 18th, 2012

Welcome everybody to something unusual. Today we’ll be looking into four-dimensional space. Skip the talk and jump to the damned simulation.

You’ll need functioning Java in order to see this.

If you happen to not know what the fourth dimension is, here’s a great explanation:




OR you could read Robert Heinlein’s hugely amusing short story “And He Built a Crooked House” – which describes the weird experience of a family that moved into a tesseract-shaped house. You can get it here and here. Or maybe here.

In our case, time will NOT be the forth dimension, but the fifth. Damn, I could have named this thing “Looking into 5D Space,” but never mind.

My goal was to offer something better than the usual tesseract animations you can find on the internet. What is a tesseract?

I wanted to make it as real as it gets – and help you experience it as fully as possible.

See, we have a basic problem – our spacial awareness is three-dimensional. We have a limitation, that needs to be overcome.

Luckily however, our brains already have a means for overcoming a similar limitation: We can perceive the world in 3D, even though our eyes can only see flat, two-dimensional images.

The way our brains do it is to gather images of the same spatial object from many perspectives – and then put all this data together for us – in the form of a 3D perception.

One way to do this is to move while looking. As our point of view shifts, near objects shift a lot whereas distant ones hardly move. Thus, we have a means to gauge the distance.

As you might have guessed, the other way is through binocular vision – by looking with both eyes. Each eye gives a slightly different perspective, and when both are put together, spatial awareness can arise.

That’s why here I’m offering you a stereoscopic simulation of a tesseract. We’ll try to tap into the brain’s capability to go one dimension further – and give it two perspectives of the 4D scene.

What you are about to see:

You’ll be shown a simulation of a tesseract, rotating in 4D space. There’ll be a separate projection for each of your eyes.

Normally, to do this, you’d have to first project the tesseract onto a 3D screen, and then make two 2D projections of that screen – one for each eyes. This didn’t sound good enough for me though, so I went for something a bit more fancy:

The simulation below projects the tesseract onto two 3D screens – one for each eye – and then projects each of them onto a 2D screen.

Obviously, here we also have to deal with the limitations of current technology. 3D displays are not the standard. Not yet. So we’ll have to use workarounds.

There are two widespread ways for looking at stereoscopic images. One requires some skill, the other one – a very cheap piece of equipment. I’m offering you implementations for both.

Anaglyphs

Anaglyphs combine two images into one, by using different colors for those images. The way each eye only gets its image is, by looking at the anaglyph with special glasses – with different color filters for both eyes.

Red and cyan are the most frequently used colors.

Through a red filter, white and red look the same, just as cyan and black look the same.

Through a cyan filter, cyan and white look the same, just as red and black look the same. Thus, each eye gets only what was meant for it.

The way I got to know anaglyphs was through a book I encountered as a kid: “Descriptive Geometry with Anaglyphic Illustrations.” It came with a pair of glasses. I was instantly hooked. While the theory seemed too dry to me – I was just a kid after all – I couldn’t get enough from the illustrations.

It was an amazing experience to look at the page through the glasses – and see all sorts of cool shapes jump into the air.

After a while, I even learned to look at the anaglyphs without glasses; and to draw my own.

And then I forgot all about it – never to remember it for many many years.

Crossed-view stereograms

On a crossed-view stereogram, the two images reside next to each-other. In order to see the spatial figure, you have to be looking with you right eye at the left image, and with the left eye at the right image. If you imagine two straight lines connecting your eyes with their respective images, the two lines will intersect somewhere in mid-air, and that’s where the spatial figure will appear.

I hope you read that well, because you’ll have to do it yourself. It’s gonna be fun …

How to look at the crossed-view stereogram:

Here’s a brief manual for how to look at the monochrome simulation below.

Look at the monitor straight. Don’t look at an angle. Do NOT tilt your head.

It’s easier if you look from some distance. An arm’s length would be a good start.

Stretch your arm toward the screen and point your finger to the middle between the two images. Almost touch the screen …

Look at your fingertip with both eyes.

While looking, slowly move your fingertip along a straight line toward the point between your eyes.

Somewhere in mid-air, you’ll see the two images align, and turn into something REALLY COOL …

Move the finger away, keep looking.

There’s one tricky part. See, each time you look at something, two different things happen simultaneously – so you’ve been conditioned to always do both. Now you’ll have to separate them. When you look at something:

  1. The lenses of your eyes focus at the object you are looking at – so that you can see it in high detail.
  2. Your eyeballs move – so that the images from both eyes align – and you see just one object and not two.

As you reach the point when both images align and it’s time to remove your finger, you’ll have to refocus the lenses of your eyes without moving your eyeballs. See, your the computer screen will be more distant than your finger, so you’ll have to switch focus from the finger to the monitor. However, your eyes will already be looking at the point in mid-air, where the tesseract should appear.

It may take a bit of practice.

Making it interactive

Watching cool stuff is fun, but you won’t learn much unless you can engage it. Our vision evolved to work in concert with movement. The best way to see is to also touch.

That’s why I didn’t just make a video, but wanted to make the simulation interactive. Admittedly, this part leaves a lot of room for improvement.

How do you touch a virtual 4D object? For now, we’ll have to use the mouse.

You’ll be able to control the rotation speed on two of the 6 possible planes. See, in 3D we can think of rotation around an axis. In 4D, this doesn’t work anymore. There, you can have rotation on a plane; and there are six possible planes (rather than just three axes).

So many controls would have cluttered the display. Feel free to suggest better ways of doing it.

The simulations – at last!

Congratulations – you’ve arrived. Now it’s time to start applying what you’ve learned.

If you skipped and don’t know how to look at these, read the instructions above.
The Crossed-View Stereographic Simulation

You need Java to watch this.

Embed on your website:

 

Can you see this? Looking at the crossed-view stereogram takes practice. To me, it’s become really easy – and it can become easy for you too – if you practice enough.
Without the need for practice, you could watch the anaglyphic simulation instead – but you’ll need a pair of glasses.
Anaglyphic Simulation

You need Java to watch this.

Embed on your website:

Some random stuff
Here are some technologies that I considered for making this simulation:
GIMP/GAP could have been good for video generation and could have offered fancy effects that Java doesn’t offer. However, it doesn’t give me the interactivity, and I’m not that proficient in Scheme scripting. I’ve done it, but it was a long time ago.
BLENDER would have offered some really cool visual effects, but I have no idea how to manipulate its data programmatically. It’s not interactive. And it’s not 4D.
I’m not aware of any framework that would do the exotic projections I did. Do YOU know any?
What’s next?
I could make a video of this stuff. Actually, I already made a short clip, but it looks just like the simulation and is of a much larger size.
One interesting thing would be to make a 3D video and put it on youtube. Does anybody know what software I need to encode one stereoscopic clip out of the two clips (one for each eye)? And I’m not buying any expensive software – unless you decide to chip in.
The interactivity part of the simulation allows for lots of improvement.
Tesseracts are cool, but they are not the only 4D figures possible. It would be interesting to see how the intersection of a 4D triangle (the 3D triangle is called tetrahedron) and a 4D cylinder (with spherical bases) looks like. If I get my head around how all of this works.
Of course, YOU might be having some even more exciting ideas worth sharing.
This is all very exciting, but also time-consuming, so show me some interest. I’d very much appreciate it.

Thank you for your attention!



“I disagree. This is wrong. I feel offended.” I am sorry about that. Your opinion is important to me, so please write down all your objections in a comment below.  Thank you.

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7 Comments
  1. howtolivehappily permalink

    For the case that you didn’t have proper Java installed and couldn’t see the simulations, here’s a short video of the crossed-view simulation:


    .
    Have some fun with it.

  2. Tyler permalink

    I’m trying to get the stereographic to work and I’m getting a focused single image between the two, but it just looks like one of the single images alone. In other words, I’m getting the same effect as if I was just looking at one of the tesseracts with both eyes. Any suggestions?

    • howtolivehappily permalink

      Hey Tyler, I’m having a bit of a problem understanding what exactly you mean.
      Which is kind of normal: Describing an unusual subjective experience can be hard.

      You may very well be on the right track, because you should be seeing one image. It should also look like both of the two images merged.

      Maybe it would be more accurate to say that you should be seeing three images, the one in the middle being the one you focus on. The one in the middle is the one you see with both eyes. The other two you’ll see with just one eye respectively – which would make them look “fainter.”
      Ignore them. Focus on the one in the middle.

      This image should look like it’s suspended in space, somewhere between your head and your screen.
      It should also have some depth. In other words, some parts of it should look further away from you than others.

      We’ve got a problem if it looks flat. So, does it look flat?
      Can you tell if it does?

      Because a tesseract is quite complex, and because looking at stereographic images may be new to you, there’s a good chance that you’re still too confused to see it correctly.

      For example, you may not yet be able to tell if it’s flat or not.

      Looking some more should do the trick. Don’t overdo it though, or you may get nauseous.

      I suggest that you look for a minute or two, then take a break – get up, walk around and look at real world stuff.

      Then come back later and look again. Wash, rinse, repeat.

      This should work. Tell me how it goes …

      • Tyler permalink

        I GOT IT! I GOT IT! That’s so cool! I still don’t understand the 4 dimensional nature of it, but I guess that’s due to our 3 dimensional spatial limitations. It looks like a 3 dimensional shape that is folding in and around and on itself. Very cool.

        Hint to those attempting this: Once I got the third and central image to be in view, it helped me focus to try to follow a specific vertex. It helped my brain understand what I was trying to do. I also listened to ambient music. Whatever works. Best of luck!

        • howtolivehappily permalink

          That’s awesome!

          And listening to relaxing music is a really good idea. It can definitely help.

          Our visual system is limited to 3D, so it’s natural that the tesseract will appear like this. If there’s a way to truly see it in 4D, I’m not aware of it. Please tell me if you ever find out …

          Until then, here’s a very good theoretical explanation on how to think about the fourth dimension: http://eusebeia.dyndns.org/4d/vis/01-intro

          I find this topic fascinating, because it just pushes you to stretch your mind.

          Most of the time, we are completely caught up within our own ways of thinking – without even realizing it. Our current understanding of things is like a prison that is very hard to break out of.

          Breaking out can be scary. That’s because holding on to a certain way of thinking gives us those three things:

          • a sense of control,
          • a sense of security,
          • a sense of pride – because knowing how things “are” makes us smart.

          Getting a new perspective requires that we let go of the old one first. It requires that we for a moment give up the control, the security and the pride.

          We have to welcome confusion and let our old understanding fall apart.

          Thinking of the fourth dimension forces us to do exactly that. While trying to see that figure suspended in space, you had to go through a phase of confusion, didn’t you?

          You had to let your old way of looking fall apart – so that it could snap into something completely new. And then you could see things that seemed impossible before.

          This is an awesome exercise in mind expansion …

          • Tyler permalink

            Absolutely. I agree with every part of that. It’s just like letting God take control. Allowing confusion, loss of pride, loss of security, and loss of control to happen is a huge benefactor to mind expansion. Seeing things from a different perspective takes time. Difficult life decisions that don’t make sense to us, but we know God would want, cause all of those things, but in the end, everything snaps into focus and new things, that we once thought impossible, are now very possible and real. Cheers!

            P.S. – Here’s a good video for mind expansion, given those criteria.

            • howtolivehappily permalink

              Admittedly, I’m not completely happy with bringing up religion in this context, and here’s why:

              Many people are allergic to the G-word, and encountering it here could easily make them cringe – and discourage them from letting go of the desire for control, security and pride. Thus, they’d be prevented from the kind of mind-expansion I’m trying to encourage.

              This kind of mind expansion doesn’t require any religious faith whatsoever.

              Even though it is greatly compatible with it – as you pointed out. So feel free to enjoy them both as much as you can.

              What is my personal view about religion? Well, it can’t be described within a single comment like this. My view is unconventional, and would probably piss off religious people and atheists alike. Here are just two ideas:

              1. Science cannot be applied to the notion of God – because it only works with strictly defined terms, and God is beyond definition.
              2. You cannot prove God by disproving science. This whole science vs. God opposition is a huge and pointless waste of time.

              One more thing: There are flawed arguments in this video that have been addressed countless times. It’s true that science cannot stand without faith – and atheists fail to realize it – but this doesn’t in any way support the idea of God presented in your video.

              Nothing is proven, ever. Whatever faith you pick is entirely your choice, and there’s no authority in this world that could ever give you a guaranteed description of how things really are. There are countless faiths and teachers claiming to know the truth and demanding that you follow their rules – or be severely punished.

              Nothing is proven, and (of course) this guy from the video didn’t prove anything.

              Since everybody has no other option but to choose their faith, here’s a choice I’ve made and stand by:

              I don’t condone the eternal torture, not even of a single soul.

              And whoever chooses to believe in the version of God presented by this video, chooses to condone eternal torture – of billions of people. In the paradise of such a god, there’s no place for people who have a heart.

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